Darmstadt Vlsi Design Course

9 Unterlagen zur Vorlesung VLSI - Entwurf h¨ ochstintegrierter Schaltungen (V3.0)

Prof. Dr. Dr. h.c. M. Glesner Dipl.-Ing. M.-D. Doan Dipl.-Inf. M. Gasteier Dipl.-Ing. H. Genther Dipl.-Ing. T. Hollstein Dipl.-Ing. P. P¨ ochm¨ uller Dr.-Ing. N. Wehn Dipl.-Ing. P. Windirsch

Technische Hochschule Darmstadt Institut f¨ ur Datentechnik FG Mikroelektronische Systeme Karlstraße 15

Bibliography

Bibliography [1] M. Anaratone. Digital CMOS Circuit Design. Kluwer Academic Publishers, 1986. [2] Stephen D. Brown, Robert J. Francis, Jonathan Rose, and Zvonko G. Vranesic. FieldProgrammable Gate Arrays. Kluwer Academic Publishers, 1992. [3] Joseph J. F. Cavanagh. Digital Computer Arithmetic - Design and Implementation. McGraw-Hill, Inc., 1985. [4] Murray Disman. The Programmable Logic IC Market. Electronic Trend Publications, 1992. [5] European Silicon Structures (ES2), Zone Industrielle, 13106 Rousset, France. Solo 2030 User Guide, e02a02 edition, June 1992. [6] Daniel D. Gajski. Silicon Compilation. Addison-Wesley Publishing Company, Inc., 1988. [7] Randall L. Geiger, Phillip E. Allen, and Noel R. Strader. VLSI Design Techniques for Analog and Digital Circuits. McGraw-Hill, Inc., 1990. [8] Abhijit Ghosh, Srinivas Devadas, and A. Richard Newton. Sequential Logic Testing and Verification. Kluwer Academic Publishers, 1992. [9] Lance A. Glasser and Daniel W. Dobberpuhl. The Design and Analysis of VLSI Circuits. Addison-Wesley Publishing Company, 1985. [10] John P. Hayes. Computer Architecture and Organization. McGraw-Hill, Inc., 1988. [11] David A. Hodges and Horace G. Jackson. Analysis and Design of Digital Integrated Circuits. McGraw-Hill, 1983. [12] Ernest E. Hollis. Design of VLSI Gate Array ICs. Prentice-Hall, 1987. [13] Kai Hwang. Computer Arithmetic – Principles, Architectures, and Design. John Wiley and Sons, 1979. [14] Barry W. Johnson. Design and Analysis of Fault-Tolerant Digital Systems. AddisonWesley Publishing Company, 1989. [15] Parak K. Lala. Digital System Design using Programmable Logic Devices. Prentice-Hall, 1990.

VLSI

Design Course

0-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Bibliography

[16] W. Maly. Atlas of IC Technologies: An Introduction to VLSI Processes. The Benjamin/Cummings Publishing Company, 1987. [17] Colin M. Maunder and Rodham E. Tulloss. The Test Access Port and Boundary Scan Architecture. IEEE Computer Society Press, 1990. [18] John Mavor, Mervyn A. Jack, and Peter B. Denyer. Introduction to MOS LSI Design. Addison Wesley, 1983. [19] William J. McClean (Editor). ASIC Outlook 1993. ICE (Integrated Circuit Engineering Corporation), 1993. [20] Dhiraj K. Pradhan, editor. Fault-Tolerant Computing: Theory and Techniques, volume I. Prentice-Hall, 1986. [21] Bryan T. Preas and Michael J. Lorenzetti. Physical Design Automation of VLSI Systems. The Benjamin/Cummings Publishing Company, 1988. [22] S. M. Sze. VLSI Technology. McGraw-Hill, Inc., 1988. [23] Takao Uehara and William M. van Cleemput. Optimal Layout of CMOS Functional Arrays . In IEEE Transactions on Computers, pages 305–312, May 1981. [24] John P. Uyemura. Fundamentals of MOS Digital Integrated Circuits. Addison Wesley, 1988. [25] John P. Uyemura. Circuit Design for CMOS VLSI. Kluwer Academic Publishers, 1992. [26] Stephen A. Ward and Robert H. Halstead. Computation Structures. MIT-Press, 1990. [27] Neil Weste and Kamran Eshraghian. Principles of CMOS VLSI design. Addison-Wesley Publishing Company, 1985. [28] T.W. Williams, editor. VLSI Testing, volume 5 of Advances in CAD for VLSI. Elsevier Science Publishers B.V., 1986.

VLSI

Design Course

0-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

pn Junction Properties

Chapter 1

Basics of CMOS Circuit Design 1.1

pn Junction Properties

Figure 1.1: Step-profile of pn junction Figure 1.1 shows the profile of a pn junction p-type region (x < 0): n-type region (x > 0):

doping Na [cm−3 ] doping Nd [cm−3 ]

The following analysis is done for the pn junction without external voltage (V = 0).

1.1.1

pn Junction Space Charge Area and Electric Field

Diffusion (statistical phenomenon) of mobile carriers over the junction lets the dopants become ionized and space charge regions arise. The diffusion is restricted by the electric field caused by the space charge (moved electrons/holes). The equation describing the relation between the space charge density ρ(x), the depletion electric field E(x) and the potential φ(x) (Poisson equation) is given by d2 φ(x) dE(x) ρ(x) = = . (1.1) − 2 dx dx Si

VLSI

Design Course

1-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

pn Junction Properties

ρ(x) is the volume charge density of ionized dopants and can idealized be written as (

+qNd [0, xn ], −qNa [−xp , 0].

ρ(x) =

(1.2)

The electric field is calculated by integration: E(x) =

Zx x0

ρ(x) dx Si

(1.3)

Integrating with the boundary conditions E(xn ) = 0 = E(−xp ) (due to V = 0) gives E(x) =

 qN d   − Si (xn − x) [0, xn ],  

a − qN Si (x

(1.4)

+ xp ) [−xp , 0].

The maximum of the field is at x = 0 and E(x = 0) has a magnitude of Emax =

1.1.2

qNd xn qNa xp = . Si Si

(1.5)

pn Junction Built-in Potential

The built-in potential is a characteristic for the doping and is found to be Zxn

φ0 =

E(x) dx.

(1.6)

−xp

The build-in potential can be derived from the following equations: The diffusion hole-current density Jp dif f (x) is proportional to the positive charge carrier gradient and is given by dp(x) Jp dif f (x) = −qDp (1.7) dx where Dp is the diffusion constant for holes and p(x) is the density of holes at x. Diffusion and charge carrier mobility µ are statistical phenomenons and the relationship between them is given by the Einstein equation kT Dp Dn = = VT = q µp µn

(1.8)

where k is the Boltzmann constant (in joules per Kelvin) and T the temperature (in K). The electic field E(x) in the analyzed junction semiconductor has not for all x the value 0 which means that also a drift current density Jdrif t exists. The equation for Jdrif t for positive charge carriers is Jp drif t (x) = qµp p(x)E(x) (1.9) The resulting hole current density is dp(x) Jp (x) = qµp p(x)E(x) − qDp dx

VLSI

Design Course

1-2



A m2



Darmstadt University of Technology Institute of Microelectronic Systems

(1.10)

0

pn Junction Properties

and equivalent for electrons Jn (x) = qµn n(x)E(x) + qDn

dn(x) dx



A . m2 

(1.11)

Setting Jp = 0 (equilibrium condition) and using the Einstein relationship Dp = µp VT we obtain dφ(x) VT dp(x) E(x) = − = (1.12) dx p(x) dx and we can calculate the potential as dp(x) . (p)

dV = −VT

(1.13)

Integration from x1 (with concentration p1 and potential V1 ) to a point x2 (with p2 and V2 ) yields p1 V21 = VT ln . (1.14) p2 For the built-in potential φ0 we obtain φ0 = VT ln

p(−xp ) . p(xn )

(1.15)

With p(−xp ) = Na

(1.16)

np = n2i n2i =⇒ p(xn ) = Nd

(1.17)

and

(1.18)

we get the final expression for φ0 φ0 = VT ln

Na Nd . n2i

(1.19)

Note: Equation 1.17 is valid independent of the amount of donor and acceptor impurity doping.

1.1.3

pn Junction Depletion Width W = xp + xn

(1.20)

With Na xp = Nd xn follows xn = xp =

Na W Na + Nd Nd W. Na + Nd

(1.21) (1.22) (1.23)

VLSI

Design Course

1-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

pn Junction Properties

From

  

dφ −E(x) = = dx  

qNd Si (xn

− x) [0, xn ], (1.24)

qNa Si (x

+ xp ) [−xp , 0].

and the integration 

φ0 =

q   Si

Zxn

Z0

Na (x + xp ) dx +

−xp



Nd (xn − x) dx 

0

(

= = =

0 xn ) Na 2 N d 2 (x + 2x xp ) + (2x xn − x ) 2 2 −xp 0 h i

q Si q Na x2p + Nd x2n 2Si "  2  2 # q Nd Na Na W + Nd W 2Si Na + Nd Na + Nd "

=

q Na Nd2 Nd Na2 + 2Si (Na + Nd )2 (Na + Nd )2

=

W2

q (Nd + Na )Na Nd W2 2Si (Na + Nd )2   q 1 1 −1 2 + W 2Si Na Nd 

=

#



(1.25)

we obtain for the depletion width W the following equation: s

W =

2Si φ0 q



1 1 + . Na Nd 

(1.26)

A one-sided junction is obtained if Nd  Na or vice versa. In this case s

W '

2Si φ0 , qN

(1.27)

where N = min(Na , Nd ).

1.1.4

pn Junction with External Voltage

Assuming that the positive side of an external voltage V is attached to the p-type area and the negative side to the n-side area (V > 0: forward bias; V < 0: reverse bias) we can modify the equilibrium equations by the transformation φ0 → (φ0 − V ) and obtain for the depletion width: s   2Si 1 1 W = (φ0 − V ) + . (1.28) q Na Nd

VLSI

Design Course

1-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

pn Junction Properties 1.1.5

pn Junction Capacitance

The junction capacitance originates from the depletion charge. It is important in reverse bias (V < 0), where it is given by Si Cj (V ) = [F/cm2 ] (1.29) W (V ) C is nonlinear since it changes with the voltage V .

1.1.6

pn Junction Current Flow

Current flow through the junction is established by tracking the minority carriers: • electron current In on the p-side • hole current Ip on the n-side • recombination-generation current originating from the depletion region In and Ip combine to give the ideal diode equation I = I0 (eqV /kT − 1), where Dn np0 Dp pn0 I0 = qA + Ln Lp

(1.30) !

(1.31)

is the reverse saturation current. The reverse generation current (V < 0) is found as Igen ' −

qAni W (V ), 2τ0

(1.32)

while the forward recombination current assumes the form Irec '

qAni W (V ) qV /2kT e , 2τ0

(1.33)

where τ0 is the average carrier lifetime. These contributions must be added to the ideal diode current.

VLSI

Design Course

1-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory 1.2

MOS Transistor Theory

1.2.1

MOSFET Structure

Figure 1.2: n-channel enhancement-mode MOSFET Quantity Xox L W

meaning gate oxide thickness channel length channel width

process parameter ×

design (layout) parameter × ×

⇒ the aspect ratio W/L is the characteristical transistor design parameter MOSFET type: Substrate material: Drain,Source material: Gate material:

VLSI

Design Course

n-channel p-channel weak p-type Silicon weak n-type Silicon strong n+ Silicon strong p+ Silicon strong doped Polysilicon → low resistance

1-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory 1.2.2

MOS Capacitor and Threshold Voltage

Figure 1.3: The basic MOS structure n-channel MOSFET: • p-type wafer (single crystal p-type silicon) uniformly doped with acceptor (e.g. boron) concentration Na (Na ' 1015 cm−3 ) • Close to the bulk electrode, the majority and minority thermal equilibrium concentrations are approximated by ppo ' Na

and npo '

n2i Na

(1.34)

where ni is the intrinsic carrier density (ni ' 1, 45 · 1010 cm−3 ) • Oxide layer (SiO2 = quartz glass) is used as insulating dielectric between metal and semiconductor layer with a resistivity > 1015 Ωcm. • State of the art MOS processes use poly silicon as gate material. The gate capacity is given by Cox

=

εox [F/cm2 ] xox

with εox

=

3, 9ε0 ,

ε0 = 8, 854 · 10−14

xox ' 50nm ⇒ Cox ' 10−8 Cges

=

(1.35) F cm

F cm2

Cox · A [F]

• the top layer of metal is used for low resistance connections of transistor structures

VLSI

Design Course

1-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

%newpage Varying the gate voltage gives three modes of operation for the MOS capacitor: 1. accumulation (VG < 0) 2. depletion (VG > 0) (VG small) and 3. inversion (VG > 0) Accumulation Positively charged majority carriers (holes) accumulate at the Si-SiO2 interface (Fig. 1.4). The MOS system behaves as a capacitor (Eq. 1.35). This state is only useful for measuring some basic MOS properties. It is no operational region.

Figure 1.4: MOS accumulation state

VLSI

Design Course

1-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Depletion

Figure 1.5: MOS fields and potentials for positive gate voltages MOS field effect: An externally applied gate voltage VG controls the semiconductor electric field E(x) and the semiconductor potential φ(x) and therefore the Silicon carrier densities p, n. E(x) = −

dφ(x) dx

(1.36)

Potential boundary condition: φ(x) → VB = 0 at the bulk electrode. The total voltage accross the semiconductor is equal to the surface potential φS = φ(x = 0).

(1.37)

VG = Vox + φS

(1.38)

Applying the KVL leads to Connection between VG and ES :

dφ ES = E(x = 0) = − dx x=0

(1.39)

ES is the maximum value of the semiconductor field and is controlled (Poisson equation) by the voltage VG and influences the surface carrier concentrations ⇒ negatively charged acceptor ions are termination points for the electric field lines. pS = pp (x = 0) and nS = np (x = 0)

(1.40)

If VG is increased to a point where pS  Na (induced by electric field ES ) is satisfied, the depletion region extends from x = 0 to x = xd . The depletion phenomenon in the MOS system is analogous to the p-side of a one-sided n+ p profile junction with the difference that there is the voltage φS across the depletion region. Replacing the built-in voltage φ0 by the surface potential φS leads to an equation for the depletion width: s 2εSi φS , εSi = 11, 8ε0 . (1.41) xd = qNa

VLSI

Design Course

1-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Figure 1.6: Depletion in the MOS system The bulk depletion charge per unit area is QB0 = −qNa xd [C/cm2 ]

(1.42)

where QB0 =

QB |VB =0 p

= − 2qεSi Na φS .

(1.43)

QS Cox

(1.44)

MOS capacitator: ⇒ QS = QB < 0 Vox = − Inversion

Figure 1.7: Surface inversion in the MOS system

VLSI

Design Course

1-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Increasing VG implies increasing φS and driving xd deeper towards the bulk electrode. When VG reaches a critical threshold value VT 0 (assuming VB = 0) the inversion phenomenon occurs: The depth of the depletion area remains constant (xd = xdm ) and a layer of minority carriers accumulates at the surface (x=0). The depth of the depletion area remains constant, because the inversion layer electrons shield the bulk substrate from the increasing field at the surface. The inversion condition is given by VG ≥ V T

(1.45)

with φS (VG = VT ) = 2|φF |   Na kT ln where |φF | = q ni

(1.46) (bulk Fermi potential).

(1.47)

The maximum depletion width is s

xdm =

2εSi (2 |φF |) , qNa

(1.48)

the bulk depletion charge density q

QB0 = − 2qεSi Na (2 |φF |) ,

(1.49)

and the total surface charge density QS (VG ) = QB0 + QI (VG )

(1.50)

(where QI (VG ) is electron inversion layer charge). At the onset of inversion, QI  QBO , so the ideal threshold voltage is VTideal = 0 =

−QB0 + 2|φF | Cox p 2qεSi Na (2 |φF |) Cox |

{z

}

(1.51) 2|φF |

+

| {z }

voltage drop across oxide

voltage drop across substrate (1.52)

In reality exists an additional term VF B (called Flatband voltage) to the oxide voltage drop: VF B = ΦGS −

1 (Qox + QSS ) Cox

(1.53)

• ΦGS = ΦG − ΦS represents the difference in work functions Φ between the gate and substrate materials (material specific contact voltages which can be taken from tables). • Qox is the oxid charge (unwanted positive ions) density • QSS is the surface state density Since Qox and QSS are positive, VF B may become negative resulting in a negative threshold voltage.

VLSI

Design Course

1-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

To ensure a positive VT 0 a additional acceptor ion implantation is introduced in the MOS process with a ion dose DI [ions/cm2 ]. Final threshold voltage for VB = 0: p

VT 0 = V F B +

2qεSi Na (2|φF |) qDI + 2|φF | + Cox Cox

(1.54)

The electron charge density in the inversion layer is QI = −Cox (VG − VT 0 )

(1.55)

MOS Transistor Threshold Voltage for Nonzero Bulk-Source Voltages

Figure 1.8: Increase in depletion charge from body bias VB Non zero bulk voltage reverse biases the pn junction. The depletion charge is q

QB = − 2qεSi Na (2|φF | + VB )

(1.56)

Threshold shift: ∆VT

VT

= VT (VB ) − VT 0 , VT 0 = VT (VB = 0) √   q 2qεSi Na q 2|φF | + VB − 2|φF | = Cox = VT 0 + γ

with γ =

q

2|φF | + VB −

(1.57)

q



2|φF |

(1.58)

√

2qεSi Na 1/2 [V ] Cox body effect constant

(1.59)

The n-channel inversion charge is given by QI = −Cox (VG − VT )

VLSI

Design Course

1-12

Darmstadt University of Technology Institute of Microelectronic Systems

(1.60)

0

MOS Transistor Theory 1.2.3

MOSFET Operation Modes

Figure 1.9: Basic MOSFET channel formation n-channel MOSFET: • Source electrode (n+ region) is at the lowest potential • Source potential is the reference potential for all voltages: VDS = VD − VS ,

VGS = VG − VS ,

VSB = (VS − VB )

(1.61)

• VSB > 0 because VB must be more negative than VS to make sure that the pn-junction from bulk to source is reverse biased.

VLSI

Design Course

1-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory MOSFET operation Modes: Cutoff, Nonsaturation, Saturation

Cutoff : VGS < VT

Figure 1.10: MOSFET in cutoff mode Nonsaturation : VGS ≥ VT and VDS ≤ (VGS − VT ) Saturation : VGS ≥ VT and VDS ≥ (VGS − VT )

VLSI

Design Course

1-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Figure 1.11: MOSFET in nonsaturation mode

Figure 1.12: MOSFET in saturation mode

VLSI

Design Course

1-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory 1.2.4

MOSFET current characteristic

The Gradual Channel Approximation • analysis with the gradual channel approximation=reduction of the three-dimensional problem to a one-dimensional current flow problem • approximation describes very well ”large devices” • analysis first done for VS = 0 • assumption for derivation of GCA equations: depletion charge is supported entirely by the vertical electric field Ex (y); (assume VT 0 (QB0 ) indep. of V (y))

Figure 1.13: MOSFET geometry used in GCA (MOSFET in linear/nonsaturated region) The channel electric field Ey (y) is established by the drain source voltage VDS is Ey (y) = −

dV (y) dy

(1.62)

with V (y = 0) = VS = 0, V (y = L) = VDS . The depletion depth has its maximum at the drain electrode because V (y) has a maximum at y = L: s 2εSi Xdm (y) ' [2|ΦF | + V (y)] (1.63) qNa The inversion charge density as a function of the position y is given by QI (y = 0) = −Cox [VGS − VT ] QI (y) = −Cox [VGS − VT − V (y)]

(1.64) (1.65)

The resistance for a differential channel increment dy is dR = −

VLSI

Design Course

dy dy = [Ω] µn W QI (y) σA

1-16

Darmstadt University of Technology Institute of Microelectronic Systems

(1.66)

0

MOS Transistor Theory

Figure 1.14: Geometry for GCA current analysis with

A µn W σ

: : : :

channel cross section electron surface mobility channel width conductivity

Rearranging dV ⇔

= ID dR = −

ID dy µn W QI (y)

ZL

VZDS

0

0

dy = −µn W

ID

QI (V )dV

(1.67) (1.68)

and Integration yields ID

W = µn Cox L

VZDS

(VGS − VT − V )dV

(1.69)

0

= k

0W

L



(VGS − VT )VDS

1 2 − VDS 2

with the process transconductance parameter k 0 = µn Cox tance parameter β =

VLSI

Design Course

h

A V2

i



(1.70)

and the device transconduc-

2 k0 W L [A/V ].

1-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

MOSFET Current Equations The resulting equation from the GCA for the nonsaturated current in a conveniant form is ID =

β 2 [2(VGS − VT )VDS − VDS ] 2

(1.71)

At the onset of saturation the current ID reaches a peak value and remains constant in the

Figure 1.15: Nonsaturated MOS current saturation region: ∂ID = 0 = β(VGS − VT − VDS ) ∂VDS

(1.72)

Evaluation of the derivation yields VDS,SAT ⇒

ID,SAT

= VGS − VT

(1.73)

= ID (VDS = VDS,SAT ) =

β (VGS − VT )2 2

(1.74)

⇒ parabolic border between saturation and nonsaturation.

VLSI

Design Course

1-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Figure 1.16: Basic MOSFET characteristics

Figure 1.17: Start of Saturation in a MOSFET Channel length modulation in saturation The effective channel lenght in saturation is L0 = L − ∆L. From GCA: ⇒ ⇒

QI (L0 ) = 0

(1.75)

0

V (L ) ' VDS,SAT

(1.76)

(VDS,SAT = VGS − VT 0 ⇒ no inversion charge is induced). ∆L may be approximated as a depletion region for a one-sided pn junction with a voltage VDS − VDS,SAT across it. s 2εSi [VDS − VDS,SAT ] (1.77) ∆L ' qNa

VLSI

Design Course

1-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Figure 1.18: Channel length modulation The saturated current is modified to ID ' '

k0 W (VGS − VT )2 2 L0 ID0 1 − ∆L L

(1.78) (1.79)

with ID0 =

β (VGS − VT 0 )2 . 2

Using the empirical relation 1−

∆L ' 1 − λVDS L

(1.80)

with λ[V−1 ] the channel length modulation factor and assuming that λVDS  1 the current can be represented by ID = = =

ID0 1 − λVDS 1 + λVDS ID0 1 − λVDS 1 + λVDS ID0 (1 + λVDS ) 1 − (λVDS )2 |

⇒

{z

1

(1.81)

}

ID ' ID0 (1 + λVDS ) =

β (VGS − VT 0 )2 (1 + λVDS ) 2

(1.82)

λ has typical values from 0.1 to 0.01V−1 and represents the influence of VDS on ID in saturation. λ is important in small geometrie devices. In the following exercises we will neglect λ.

VLSI

Design Course

1-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Figure 1.19: MOSFET characteristics with channel length modulation

1.2.5

Biased MOSFET Current Equations

Figure 1.20: General MOSFET bias

VT

q

= VT 0 + γ( 2|φF | + VSB −

q

2|φF |)

ID ' 0 (VGS < VT ) i βh 2 ID = 2(VGS − VT )VDS − VDS (VGS > VT , VDS < VDS,sat ) 2 VDS,sat = VGS − VT β ID = (VGS − VT )2 (1 + λVDS ) (VGS > VT , VDS ≥ VDS,sat ) 2

VLSI

Design Course

1-21

Darmstadt University of Technology Institute of Microelectronic Systems

(1.83) (1.84) (1.85) (1.86) (1.87)

0

MOS Transistor Theory

Figure 1.21: Body bias effects

1.2.6

Measurement of device parameters

Figure 1.22: Device parameter measurement (a) Get (1) VT 0 from intercept √ √ 2ID 0W (2) k = k from slope: k = L VGS − VT VT (VSB ) − VT 0 p (3) γ = p 2|φF | + VSB − 2|φF |

and λ from (4)

VLSI

Design Course

ID2 1 + λVD2 = ID1 1 + λVD1

1-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Figure 1.23: Device parameter measurement (b)

1.2.7

The Complete MOSFET GCA Analysis

• includes additional depletion charge created by the channel voltage V (y), which is reverse bias across the n+ p junction at the channel-substrate boundary • assume VS = 0 = VB • calculation for nonsaturated MOSFET VT 0 (V ) = VF B + 2|φF | +

qDI 1 q + 2qSi Na (2|φF | + V ) Cox Cox

(1.88)

The basic GCA integral VZDS

ID =

[VGS − VT 0 (V ) − V ] dV

(1.89)

0

is modified to (now: VT 0 not constant and dependent of QB0 ) VZDS 



VGS − VF B

ID = β

qDI − 2|φF | − −V Cox

0

1 q 2qSi Na (2|φF | + V ) dV − Cox 

(1.90)

which gives for the nonsaturated drain current 

ID = β

VGS − VF B − 2|φF | −

qDI Cox



1 2 VDS − VDS 2

2 p 2qSi Na [(2|φF | + VDS )3/2 − (2|φF |)3/2 ] . 3Cox 

−

(1.91)

Introduction of a “reduction factor” M < 1 modifies the nonsaturated current equation to β 2 ID = M [2(VGS − VT 0 )VDS − VDS ]. 2 The saturated current is then given by β ID,sat = M (VGS − VT 0 )2 2

VLSI

Design Course

1-23

Darmstadt University of Technology Institute of Microelectronic Systems

(1.92)

(1.93)

0

MOS Transistor Theory

Figure 1.24: Comparision of circuit equations with the complete GCA model

Figure 1.25: Comparision of modified circuit equations with the complete GCA model

1.2.8

Depletion mode n–channel MOSFET

⇒ only used in NMOS as load device.

VLSI

Design Course

1-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

With the donator implant dose DI , VT is modified to 1 q qDI 2qεSi Na (2|ΦF | + VSB ) − Cox Cox

VT = VF B + 2|ΦF | +

(1.94)

so that VT of a depletion MOSFET is negative. The n-type layer resulting from donor doping

Figure 1.26: Depletion-mode MOSFET is modeled by (Nd − Na ) > 0.

(1.95)

The current ID can be modeled by 

ID = −µn

W L

Z

VDS

QC (V )dV

(1.96)

0

with QC (V ) the channel charge density QC (V ) = −Qn + QS (V ) + Qj (V )

VLSI

Design Course

1-25

Darmstadt University of Technology Institute of Microelectronic Systems

(1.97)

0

MOS Transistor Theory

Figure 1.27: Simplified depletion-mode MOSFET model Qn : total charge density of electrons in the n-type layer QS : MOS surface charge density (VF B gives the voltage necessary to create a charge-neutral flatband state at the surface of the semiconductor) Qj : amount of depletion charge on the n-side of the pn junction n-type layer ←→ substrate Qn = −q(Nd − Na )a

(1.98)

QS (V ) = −Cox [VGS − VF B − V ]

(1.99)

q

Qj (V ) =

2qSi N (φ0 + V ) 

φ0 ' N=

kT q

"



ln

(1.100)

(Nd − Na )Na Ni2

#

(built-in voltage)

(Nd − Na )Na Na = (Nd − Na ) (Nd − Na ) + Na Nd

(1.101) (1.102)

Using these charge densities gives 

ID = −µn

W L

Z 0

VDS

[q(Nd − Na )a + Cox (VGS − VF B − V )

q

− 2qSi N (φ0 + V )]dV q(Nd − Na )a 1 2 = β VDS + (VGS − VF B )VDS − VDS Cox 2  2 p 2qSi N [(φ0 + VDS )3/2 − (φ0 )3/2 ] . − 3Cox 





(1.103)

This equation is too complicate for hand-calculations, so usually the D-mode MOSFET is described by β 2 ID = [2(VGS − VT 0 )VDS − VDS ], (1.104) 2

VLSI

Design Course

1-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

where VT 0 < 0. Saturation current: ID,sat =

β (VGS + |VT 0 |)2 2

(1.105)

Application of D-mode MOSFETs often as Depletion load (saturation region):

Figure 1.28: Depletion-mode MOSFET characteristics

VLSI

Design Course

1-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Figure 1.29: Square root of saturated depletion-mode MOSFET current

1.2.9

p–channel MOSFET

Figure 1.30: p-channel MOSFET The source electrode is connected to VDD .

VLSI

Design Course

1-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

Threshold voltage: VTP =ΦGS − 2ΦFn − ΦFn = kT q ln



Nd ni



1 Cox (QSS

>0

+ Qox ) −

1 Cox QBn

Nd : n − type substrate doping

q

QBn = 2qεSi Nd [2ΦFn + VBSp ] VTp =VT Op − γp √

with γp =

q

(1.106)

VBSp + 2ΦFn −

p

2ΦFn



2qNd εSi Cox

VTp is negative for enhancement p-channel MOSFET. Current equations are similar to nchannel MOSFET but all the signs are opposite.

1.2.10

VLSI

Conclusions

Design Course

1-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory

n − channel transistor ΦFp

=

kT q

ln



ni Na



p − channel transistor Fermipotential ΦFn =

<0

Threshold

kT q

ln



Nd ni

negative

VTn = VT 0n + γn (|2ΦFp | − VBS ) − √ γn = 2qNa εSi /Cox

q

|2ΦFp |

Current Cutoff : VGS < VTn



q

VTp = VT 0p − γp (VBSp + 2ΦFn ) − √ γp = 2qNd εSi /Cox

h



Nonsaturation and VDS ≤ (VGS − VTn ) |VGSp | > |VTp | and |VDSp | ≤ |VGSp − VTp |

2 2(VGSn − VTn )VDSn − VDS n

VGS > VTn βn 2 (VGS

1.2.11

2ΦFn

ID = 0

VGS > VTn

ID =

p

Equations |VGS | < |VTp |

ID = 0

βn 2

>0

Voltage

positive q

ID =



and VDS ≥ (VGS

i

IDp

=

βp 2

h

2 2(VSGp + VTp )VSDp − VSD p

i

Saturation − VTn ) |VGSp | > |VTp | and |VDSp | ≥ |VGSp − VTp |

− VTn )2

ID =

βp 2 (VSGp

+ VTp )2

Modelling the MOS Transistor for Circuit simulation

MOSFET SPICE Parameters SPICE=(Simulation Program with IC Emphasis)

VLSI

Design Course

1-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

MOS Transistor Theory Symbol

Name LEVEL VTO KP GAMMA PHI LAMBDA RD RS CBD CBS IS PB CGSO

VT 0 k0 γ 2|φF | λ rd rs Cbd Cbs Is φ0

CGDO CGBO RSH Cj0

CJ

m

MJ CJSW

m

MJSW JS

tox NA or ND QSS /q

TOX NSUB NSS NFS TPG

Xj LD µ

XJ LD UO

VLSI

Design Course

Parameter Model Index Zero-bias threshold voltage Transconductance parameter Bulk threshold parameter surface potential Channel-length modulation Drain ohmic resistance Source ohmic resistance Zero-bias B-D junction capacitance Zero-bias B-S junction capacitance Bulk junction saturation current Bulk junction potential Gate-source overlap capacitance per meter channel width Gate-drain overlap capacitance per meter channel width Gate-bulk overlap capacitance per meter channel length Drain and source diffusion sheet resistance Zero-bias bulk junction bottom capacitance per square meter of junction area Bulk junction bottom grading coefficient Zero-bias bulk junction sidewall capacitance per meter of junction perimeter Bulk junction sidewall grading coefficient Bulk junction saturation current per square meter of junction area Oxide thickness Substrate doping Surface state density Fast surface state density Type of gate material +1 opposite to substrate -1 same as substrate 0 Al gate Metallurgical junction depth Lateral diffusion Surface mobility

1-31

Units

Example

V A/V2 V1/2 0.0 V 1/V Ω Ω F F A V

Default 1 0.0 2.0E-5 0.37 0.6 0.0 0.0 0.0 0.0 0.0 1.0E-14 0.8

F/m

0.0

4.0E-11

F/m

0.0

4.0E-11

F/m

0.0

2.0E-10

Ω/2

0.0

10.0

F/m2

0.0 0.0

2.0E-4 0.5

F/m

0.0 0.33

1.0E-9

A/m2 m 1/cm3 1/cm2 1/cm2

m m cm2 /Vs

1.0E-7 0.0 0.0 0.0 1.0

0.0 0.0 600

1.0 3.1E-5 0.65 0.02 1.0 1.0 2.0E-14 2.0E-14 1.0E-15 0.87

1.0E-8 1.0E-7 4.0E15 1.0E10 1.0E10

1.0E-6 0.8E-6 700

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters 1.3

DC Characteristics of MOS Inverters

Figure 1.31: Ideal inverter properties

VLSI

Design Course

1-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters 1.3.1

Basic Inverter characteristics

Figure 1.32: Basic nMOS inverter structure

The voltage transfer curve for DC voltages is defined as Vout (Vin ). The DC equation for the load current IL is IL = ID (Vin , Vout )

(1.107)

Vout = VDD − VL (IL ).

(1.108)

and for the output voltage we get

If Vin is increased from 0 (Vout = VDD initially) to values greater than VT : VDS = Vout > (VGS − VT ) ⇒ the driver changes from cutoff mode to saturation: βD (Vin − VT )2 (1 + λVout ) = IL (VL ) 2 = IL (VDD − Vout )

(1.109)

If Vin is more increased and when the point is reached where Vout < (VGS − VT ) then the driver is in ohmic mode: βD 2 [2(Vin − VT )Vout − Vout ] = IL (VL ) 2 = IL (VDD − Vout )

VLSI

Design Course

1-33

Darmstadt University of Technology Institute of Microelectronic Systems

(1.110)

0

DC Characteristics of MOS Inverters

Figure 1.33: Voltage transfer curve of an nMOS inverter

Characteristical points of the Voltage transfer curve: VOL : output low voltage of the inverter VOH : output high voltage of the inverter VIL : input low voltage of the inverter VIH : input high voltage of the inverter

)

at the point

dVout dVin

= −1

VT H : Inverter threshold voltage at Vout = Vin

VLSI

Design Course

1-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Figure 1.34: Definition: Noise margins Noise margins

N MH N ML

= =

VOH − VIH VIL − VOL

Input voltage ranges for

Logic 1 Logic 0

: :

VIH to VDD 0 to VIL

Output voltage ranges for

Logic 1 Logic 0

: :

VOH to VDD 0 to VOL

Figure 1.35: Base for NM definitions: cascaded inverter stages

VLSI

Design Course

1-35

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Figure 1.36: Model for transmission network problem

VLSI

Design Course

1-36

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Figure 1.37: Simplified AC circuit model for noise margins Inverter Transient Response Current equation for change of Vin from VOL to VOH : ID = −Cout

dVout + IL dt

(1.111)

and for change of Vin from VOH to VOL : IL (Vout ) = Cout

VLSI

Design Course

1-37

dVout dt

Darmstadt University of Technology Institute of Microelectronic Systems

(1.112)

0

DC Characteristics of MOS Inverters

Figure 1.38: Inverter transient response definitions

1.3.2

Inverter with Linear Resistor Load

The description of the load is given by Vout = VDD − IL RL VDD − Vout IL = RL

(1.113) (1.114)

To obtain the VTC, the load current must be set equal to the driver current (IL = ID ) (assuming a slow change of Vin ). When the driver is in cutoff (Vin < VT ⇒ ID = 0), there is a zero voltage drop across RL and Vout = VDS = VOH . When Vin is increased, the driver starts conduction in saturation mode, because the output voltage is initially high, so Vout = VDS > (VGS − VT ). In this case, the VTC equation is β Vout = VDD − RL (Vin − VT )2 . (1.115) 2 When Vin is more increased, Vout = VDS drops to the value (Vin − VT ) and the driver changes to ohmic mode, where the VTC equation is given by Vout = VDD −

VLSI

Design Course

β 2 RL [2(Vin − VT )Vout − Vout ]. 2

1-38

Darmstadt University of Technology Institute of Microelectronic Systems

(1.116)

0

DC Characteristics of MOS Inverters

Figure 1.39: Physical reason for transition times Calculation of VOH VOH = VDD because ID = 0 when driver in cutoff. Calculation of VOL Vin = VOH and the driver is nonsaturated, because Vout < Vin − VT . VDD − VOL βD 2 = [2(VOH − VT )VOL − VOL ] RL 2 ⇔

2 VOL −2



1 2VDD + VDD − VT VOL + =0 βD RL βD RL

(1.117)



(1.118)

Solving quadratic equation ⇒ VOL .

VLSI

Design Course

1-39

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Figure 1.40: Inverter with linear resistor load Calculation of VIL For Vin = VIL the driver transistor is saturated, because Vout is slightly below VOH . From ID = IL follows: βD VDD − Vout (Vin − VT )2 = (1.119) 2 RL VIL is defined as the point where

dVout = −1 dVin

(1.120)

Differentials of both sides of ID (Vin ) = IL (Vout ):

VLSI

Design Course

dID dVin = dVin

dIL dVout dVout

(1.121)

dVout ⇔ dVin

=

dID dVin dIL dVout

(1.122)

=

βD (Vin − VT ) − R1L

1-40

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Figure 1.41: VTC for linear resistor load nMOS inverter = −βD RL (Vin − VT ) = −1

(1.123)

1 βD RL

(1.124)

With Vin = VIL : VIL = VT +

Replacing Vin in equation 1.119 by the preceding equation term yields for Vout : 1 2βD RL

Vout (VIL ) = VDD −

(1.125)

Calculation of VIH For Vin = VIH , Vout < (VGS −VT ), so the driver is in the ohmic (nonsaturated) mode. Equating ID and IL gives 1 βD 2 [2(VIH − VT )Vout − Vout ]= (VDD − Vout ) (1.126) 2 RL Evaluation of the condition (dVout /dVin ) = -1 for ID (Vin , Vout ) = IL (Vout ) gives ∂ID dIL ∂ID dVin + dVout = dVout . ∂Vin ∂Vout dVout

(1.127)

Rearranging, dVout = dVin

VLSI

Design Course

∂ID ∂Vin dIL dVout

1-41

−

∂ID ∂Vout

Darmstadt University of Technology Institute of Microelectronic Systems

(1.128)

0

DC Characteristics of MOS Inverters

computing the derivatives, 1 RL

βD Vout =1 + βD (Vin − VT − Vout )

(1.129)

rearranging and setting Vin = VIH yields 1 1 Vout = (VIH − VT ) + 2 2βD RL

(1.130)

Substitution of this expression for Vout in equation 1.126 gives (VIH

2 (VIH − VT ) − − VT ) + βD RL 2

8VDD 1 − 2 2 3βD RL βD RL

!

=0

(1.131)

VIH can be computed by solving this quadratic equation and selecting the proper physical root. Calculation of Vth The inverter threshold voltage is defined as the VTC point where Vin = Vout . The current equation can be written as (with Vth = Vin = Vout ): βD VDD − Vth (Vth − VT )2 = 2 RL

(1.132)

Rearranging and solving the equation 2 Vth

1 2VDD − 2 VT − Vth + VT2 − βD RL βD RL 







=0

(1.133)

yields Vth .

1.3.3

Inverter Design: Resistor Model

In this approach VOH and VOL are of first and VIH and VIL of secondary importance. The inverter is modeled as series resistive voltage divider.

Figure 1.42: VOH resistor model VOH =

VLSI

Design Course

Rof f VDD Rof f + RL

1-42

Darmstadt University of Technology Institute of Microelectronic Systems

(1.134)

0

DC Characteristics of MOS Inverters

Figure 1.43: VOL resistor model For RL  Rof f is VOH ' VDD . Current equations for VOL (assuming Vin = VOH ): βD VDD − VOL 2 [2(VOH − VT )VOL − VOL ]= 2 RL

(1.135)

Rearrangement yields 

RL

W L



= D

k 0 [2(V

2(VDD − VOL ) 2 OH − VT )VOL − VOL ]

(1.136)

with βD = k 0 (W/L). This equation describes the needed product RL (W/L) for a given voltage VOH . The driver on resistance can be written as follows: Ron =

VOL 1 i =   h W 0 ID k L (VOH − VT ) − 12 VOL

(1.137)

D

Ron → as small as possible ⇒ (W/L) → as high as possible (ratio logic)

VLSI

Design Course

1-43

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters 1.3.4

Inverter with Saturated Enhancement Load

Figure 1.44: Saturated enhancement load nMOS inverter With VGSL = VDSL ⇒ VDSL > (VGSL − VT L ) the load is automatically saturated and the current is given by   k0 W IL = (VGSL − VT L )2 (1.138) 2 L L Since VGSL = (VDD − Vout ) and Vout = VDSD , k0 ID = IL = 2



W L



[VDD − VDSD − VT L (VDSD )]2

(1.139)

L

VSBL = Vout , so q

VT L = VT 0L + γ( Vout + 2|φF | −

q

2|φF |)

(1.140)

The driver is in cutoff for Vin < VT D ⇒ Vout = VOH . As Vin increases above VT D the driver is saturated, so βD βL (Vin − VT D )2 = [VDD − Vout − VT L (Vout )]2 (1.141) 2 2

VLSI

Design Course

1-44

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Figure 1.45: VTC for saturated enhancement load nMOS inverter When Vin is increased further and the condition Vout < (Vin − VT D ) becomes true, then the current is βD βL 2 [2(Vin − VT D )Vout − Vout ]= [VDD − Vout − VT L (Vout )]2 . (1.142) 2 2

1.3.5

Inverter with Nonsaturated Enhancement Load

The condition for the load being in nonsaturated region is

⇔

VDSL < VGSL − VT L (VBSL )

(1.143)

VGG > VDD + VT L (VDD )

(1.144)

This extra bias ensures that VOH = VDD . Writing VDSL = (VDD − Vout ) and VGSL = (VGG − Vout ), the nonsaturated load current is given by βL IL = [2(VGG − Vout − VT L )(VDD − Vout ) − (VDD − Vout )2 ]. (1.145) 2 The load line is got from this equation by setting ID = IL , Vout = VDSD and rearranging: ID =

VLSI

Design Course

βL (2VGG − VDD − 2VT L − VDSD )(VDD − VDSD ). 2

1-45

Darmstadt University of Technology Institute of Microelectronic Systems

(1.146)

0

DC Characteristics of MOS Inverters

Figure 1.46: Nonsaturated enhancement load nMOS inverter

1.3.6

Inverter with Depletion mode MOSFET Load

The ideal load line in fig. 1.49 is for the case, that the load transistor body bias effects are ignored. Because VGSL = 0 > VT L is always satisfied ⇒ there always exists a conducting channel in the depletion load. VDSL,sat = (VGSL − VT L ) = |VT L | (1.147) Border between saturated and nonsaturated load region: VDD − Vout = |VT L |. q

VT L (Vout ) = VT 0L + γL ( Vout + 2|φF,L | −

(1.148) q

2|φF,L |)

(1.149)

Condition for load beeing in saturation: Vout small ⇒ (VDD − Vout ) > |VT L (Vout )| IL =

VLSI

Design Course

βL βL [VGSL − VT L (Vout )]2 = [−VT L (Vout )]2 2 2

1-46

Darmstadt University of Technology Institute of Microelectronic Systems

(1.150)

0

DC Characteristics of MOS Inverters

Figure 1.47: VTC for nonsaturated enhancement load nMOS inverter

Figure 1.48: Symbol for depletion mode MOSFET Condition for load beeing in nonsaturation: (VDD − Vout ) < |VT L (Vout )| IL =

βL [2|VT L (Vout )|(VDD − Vout ) − (VDD − Vout )2 ] 2

(1.151)

For the following discussion is assumed that VT D < |VT L | < VDD

(1.152)

When Vin < VT D then the driver is in cutoff and the load provides a conduction path between VDD and Vout , so Vout ' VOH ' VDD . When Vin is increased above VT D the driver enters the saturation region while the load remains ohmic (VDD − Vout < |VT L |): βD βL (Vin − VT D )2 = [2|VT L (Vout )|(VDD − Vout ) − (VDD − Vout )2 ] 2 2

VLSI

Design Course

1-47

Darmstadt University of Technology Institute of Microelectronic Systems

(1.153)

0

DC Characteristics of MOS Inverters

Figure 1.49: Depletion mode MOSFET load When Vin is increased further then either the driver or the load changes its operational region. If Vout < VDD − |VT L | (1.154) is satisfied first, then the load will change to saturation while the driver remains in saturation, otherwise Vout < Vin − VT D (1.155) is satisfied first and the driver becomes nonsaturated while the load is still nonsaturated. When Vin is further increased to a voltage few less than VDD the driver is nonsaturated and the load is in saturation region: βD βL 2 [2(Vin − VT D )Vout − Vout ]= [−VT L (Vout )]2 2 2

(1.156)

VOH ' VDD

(1.157)

Calculation of VOH Usually taken:

VLSI

Design Course

1-48

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Figure 1.50: VTC for inverter with depletion mode MOSFET load Taking into consideration the resistance of the load device: VOH = VDD − VDSL |Vin =0

(1.158)

The current IL is in this case the driver leakage current. The conductance of the nonsaturated load is: IL βL GDSL = = [2|VT L (VOH )| − (VDD − VOH )] (1.159) VDSL 2 With VDSL = IL /GDSL results: VOH = VDD −

IL 0 kL 2



W L

 L

(1.160)

[2|VT L (VOH )| − (VDD − VOH )]

Calculation of VOL

Setting Vin = VOH

βD βL 2 [2(Vin − VT D )Vout − Vout ]= [−VT L (Vout )]2 2 2 and Vout = VOL yields 2 βR [2(VOH − VT D )VOL − VOL ] = |VT L (VOL )|2

(1.161)

(1.162)

Rearranging 2 VOL − 2(VOH − VT D )VOL +

1 |VT L (VOL )|2 = 0 βR

(1.163)

and solution of this quadratic equation (body bias is ignored at this step) yields s

VOL = (VOH − VT D ) −

(VOH − VT D )2 −

1 |VT L (VOL )|2 . βR

(1.164)

⇒ final result for VOL by iteration of this equation

VLSI

Design Course

1-49

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Design of Depletion Mode Inverters The output voltages VOL and VOH are tuned to predefined values by adjusting the (W/L) ratios. For VOH the following equation has been given before VOH = VDD −

IL 0 kL 2



W L

 L

,

(1.165)

[2|VT L (VOH )| − (VDD − VOH )]

where IL is constrained by the driver leakage current. The difference VDD − VOH may be decreased by • increasing (W/L)L by the designer (more chip area required) • adjusting a proper process parameter VT 0L q

VT L (VOH ) = VT 0L + γL ( VOH + 2|φF,L | −

q

2|φF,L |)

(1.166)

Setting VOL : rearranging the current equation for VOL gives βR =

|VT L (VOL )|2 2 2(VOH − VT D )VOL − VOL

where the driver-load ratio is



(1.167)



W 0 kD βD L  D βR = = βL kL0 W L

(1.168)

L

If the design problem is described by a simplified resistive network, the driver on resistance

Figure 1.51: Driver-load ratio for depletion-load inverter

VLSI

Design Course

1-50

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

can be written as Ron =

VOL = ID

1 0 kD 2



W L

 D

=

[2(VOH − VT D ) − VOL ]

1 Gon

(1.169)

With load in saturation the drain-source resistance of the depletion-mode MOSFET is RDSL =

1 GDSL

=

VDD − VOL 0 kL 2



W L

 L

(1.170)

|VT L (VOL )|2

The equation VOL =

Ron VDD Ron + RDSL

(1.171)

implies that the value of VOL is lowered by increasing βR . The transistor conductances are proportional to their (W/L) ratios.

1.3.7

CMOS inverter

Advantages of CMOS:

Disadvantages of CMOS:

• CMOS circuits dissipate power only during switching events. When the inputs are stable, only leakage currents are required from the power supply. (NMOS: current flow, when driver is on)

• processing is more complex than for NMOS: extra processing s.pdf must be added to create n-tub areas for ptransistor realizations (including extra step for adjusting the threshold voltage of the p-channel device)

• VOH = VDD and VOL = 0V

• additional processing s.pdf for latchup prevention: guard rings prevent from unwanted forward biased pn junctions

• the voltage transfer curve of a CMOS inverter will exhibit a sharp transition

• CMOS realizations of circuits generally require more transistors than equivalent NMOS-designs CMOS Inverter Characteristics Vin = VGSn = VDD + VGSp

(1.172)

Vout = VDSn = VDD + VDSp

(1.173)

For Vin < VT n ⇒ Vout = VDD the nMOS transistor is in cutoff while the pMOS transistor is in nonsaturation (|VDSp | = |Vout − VDD | < |VGSp − VT p | = |Vin − VDD − VT p |). When Vin is increased to values above VT n , the nMOS transitor starts conducting in saturation mode while the pMOS transistor is still in ohmic region: βn βp (Vin − VT n )2 = [2(VDD − Vin − |VT p |)(VDD − Vout ) − (VDD − Vout )2 ] 2 2

VLSI

Design Course

1-51

Darmstadt University of Technology Institute of Microelectronic Systems

(1.174)

0

DC Characteristics of MOS Inverters

As Vin is increased further, Vout is decreased. When the point is reached, where (VDD − Vout ) > (VDD − Vin − |VT p |),

(1.175)

both transistors are in saturation: βn βp (Vin − VT n )2 = (VDD − Vin − |VT p |)2 2 2

(1.176)

When Vout falls to a level where Vout < (Vin − VT n ),

(1.177)

the nMOS transistor becomes nonsaturated: βp βn 2 [2(Vin − VT n )Vout − Vout ] = (VDD − Vin − |VT p |)2 . 2 2

(1.178)

When the point is reached, where (VDD − Vin ) < |VT p |

(1.179)

the pMOS transistor goes into cutoff (⇒ IDn = IDp = 0, Vout = 0). Calculation of VOH VOH ' VDD when Vin < VT n (n-channel transistor in cutoff, current is leakage current only) Calculation of VOL VOL ' 0 when (VDD − Vin ) < |VT p | (p-channel transistor in cutoff) Calculation of VIL Equating currents for saturated nMOS and nonsaturated pMOS device: βp βn (VIL − VT n )2 = [2(VDD − VIL − |VT p |)(VDD − Vout ) − (VDD − Vout )2 ] 2 2

(1.180)

Evaluation of condition (dVout /dVin ) = −1 for IDn (Vin ) = IDp (Vin , Vout ): (dIDn /dVin ) − (∂IDp /∂Vin ) dVout = = −1 dVin ∂IDp /∂Vout

(1.181)

Evaluating the derivation gives VIL

βn 1+ βp

!

= 2Vout +

βn VT n − VDD − |VT p | βp

(1.182)

This equation has to be solved together with equation 1.180 ⇒ VIL .

VLSI

Design Course

1-52

Darmstadt University of Technology Institute of Microelectronic Systems

0

DC Characteristics of MOS Inverters

Calculation of VIH At this point of the VTC the nMOS device is nonsaturated and the pMOS transistor is saturated. βn βp 2 [2(VIH − VT n )Vout − Vout ] = (VDD − VIH − |VT p |)2 . (1.183) 2 2 The derivation condition (dVout /dVin ) = −1 has to be evaluated for IDn (Vin , Vout ) = IDp (Vin ): dVout (dIDp /dVin ) − (∂IDn /∂Vin ) = = −1 dVin ∂IDn /∂Vout

(1.184)

which gives βp βp VIH 1 + = 2Vout + VT n + (VDD − |VT p |) (1.185) βn βn This equations forms together with equation 1.183 a quadratic in VIH which has to be solved. 



Calculation of Vth For Vth = Vin = Vout both transistors are saturated. βn βp (Vth − VT n )2 = (VDD − Vth − |VT p |)2 2 2

(1.186)

Solving for Vth yields: Vth =

VT n +

q

βp /βn (VDD − |VT p |)

(1 +

q

(1.187)

βp /βn )

Design While at nMOS design a lot of efforts have to be made to optimize the levels of VOH and VOL , the ratio (W/L) in CMOS design is used to set the level of Vth (VOH = VDD , VOL = 0). µp



W L



βp  p = βn µn W L

(1.188)

n

The ratio required to establish a given inverter threshold voltage is s

βn (VDD − Vth − |VT p |) = . βp (Vth − VT n )

(1.189)

To get a symmetrical VTC, Vth is set to VDD /2: s

If in a process is set |VT p | = VT n

VLSI

Design Course



1 2 VDD



− |VT p |

βn . =  1 βp V − V Tn 2 DD

⇒

(1.190)

βp = βn then the device aspect ratios are related by 

W L



W L

 p =

1-53

µn . µp

(1.191)

n

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters Since µn /µp ' 2.5 a minimum area CMOS inverter will have (W/L)n ' 1 and (W/L)p ' 2.5 In this case the VTC is completely symmetric.

1.4

Switching of MOS Inverters

1.4.1

The output High-to-Low Time tHL

dVOU T , tHL = t2 − t1 , (1.192) dt Driver goes from Cutoff over Saturation into Nonsaturation region. Border between Saturation and Nonsaturation is reached at the time tx and output voltage Vout = VOH − VT D . In order to simplify the final expressions, the following integrations for computing tHL are done with the borders from VOH to VOL (correct borders would be from V1 = VOL + 0.9(VOH − VOL ) to V0 = VOL + 0.1(VOH − VOL )). IDS (VOU T ) = −COU T

VOH Z −VT

Saturation : tx − t1 = −COU T

VOH V ZOL

Nonsaturation : t2 − tx = −COU T

VOH −VT

⇒ t x − t1 =

dVOU T β 2 2 (VOH − VT )

(1.193)

dVOU T β 2

2 2(VOH − VT )VOU T − VOU T



2COU T VT , β(VOH − VT )2 Z

with

(1.195)

dx 1 xn = ln x(a + bxn ) an a + bxn 



⇒ tHL = τ with τ

=

2(VOH − VT ) 2VT + ln −1 VOH − VT VOL 

1.4.2

RLIN E

(1.200)



β(VOH − VT )

+ RLIN E

(1.201)

Rise Time tLH IL (VOU T ) = COU T

VLSI

(1.198) (1.199)

1



(1.197)



COU T β(VOH − VT )

= COU T

(1.196)



and interconnection resistance τ



COU T 2(VOU T − VT ) ln −1 ; β(VOH − VT ) VOL 

follows : t2 − tx =

 (1.194)

Design Course

1-54

dVOU T dt

(1.202)

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters ZV1

Zt2

tLH

=

dt = COU T t1

V0

dVOU T IL (VOU T )

(1.203)

NMOS Rise Time for Resistor Load

IL =

VDD − Vout RL ZV1

tLH

= RL COU T V0

(1.204) dVOU T VDD − V0 = RL COU T ln VDD − VOU T VDD − V1 



(1.205)

with V0 = 10% of the whole Voltage swing

(1.206)

V0 ' VOL + 0.1(VDD − VOL ) ,

(1.207)

and V1 = 90% of the whole swing

(1.208)

V1 ' VOL + 0.9(VDD − VOL )

(1.209)

NMOS Rise Time for Depletion Load Inverter First Approximation : IL tLH

|VT L (VOU T )|2

=

βL 2

=

COU T ·∆V IL

=

(1.210)

2COU T (V1 −V0 ) βL |VT L |2

With more accuracy : VT L is not constant because of the substrate effect (=body bias effect). Depletion MOSFET changes from saturation to nonsaturated mode, if VDD − VOU T < |VT L |. Nonsaturation IL =

i βL h 2 |VT L (VOU T )| (VDD − VOU T ) − (VDD − VOU T )2 2 VDDZ−|VT L |

tLH

= COU T V0

=

COU T βL |VT L |



dVOU T + COU T IL(SAT )

VDD −|VT L |



COU T βL |VT L |

interconnect line resistance RLIN E : τL = max. switching frequency fmax =

Design Course

dVOU T IL(nonSAT )

2(VDD − |VT L | − V0 ) 2|VT L | − (VDD − V1 ) + ln |VT L | VDD − V1

Load Charge Time constant τL =

VLSI

ZV1

(1.211)

(1.212)



(1.213)

with 

1 βL |VT L |



+ RLIN E COU T

1 tHL +tLH

1-55

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters 1.4.3

NMOS Propagation Delay Time 1 tP = (tP HL + tP LH ) , 2

1 with V1/2 = (VOL + VOH ) 2

(1.214)

V1/2

tP HL = −COU T

Z VOH

= −COU T

dVOU T ID (VOU T )

VOHZ−VT D VOH

(1.215)

dVOU T βD 2 2 (VOH − VT D )

V1/2

−COU T

VOH −VT D



= τD

with τD =

dVOU T

Z βD 2

2 2(VOH − VT D )VOU T − VOU T



(1.216)



2VT D 4(VOH − VT D ) + ln −1 (VOH − VT D ) (VOH + VOL ) 



(1.217)

COU T βD (VOH − VT D )

(1.218) (1.219)

Depletion load V1/2

VDDZ−|VT L |

tP LH

= COU T VOL

tP LH

VLSI

Design Course

=

COU T βL |VT L |

(

dVOU T + COU T IL(SAT )

dVOU T

Z

VDD −|VT L |

"

2|VT L | − (VDD − V1/2 ) 2(VDD − |VT L | − VOL ) + ln |VT L | (VDD − V1/2 )

1-56

(1.220)

IL(nonSAT ) #)

Darmstadt University of Technology Institute of Microelectronic Systems

(1.221)

0

Switching of MOS Inverters 1.4.4

CMOS Inverter Transient Response

The CMOS Inverter has a full supply voltage swing: VOH = VDD

and

VOL = 0V

(1.222)

⇒ V0 = 0.1VDD

and

V1 = 0.9VDD .

(1.223)

The high-to-low time tHL is similar to the NMOS Inverter COU T βn (V1 − VTn )

tHL =



2VTn 2(V1 − VTn ) + ln −1 (V1 − VTn ) V0 



(1.224)

From symmetry (VT n → VT p ; βn → βp ) follows: tLH

COU T = βp (V1 − |VTp |)

(

"

#)

2|VTp | 2(V1 − |VTp |) + ln −1 (V1 − |VTp |) V0

(1.225)

If VT n = VT p and βn = βp ⇒ tHL = tLH .

1.4.5

Propagation Delay Time tp of CMOS Inverters 

tP HL = τn

2VTn 4(VOH − VTn ) + ln −1 (VOH − VTn ) (VOH − VOL ) 



.

(1.226)

From symmetry follows: (

tP LH = τp

tp =

"

1 (tP HL + tP LH ) 2 

τn = "

τp =

#)

2|VTp | 4(VOH − |VTp |) + ln −1 (VOH − |VTp |) (VOH − VOL )

.

with

(1.227)

(1.228)

1 + RLIN E COU T βn (V1 − VTn ) 

and

(1.229)

#

1 + RLIN E COU T . βp (V1 − |VTp |)

(1.230) (1.231)

Symmetrical CMOS inverter (VT n = VT p and βn = βp ): tP HL = tP LH = tP 

= τn

VLSI

Design Course

2VT 4(VDD − VT ) + ln −1 VDD − VT VDD 

1-57



Darmstadt University of Technology Institute of Microelectronic Systems

(1.232)

0

Switching of MOS Inverters

Figure 1.52: βR for various VOL choices

VLSI

Design Course

1-58

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.53: Basic CMOS inverter structure

VLSI

Design Course

1-59

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.54: CMOS inverter characteristics

VLSI

Design Course

1-60

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.55: Output high to low time

VLSI

Design Course

1-61

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.56: Rise time circuit

Figure 1.57: Depletion load rise time

VLSI

Design Course

1-62

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.58: Propagation delay time definitions

VLSI

Design Course

1-63

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.59: CMOS transient analysis

VLSI

Design Course

1-64

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters 1.4.6

Power-Delay-Product (PDP)

The power-delay-product characterizes the overall performance of a digital circuit: P DP = Pav tp

(1.233)

where Pav is the average power dissipated by the circuit and tp is the average propagation delay time. ⇒ a small PDP is desirabel. For PDP computation the input signal waveform must be taken into consideration (Fig. 1.60). For the following PDP analysis, simplified versions of propagation delay time equations will

Figure 1.60: PDP: input signal waveforms be used: tP HL ' τD = Ron Cout tP LH

' τL = RL Cout

⇒ tp '

VLSI

Design Course

(1.234)

1 (Ron + RL )Cout 2

1-65

(1.235) average propagation delay

Darmstadt University of Technology Institute of Microelectronic Systems

(1.236)

0

Switching of MOS Inverters

PDP for Resistor-Load Inverter

Figure 1.61: PDP for inverter with resistor load With Iav (average power supply current) the power dissipated by the circuit is Pav = Iav VDD

(1.237)

Static State Contribution to the PDP: P av '

2 VDD 2(Ron + RL )

(1.238)

(factor 12 because resistively loaded inverter is considered to be half of time in output low state – in output high state no power is dissipated) 1 2 (P DP )DC ' Cout VDD 4 Output Rise Interval Contribution to the PDP: With driver in cutoff ⇒: Vl ∆V Iav ' Cout = Cout ∆t tLH with Vl = VDD (Vout : 0 → VDD ). 2 (P DP )LH ' Cout VDD

VLSI

Design Course

1-66

tp tLH

Darmstadt University of Technology Institute of Microelectronic Systems

(1.239)

(1.240)

(1.241)

0

Switching of MOS Inverters

Output Fall Interval Contribution to the PDP: 1 Iav ' (Iinitial + Ifinal ) 2 where Iinitial =

1 (VDD − VOH ), RL

Assuming VOL  VOH = VDD ⇒ Iav '

Ifinal =

(1.242) 1 (VDD − VOL ) RL

VDD 2RL

(1.243)

(1.244)

With tP HL ' τD , tHL can be estimated as tHL ' 2τD = 2Ron Cout 2 (P DP )HL ' Cout VDD

(1.245)

Ron tp RL tHL

(1.246)

The final PDP expression is obtained by adding all contributions: 2 P DP ' Cout VDD



1 tp Ron tp + + 4 tLH RL tHL



.

(1.247)

For well-designed inverters is Ron  RL . The propagation delay time is then tp ' (τL /2). With the approximations tLH = 2τL and tHL = 2τD follows: 3 2 P DP ' Cout VDD 4

(1.248)

PDP for Depletion-Load nMOS Inverter Static State Contribution to the PDP: Average DC power dissipation: 1 (Pav )DC ' Imax VDD (1.249) 2 where Imax is the maximum power supply current (this is for Vout = VOL ⇒ Imax = ID (Vout = VOL )). Assuming that the probability for the inverter being in this state is 50% ⇒ (Pav )DC

' '

βD 2 [2(VOH − VT D )VOL − VOL ]VDD 4 βL [VT L (VOL )]2 VDD 4

(1.250) (1.251)

Output Rise and Fall Interval Contributions to the PDP: (Iav )LH =

1 T

Z

tLH

IL (t)dt

(1.252)

dVout dt

(1.253)

0

with IL (t) = ID (t) + Cout

VLSI

Design Course

1-67

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.62: Power supply currents ⇒

1 T The first term may be rewritten as

Z

(Iav )LH =

tLH

ID (t)dt + 0

ID,LH ≡

1 tLH

Z

1 Cout T

Z

tLH

0

dVout dt dt

(1.254)

tLH

ID (t)dt .

(1.255)

0

ID,LH = 0 if Vin is an ideal square wave (driver in cutoff). The second term can be evaluated as follows Z tLH Z V1 dVout dt = dVout (1.256) dt V0 0 ⇒ 1 (Iav )LH = [ID,LH tLH + Cout (V1 − V0 )] (1.257) T

VLSI

Design Course

1-68

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

The equations for the discharge time are similar: 1 T

(Iav )HL =

Z

tHL

IL (t)dt

(1.258)

dVout dt

(1.259)

0

IL (t) = ID (t) + Cout

1 [ID,HL tHL − Cout (V1 − V0 )] (1.260) T Z tHL 1 ID,HL ≡ ID (t)dt . (1.261) tHL 0 So the transient power supply current is 1 (Iav )transient = (ID,LH tLH + ID,HL tHL ) (1.262) T For the total PDP of the depletion-load inverter follows: 1 tp P DP ' Imax VDD tp + (ID,LH tLH + ID,HL tHL )VDD (1.263) 2 T To understand this expression, assume that ID,LH = ID,HL = ID,av . The logic switching frequency is f = 1/T and the maximum switching frequency is (Iav )HL =

fmax =

1 . tHL + tLH

(1.264)

⇒

1 f P DP ' Imax VDD tp + ID,av VDD tp (1.265) 2 fmax For f  fmax the DC term of this equation is dominating. When f = fmax , the inverter is never in the stable state where Vout = VOL , so P DP ' ID,av VDD tp

(1.266)

P DP ∼ Cout VDD × (Voltage)

(1.267)

PDP dependence:

PDP for CMOS Inverter Current flows only during a switching event so the average current in a logic cycle T can be written as 1 Iav = [IDn ,LH tLH + IDn ,HL tHL ] . (1.268) T In this equation Z tLH 1 IDn ,LH ≡ IDn (t)dt (1.269) tLH 0 gives the average current during the rise time, while IDn ,HL ≡

1

Z

tHL

IDn (t)dt (1.270) tHL 0 is the average fall time current. For a completely symmetric CMOS inverter IDn ,LH = IDn ,HL = IDn ,av , so the power-delay product is given by P DPCMOS = IDn ,av VDD tp

VLSI

Design Course

1-69

f fmax

Darmstadt University of Technology Institute of Microelectronic Systems

(1.271)

0

Switching of MOS Inverters 1.4.7

MOSFET Capacitances

• MOSFET capacitances are complicated functions of the fabrication processes and the layout geometry • nonlinear, voltage-dependent capacitances • exact analysis not possible (⇒ computer simulation) • here: hand computations/estimations in an average sense

Figure 1.63: Capacitances: basic MOSFET structure

MOS Overlap Capacitors Refering to Fig. 1.64 the physical length of a polysilicon gate is given by L0 = Ls + L + LD

(1.272)

The gate overlap is necessary to ensure the contact of the channel and the n+ regions. The overlap capacitances are given by Cols = Cox W Ls ,

Cold = Cox W Ld

(1.273)

with Cox = εox /xox (gate capacitance per unit area). Self-aligned process: polysilicon gate is employed as a mask to define the n+ source and drain regions. The overlaps occur, because the following processing s.pdf require heating of the wafer (→ lateral diffusion). The overlap capacitances may only be influenced by the designer by varying the channel width W . In design rule sets the overlap capacitance is often defined by: Co = Cox Lo

VLSI

Design Course

⇒

1-70

Cols = Cold = Co W

Darmstadt University of Technology Institute of Microelectronic Systems

(1.274)

0

Switching of MOS Inverters

Figure 1.64: MOSFET capacitor model MOSFET Gate Capacitances Cgs = Cox W Lf1 (VGS , VGD )

(1.275)

Cgd = Cox W Lf2 (VGS , VGD )

(1.276)

Cgb = Cox W Lf3 (VGS , VGD , VSB )

(1.277)

The gate-bulk capacitance consists of the gate capacitance in series with the depletion capacitance of the depletion region. 1. Cutoff: no inversion layer channel ⇒

VLSI

Design Course

Cgb ' Cox W L

(1.278)

Cgs ' 0

(1.279)

Cgd ' 0

(1.280)

1-71

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.65: MOSFET gate capacitances in the three operational regions 2. Nonsaturation: the channel shields the bulk electrode from the gate since the inversion layer acts as conductor between drain and source ⇒ Cgb = 0 Cgb ' 0

(1.281)

Cgs '

1 VDS Cox W L 1 + 2 3VDS,sat

Cgd '

1 VDS Cox W L 1 − 2 VDS,sat

!

(1.282)

!

(1.283)

3. Saturation: the channel shields the bulk electrode from the gate since the inversion layer acts as conductor between drain and source ⇒ Cgb = 0. The channel is pinched off and does not contact the drain n+ region. Cgb ' 0 2 Cgs ' Cox W L 3 Cgd ' 0

(1.284) (1.285) (1.286)

Combination of the gate capacitances with the overlap contributions: CG = Cox W L0 where

VLSI

Design Course

(1.287) 0

L = L + 2Lo

CGS = Cols + Cgs

(1.288)

CGD = Cold + Cgd

(1.289)

1-72

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Figure 1.66: Gate capacitances as functions of gate-source voltage The Bulk Junction Capacitances

Figure 1.67: Expanded view of an n+ drain or source region for computing depletion capacitances The reverse-biased depletion capacitance per unit area of a pn junction is given by C=

Cj0 1+

Vr φ0

1/2

(1.290)

where Vr is the magnitude of the reverse-bias voltage applied to the junction. φ0 is the built-in

VLSI

Design Course

1-73

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

potential 

φ0 =

kT q



Nd Na ln n2i

!

(1.291)

and Cj0 is the zero-bias (Vr = 0) capacitance per unit area. Cj0

v u =u t 

2

qεSi 1 Na

+

1 Nd



(1.292) φ0

The bottom capacitance can be computed simply using the doping concentrations Nd and Na for the pn junction: Cj0 W Y Cbottom =  (1.293) 1/2 Vr 1 + φ0 For computing the sidewall capacitance the p+ channel stop doping must be taken into consideration (−→ see also technology description later on). The sidewall capacitance is usually computed by first taking the sidewall capacitance per unit area as Cj0sw

v u =u t 

2

qεSi 1 Na,sw

+

1 Nd



(1.294) φ0sw

where 

φ0sw =

kT q



Nd Na,sw ln n2i

!

(1.295)

is the sidewall built-in potential. Because the n+ area has a junction depth of xj , the sidewall capacitance per unit length Cjsw is taken as Cjsw = Cj0sw xj

(1.296)

The total sidewall capacitance is then given by Csw = 

Cjsw l 1+

Vr φ0 sw

(1.297)

1/2

where l is the total sidewall perimeter length (2W + 2Y ). Assuming φ0 = φ0sw , the total depletion capacitance for a drain or source area is given by Cd (Vr ) = Cbottom + Csw Cj0 W Y + Cjsw l =  1/2 . Vr 1 + φ0

(1.298)

For drain regions Vr = VDB and for source regions Vr = VSB ⇒ the depletion capacitance depends on actual voltages. An average depletion capacitance may be defined by Cav = =

VLSI

Design Course

1 V2 − V1

Z

V2

V1

2φ0 CT (V2 − V1 )

Cd (Vr )dVr

"

V2 1+ φ0

1-74

(1.299)

1/2

V1 − 1+ φ0 

1/2 #

Darmstadt University of Technology Institute of Microelectronic Systems

(1.300)

0

Switching of MOS Inverters

where CT = Cj0 W Y + Cjsw l .

(1.301)

Defining a dimensionless voltage factor Cav 2φ0 K(V1 , V2 ) = = CT (V2 − V1 )

"

V2 1+ φ0

1/2

V1 − 1+ φ0 

1/2 #

<1

(1.302)

yields Cav = K(V1 , V2 )CT

1.4.8

(1.303)

Inverter Output Capacitance

Figure 1.68: Approximation used for Cout in cascaded nMOS inverters

Figure 1.69: Simplified interconnect scheme for line capacitance

VLSI

Design Course

1-75

Darmstadt University of Technology Institute of Microelectronic Systems

0

Switching of MOS Inverters

Cout = CGD1 + CGD2 + K(VOL , VOH )[Cdb1 + Csb2 ] + Cline + CG3

(1.304)

For computation of the line capacitance transmission line theory should be used (parasitic capacitances, structures must be treated in a distributed manner). The problem can be reduced by a lumped-element approximation: Cline ' Cint Aline with Cint =

εox [F/cm2 ]. xint

(1.305)

(1.306)

Cint is the capacitance per unit area formed between the line and the substrate, xint is the oxide thickness between line and substrate. The line resistance can be estimated in a similar manner by Rline = nR2 [Ω] (1.307) where n = (d/w) is the number of squares (2) with area w2 as seen in the direction of current flow. Fig. 1.70 gives an example for cascaded stages with a fanout of three:

Figure 1.70: Capacitance calculation for FO = 3 C → CG3 + CG4 + CG5 + (∆Cline )

(1.308)

The output capacitance of CMOS inverters can be computed using similar techniques. In Fig. 1.71 two cascaded CMOS inverters are shown. Cout ' CGDn + CGDp + K(VOL , VOH )(Cdbp + Cdbn ) + Cline + CG

VLSI

Design Course

1-76

Darmstadt University of Technology Institute of Microelectronic Systems

(1.309)

0

Switching of MOS Inverters

Figure 1.71: Approximation used for Cout in cascaded CMOS inverters with CG the input capacitance of the next stage, which is given by CG = CGn + CGp

VLSI

Design Course

1-77

Darmstadt University of Technology Institute of Microelectronic Systems

(1.310)

0

Switching of MOS Inverters 1.4.9

Scaled Inverter Performance

Assuming that device dimensions are scaled with S > 1, such that Length S

Length’ =

(1.311)

This length reduction applies to all geometries in the chip. nMOS high-to-low time: 

tHL = τD

2VT D 2(VOH − VT D ) + ln −1 VOH − VT D VOL 



(1.312)

Scaling: also voltage reduction by V 0 = (V /S). The term enclosed by curly brackets in the previous equation remains constant, but τD is modified: τD =

Cout βD (VOH − VT D )

(VOH − VT D )0 = 0

(VOH − VT D ) S

⇒

Cox = SCox

0

(1.313)

(1.314)

βD = SβD

(1.315)

(C)oxide S

(1.316)

Cout consists of oxide and depletion capacitances: 0

(C 0 )oxide = Cox (Area)0 = (C)junction S Cout S τD S

(C 0 )junction ' 0

⇒ Cout = 0

⇒ τD '

(approximation)

(1.317) (1.318) (1.319)

The maximum switching frequency is 0

fmax =

1 ' Sfmax 0 tHL + tLH 0

(1.320)

If the voltage is kept constant (only lengths are scaled): 0

τD S2 = S 2 fmax

τD ' 0

fmax

VLSI

Design Course

1-78

Darmstadt University of Technology Institute of Microelectronic Systems

(1.321) (1.322)

0

CMOS Technology 1.5

CMOS Technology

1.5.1

CMOS Process Flow

Figure 1.72: CMOS process flow

VLSI

Design Course

1-79

Darmstadt University of Technology Institute of Microelectronic Systems

0

CMOS Technology 1.5.2

The Latch-Up Effect

Figure 1.73: Latch-up in n-tub CMOS inverter −→ significant problem in CMOS circuits If the base-emitter junction of the pnp transistor becomes forward biased, the transistor is switched on and I begins to flow, causing the npn transistor to be forward biased. The collector current of the npn transistor forces the pnp transistor to conduct more current. This feedback leads to latch-up and the circuit will be destroyed by heat.

VLSI

Design Course

1-80

Darmstadt University of Technology Institute of Microelectronic Systems

0

CMOS Technology

Figure 1.74: Guard rings for latch-up prevention The circuit can be prevented from latch-up by placing heavily doped guard ring around the MOSFETs. This reduces the effectiveness of the base and emitter regions in both transistors.

VLSI

Design Course

1-81

Darmstadt University of Technology Institute of Microelectronic Systems

0

Overview: Combinational Logic

Chapter 2

Static CMOS Logic Design and Combinational Circuits 2.1

Overview: Combinational Logic

Several kinds of combinational logic: • Random Logic: Circuit design using NAND gates, NOR gates and Inverters (often called “AOI Logic Gate Representation” = AND-OR-Inverter Logic)

Figure 2.1: Example for random logic: adder

VLSI

Design Course

2-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Overview: Combinational Logic • Complex MOS Logic: A boolean function is realized by a pull-up network (realizes the product terms for logic ’1’) and a pull-down network (realizes logic ’0’). Productterm realization is done by parallel/serial combinations of MOS tranistors which inputs are controlled by the literals of the boolean equation.

Figure 2.2: Complex gate logic primitive: CMOS inverter • Passtransistor Logic: transistors are used as switches which are controlled by input literals.

Figure 2.3: MOS transistors viewed as switches

VLSI

Design Course

2-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Overview: Combinational Logic

Figure 2.4: A complementary switch • Logic Arrays: PLA (programmable logic arrays), gate-matrix layout, Weinberger Arrays and regular layout achieved by application of the Euler-Graph method

VLSI

Design Course

2-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Overview: Combinational Logic

Figure 2.5: Example for regular design: gate-matrix layout

VLSI

Design Course

2-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex nMOS Logic 2.2

Complex nMOS Logic

2.2.1

nMOS NOR Gates

Figure 2.6: nMOS 2-input NOR gate

Figure 2.7: nMOS N-input NOR gate

VLSI

Design Course

2-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex nMOS Logic 2.2.2

nMOS NAND Gates

Figure 2.8: nMOS 2-input NAND gate

VLSI

Design Course

2-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex nMOS Logic 2.2.3

nMOS Complex Gates

Figure 2.9: Example of a complex nMOS circuit

VLSI

Design Course

2-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex nMOS Logic

Figure 2.10: Evolution of a nMOS XOR circuit

VLSI

Design Course

2-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex nMOS Logic

Figure 2.11: Direct NOT XOR complex gate implementation

VLSI

Design Course

2-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic 2.3

Complex Static CMOS Logic

2.3.1

CMOS NAND and NOR Gates

Figure 2.12: CMOS NAND gate

VLSI

Design Course

2-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Figure 2.13: CMOS NAND gate layout

VLSI

Design Course

2-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Figure 2.14: CMOS NOR gate

VLSI

Design Course

2-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic 2.3.2

Static CMOS Logic Design

Figure 2.15: General CMOS static logic gate

Static CMOS Complex Gate Logic Properties • Build logic gates as shown in figure 2.15 where transistors are represented as switches • The pMOS pull-up network replaces resistive or depletion loads used in nMOS technique • Configure so that for each input combination: – either a p-chain pulls the output up – or an n-chain pulls the output down ⇒ pull-up and pull-down networks implement complementary functions, when one conducts the other does not • No quiescent current through the gate means zero or very low static power dissipation • Active pull-up chains are faster than resistive loads • Switching time is the same for both kind of output changes

VLSI

Design Course

2-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Figure 2.16: CMOS complex gate construction

VLSI

Design Course

2-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Design Method • nMOS devices pull the output to ’0’ when the gate inputs are ’1’ • pMOS devices pull the output to ’1’ when the gate inputs are ’0’ Consider a function to be realized: F (A, B, C, . . .) • nMOS pull-down network must realize the pull-down function FP D = F (A, B, C, . . .) • pMOS pull-up network must realize the pull-up function FP U = F (A, B, C, . . .) The literals in FP U have to be inverted, because the p-channel transistors conduct, if their gate input is ’0’ (low). • Example: Realization of F = A + B + C (NOR) FP D = A + B + C FP U

= A+B+C =A∗B∗C

(Boolean expression transformation is to be done by applying the Shannon inversion theorem – De Morgan’s law) ⇒ Synthesis can use conventional logic design techniques (Boolean functions, Karnaugh maps, logic minimization) and express the results in AND/OR form for realisation in series and parallel connections for devices

VLSI

Design Course

2-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Rules for Logic Formation Rule 1: nMOS transistors in series implement the AND operation Rule 2: nMOS transistors in parallel implement the OR operation

Rule 3: Logic functions in series are ANDed together Rule 4: Parallel nMOS branches OR the individual branch functions

First the logic nMOS transistors are structured according to the rules above. The output of the function is the complement of the nMOS logic. Now the pMOS transistor network has to be structured according to the following rules:

VLSI

Design Course

2-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Rule 5: Parallel connections of nMOS transistors have to be transformed to serial connections of pMOS transistors. The input literals applied to the pMOS transistors are identical with the gate inputs of the nMOS transistors (no inversion needed) Rule 6: Serial connections of nMOS transistors have to be transformed to parallel connections of pMOS transistors. Input literals remain unchanged Rule 7: Parallel connected logic blocks of the nMOS network −→ serial connection in the pMOS network Rule 8: Serial connected logic blocks of the nMOS network −→ parallel connection in the pMOS network

VLSI

Design Course

2-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Figure 2.17: Systematic function construction

VLSI

Design Course

2-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Example: Basic AOI Logic Realization as Complex Gate F = A(BC + D)

(2.1)

F = D0 S0 S1 + D2 S0 S1 + D1 S0 S1 + D3 S0 S1

(2.2)

Example: 4-to-1 Multiplexer

VLSI

Design Course

2-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic ⇒ several kinds of complex gate realisations possible: • hierarchical connection of three 2-input MUX complex gates • full complex gate realization of one 4-input MUX ⇒ ... Example: AOI Logic Circuit F = AB + (A + B)C

VLSI

Design Course

2-20

Darmstadt University of Technology Institute of Microelectronic Systems

(2.3)

0

Complex Static CMOS Logic

Example: Combinational Adder CARRY = AB + AC + BC = AB + C(A + B)

(2.4)

SUM = ABC + AB C + A BC + ABC = ABC + (A B + B C + A C)(A + B + C) = ABC + CARRY(A + B + C)

(2.5)

Figure 2.18: Combinational adder schematic

VLSI

Design Course

2-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic

Figure 2.19: Combinational adder layout possibilities for one adder circuit

VLSI

Design Course

2-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Complex Static CMOS Logic 2.3.3

Pseudo nMOS Logic

Figure 2.20: Pseudo nMOS logic • Substitute the pMOS network by one single pMOS load transistor • Consists of a single pMOS load per gate (emulating the nMOS depletion load, without body effect) and a nMOS pull-down network • Needs ratioed devices • Dissipates static power, when pull-down network is on • Provides a method of emulating nMOS circuits in CMOS • Reduced noise margin

VLSI

Design Course

2-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic 2.4

Passtransistor and Transmission Gate Logic

Figure 2.21: Pass transistor logic model

Example: Pass Transistor NXOR Realisation A 0 0 1 1

B 0 1 0 1

A B 1 0 0 1

Pass Function A+B A+B A+B A+B

Figure 2.22: Pass transistor structure for NXOR function

VLSI

Design Course

2-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic 2.4.1

Passtransistor Charging Characteristics

Figure 2.23: Pass transistor charging characteristics

VGS,P = VDD − Vin = VDS,P

(2.6)

Since the passtransistor is always saturated, the charging current equation can be written as: Cin

dVin βP = (VDD − Vin − VT P )2 dt 2

where



βP = (µn Cox )

W L

(2.7)



(2.8) P

Ignoring the body bias effect the solution of this differential equation is given by (initial condition: Vin (0) = 0): Vin (t) = (VDD − VT P ) − h With τch ≡

VLSI

Design Course

(VDD − VT P ) 1+

βP t 2Cin (VDD

i .

2Cin βP (VDD − VT P )

2-25

(2.9)

− VT P )

Darmstadt University of Technology Institute of Microelectronic Systems

(2.10)

0

Passtransistor and Transmission Gate Logic

this solution may be written as 

Vin (t) = (VDD − VT P )

(t/τch ) 1 + (t/τch )



.

(2.11)

The maximum load voltage is given by Vin (t → ∞) = (VDD − VT P ) = Vmax

(2.12)

or taking into account the body bias with q

VT P (Vin ) = VT 0P + γ( 2|φF | + Vin −

q

2|φF |)

(2.13)

for the maximum voltage follows: Vmax = VDD − VT P (Vmax ) q

= (VDD − VT 0P ) − γ( 2|φF | + Vmax −

q

2|φF |) .

(2.14)

Consequences of the Passtransistor Charging Characteristics for the Design of Passtransistor Networks 1. Cascaded Passtransistor Chain: Vchainout = Vmax = (VDD − VT P ) ⇒ Vmax is propagated through the passtransistor chain

2. Pass Transistor driving another Pass Transistor: V1,max = (VDD − VT P 1 ) and V2,max = (V1,max − VT P 2 ) ⇒ reduction of Vmax !

2.4.2

Passtransistor Discharging Characteristics VGS,P = VDD − VP = VDD

VLSI

Design Course

2-26

(2.15)

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Since the passtransistor is always nonsaturated, the charging current differential equation can be written as: dVin βP 2 −Cin = [2(VDD − VT P )Vin − Vin ] (2.16) dt 2

Figure 2.24: Pass transistor discharge characteristics

VLSI

Design Course

2-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Ignoring the body bias effect the solution of this differential equation is given by: 2e−t/τdis Vin (t) = (VDD − VT P ) 1 + e−t/τdis where τdis ≡

!

.

Cin βP (VDD − VT P )

1 τdis ' τch 2 ⇒ Discharging much faster than charging.

(2.17)

(2.18) (2.19)

Figure 2.25: nMOS pass characteristics

2.4.3

CMOS Transmission Gates

Figure 2.26: CMOS transmission gate symbols

VLSI

Design Course

2-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Figure 2.27: CMOS transmission gate realisation

Figure 2.28: pMOS pass transistor pMOS Transmission Characteristics It’s not possible to discharge the capacitator to 0 Volts because Vout (t → ∞) = |VT P | = Vmin

(2.20)

Transmission Gate Model Logic Level Logic 0 Logic 1

nMOS 0 (VDD − VT n )

IDn + IDp = Cout

pMOS |VT p | VDD

CMOS 0 VDD

dVout dt

(2.21)

Logic 1 transfer: Vout (t) = VDD [1 − e−(t/τT G ) ]

(2.22)

τT G = RT G Cout

(2.23)

Vout (t) = VDD e−(t/τT G )

(2.24)

with Logic 0 transfer:

VLSI

Design Course

2-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Figure 2.29: pMOS pass characteristics

Figure 2.30: CMOS transmission gate Equivalent Resistance RT G =

Rn = Rp =

VLSI

Design Course

VT G IDn + IDp

1 βn (VDD − VT n ) 1 βp (VDD − |VT p |)

2-30

Darmstadt University of Technology Institute of Microelectronic Systems

(2.25)

(2.26) (2.27)

0

Passtransistor and Transmission Gate Logic

Figure 2.31: MOSFET operational states

Figure 2.32: Transmission gate: resistor switch model

VLSI

Design Course

2-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Figure 2.33: Transmission gate: RC switch logic transfer

Figure 2.34: Transmission gate: equivalent resistances

VLSI

Design Course

2-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Figure 2.35: Transmission gate: basic layout

VLSI

Design Course

2-33

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

TG-Based Logic Gates S=1:

B←A

(2.28)

Figure 2.36: Transmission gate logic

Path Selector F

= AS + BS

S=1

:

F =A

S=0

:

F =B

(2.29)

Figure 2.37: TG-logic: 2-input path selector

VLSI

Design Course

2-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

OR Gate F

= A + AB = A+B

(2.30)

Figure 2.38: TG-logic: OR gate

XOR and Equivalence F1 = A ⊕ B = AB + AB

(2.31)

F2 = A B = AB + A B

VLSI

Design Course

2-35

Darmstadt University of Technology Institute of Microelectronic Systems

(2.32)

0

Passtransistor and Transmission Gate Logic

Figure 2.39: TG-logic: XOR and equivalence

Figure 2.40: TG-logic: alternate equivalence logic circuit

VLSI

Design Course

2-36

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Adders S0 = A0 ⊕ B0

(2.33)

C0 = A0 B0

(2.34)

Figure 2.41: Half adder logic symbol

Figure 2.42: TG-logic: Half adder

VLSI

Design Course

2-37

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Full adder equations: Sn = (An ⊕ Bn )C n−1 + (An ⊕ Bn )Cn−1

(2.35)

Cn = (An ⊕ Bn )Cn−1 + (An ⊕ Bn )An

(2.36)

Figure 2.43: TG-logic: Full adder

VLSI

Design Course

2-38

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Array Logic Multiplexers/Demultiplexers

Figure 2.44: Multiplex/Demultiplex operations 4-to-1 Multiplexer: F = D0(AB) + D1(AB) + D2(AB) + D3(A B)

(2.37)

⇒ Multiplexers can be used as function generators

Figure 2.45: TG-logic: 4-to-1 multiplexer (example: for D0=1, D1=0, D2=0, D3=0 an AND function is realized)

VLSI

Design Course

2-39

Darmstadt University of Technology Institute of Microelectronic Systems

0

Passtransistor and Transmission Gate Logic

Split Arrays ⇒ improvement of the layout efficiency by separating pMOS and nMOS transistors into two distinct areas (physical separation)

Figure 2.46: TG-logic: Split-Array MUX

Pass Transistor Logic with pMOS Pull-Up For reduction of device count and area an nMOS version with pMOS pull-up can also be useful (→ kind of pseudo nMOS).

Figure 2.47: Pass transistor logic with pMOS pull-up

VLSI

Design Course

2-40

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clocking

Chapter 3

Synchronous MOS Logic 3.1

Clocking

Clock Signal: • used to synchronize data flow through a digital network ⇒ clocked static or dynamic circuits • problems: clock skew (delay caused by clock distribution wires)

Figure 3.1: Ideal nonoverlapping 2-phase clocks Condition for nonoverlapping clock signals φ1 (t) and φ2 (t): φ1 (t)φ2 (t) = 0

VLSI

Design Course

3-1

∀t

Darmstadt University of Technology Institute of Microelectronic Systems

(3.1)

0

Clocking

Figure 3.2: Basic 2-phase clocking

3.1.1

Single and Multiple Clock Signals

Figure 3.3: Single clock 2-phase timing ⇒ For nonoverlapping clock phases φ and φ fine tuned and well designed delay lines (realized as Transmission gates) have to be inserted in order to avoid overlapping of φ and φ.

VLSI

Design Course

3-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clocking

Figure 3.4: Generation of inverted clock phase

Figure 3.5: TG delay circuit

VLSI

Design Course

3-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clocking

Figure 3.6: Pseudo 2-φ clocking

VLSI

Design Course

3-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clocked Static Logic 3.2

Clocked Static Logic

⇒ Synchronized data transfer

Figure 3.7: Shift register

Upper Frequency Limitation: Charging and Discharging Times

Figure 3.8: Clocked shift register circuit Time constant for charging and discharging: τT G = RT G CL

(3.2)

CL = CT G + Cin + Cline

(3.3)

Vin (t) ' VDD [1 − e−t/τT G ]

(3.4)

where VA = VDD :

(Vin (0) = 0)

Inverter is switched, when Vin = VIH which occurs after VIH t1 ' −τT G ln 1 − VDD 



Cin = Cox [(W L)n + (W L)p ]

VLSI

Design Course

3-5

Darmstadt University of Technology Institute of Microelectronic Systems

(3.5) (3.6)

0

Clocked Static Logic

VA = 0 :

(Vin (0) = VDD ) Vin (t) ' VDD e−t/τT G

(3.7)

The time until Vin reaches VIL is given by VIL t0 = −τT G ln VDD 



(3.8)

Lower Frequency Limitation: Charge Leakage

Figure 3.9: Leakage path in a CMOS TG The load capacitance, seen by the transmission gate (TG) is CL = CT G + Cline + Cin The depletion capacitance contributions to CL are due to the reversed pn junctions MOS transistors. As shown in fig. 3.9 a leakage current flow exists across the reverse pn junctions. The influence of this leakage current on the charge stored in CL depends values of ILp and ILn . With IL = ILn − ILp

(3.9) in the biased on the (3.10)

the leakage current influence on Vin is given by CL

dVin = −IL dt

(3.11)

If ILp > ILn the capacitance is charged by IL otherwise it is discharged or remains constant when the ideal condition ILp = ILn is true. dQstore dt

= ILp − ILn

Cstore =

dQstore dV

(3.12) (3.13)

Assuming that the leakage currents ILp and ILn are constant and that the node charge voltage relation is linear of the form Qstore = Cstore V (3.14)

VLSI

Design Course

3-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clocked Static Logic

Figure 3.10: Charge leakage problem in CMOS TG follows (because Cstore is const.) Cstore

dV = ILp − ILn . dt

(3.15)

The solution of this equation is V (t) =

(ILp − ILn ) t + V (0) Cstore

(3.16)

If ∆V is the maximum allowed voltage change: tmax =

VLSI

Design Course

3-7

Cstore ∆V IL

Darmstadt University of Technology Institute of Microelectronic Systems

(3.17)

0

Clocked Static Logic

Figure 3.11: Charge leakage circuit With Tmax = 2tmax (the longest allowed clock period) follows for the minimum frequency fmin ' '

1 2tmax IL 2Cstore ∆V

(3.18)

The transmission gate capacitance is

Figure 3.12: Transmission gate capacitance CT ' CG + Cline + Cols + Cold + CSBp (V ) + CDBn (V ) .

(3.19)

So the storage capacitance can be estimated by voltage averaging of this expression: Cstore ' CG + Cline + Cols + Cold + K(0, VDD )[CSBp + CDBn ]

VLSI

Design Course

3-8

Darmstadt University of Technology Institute of Microelectronic Systems

(3.20)

0

Clocked Static Logic

For a realistic analysis of the charge leakage problems the dependence of the leakage currents from the reverse voltage bias has to be taken into consideration (see [25]).

VLSI

Design Course

3-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Charge Sharing 3.3

Charge Sharing

Figure 3.13: Basic charge sharing circuit t<0:

(TG switched off) V1 (t < 0) = VDD

(3.21)

V2 (t < 0) = 0

(3.22)

QT t>0:

= C1 VDD

(3.23)

(TG switched on) QT Vf

= (C1 + C2 )Vf

(3.24)

= V1 (t > 0) = V2 (t > 0) C1 = VDD C1 + C2 1 = VDD 1 + (C2 /C1 )

(3.25)

Charge sharing among N TG-connected capacitators Initial charge: QT =

N X

Ci Vi (0)

(3.26)

i=1

After connecting nodes: QT =

N X

!

Ci Vf

(3.27)

i=1 Ci Vi (0) PN i=1 Ci

(3.28)

i=1

Final voltage: PN

Vf =

VLSI

Design Course

3-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Charge Sharing

Figure 3.14: Transient voltage behaviour

VLSI

Design Course

3-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Dynamic Logic 3.4

Dynamic Logic

• Pull-up (pull-down) network of static CMOS is replaced by a single precharge (discharge) transistor. The remaining network then conditionally discharges (charges up) the output in a second operation phase • One logic level is held by dynamic charge storage • Transistor count is reduced from 2n (static CMOS) to n+2 for dynamic precharged CMOS (but now: 2 phases of operation)

3.4.1

Dynamic nMOS Inverter

Figure 3.15: Basic dynamic nMOS inverter

Precharge Phase If Vin = 0 then τch =

Cout = Rp Cout βp (VDD − |VT p |)

(3.29)

Worst case (Vin = VDD ): τch,max = Rp (Cout + Cn ) "

tch,max = τch,max

VLSI

Design Course

(3.30) #

2|VT p | 2(VDD − |VT p |) + ln −1 (VDD − |VT p |) V0 

3-12

Darmstadt University of Technology Institute of Microelectronic Systems

(3.31)

0

Dynamic Logic

Figure 3.16: Dynamic nMOS inverter: precharge and evaluate Evaluation Phase For the case that M1 is switched on and identically designed channel width for M1 and Mn the discharge time constant is given by τdis =

VLSI

Design Course

(L1 + Ln )Cout kn W (VDD − VT n ) 0

3-13

Darmstadt University of Technology Institute of Microelectronic Systems

(3.32)

0

Dynamic Logic

Figure 3.17: Precharge network for worst case

Figure 3.18: Evaluation discharge network 

tdis = τdis

2VT n 2(VDD − VT n ) + ln −1 (VDD − VT n ) V0 



(3.33)

Maximum Clock Frequency tM = max(tch,max , tdis )

VLSI

Design Course

3-14

Darmstadt University of Technology Institute of Microelectronic Systems

(3.34)

0

Dynamic Logic

fmax '

3.4.2

1 2tM

(3.35)

Dynamic pMOS Inverter

Figure 3.19: Basic dynamic pMOS inverter

3.4.3

Dynamic CMOS Properties and Conditions

• single phase clock • input should change during precharge only • input must be stable at the end of the precharge phase • in the evaluation phase the output remains HIGH (LOW) or is optionally discharged (charged)

VLSI

Design Course

3-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Dynamic Logic 3.4.4

Complex Logic

Figure 3.20: Complex dynamic logic

VLSI

Design Course

3-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Dynamic Logic 3.4.5

Dynamic Cascades

pMOS blocks and nMOS blocks have to be installed alternated in order to avoid glitches

Figure 3.21: Cascaded nMOS-nMOS glitch problem

Figure 3.22: Dynamic cascades

VLSI

Design Course

3-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Domino CMOS Logic 3.5

Domino CMOS Logic

Figure 3.23: Basic domino logic circuit • Domino Logic: design method for glitch-free cascading of nMOS logic blocks • Each stage is driven by φ – Precharge during φ = 0 – Evaluation when φ = 1 • Domino logic blocks consist of a precharge/evaluation block and an output inverter Precharge Phase: The gate output is precharged to logic 1 and the inverter output is going to logic 0. Logic transmission errors are avoided by providing a logic 0 at the inverter output (avoiding discharge of the next logic stage). Evaluation Phase: The inverter output stays according to the actual input values at logic 0 or is set to logic 1. The correct result signal is provided at the end of the domino cascade after stabilization of all stages.

VLSI

Design Course

3-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Domino CMOS Logic

Figure 3.24: Domino AND gate

Figure 3.25: Cascaded domino logic

Figure 3.26: Visualization of domino effect

VLSI

Design Course

3-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Domino CMOS Logic

$\phi_N$

B

A

n

D

C

n

n

$\phi_N$

A

B

C

D

Figure 3.27: Domino timing

VLSI

Design Course

3-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Domino CMOS Logic

Figure 3.28: Cascaded domino circuit with fanout = 2

VLSI

Design Course

3-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Domino CMOS Logic 3.5.1

Domino Logic Properties

out

out

n-channel

p-channel

only

only

clk

$\overline{\rm clk}$

Figure 3.29: Cascaded domino logic

• Domino logic consists of either n-type or p-type blocks • small load capacity to be driven by logic (one inverter only) =⇒ low dimension of transistors • only one clock signal required • only positive logic realizations possible because of the input inverters ⇒ domino logic is noninverting Functions as F1 = A ⊕ B = AB + AB F2 = A B = AB + A B

(3.36)

cannot be directly realized in a domino chain

VLSI

Design Course

3-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Domino CMOS Logic 3.5.2

Analysis

Figure 3.30: Domino AND4 gate

Precharge Assuming that all Ai (coming from previous stages) are zero, the capacitance CX is charged, where CX

= C0 + CT

(3.37)

' (CGDn1 + CBDn1 ) + (CGDp1 + CBDp1 ) + CG + Cline

(3.38)

Evaluate If all inputs Ai are set to logic 1, the worst case delay time can be estimated by tD ' Rn Cn + (Rn + R3 )C3 + (Rn + R3 + R2 )C2 + +(Rn + R3 + R2 + R1 )C1 + (Rn + R3 + R2 + R1 + R0 )CX with Rj =

VLSI

Design Course

1 kn0 (W/L)j (VDD − VT n )

3-23

Darmstadt University of Technology Institute of Microelectronic Systems

(3.39)

(3.40)

0

Domino CMOS Logic 3.5.3

Charge Leakage and Charge Sharing

Figure 3.31: Domino stage with pull-up MOSFET

VLSI

Design Course

3-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Domino CMOS Logic

Figure 3.32: Charge sharing in a domino chain

Figure 3.33: Use of feedback to control a pull-up MOSFET for charge sharing problem

VLSI

Design Course

3-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

NORA Logic 3.6

NORA Logic

(NORA = NO RAce)

3.6.1

NORA Properties

• NORA is very insensitive to clock delay • one clock signal and the inverted clock signal with short slopes rise times are sufficient • no inverter is needed between the logik stages, because of alternate use of n-type and p-type blocks • the last stage is a clocked inverter, a C2 MOS latch

3.6.2

The Signal Race Problem

Figure 3.34: Signal race problem From fig. 3.34 the signal race problem can be seen: A signal race can arise, when both transmission gates conduct at the same time. If the new input from TG1 reaches the input of TG2 while TG2 is still transmitting the output, the output information will be lost. Imperfect TG synchronization occurs because of normal transition intervals or clock skew.

VLSI

Design Course

3-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

NORA Logic

Figure 3.35: Clock skew

VLSI

Design Course

3-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

NORA Logic 3.6.3

NORA Structuring

$\overline{clk2}$ in

out clk2

clk1

$\overline{clk1}$

clk1

clk2

Figure 3.36: NORA structuring

VLSI

Design Course

3-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

NORA Logic

Figure 3.37: NORA φ and φ sections

VLSI

Design Course

3-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

NORA Logic

Figure 3.38: C2 MOS latch

Figure 3.39: NORA pipelined logic

VLSI

Design Course

3-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures 3.7

Memory Structures

3.7.1

Principle of CMOS Information Storage

Figure 3.40: Connection of components for a simple CMOS flip-flop Behaviour: LD = 1 :

Q←D

Q←D

LD = 0 : store current state

VLSI

Design Course

3-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

Figure 3.41: Physical Construction of a CMOS flip-flop

VLSI

Design Course

3-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures 3.7.2

Dynamic Flip-Flops: Pseudo 2-Phase Clocking

Figure 3.42: Pseudo 2-phase clocking (a) waveforms and simple latch, (b) clock skew, and (c) slow clock edges

VLSI

Design Course

3-33

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.3

Pseudo 2-Phase Memory Structures

Figure 3.43: Pseudo 2-phase latches (! charge redistribution problem in (b))

VLSI

Design Course

3-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

Figure 3.44: Pseudo 2-phase latch layouts

VLSI

Design Course

3-35

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

Figure 3.45: Shift register array layout

VLSI

Design Course

3-36

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.4

Dynamic Flip-Flop with reduced Transistor Count and Clock Connection

(Reduced Noise Margins – Poor “1” in the Slave)

Figure 3.46: Reduced transistor count latch better with high impedance sustainer transistor: (accurate simulation is required for correct function)

D

Q

$\phi_1$

$\phi_2$

Figure 3.47: Reduced transistor count latch with high impedance sustainer transistor

VLSI

Design Course

3-37

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.5

Dynamic D-Latches

Figure 3.48: Dynamic D-Latches Characteristic Equation: Q(t) = D(t) and LD = 1 = Q(t − 1) and LD = 0 where D(t) is the state of the data at time t Q(t) is the state of the latch at time t Q(t-1) is the state of the latch at time t-1

VLSI

Design Course

3-38

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.6

Pseudo 2-Phase Logic Structures

Figure 3.49: Pseudo 2-phase dynamic logic

VLSI

Design Course

3-39

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.7

Pseudo 2-Phase Logic Structures: Domino Logic

a number of logic stages may be cascaded before latching the result

Figure 3.50: Pseudo 2-phase domino logic

VLSI

Design Course

3-40

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.8

2-Phase Memory Structures: Skew Reduction

Figure 3.51: 2-phase flip-flop and skew reduction

VLSI

Design Course

3-41

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.9

2-Phase Memory Structures: Chain Latch

Figure 3.52: Chain latch

VLSI

Design Course

3-42

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.10

2-Phase Memory Structures: Static Flip-Flops

Figure 3.53: 2-phase static flip-flops

VLSI

Design Course

3-43

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.11

2-Phase Memory Structures: Static D Flip-Flops

Figure 3.54: 2-phase static D flip-flops

VLSI

Design Course

3-44

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

Figure 3.55: 2-phase static D flip-flops (continued)

VLSI

Design Course

3-45

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures 2-Phase D Flip-Flops layouts of Fig 3.53a, 3.54a and 3.54b

Figure 3.56: 2-phase D flip-flops layouts

VLSI

Design Course

3-46

Darmstadt University of Technology Institute of Microelectronic Systems

0

Memory Structures

3.7.12

Static D Flip-Flop with Set and Reset

Figure 3.57: Static D flip-flop with set and reset

INPUTS CL D R X X 1 X X 0 X X 1

S 0 1 1

OUTPUT Q 0 1 NA

Table 3.1: Static D flip-flop set/reset truth table

VLSI

Design Course

3-47

Darmstadt University of Technology Institute of Microelectronic Systems

0

Signaldelay

Chapter 4

Performance 4.1

Signaldelay

4.1.1

Resistance Estimation

The resistance of an uniform slab of conducting material may be expressed as ρ t

 

R=

l w



where ρ t l w

= = = =

resistivity thickness conductor length conductor width

This expression may be rewritten as R = Rs

  l w

, where Rs is the sheet resistance having

Ω 2

units of (ohms per square). Thus to obtain the resistance of a layer, one would simply multiply the sheet resistance Rs , by the ratio of the length to width of the conductor. Note that for metal having a given thickness t, the resistivity is known, while for poly and diffusion the resistivities are significantly influenced by the concentration density of the impurities that have been introduced into the conducting regions during implantation. This means that the process parameters have to be known to accurately estimate these quantities. Although the voltage-current characteristic of a MOS transistor is generally nonlinear, it is sometimes useful to approximate its behavior in terms of a channel resistance to estimate performance. The channel resistance may be expressed by 

Rc = k with 0 r k= µ tox  

VLSI

Design Course

4-1



L W



−1

(Vgs − Vt )

Darmstadt University of Technology Institute of Microelectronic Systems

0

Signaldelay


    

 ! "

#%$

#%$ & '! "

-/. 01/23  41$ -/. 01% (

41$ -/. 0156 (

(*),+ 

Figure 4.1: Basic LOCOS MOSFET structure. For both the n-channel and p-channel devices, k may take a value within the range 50, 000 to 30, 000 Ω 2 . The equation for k as given above demonstrates the dependence of channel resistance on the surface mobility µ of the majority carriers. Since the mobility is also a function of temperature, the channel resistance and therefore switching time parameters, as well as power dissipation, change with temperature variations. The increase in channel resistance may be approximated by +0.25% per ◦ C for an increase in temperature above 25◦ C.

4.1.2

Capacitance Estimation

The dynamic response of MOS systems are very much dependent on the parasitic capacitances associated with the MOS device and interconnection capacitances that are formed by metal, poly, and diffusion wires in concert with transistor and conductor resistances. The total load capacitance on the output of a MOS gate is the sum of: • gate capacitance (of other inputs connected to the output of the gate) • diffusion capacitance (of the drain regions connected to the output) • routing capacitance (of connections between the output and other inputs). Gate Capacitances The large-signal MOSFET capacitance model that will be used to compute Cgate is based on the self-aligned, poly gate LOCOS (local oxidation of silicon) structure depicted in Fig. 4.1.

VLSI

Design Course

4-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Signaldelay Gate (Oxide thickness xox)

Source

Drain

field oxide

Cols

Cold Cgs

field oxide

Cgd

n+

n+ Cgb Csb

Cdb

p+

p+ p-substrate

Basic model (a)

Poly gate

Drain n+

L

Ls

Ld

Source n+ W

Ys

Yd

Top view geometry (b)

Figure 4.2: MOSFET capacitor model. Although the LOCOS MOSFET has been singled out for the analysis, the model developed here is generally applicable to any MOSFET regardless of the technology base. Figure 4.2a shows the basic lumped-element capacitances and their physical origins in terms of the device cross section. This particular model is chosen because it allows the capacitors to be divided into contributions that may be computed directly from the device and processing parameters. 1. The overlap capacitances Cols and Cold are parasitic elements that originate from the basic fabrication steps. In the self-aligned process, the polysilicon gate is employed as a mask to define the n+ drain and source regions. Directly after this step, Ls = Ld = 0 and L0 = L. The overlaps occure because the remaining steps require heating of the wafer. This gives rise to lateral diffusion of the n+ dopants. Typically, these overlap

VLSI

Design Course

4-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Signaldelay capacitance

Off

Linear

Saturation

Cgb

A tox

0

0

Cgs

0

1 2



A tox



Cgd

0

1 2



A tox



Cg = Cgb + Cgs + Cgd

A tox

A tox

2 3



A tox



0

2 3



A tox



Table 4.1: Approximation of intrinsic MOS gate capacitance

distances are less than a few tenths of a micron. Cols = Cox W Ls , where Cox =

Cold = Cox W Ld

ox tox

2. The gate-source capacitance Cgs is really the gate-to-channel capacitance as seen between the gate and source; similarly, Cgd represents the gate-drain capacitance when the channel is acting as a conductor to the drain n+ region. The voltage-dependent nature of the channel implies that these elements are nonlinear. Cgb is the gate-bulk capacitance and consists of the gate capacitance in series with the depletion capacitance established by the p-type space charge region. Table 4.1 shows approximated values of these three capacitances in various states of the MOS transistor.

Diffusion Capacitances The two remaining capacitors in the model of Fig. 4.2a are Csb and Cdb . These represent the voltage-dependent depletion capacitances that result from the pn junctions at the drain and source regions. The problem of determining these elements is aided by using the expanded drawing in Fig. 4.3. This shows an n+ well in a p-type bulk region and is representative of either a drain or a source; note that a p+ region surrounds the n+ sidewalls. The actual doping profile around the pn junction is generally quite complicated. A step doping will be assumed for simplicity. The total depletion capacitance Cd can be presented by Cd = Cja · (W · Yd ) + Cjp · (2W + 2Yd ) where

VLSI

Design Course

4-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Signaldelay

Y

p+ n+ Drain or source well W n+

p+

Nd

p+

xj

p+

p-type substrate Na Depletion region

Figure 4.3: Expanded view of an n+ drain or source region for computing depletion capacitances. Cja Cjp W Yd

= = = =

juntion capacitance per µm2 periphery capacitance per µm width of diffusion region extent of diffusion region

Since the thickness of depletion layer depends on the voltage across the junction, both Cja and Cjp are functions of junction voltage Vj . A general expression that describes the junction capacitance is   Vj −m Cj = Cj0 1 − ΦB where Vj is the junction voltage (negative for reverse bias), Cj0 zero bias capacitance (Vj = 0), and ΦB the build-in junction potential (∼ 0.6V ). m is a constant, which depends on the distribution of impurities near the junction, and has a value of the order of 0.3 to 0.5. Routing Capacitances: Routing capacitances between metal and poly layers and the substrate can be approximated using a parallel plate model (C = t A), where A is the area of the plate capacitor, t is the insulator thickness, and  is the dielectric constant of the insulating material between the plates. The parallel-plate approximation, however, ignores fringing fields. The effect of fringing fields is to increase the effective area of the plates. Consequently, poly and metal lines will actually have a higher capacitance (up to twice as large) than that predicted by the model. Interlayer capacitance such as metal-poly capacitance is also enhanced by fringing. As line width are scaled, the width (w) and heights of wires tend to reduce less than their separations (l). Accordingly, this fringing effect increases in importance. For current processes, a factor of 1.5 − 3 should be used. Another factor, which should be taken into account for small

VLSI

Design Course

4-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Signaldelay Ij-1 R

Ij

R

Vj-1

R

Vj

C

R

Vj+1

C

C

C

Figure 4.4: Representation of long wire in terms of distributed RC sections

geometries when using the parallel plate model, is that a drawn shape (on mask) will not be the same as the actual physical shape produced on silicon.

4.1.3

RC-line model

The propagation of a signal along a wire depends on many factors, including the distributed resistance and capacitance of the wire, the impedance of the driving source, and the load impedance. For very long wires propagation delays caused by distributed resistance capacitance (RC) in the wiring layer tend to dominate. This transmission line effect is particularly severe in poly wires because of the relatively high resistance of this layer. A long wire can be represented in terms of several RC sections, as shown in Fig. 4.4. The response at node Vj with respect to time is then given by C

(Vj−1 − Vj ) (Vj − Vj+1 ) dVj = (Ij−1 − Ij ) = − dt R R

As the number of sections in the network becomes large (and the sections become small), the above expression reduces to the differential form: rc

dV d2 V = dt dx2

where x r c

= = =

distance from input resistance per unit length capacitance per unit length

Solution of this differential form yields an approximate signal delay of: tl =

rcl2 2

where r c l

VLSI

Design Course

= = =

resistance per unit length capacitance per unit length length of the wire

4-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Signaldelay

1mm

1mm Buffer

Input

Output

taubuf

Figure 4.5: Segmentation of polysilicon line

Rs

Rt tau

Cl

Ct

V

Figure 4.6: Simple model for rc delay calculation

The l2 term in the equation above shows that signal delay will be totally dominated by this RC effect for very long signal paths. In order to optimize speed in a long poly line, one possible strategy is to segment the line into several sections and insert buffers within these sections as shown in Fig. 4.5. A model for the distributed RC delay, which takes driver and receiver loading into account, is shown in Fig. 4.6. Rs is the output resistance of the driver. Cl is the receiver input capacitance. Rt and Ct are the total lumped resistance and capacitance of the line. τ is the 2 RC delay calculated using the equation τ = rc.l 2 . The concept of using RC time constants for delay estimations is based upon the assumption that the time taken for a signal to reach 63% of its final value approximates the switching point of an inverter. Wire length design guide For the purpose of timing analysis, an electrical mode may be defined as that region of connected paths in which the delay associated with signal propagation is small in comparison with gate delays. For sufficiently small wire lengths, RC delays can be ignored. Wires can then be treated as one electrical node and modeled as simple capacitive loads. It is therefore useful to define simple electrical rules that can be used as a guide in determining the maximum length of communication paths for the various interconnect levels. To do this we required that wire delay τw and gate delay τg satisfy the following condition: τw  τg

VLSI

Design Course

4-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

CMOS Gate Transistor Sizing

To fulfil this condition, the maximum length of the wire is given by: r

l

2τg rc

This establishes an upper bound on the allowable length of the interconnects where the above approximations are valid.

4.2

CMOS Gate Transistor Sizing

To have the same rise and fall times for an inverter, we must make Wp = 2Wn where Wp is the channel width of the p-device and Wn is the channel width of the n-device. This, of course increases layout area and dynamic power dissipation. In some cascaded structures it is possible to use minimum size devices without compromising the switching response. This is illustrated in the following analysis, in which the delay response for an inverter pair (Fig. 4.7a) with Wp = 2Wn is given by

tinv.pair = tf all + trise R 3Ceq 2 = 3RCeq + 3RCeq 



= R.3Ceq + 2 = 6RCeq

where R is the effective on resistance of a unit-sized n-transistor and Ceq = Cg + Cd is the capacitance of a unit-size gate and drain region. The inverter pair delay with Wp = Wn is

tinv.pair = 4RCeq + 2RCeq = 6RCeq

Thus we find similar responses are obtained for the two different conditions.

4.3

Power Dissipation

There are two components that establish the amount of power dissipated in a CMOS circuit. These are: 1. Static dissipation − due to leakage current.

VLSI

Design Course

4-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power Dissipation tinv.pair R

R 3Ceq

3Ceq

(b) Wp=2Wn

tinv.pair 2R

R 2Ceq

2Ceq

(b) Wp=Wn

Figure 4.7: CMOS inverter pair timing response

2. Dynamic dissipation − due to: (a) switching transient current (b) charging and discharging of load capacitances

4.3.1

Static power dissipation

Considering a complementary CMOS gate, if the input=‘0’, the associated n-device is ‘OFF’ and the p-device is ‘ON’. The output voltage is VDD or logic ‘1’. When the input=‘1’, the associated n-channel is biased ‘ON’ and the p-channel device is ‘OFF’. The output voltage is 0V (VSS ). Note that one of the transistors is always ‘OFF’ when the gate is in either of these logic states. Since no current flows into the gate terminal, and there is no D.C. current, and hence power Ps , is zero. However, there is some small static dissipation due to reverse bias leakage between diffusion regions and the substrate. The source-drain diffusion and the p-well diffusion form parasitic diodes. Since the diodes are reverse biased, only their leakage current contributes to static power dissipation. The leakage current is described by the diode equation V

i0 = is (e kT /q − 1) where

VLSI

Design Course

4-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power Dissipation is V q k T

= = = = =

reverse saturation current diode voltage electronic charge Boltzmann’s constant temperature

The static power dissipation is the product of the device leakage current and the supply voltage. A useful estimate is to allow a leakage current of 0.1nA to 0.5nA per gate at room temperature. Then total static power dissipation Ps is obtained from Pn

Ps = (

1 leakage

current) × suply voltage

For example, typical static power dissipation due to leakage for an inverter operating at 5V is between 1 − 2nW (nano-watts).

4.3.2

Dynamic power dissipation:

During transition from either ‘0’ to ‘1’ or, alternatively, from ‘1’ to ‘0’, both n- and p-transistors are on for a short period of time. This results in a short current pulse from VDD to VSS . Current is also required to charge and discharge the output capacitive load. This latter term is generally the dominant term. The current pulse from VDD to VSS results in a ”short circuit” dissipation which is dependent on the load capacitance and the gate design. This is of relevance to I/O buffer design. The dynamic dissipation can be modeled by assuming the rise and fall time of the step input is much less than the repetition period. The average dynamic power, Pd , dissipated during switching for a square-wave input Vin , having a repetition frequency of fp = 1/tp , as shown by Fig. 4.8, is given by 1 Pd = tp

tZp /2 0

1 in (t)Vo .dt + tp

Ztp

ip (t)(VDD − Vo ).dt

tp /2

where in ip

= =

n-device transient current p-device transient current

For a step input with in (t) = CL dVo /dt (CL =load capacitance) Pd =

= with fp =

1 tp ,

CL tp

VZDD

0 2 CL VDD

CL Vo .dVo + tp

Z0

(VDD − Vo ).d(VDD − Vo )

VDD

tp

resulting in 2 Pd = CL VDD fp

VLSI

Design Course

4-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power Dissipation $t_p$ $V_{in}$

$V_{DD}$

$0$

$t$ $t_f$

$t_r$

$V_o$

$V_{DD}$

$0$

$t$

$I_d$

$I_{dn}$ $I_{pn}$

$0$

$t$

Figure 4.8: Waveforms for determination of dynamic power dissipation

Thus for the repetitive step input the average power that is dissipated is proportional to the energy required to charge and discharge the circuit capacitance. The important factor to be noted here is that the lattest equation shows power to be proportional to switching frequency but independent of the device parameters.

4.3.3

Power delay product

The power delay product (PDP) is used to characterize the overall performance of a digital gate circuit. It is given by P DP = Pav tp where Pav is the average power dissipated by the gate and tp is the average propagation delay time. Typically, MOS-based digital gates display power-delay products on the order of a few picojoules (pJ). The PDP is commonly used to compare the performance of various logic families or processing technologies. A small PDP is desirable, as this implies both low power consumption and fast switching speeds. As a first step towards understanding the meaning of the PDP, suppose that an ideal square

VLSI

Design Course

4-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power Dissipation

Vin(t)

One logic cycle

VOH

VOL t 0

T/2

T

Ideal square wave (a)

Vin(t)

VOH

V_{1/2}

VOL t 0

T/2

T

Finite rise and fall time waveform (b)

Figure 4.9: Input voltage waveforms for the power-delay products

wave Vin (t) (Fig. 4.9a) is applied to the resistively load nMOS inverter shown in Fig. 4.10a; the output voltage Vout (t) then assumes the form drawn in Fig. 4.10b. The average propagation delay is 1 tp ≈ (Ron + RL )Cout 2 with approximations as followed tP HL ≈ τD = Ron Cout tP LH ≈ τL = RL Cout where Ron is the on-resistance of the driver; note that Ron = RDS . The average power dissipated by the circuit is given by Pav = Iav VDD Iav is the average power supply current and is separated into two contributions: the constant (DC) current flow when the output is stable with Vout = VOL and the transient current that flows during the rise and fall times. Using Ohms’s law, the average DC power dissipation during the period T is 2 VDD Pav = 2(Ron + RL ) The PDP that results from the constant DC current flow only is given by 1 2 (P DP )DC ≈ Cout VDD 4

VLSI

Design Course

4-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power Dissipation

$V_{DD}$

$R_L$

$+$

$+$

$V_{out}(t)$

$C_{out}$

$-$

$V_{in}(t)$ $-$

{\it Basic inverter (a)}

$V_{DD}$ $V_{out}$ $R_L$

$V_{OH}$

$+$ $V_{1/2}$ $V_{out}$ $R_{on}$ $V_{OL}$

$-$

$t$ $T/2$

$T$

{\it Output voltage (b)}

{\it Resistor analogy for $V_{out}=V_{OL}$ (c)}

Figure 4.10: Power-delay product in a resistively loaded inverter.

The total power-delay product for the circuit must also account for the average power consumed by the gate during the rise and fall time intervals. Consider first the charging current supplied by VDD during the rise time tLH . Since the driver is in cutoff, this can be estimated by Vl (∆V ) Iav ≈ Cout = Cout (∆t) tLH with Vl = VDD being the logic swing. The resulting PDP contribution due to this current is then tp 2 (P DP )LH ≈ Cout VDD tLH The power supply current used by the inverter during the discharge time tHL is approximated by   1 1 (VDD − VOH ) (VDD − VOL ) Iav ≈ (Iinitial + If inal ) = + 2 2 RL RL Iinitial and If inal give the current at the beginning and end of the discharging event. Thus,

VLSI

Design Course

4-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power Dissipation $V_{in}(t)$ $V_{OH}$

$V_{1/2}$

$V_{OL}$ $t$ $0$

$T/2$

$T$

{\it Input voltage waveform} {\it (a)}

$I(t)$ $I_{max}$

$I_{leak}$ $t$ $0$

$T/2$

$T$

{\it Power supply current for an NMOS inverter} {\it (b)}

$I(t)$ $I_{peak}$

$t$ $0$

$T/2$

$T$

{\it Power supply current for a CMOS inverter} {\it (c)}

Figure 4.11: Current waveforms for the power-delay product calculations.

assuming VOL  VOH = VDD , Iav ≈

VDD 2RL

Now, noting that tP HL ≈ τD , a first-order estimate for the discharge time tHL is tHL ≈ 2τD = 2Ron Cout . Forming the power-delay product for this time interval gives the term 2 (P DP )HL ≈ Cout VDD

Ron tp RL tHL

The complete expression for the PDP is obtained by summing all contributions: P DP ≈

2 Cout VDD



tp Ron tp 1 + + 4 tLH RL tHL



This can be simplified by noting that Ron  RL will be valid in a well-designed inverter. The propagation delay time is then tp ≈ (τL /2). Using this in conjunction with the approximations tLH ≈ 2τL and tHL ≈ 2τD gives 3 2 P DP ≈ Cout VDD 4 as the lowest-order approximation for the total PDP.

VLSI

Design Course

4-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Scaling

The power-delay product for the CMOS inverter is computed by using the current waveform in Fig. 4.11c. Since current flows only during a switching event, the average power supply current required during a single logic cycle T can be written by Iav =

1 [IDn,LH tLH + IDn,HL tHL ] T

In this equation IDn,LH gives the average current during the rise time, while IDn,HL is the average fall time current. For a completely symmetric CMOS inverter, the two currents are the same, so the power-delay product is given by P DPCM OS = IDn,av VDD tp

4.4

f fmax

Scaling

Very large-scale integration (VLSI) requires dense circuit layouts on silicon. The level of integration depends on the smallest-size feature permitted by the fabrication processes. To obtain the highest packing density, the size of the transistors must be made as small as possible. This, however, changes the internal operating physics of the MOSFETs. Phenomena that are negligible in “large” devices become limiting factors as device geometries are reduced. This section discusses some of the important aspects involved in describing small MOSFETs. The level is introductory, with emphasis on parameters that affect circuit design. The model we use is a simple first-order constant field scaling.

4.4.1

Scaling principles

First-order MOS scaling theory indicates that the characteristics of an MOS device can be maintained and the basic operational characteristics preserved if the critical parameters of a device are scaled in accordance to a given criterion. Such an approach has shown to be very effective in scaling from the range 5µm to 10µm minimum features to the range 1µm to 3µm minimum feature size. Although first-order scaling does not give optimized device performance at small dimensions, the technique is very powerful in providing the necessary guidelines to identify the improvements (or otherwise) that can be expected as processes are scaled. Basically the scaled device is obtained by applying a dimensionless factor α to • all dimensions, including those vertical to the surface • device voltages • the concentration densities. The resultant effect of the first-order scaling process is illustrated in Table 4.2. Table 4.2 shows that if device dimensions (which include channel length L, channel width W , oxide thickness Tox , junction depth Xj , applied voltages, and substrate concentration density N ) are scaled by the constant parameter α, then the depletion thickness d, the threshold voltage

VLSI

Design Course

4-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Scaling

DEVICE PARAMETER

RESULTANT INFLUENCE

PARAMETER Length; L Width; W Gate oxide thickness; tox Junction depth; Xj Substrate doping; Na or Nd Supply voltage; VDD Electric field across gate oxide; E Depletion layer thickness; d Parasitic capacitance; W L/tox Gate delay; (V C/I) DC power dissipation; Ps Dynamic power dissipation; Pd Power speed product Gate area Power density; (V I/A) Current density; (I/A) Transconductance; gm

SCALING FACTOR 1/α 1/α 1/α 1/α α 1/α 1 1/α 1/α 1/α 1/α2 1/α2 1/α3 1/α2 1 α 1

Table 4.2: Influence of first-order scaling on MOS device characteristics

Vt , and drain-to-source current Ids are also scaled. One of the important factors to be noted is that since the voltage is scaled, electric field E in the device remains constant. This has the desirable effect that many nonlinear factors essentially remain uneffected. A further point is that reduction in oxide thickness would require the fabrication process to provide thinner oxides with comparable yield to conventional oxide thicknesses. The depletion regions associated with the pn junctions of the source and drain determine how small we can make the channel. As a rule, the source-drain distance must be greater than the sum of the widths of the depletion layers to ensure that the gate is able to exercise control over the conductance of the channel. Thus in order to reduce the length of the channel one needs to reduce the width of the depletion layers. This is accomplished by increasing the doping level of the substrate silicon. As we scale device dimensions by 1/α, the drain-to-source current Ids per transistor reduces by α, the number of transistors per unit area; that is, circuit density scales up by α2 , which subsequently results in the current density scaling linearly with α. Thus wider metal conductors will be necessary for densly packed structures. A second characteristic illustrated in Table 4.2 is power density. Both the static power dissipation Ps and frequency dependent dissipation Pd decrease by 1/α2 as the result of scaling. However, since the number of devices per unit area increases by α2 , the resultant effect is that the power density remains constant. An estimation of the limit in power density is derived from the thermodynamic relationship given by Tj = Tamb + θjA .P where

VLSI

Design Course

4-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Scaling Tj Tamb θjA P

= = = =

temperature of silicon chip ambient temperature thermal resistance of the package power dissipation.

Generally the thermal resistance is expressed as ∆◦ C per watt, which means one watt of heat energy will raise the temperature by ∆◦ C. As the temperature increases, the carrier mobility falls, thus reducing the gain of devices. This, in turn, would reduce the speed of circuits. If high temperature, high speed circuits are required, then special consideration during design is necessary. One of the limitations of first-order scaling is that it gives the wrong impression of being able to scale proportionally to zero dimension, or to zero threshold voltages. In reality, both theoretical and practical considerations do not permit such behavior. This is highlighted when the surface concentrations become larger than surface concentrations become larger than 1 × 1019 cm−3 , above which the gate oxide breaks down, before surface inversion can take place for the formation of the channel.

4.4.2

Interconnect layer scaling

Although constant-field (first-order) scaling gives a number of improvements, there are a number of curcuit parameters such as voltage drop, line propagation delay, current density, and contact resistance that exhibit significant degradation with scaling. For example scaling the thickness and width of a conductor by α, reduces the cross-sectional area by α2 . The scaled line resistance r0 is given by R

0

ρ L/α = t/α W/α = αR 



where ρ is the conductivity term and t is conductor thickness. The voltage drop along such a line can now be expressed as Vd0 = (I/α)(αR) = IR which is a constant. However, for constant chip size, the length of some of the signal paths that traverse across the chip, as a rule, do not scale down. This gives the principal result that voltage drops along communication paths are larger by a factor of α with respect to the scaled voltages. In a similiar manner, we can derive the line response time as τs0 = (αR)(C/α) = RC which is a constant. However, as before, for a constant chip size many of the communication paths do not scale. Thus the line response time normalize to scaled line response is larger by a factor of α. The significance of this result is that it is somewhat difficult to take the full advantage of the higher switching speeds inherent in scaled devices when signals are required to propagate over long paths. Thus the distribution an organization of clocking signals becomes a major problem as geometries are scaled. The influence of scaling on interconnection paths is summarized in Table 4.3. As seen from Table 4.3, metal lines must carry a higher current with respect to cross-sectional area; thus

VLSI

Design Course

4-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power and Clock Distribution PARAMETERS Line resistance; r Line response; rc Normalized line response Line voltage drop; Vd Normalize line voltage drop Current density; J Normalized contact voltage drop; Vc /V

SCALING FACTOR α 1 α 1 α α α2

Table 4.3: Influence of scaling on interconnect media

electron migration becomes a major factor to consider. The second problem relates to an increase in the capacitance of wiring. As the level of integration increases, the average line length on a chip tends to increase also. However the power dissipation per gate decreases, which diminishes the ability of gates driving wiring capacitances. Under such condition, average gate delay is determined by the interconnection rather than the gate itself. Many of these limitations are being overcome by scaling lateral dimensions while keeping vertical dimensions approximately constant.

4.5

Power and Clock Distribution

4.5.1

Power distribution

One of the most important issues in chip planning is the routing of power. In technologies in which there is only one level of metal, VDD and ground are routed in interdigitated trees. This is illustrated in Fig. 4.12. Crossunders are very difficult. When necessary, these are done in low resistance interconnect (poly over buried contact over active area) with a multiplicity of contact cuts. Consider the extreme case of a crossunder that must cary 100mA. One square of low resistance interconnect might have a maximum resistance of, say, 10Ω/2. Thus a square crossunder would drop 1 volt. Over 50 contact 2µm cuts to the metal on each side would be needed because of metal migration limits. Obviously, 100mA is an awful lot of current to squeeze through a crossunder. Even 10mA can be difficult, and 10mA corresponds only to about twenty nMOS inverters. Power is usually distributed locally in diffusion since it must get to the sources and drains anyway. For low-power gates, this local power distribution is not too bad, but for high performance devices, great care must be taken. When two levels of metal are available the general power distribution is much easier, though by no means trivial. Clearly, one of the worst scenarios for power supply noise is when large segments of the chip transition simultaneously. One strategy, therefore, is to distribute power in such a way that parts of the chip that are likely to transition all at once are routed separately. If power is distributed across these simultaneously switching segments, we would expect large surges on the power lines, but if power is distributed along the signal lines, then surge currents should be much smaller. A major problem of high performance chips is bringing power onto the chip. Bonding wires

VLSI

Design Course

4-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power and Clock Distribution

Vdd Vss

Vss Vdd

Vdd

Vdd OUTPUT PADS

Vdd

Vss

Vss

Vss

Vdd

Vss

Vdd

Vdd

Figure 4.12: Layout pattern for VDD and VSS lines.

can bave anywhere from 0.25 to 2nH of inductance (about 0.5 to 1nH/mm). VDD and ground are often double-bonded (two wires to the bonding pad) but while this lowers the inductance somewhat, it does not give the expected factor of two unless the wires are kept far apart. This is because there is mutual coupling between the wires. Seperate power pins might be used for the output driver, since these drivers cause huge switching transients and can tolerate more power supply noise than the internal circuitry.

4.5.2

Clock distribution

Synchronizing machine operations and data transfers with clock pulses provides us with a structured framework for dealing with the complexities of large system designs. Clocking is a global control technique which provides the “glue” for system operation. It is equally important at the circuit level, particularly in a dynamic logic stage.

VLSI

Design Course

4-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power and Clock Distribution 4.5.3

Clock and Timing Circles

System level timing can be described using circular timing charts. Consider an ideal pseudo 2-phase scheme with mutually-exclusive pulses φ1 and φ2 : φ1 (t) · φ2 (t) = 0 System timing can be described by constructing the chart shown in Fig. 4.13. Time increases in a counter-clockwise direction with one full rotation corresponding to the clock periode T . Segments are labeled according to time intervals when a clock signal is high. In this example, φ1 = 1 during the first half-period, while φ2 = 1 during the last half-period.

Figure 4.13: Pseudo 2-Phase Clocking Chart A more realistic clocking arrangement is depicted by the clocking circle in Fig. 4.14. If both clocks have 50% duty cycles, normal operation gives φ1 (t) · φ2 (t) = 0 except during the transition times. Mutually-exclusive clock signals provide timing intervals for logical operations, and are used to allow for normal gate delay times. Overlapped segments are avoided to prevent ill-defined movement of data, instructions, or control signals. Transtion times can be made small by proper clock generator design.

Figure 4.14: Pseudo 2-Phase Overlap Times Clock skew is represented by rotating one of the clocks as shown in Fig. 4.15. The skew time ts is defined as the time interval where φ1 (t) · φ2 (t) = 1

VLSI

Design Course

4-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power and Clock Distribution

and indicates the possibility of unwanted simultaneous bit transfers. This may lead to severe conflict problems in the operation.

Figure 4.15: Clock Skew

4.5.4

Clock Generation Circuits

A basic 2-phase clock generator circuit is designed to generate φ and φ¯ from a single input CLK signal. This is often a matter of convenience to the user: requiring only a single external clock makes the chip’s usage more attractive to the board designer. Various circuits have been developed for use in clock generation. Fig. 4.16 provides a CMOS generator/driver which uses a transmission gate as a delay element. MOSFETs M n1 and M p1 form an inverter which acts as the first driver for the chain. The upper branch of the circuit consists of two cascaded inverters and generator the signal φ¯ = CLK while the lower branch only has a single inverter and gives φ = CLK. Transmission gate T G is used as a delay ¯ Since it is biased into active conduction, element to minimize clock skew between φ and φ. we will model it using an equivalent resistance RT G , and introduce the time constant tD ' RT G Cin If the propagation delay through an inverter is tp , then choosing tD ' t P equalizes the delay between the upper and lower branches. Recalling that the transmission gate conductance can be approximated by GT G ' βn (VDD − VT n ) + βp (VDD − |VT p |) we see that clocking skew can be controlled by adjusting the size of the TG transistors. Another straightforward approach uses an SR latch as shown in Fig. 4.17. The clocking signal CLK is inverted, and CLK and CLK are used to drive the SR circuit. The 2-phase clock signals φ and φ¯ are taken from the latch outputs. This logic can also be used to generate pseudo 2-phase clocks φ1 and φ2 by redefining the outputs.

VLSI

Design Course

4-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Power and Clock Distribution

Figure 4.16: Clock Generator With a TG Delay

Figure 4.17: Latch-Based Clock Generator

4.5.5

Clock Drivers and Distribution Techniques

Once the clocking pulses are generated they must be destributed throughout the chip in a manner which minimizes clock skew. Fig. 4.18 illustrates the problem in a pseudo 2-phase circuit by showing timing circles at various points on a chip. Skew problems originate mostly from • Unbalanced loads at the driver, • Unequal RC line delays, so that the driver circuits and associated distribution schemes are important in maintaining the synchronous logic design. A related problem is that the drive capability of the circuit must be able to handle large capacitive loads at the required clock frequency.

VLSI

Design Course

4-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Input Protection Circuits

Figure 4.18: Clock Skew Due to Distribution One approach to designing a clock distribution network is to use a cascaded chain of inverting buffers that matches the clock generator to the distribution line. Also careful global planning and structured distribution patterns can be used to solve the problem. Clock distribution can also be accomplished by using a balanced tree network with multiple fanouts as shown in Fig. 4.19. Identical drivers can be used within a given stage. Moreover, the drive requirements of the output circuits are reduced from the single inverter design since the FO has been split into groups. Each inverter reshapes the clocking waveform, making the performance less sensitive to variations in the interconnect routing. Clock skew problems can be minimized by using symmetrical geometries for the clock distribution lines. An example is the “H-tree” network shown in Fig. 4.20. Every clock distribution point O is the same distance from the driver D, giving equal delay times. If the load capacitance is the same at every O-point, then the clocks will all be in phase with one another. Other geometrical patterns can be used so long as the general design criteria are unchanged.

4.6

Input Protection Circuits

Input pads connect data, control, or clocking signals to on-chip logic gates. When the pads are directly connected to the gate electrodes of MOSFETs, care must be taken to insure that excessive static electrical charge does not destroy the transistor. Protection circuits are designed to drain excessive charge away from the MOS capacitance to avoid static burnout. To understand the origin of the problem, recall that a MOSFET gate is basically a capacitor of value Cg = Cox W L With a gate-substrate voltage VG applied to the transistor, the internal oxide electric field is

VLSI

Design Course

4-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Input Protection Circuits

Figure 4.19: Clock Line Capacitance

Figure 4.20: Clock Line Capacitance given by Eox '

VG xox

where we have ignored any trapped oxide or surface charge. Breakdown occurs because of the fact that silicon dioxide has a breakdown field value of approximately EBD ∼ 7.5 × 106 V cm If Eox exceeds this value, the oxide insulating properties break down and charge is tranported

VLSI

Design Course

4-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Static Gate Sizing

through the material. This usually results in destruction of the device. Since xox is usually less than about 450 ˚ A, the maximum gate voltage VG,max ' EBD · xox which can be applied to the device is a relatively small number. The basic idea of an input protection circuit is to allow for alternate charge flow paths when the input voltage gets too large. Diode structures are very useful in this application since they have relatively breakdown voltages which can be controlled. Moreover, reverse breakdown in a pn-junction is non-destructive, so that the protection circuit is reusable. Junctions which are purposely used at the reverse-bias breakdown voltage are generally termed Zener diodes. Fig. 4.21 illustrates a simple input protection circuit for CMOS IC. Reverse biased pn-junctions are used as protection diodes, and a series connected resistor is included to drop some of the voltage. Both diode pairs (D1 , D2 ) and (D3 , D4 ) are designed to undergo breakdown for positive or negative voltage surges. R is designed to reduce the voltage that reaches (D3 , D4 ); this effectively increases the level of protection to the transistor gate.

Figure 4.21: Input Protection Circuit One problem that exists with this input protection circuits is the introduction of parasitic RC time constants into the network. Other input protection schemes are used. Fig. 4.22 shows a common circuit based on the properties of a thick field oxide MOSFET. The transistor has an threshold voltage of VT,F > VDD and is in cutoff during normal operation. A large input voltage V > VT,F drives the transistor into conduction, providing a path to ground to drain off the excessive charge. The breakdown voltage of the FOX MOSFET is large enough to withstand the high voltages since XF OX is large.

4.7

Static Gate Sizing

An interesting and useful problem is that of optimizing a chain of static gates to minimize the overall propagation delay. This type of situation arises in many different situations and is important to high-performance circuits. In particular, it is relevant to the output drivers and clocking circuits.

VLSI

Design Course

4-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Static Gate Sizing

Figure 4.22: Thin Oxide MOSFET Protection Circuit A classic example is shown in Fig. 4.23 where the objective is to design the fastest network for driving a large capacitance. For the problem at had, we will assume a series of inverting buffers for the driving network. At first sight, it may appear that we could want the fewest possible gates between the input and the load. This simple solution, however, ignores the effect of capacitive loading on successive stages. Accounting for these factors shows that the sizing of the transistors in the chain allows for minimization of the delay. This gives the interesting result that additional logic gates are often inserted to reduce the overall propagation delay between two points.

Figure 4.23: Capacitive Loading Problem Consider the scaled inverter chain shown in Fig. 4.24. Each gate is characterized by a sizing factor Sj which is normalized to the first stage such that S1 = 1, while Sj > 1 for (j > 1). By definition, the first stage has a MOSFET conduction factor β1 = k 0



W L

 1

while the j-th stage is described by βj = Sj β1 The values of Ci and C0 are determined by gate 1, and scaled for successive gates. Note that an additional capacitive component Cw has been added between stages. This represents

VLSI

Design Course

4-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Static Gate Sizing

the wiring contribution. We assume that the wiring capacitance is between two stages is proportional to the sizing factor of the second stage. The capacitance between the j-th gate and the (j + 1)-st gate can be summarized as follows: • Sj Co , output capacitance from gate j • Sj+1 Ci , input capacitance to gate (j + 1) • Sj+1 Cw , wiring capacitance into gate (j + 1). The time delay through gate j is thus estimated by R Sj

tD,j =

!

[Sj Co + Sj+1 (Ci + Cw )]

Our calculation is to determine the values of Sj for (j = 2, ...) which minimizes the total delay through the chain.

Figure 4.24: Inverter Sizing Problem Suppose that there are N stages in the chain. The total time delay is given by TD =

N X R[Sj Co + Sj+1 (Ci + Cw )]

Sj

j=1

To minimize TD , we differentiate with respect to Sj and look for zero slope points via δTD = 0; δSj this results in the recursion relation Sj+1 Sj = Sj Sj−1

VLSI

Design Course

4-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Static Gate Sizing

for j = 2, 3, .., N . If this to hold for arbitrary values of j, then Sj+1 = K = constant Sj must be true. Now then, the boundary conditions of the problems are

S1 = 1 CL SN +1 = Ci and the ends of the chain. Forming the product S 2 S3 S4 SN +1 · · ··· = KN S 1 S2 S3 SN and using the boundary conditions gives KN =

CL Ci

Thus, we obtain the scaling ratio in the form 

K=

CL Ci

1

N

which is our final result. Explicitly, the scaling factors are given by S1 = 1 S2 = K S3 = K 2 . . . SN

= K N −1

as the scaling required to optimize the chain. The minimum delay is then TD,min =

N X

R[Co + K(Ci + Cw )]

j=1

= N R[Co + K(Ci + Cw )]

as verified by direct substitution.

VLSI

Design Course

4-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Off-Chip Driver Circuits

One important point which is obtained from the above analysis deals with the delay time. S The equation K = ( Sj+1 ) says physically that the minimum chain delay occurs when every j stage has the same individual time delay tD . The final question which must be answered is the number of stages N needed to optimize the delay. To calculate this, we differentiate TD with respect to N and set the result to 0. This gives the general equation CL RCo + R(Ci + Cw ) Ci 

1  N

ln(CL Ci ) 1− =0 N 

If Co is small, this reduces to the well-publicized result 

N = ln

CL Ci



which is chosen to the nearest integer for given values of Ci and CL .

4.8

Off-Chip Driver Circuits

Off-chip driver circuits are critical to the overall chip design. Much effort is put into speeding up internal switching networks. Careful output design insures that the high-performance specifications apply to the external characteristics as well. Some important problems which must be addressed include • Efficient buffer circuitry between internal and off-chip drivers • Minimization of transmission line effects • Fast switching • Static charge protection as well as interface-specific items such as a CMOS-TTL level converter. An inverter circuit can be used as a basic off-chip driver. The dominant performance factors are the transient switching times tLH and tHL . Transmission line effects also enter into the problem; this is complicated by the fact that the line characteristics such as Z0 depend on the specifics of the mounting and circuit traces.

4.8.1

Basic Off-Chip Driver Design

The simplest off-chip driver circuit consists of an inverter chain which is designed to handle a large capacitive load. Cout includes contributions from the bonding pad, the package wiring, and the circuit board trace. Since this easily amounts to tens or a few hundred of picofarads depending on the interface specifications, the transistors must be relatively large.

VLSI

Design Course

4-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Off-Chip Driver Circuits

Consider the 2-stage off-chip driver network shown in Fig. 4.25. We may use time constants to obtain first-order design estimates for the sizes of the output transistors M n2 and M p2 by writing W = L n2   W = L p2





Cout 0 τn kn (VDD −

VT n ) Cout τp kp0 (VDD − |VT p |)

where τn and τp are the high-to-low and low-to-high time constants, respectively. Since the output capacitance seen by an off-chip driver can be large, the MOSFET aspect ratios are also quite large. These are obtained using several parallel-connected transistors to aid in layout and parasitic control. Sizing theory may be used to determine the sizes of the first stage transistors M n1 and M p1.

Figure 4.25: Double-Inverter Off-Chip Driver Circuit The actual values of the fall and rise times can be estimated from 

2VT n 2(VDD − VT n ) + ln −1 (VDD − VT n ) Vo

"

2|VT p | 2(VDD − |VT p |) + ln −1 (VDD − |VT p |) Vo

tHL = τn tLH

4.8.2

= τp





 #

Tri-State and Bidirectional I/O

Tri-state off-chip driver circuits are constructed by splitting the input signal to individually control each output transistor. Normal operation gives high and low voltages, while the highimpedance state is obtained by driving both the nMOS and pMOS devices into cutoff. An inverting tri-state circuit is shown in Fig. 4.26. When the tri-state variable Z = 1, pMOSFETs M p1 and M p2 are off, while nMOSFET M n conducts. This gives normal circuit operation. If Z = 0, then the gate voltages to output transistors are given by

VLSI

Design Course

4-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Off-Chip Driver Circuits

Figure 4.26: Tri-State Output Circuit

Vp = VDD Vn = 0

so that both are in cutoff. A condition of Z = 0 thus provides the necessary high-impedance state. Bi-directional input/output (I/O) circuits are also quite useful. An example is shown in Fig. 4.27. The tri-state section of the circuit is a non-inverting buffer with an enable control E, where E = 0 gives the High-Z state. Operation is straight forward and easily understood by examining the circuit.

VLSI

Design Course

4-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Off-Chip Driver Circuits

Figure 4.27: Bi-Directional I/O Circuit

VLSI

Design Course

4-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Chapter 5

CMOS Process and Layout Design of Integrated Circuits 5.1

Processing Steps

The fabrication of an integrated circuit consists of a series of steps carried out in a specific order. These steps convert the circuit design into an operable silicon integrated circuit chip. The way in which individual IC fabrication steps are carried out is of critical importance to the outcome of the manufacturing process. The main objective is to minimize the departure of geometrical features of the processed circuit from those determined during the design. To achieve this, a high degree of control over the parameters of each processing step is required. Equally rigid requirements apply to the physical and chemical properties of materials used for IC fabrication as well as to the cleanliness of the production environment.

5.1.1

Wafer Processing

The basic raw material used in semiconductor plants is a wafer or disk of silicon, which varies from 75mm to 150mm in diameter and is less than 1mm thick. Wafers are cut from ingots of single crystal silicon that have been pulled from a crucible melt of pure molten polycrystalline silicon. Controlled amounts of impurities are added to the melt to provide the crystal with the required electrical properties. The crystal orientation is determined by a seed crystal that is dipped into the melt to initiate single crystal growth. The seed is then gradually withdrawn vertically from the melt while simultaneously being rotated. Slicing into wafers is usually carried out using internal cutting edge diamond blades.

5.1.2

The n-Well CMOS Process

A common approach to n-well CMOS fabrication has been to start with a moderately doped p-type substrate (wafer), create the n-type well for the p-channel devices, and build the nchannel transistors in the native p-substrate. The mask that is used in each process step is shown in addition to a sample cross-section through an n-device and a p-device.

VLSI

Design Course

5-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Figure 5.1: Cazochalski process for manufacturing silicon ingots 1. The first mask defines the n-well (or n-tub). p-channel transistors will be fabricated in this well. Field oxide is etched away to allow a deep diffusion. 2. The next mask is called the “thin oxide” or “thinox” mask, as it defines where areas of thin oxide are needed to implement transistor gates and allow implantation to form por n-type diffusions for transistor source/drain regions. The field oxide areas are etched to the silicon surface and then the thin oxide is grown on these areas. Other terms for this mask include active area, island, and mesa. 3. Polysilicon gate definition is then completed. This involves covering the surface with polysilicon and then etching the required pattern. In a self-aligned process, the poly gate regions lead to aligned source-drain regions. 4. A n+ -mask is then used to indicate those thin-oxide areas (and polysilicon) that are to be implanted n+ . Hence the thin-oxide area exposed by the n+ -mask will become a n+ diffusion area. If the n+ -area is in the p-substrate, then a n-channel transistor or n-type wire may be constructed. If the n+ area is in the n-well, then an ohmic contact to the n-well may be constructed. An ohmic contact is one which is only resistive in nature and is not rectifying (as in the case of a diode). In other words, there is no junction and current can flow in both directions in an ohmic contact. This typ of mask is sometimes called the select mask as it selects those transistor regions that are to be p-type. 5. The next step ussually uses the complement of the n+ -mask, although an extra mask is

VLSI

Design Course

5-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Figure 5.2: The n-Well Mask

Figure 5.3: The Active Mask

VLSI

Design Course

5-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Figure 5.4: The Poly Mask

Figure 5.5: The n+ Mask

VLSI

Design Course

5-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps normally not needed. The “absence” of a n+ -region over a thin oxide area indicates that the area will be an p+ -diffusion. p+ -diffusion in the n-well defines possible p-transistors and wires. An n+ -diffusion in the n-substrate allows an ohmic contact to be made. Following this step, the surface of the chip is covered with a layer of SiO2 .

Figure 5.6: The p+ Mask 6. Contact cuts are then defined. This involves etching any SiO2 down to the contacted surface. These allow metal to contact diffusion regions or polysilicon regions. 7. Metallization is then applied to the surface and selectively etched. 8. As a final step, the wafer is passivated and openings to the bond pads are etched to allow for wire bonding. Passivation protects the silicon surface against the ingress of contaminants that can modify circuit behavior in deleterious ways. Additional steps might include threshold adjust steps to set the threshold voltages of the nand p-devices. In current fabrication processes the polysilicon is normally doped n+ . The p+ doping phase reduces the poly doping such that the polysilicon inside the p+ regions have a higher sheet resistence than the polysilicon outside the p+ region. The extent of this reduction may influence the qulaity of metal-poly contacts within p+ regions.

VLSI

Design Course

5-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Figure 5.7: The Contact Mask

Figure 5.8: The Metalisation Mask

VLSI

Design Course

5-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps 5.1.3

The p-Well CMOS Process

Typical p-well fabrication steps are similar to an n-well process, except that a p-well is used. The first masking step defines the p-well regions. This is followed by a low-dose boron implant driven in by a high-temperature step for the formation of the p-well. The next steps are to define the devices and other diffusions, to grow fiels oxide, contact cuts, and metallization. An p-well mask is used to define a p-well regions, as opposed to a n-well mask in a n-well process. An p+ -mask may be used to define the p-channel transistors and VSS contacts. Alternatively, we could use a n+ -mask to define the n-channel transistors, as the masks usually are the complement of each other.

Figure 5.9: An Example of a p-Well CMOS Process

5.1.4

The Twin-Tub Process

Twin-tub CMOS technology provides the basis for seperate optimization of the p-type and n-type transistors, thus making it possible for threshold voltage, body effect, and the gain associated with n- and p-devices to be independently optimized. Generally the starting material is either an n+ or p+ -substrate with a lightly doped epitaxial or epi layer, which is

VLSI

Design Course

5-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Figure 5.10: continued

VLSI

Design Course

5-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

used for protection against latch-up. The aim of epitaxy (which means “arranged upon”) is to grow high purity silicon layers of controlled thickness with accurately determined dopant concentrations distributed homogeneously throughout the layer. The electrical properties for this layer are determined by the dopant and its concentration in the silicon. The process sequence, which is similar to the p-well process apart from the tub formation where both p-well and n-well are utilized, entails the following steps: • tub formation • thin oxide etching • source and drain implantations • contact cut definition • metallization. Fig. 5.11 illustrates the cross-sections of the 3 processes on an example of an inverter.

Figure 5.11: Twin-tub process cross-section and layout of an inverter

VLSI

Design Course

5-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps 5.1.5

Isolation

Device isolation deals with electrically decoupling neighboring transistors on a densely-packed integrated circuit. Unwanted conduction channels must be eliminated by preventing both direct and indirect current flow paths. The most common isolation techniques used in bulk CMOS are LOCOS and trench isolation. LOCOS The Local Oxidation of Silicon (LOCOS) achieves device isolation by selective oxide growth. A typical LOCOS process starts by growing a thin stress relief thermal oxide (SiO2 ) layer on the silicon surface. Next, silicon nitride (Si3 N4 ) is deposited and patterned, keeping nitride in the areas where transistors will be built. The entire surface is then exposed to an oxidizing ambient. Nitride does not oxidize, but any exposed silicon will react to form SiO2 . The resulting LOCOS structure is illustrated in Fig 5.12.

Figure 5.12: LOCOS Isolation Simple analysis shows that XR = 0.46XF OX where XR is the depth of recession and XF OX is the thickness of the grown field oxide (FOX) which separates device locations. In general, the patterned nitride regions are called active areas, while the oxide growth defines the field regions between active transistor sections. LOCOS is a widely used isolation technique in many processing lines. However, a major limitation is the problem of active area encroachment which occurs during the FOX growth process and reduces the usable size of the region. The Problem is illustrated in Fig. 5.13. Even though the nitride protects the silicon surface, oxygen diffuses through the sides of the stressrelief oxide layer during the FOX growth. SiO2 is thus formed arround the edges, lifting the nitride upwards and forming a characteristic bird’s beak transition region between the active area and the field oxide. Encroachment cannot be avoided and affects the integration density.

VLSI

Design Course

5-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Figure 5.13: Encroachment in LOCOS

VLSI

Design Course

5-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Trench Isolation Trench isolation uses reactive ion etching (RIE) to form small trenches in the silicon. The trenches are then filled with oxide and polysilicon to electrically isolate neighboring device regions from one another. High integration levels are possible since the trench widths can be reduced to the order of a few microns. Trench isolation is illustrated in Fig. 5.14. A field implant may be used to increase the trench threshold voltage VT,T r . Small trench dimensions makes this approach particularly important for high-density integration.

Figure 5.14: Trench Isolation The vertical trench regions may also be used to create large-value capacitors without consuming valuable surface real estate. An example geometry which uses doped poly and p+ as capacitor plates is shown in Fig. 5.15. Trench capacitors are commonly used in advanced dynamic RAM (DRAM) cell design since they conserve surface real estate. Trench isolation has been developed to the point where it is a viable production line technique. It eliminates almost the problem of active area encroachment found in LOCOS and is useful when increasing the logic integration density.

5.1.6

Latchup

Bulk CMOS technologies are susceptible to latchup. This condition occurs when a parasitic conducting path is established between VDD and ground, directing current away from the circuit. Once latchup occurs, it can only be stopped by removing the power supply and restarting the circuit. In addition to halting the circuit operation, latchup may induce catastrophic failure from heating. Fig. 5.16 shows the cross-section of a n-well CMOS substrate region where the latchup problem originates. To understand the origin of the latchup problem, note that the voltage across parasitic resistor Rw1 acts to forward bias the emitter-base junction of Q2 . If VEB2 reaches the turn-on voltage of about 0.7 volts, IC2 flows. This current flowing through Rs1 develops a forward bias VBE1 across the base-emitter junction of Q1 , causing IC1 to increase. The

VLSI

Design Course

5-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Processing Steps

Figure 5.15: Trench Capacitor transistor pair Q1 and Q2 are connected to form a positive feedback loop, so that the buildup continues.

Figure 5.16: Origin of CMOS Latchup Latchup triggering may occur anytime the circuit voltages exceed normal levels. Causes include • Voltage overshoot/undershoot • Avalanche breakdown

VLSI

Design Course

5-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules • Punchthrough • Parasitic MOSFETs • Photocurrent and others. Although careful circuit design may reduce the possibility of inducing latchup, it is generally worthwhile to take extra precautions. There are two main approaches to dealing with the latchup problem: (a) reduce the transistor current gains, or (b) decouple the transistor feedback loop; it is common to use both in practice. Deep trench isolation can also be used to reduce the possibility of latchup. Fig. 5.17 illustrates adjacent nMOS and pMOS transistors separated by deep trenches. Parasitic bipolar transistors are not found in the structure since the isolating pn-junctions have been replaced by an oxide barrier.

Figure 5.17: Trench-isolated CMOS Latchup prevention is an important aspect of CMOS chip layout and design. One should always check to insure that all suggested rules have been followed to guard against the problem.

5.2

Design Rules

Design rules are sets of geometrical specifications which govern chip design for a given fabrication process. The layout rules are statements of the geometrical limits placed on the mask patterns and include items such as minimum widths, dimensions, and spacings. Violating the design rules can lead to a geometry which cannot be replicated in the fabrication line, yielding a non-functional circuit. Designers are often saved from simple mistakes by the omnipotent design rule checker (DRC) used to find layout violations. Another important fact is that parasitic circuit component values are a direct consequence of the layout geometry. Since the layout is an integral part of the circuit design, it is important to examine how a design rule set affets the overall performance.

5.2.1

Lithography and Fabrication

Microelectronic lithography is the science of transferring a pattern to each layer of material in an integrated circuit. The resolution of the lithography limits the smallest line dimension

VLSI

Design Course

5-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules

and constitutes a metric for the surface dimensions. The most common approach is optical lithography which uses an ultraviolet light source through a patterned mask to selectively expose a light-sensitive photoresist layer. Alternate approaches include electron-beam and X-ray sources; these offer finer resolution but introduce other problems. X-ray lithography currently appears to be the likely winner in the next generation, but recent advances in e-beam systems still look promising. Regardless of the approach, the resolution is limited by diffraction effects which occur whenever a wave passes by an opaque edge. This result in the minimum linewidth specification in the design rule set and may be viewed as the smallest mask dimension which can be reliably transferred to the chip surface. U V optical lithography has a minimum linewidth on the order of about 0.5 microns; e-beam systems can pattern down to one-tenth of a micron or less. Diffraction also limits how small we can make the spacing between two lines; this consideration gives a set of minimum spacing allowances in the design rule set. Minimum spacings also are needed to account for misaligned masking steps, lateral spreading, and other problems which occur during the many weeks it takes to fabricate a wafer. Yield enhancement plays an important role in setting the final numbers.

5.2.2

Basic Design Rule Set

Design rules are best illustrated by example. We consider a 1.5-micron n-well, single-poly, double-metal process which uses 10 masks. The process flow description in Table 5.2 lists the major steps in the fabrication and indicates each mask in proper sequence. Geometrical layout rules specify minimum mask feature sizes. Rules are provided for each masking layer, and also for spacings between different layers. The former originates from lithographic constraints or physical considerations. Bloats and shrinks may be applied to selected layers during the fabrication process, but the resulting physical overlay for the structure is still represented by the layout drawing. Table 5.1 provides a listing of design rules for a 2-micron CMOS process. These consist of minimum widths or dimensions, minimum spacings between features on the same or other layers, overlap distances, and other item of importance to the chip layout. Some examples of the design rules are shown below. Ground rules are usually accompanied by a complete set of drawings to illustrate each specification.

VLSI

Design Course

5-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules Mask 01 NWELL

Value (µ) 3.0 2.0 13.0 1.5 2.25 2.25 2.50 3.0

02 ACTIVE

3.75 0.0 6.0 03 POLY

1.5 2.0 1.25 0.75 2.25 1.5 1.25

04 NPLUS 05 PPLUS 06 CONTACT

07 METAL1 08 VIA

09 METAL2 10 PAD

1.5×1.5 1.5 1.25 1.75 1.0 1.75 2.0 2.25 1.5 2.0 1.0 1.5 2.0 1.5 2.75 3.0 100×100 5

Description Minimum width Minimum spacing (same polarity) Minimum spacing (different polarity) Minimum width (diffusion line) Minimum width under POLY Minimum spacing (same polarity) Minimum spacing (different polarity) p-ACTIVE inside of NWELL to NWELL-edge: pMOSFET p-ACTIVE outside of NWELL to NWELL-edge: substrate contact n-ACTIVE inside of NWELL to NWELL-edge: well contact n-ACTIVE outside of NWELL to NWELL-edge: nMOSFET Minimum width Minimum spacing Gate Overlap with ACTIVE POLY outside of ACTIVE to ACTIVE edge POLY inside of ACTIVE to ACTIVE edge Minimum spacing Spacing to ACTIVE PPLUS is reverse of NPLUS Size Minimum spacing Spacing to POLY edge (from inside) Spacing to POLY (contact outside of POLY) Spacing to ACTIVE edge (from inside) Spacing to ACTIVE (contact outside of POLY) Minimum width Minimum spacing Size Minimum spacing Overlap with METAL1 Overlap with METAL2 Spacing POLY or ACTIVE Spacing to CONTACT Minimum width Minimum spacing Dimensions Spacing to glass edge

Table 5.1: CMOS 1.5-Micron Design Rule Example

An integrated circuit may be viewed as a set of overlaid geometric patterns. Each layer is

VLSI

Design Course

5-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules

Design Rules for 1.50µm CMOS Process n-well

scribe lane

3µ 

-

differ.

6

2µ 35µ

Potential 

? same

10µ



-

-

Potent.

1.50µ

Active Area

-



n-well p-active Poly

 3.75µ 

30µ



-

p-active

-

2.25µ

6

2.50µ

6

2.25µ

?

?

p-active 2.50µ-n-active

6.00µ

- n-active

6 6

3.0µ

2.25µ scribe

? ?

n-active

lane

0.75µ 2.0µ

Poly

Active Area

 -

 -

scribe 6

2.25µ

lane

?

?



30µ

-

-

6

1.50µ

1.25µ

 -

1.50µ

minimum channel length for VDD = 5V is 1.5µ and for VDD > 5V 2.25µ.

VLSI

Design Course

5-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules

n+

Active Area

n+ diffusion

Poly 6

2.25µ

p+

is reverse of

n+

? 6

2.0µ

?

p-active -

1.25µ

 - 1.50µ

n+ 61.25µ ?

n+

Contact

6

2.75µ ? 6

2.75µ

Active Area

?

1.75µ

Poly

 -

6 ? 1.50µ -

61.25µ ?

1.75µ 6 ?

1.0µ -

1.50µ

VLSI

Design Course

5-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules 2.25µ 

metal1

metal1 1.0µ

scribe lane



30µ

-

 -

6 ?

2.0µ

maximum metal1 line width: 30µ max. current density: 0.5mA/µ 1.5µ

Via

metal1

metal1

-

metal1

metal2

2.0µ

 - ? @ @ 6

6@  -@ ? @ @ 6 1.5µ 6

2.0µ

?

?

2.0µ

Poly

Active Area

? @ @ 6

? Area Active

2.0µ ?

6 2.0µ

6

1.0µ 2.0µ

2.0µ

metal2 metal2 metal2

2.75µ3.0µ 

VLSI

Design Course

scribe lane

metal1 

Poly

6 1.5µ ?  @ @

30µ

-

-

5-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules STEP NO. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

MASK NO.

LAYER NAME

01 02

NWELL ACTIVE THIN OXIDE POLY POLY NPLUS PPLUS

03 04 05 06 07 08 09 10

CONTACT METAL1 METAL1 VIA METAL2 METAL2 GLASS PAD

Process STEP Start with n-type wafer n-tub diffusion Active area definition Grow gate oxide Deposit polysilicon Pattern polysilicon n+ implant p+ implant Deposit oxide Pattern poly contacts Deposit metal 1 Pattern metal 1 Deposit CVD oxide Pattern metal 2 contacts Deposit metal 2 Pattern metal 2 Nitride passivation Pattern pad openings

Table 5.2: Basic n-well CMOS Process

shaped to provide the proper characteristics when referenced to every other layer. High-density circuit design requires compacting the geometrical patterns into a small area without violating the design rules. Active Areas Dimensional specifications for active device areas are larger than that permitted by the lithography to account for encroachment from the isolation. As shown in the sequence of Fig. 5.18, growth of the field oxide creates the bird’s beak region which must be avoided when patterning the device. Gate Dimensions Basic self-aligned MOSFETs are fabricated using the polysilicon gate as a mask for a n+ or p+ drain/source ion implant. Lateral doping affects give effective channel lengths which are smaller than the drawn values shown on the poly mask. Gate Overhang Self-aligned MOSFETs use the gate polysilicon as a mask to the drain and source implants. To insure a functional MOSFET we require that the masks are drawn so that the poly gate extends further than required in the W direction. Fig. 5.20 shows the geometry. Providing

VLSI

Design Course

5-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Rules

Figure 5.18: Active Area Encroachment in LOCOS for a gate overhang allowance compensates for mask misalignment between the poly and n+ or p+ regions. If the gate over hang is reduced to zero, then even a minor registration error would result in a shorted transistor. Contacts and Vias Contact and via etches in the oxide can be troublesome failure points in a high-density layout. If the contact windows are too large, nonuniform coverage may result in void formation and other problems. The same comment also applies to oxide cuts which are too small. To avoid inducing contact-related failure modes, it is common practice to allow only one size for contact windows; large areas are connected by multiple contacts. This is illustrated in Fig. 5.21. Metal Dimensions Metal layers are deposited at the end of the fabrication sequence. They generally encounter a very rugged terrain due to patterning of the previous layers. Owing to this fact, the design rule widths and spacing must be large to insure electrical current flow. Another reason for

VLSI

Design Course

5-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Circuit Extraction and Electrical Process Parameters

Figure 5.19: Effective Channel Length increased widths is to allow larger current flow levels for power and ground connections.

5.3

Circuit Extraction and Electrical Process Parameters

The title circuit extraction includes a broad class of layout analysis problems. The fundamental problem is connectivity extraction, which derives a list of interconnections among the terminals from a layout description. There are several parameter extraction, which augment the basic connectivity information with measurements of features that are related to the (analog) electrical characteristics of the chip. Consider the problem of finding transistors. Transistors are formed by intersecting the polysilicon and diffusion layers; their type depends on the presence or absence of different kinds of implant or tub. Most circuit extractor treat two points (on the same or different layers) as electrically connected if they lie in the same region of a single layer or if they can be joined by a sequence of regions on several layers that are connected explicitly by contact windows. A common circuit extraction operation is to find maximal regions of electrically connected points, more commonly called nodes. This operation involves labeling the contents of each layer so that items belong to the same node if and only if they have the same label.

VLSI

Design Course

5-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Circuit Extraction and Electrical Process Parameters

Figure 5.20: Design-mask transformation

Figure 5.21: Contact Cuts

5.3.1

Connectivity Extraction

The output of connectivity extraction is a list of transistors on the chip, together with node numbers on each transistor’s gate, source, and drain. This transistor list is adequate for

VLSI

Design Course

5-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Circuit Extraction and Electrical Process Parameters

checking the logical correctness of the circuit. In order to check analog characteristics of the circuit, it is necessary to extract parasitic capacitances and resistances and transistor size information. The first step in connectivity extraction is to create derived layers that correspond to transistor of different kinds and to electrically connected regions on single layers. To illustrate the creation of derived layers using the edge representation, suppose the artwork for an nMOS chip includes the following six levels: Dmask (the diffusion mask), P mask ( the polysilicon mask), M mask (the metal mask), Cmask (contact windows from metal to underlying layers), Bmask (buried contact windows between polysilicon and diffusion), and Imask ( the depletion transistor implant). Then we could create five derive layers as follows: trans dwires PDcuts MPcuts MDcuts

← ← ← ← ←

Dmask and Pmask and not Bmask Dmask and not trans Pmask and Dmask and Bmask Mmask and Pmask and Cmask Mmask and Dmask and Cmask and Pmask

Regions in layer trans are transitor channels, that is, places where polysilicon crosses diffusion outside of a buried contact region. Conduction diffusion regions are represented in layers dwires. Files P Dcuts, M P cuts, and M Dcuts contain pricisely the places where materials of the appopriate types make electrical contact. The next step is to assign globally consistent signal labels to the items on each conducting layer that belong to a node, using the contact windows to merge signals between layers. The final step in connectivity extraction is to find for each transistor the signal labels on the nodes that are its terminals. This requires examinig all regions that abut a transistor region.

5.3.2

Parasitic Capacitance Extraction

To extract capacitance we still treat each node as equipotential but also consider it as the terminal of one or more capacitors. Each region has a capacitance between itself and the chip substrate and also internodal capacitances between itself and other overlapping or nearby nodes. Substrate capacitance can be accurately approximated as a function of the area and perimeter of each region on each layer. Capacitance between two nodes of the circuit is much harder to compute accurately. Internodal capacitance is not a simple function of area and perimeter.

5.3.3

Transistor Size Extraction

Analog characteristics such as the drive of an MOS transistor are a function of its channel length and width. For a rectangular transistor formed by polysilicon that completely overlaps diffusion, length is one-half of the transistor’s perimeter with polysilicon, and width is one-half of the transistor’s perimeter with diffusion.

VLSI

Design Course

5-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Circuit Extraction and Electrical Process Parameters 5.3.4

Parasitic Resitance Extraction

When we consider the problem of extracting resistances from a layout, the abstraction of transistors connected by equipotential nodes breaks down completely. It does not make sense to associate resistance with a node: resistance is defined between pairs of points. Thus, a node attached to the terminals of k transistors gives rise to k(k−1) resistances, one between 2 each pair of terminals. One idea is to reduce the number of resistances we must compute by chopping the region into electrically isolated regions. If we add the appropriate k − 2 junctions to a node attached to k . (See Fig. 5.22) terminals, then we need to compute only O(k) resistances, instead of k(k−2) 2

Figure 5.22: A region with eight terminals has 28 interconnection resistances. Making the cross-hatched juntions into new nodes splits the region into 10 electrically isolated regions and reduces the number of interconnection resistances to 10 A second way to reduce the number of resistances is to break nodes into rectangles by introducing artificial junctions at corners. Thus, resistances can be more easily computed. Careful resistance extraction is the hardest and most expensive problem. Indeed, most chips are manufactured without ever undergoing a complete resistance extraction because such an extraction would result in a prohibitively large network of resistors.

5.3.5

Process Parameter and Technology Description

The technology description file contains all information specific for a particular technology. Among this information, and of particular importance for the extractor, is the specification of the layers that can be used in a process and electrical parameters of that process. Layers are specified by their name and their type. The type of a layer distinguishes between auxiliary layers, implantation layers, and interconnect layers. Auxiliary layers are ignored by the extractor. Interconnect layers form the conducting patterns in a chip layout, so in a chip all interconnections will always be made via such layers. If the layers is of type interconnect, an associated terminal layer must be specified for it. Given the interconnect layers, the extractor is able to determine where the nodes of an element are located. Another important part of the technology description is the specification of the elements to be extracted. For extraction of parasitic elements, electrical process parameters must be known. The layer capacities or layer and contact resistances are necessary for exact modelling of parasitic ca-

VLSI

Design Course

5-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout

pacitances and resistances on a wafer, e.g.: for calculating load capacities (gates) and coupling (between wires). Furthermore, process parameters must be involved during the design. So poly lines can not be designed too long because of the high layer capacity and resistance of polysilicon. Example parameter of an n-well CMOS process are listed in Table 5.3 and 5.4. Capacities Gate-Oxide n+ –diff to substrate (bottom) n+ –diff to substrat (sidewall) p+ –diff to n-well (bottom) p+ –diff to n-well (sidewall) Poly–substrate Metal1–substrate Metal2–substrate Metal1–metal2 Metal1–poly Metal2–poly Metal1–n+ -diff. Metal1–p+ -diff. Metal2–n+ -diff. Metal2–p+ -diff.

nF Value ( cm 2) 135 25 4 (pF /cm) 38 4 (pF /cm) 5.9 3.2 2 3.9 5.4 2.5 5.2 5.5 2.4 2.5

Table 5.3: Layer capacitances of an n-well CMOS process

Resistances n-well n+ -diffusion p+ -diffusion Poly Metal1 Metal2 Contact Via

Value 2.5 kΩ/2 50 Ω/2 150 Ω/2 50Ω/2 60 mΩ/2 40 mΩ/2 100 Ω/contact 1 Ω/via

Table 5.4: Layer resistances of an n-well CMOS process

5.4

Basic Layout

Transforming schematics into physical circuits occurs during the layout process. All aspects of the circuit performance are structured by the patterning. Parasitics, interconnect coupling, and logic integration density are also determined by the geometries used in the layout artwork. Although layout is easy to learn, the interplay between the geometrical shapes and the resulting electrical behavior makes it difficult to master.

VLSI

Design Course

5-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout 5.4.1

IC Design

IC design is a very complex process that involves hundreds of decisions dealing with the variety of IC performances and manufacturing-related issues. The final phase in the design is the creation of an IC layout; i.e. the creation of the drawing representing the geometry of the designed circuit. For a given process such a drawing uniquely defines the IC geometry and therefore the performance of the designed circuit. The layout of an IC is defined as a set of polygons that determines the presence or absence of regions in a number of conducting and isolating layers. In other words, an IC layout shows from which part of the IC surface such materials as metal, silicon dioxide, photoresist, and so on should be removed, and where other materials should be deposited. During the design the IC is represented by a set of numbers that can be manipulated to create a composite drawing of IC masks on the screen of the terminal or on the color plotter. In the manufacturing process a “hard copy” of this layout is needed in the form of photolithographic masks. Typically, the IC design is transformed into a set of masks in a sequence of steps illustrated in Fig. 5.23. First, coordinates of all elements of the IC composite drawing are computed. Then data representing different layers are separated(Fig. 5.23 (c) and (d)) and an image of each IC layer is produced. Typically, such images are engraved on the surface of glass plates covered with chromium, using a photographic technique and pattern generator or E-beam equipment. Masks created in this way are called master mask. Next master masks are scaled down (Fig. 5.23 (e-f)) and duplicated (Fig. 5.23 (g-h)) so that working masks made in this way contain a couple of tens to a couple of hundreds of the same images as tte master masks. The size of the working mask is such that with a single exposure the entire area of a single manufacturing wafer can be covered. In the new lithography techniques, working masks are not needed and the image from the mask is transferred directly onto the surface of the wafer (the master mask is then called a reticle). Special high-precision optical step-and-repeat cameras are used for this purpose. Data that describe a single IC layer can also be used to project an image directly onto the surface of the manufacturing wafer using an electron beam technique. In this technique a deflected beam of electrons exposes appropriate regions directly on the surface of the photoresist.

5.4.2

General Layout Strategies

Structured layout is based on the idea of grids and cells. The simplest approaches start with the power distribution lines VDD and VSS and structure the circuits as needed. Each gate is placed in a semi-rectangular cell, and cascaded logic is achieved using adjacent cells. Fig. 5.24 illustrates the general idea. Both signal and power lines run horizontally in the network. Logical gates are built between metal VDD and VSS lines, while the signals may move between poly and metal layers when necessary. Minimization of the area is achieved by creative placement and shaping of the MOSFETs, interconnects, and cells in the overall grid structure. It is important to remember that the dimensions set the electrical characteristics and must adhere to the design rules set. CMOS has the added complications of complementary nMOS/pMOS logic blocks and physical separation of nMOS and pMOS transistors, which affect the layout.

VLSI

Design Course

5-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout

Figure 5.23: Design-mask transformation Complementary structuring is illustrated in Fig. 5.25. Each input is connected to both nMOS and pMOS transistors which are physically separated from one another due to the opposite background polarity requirements.

5.4.3

Equivalent Load Concept

High-speed switching requires large currents and small Cout to insure small charging and discharging time constants. It is evident that this leads to a design problem: to increase current flow, we must use large ( W L ) values for the MOSFETs, which in turn increases the

VLSI

Design Course

5-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout

Figure 5.24: General Layout Grid

Figure 5.25: Complementary Transistor/Logic Blocks transistor capacitances. Increasing the aspect ratios in a CMOS circuit gives larger values for both Cin and Cout , affecting the performance of the entire logic chain. In bottom-up design, we attempt to optimize each gate, both intrinsically and with respect to its nearest neighbors. The concept of the equivalent load helps the initial layout problem by defining “standard” transistor or logic gate capacitances which are used as a reference. All loads are then specified by the number of equivalent loads. A common choice is a minimum-area transistor as shown

VLSI

Design Course

5-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout in Fig. 5.26. Assuming drawn gate dimensions of (W × L), the gate input capacitance is approximated by CG ≈ Cox W L. An inverter made using minimum area nMOS and pMOS transistors has an input capacitance of approximately Cin = 2CG which becomes our reference value. To use the equivalent load concept, we assume that the circuit we are designing must drive a load of value CL = nCin , where n is a scaling factor indicating the size of the transistors used in the next gate. For example, n = 2 may imply a single gate with MOSFETs which are twice as large as the reference, or a fan-out F O = 2 into two minimum size gates. The circuit is designed according to the assumed load value. After the design of the logic chain is completed, we recheck the circuit to insure that the actual switching performance is acceptable.

Figure 5.26: Equivalent Load Optimization of the circuit performance can also be specified at the system level and then applied to each gate. This type of top-down approach has been used to estimate gate sizing rules to speed up the response of a static logic chain. In general, combining the two views offered by bottom-up (circuit level) and top-dowm (system level) design provides the most powerful approach to high-performance design. Large digital networks contain both critical and non-critical logic paths so that intermixing design philosophies are often required.

VLSI

Design Course

5-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout 5.4.4

Latch-Up Prevention

Circuits which are fabricated in bulk CMOS require additional safeguards to aviod latch-up. A common approach is to use guard rings, which are heavily doped n+ or p+ regions around MOSFETs as shown in Fig. 5.27. Guard rings reduce the transistor current gain and offset the potential and are effective in preventing latch-up. Another common preventative measure is providing substrate bias contacts next to every MOSFET which is connected to the power supply or ground.

Figure 5.27: Guard Ring Example

5.4.5

Static Gate Layout

Static CMOS gates are based on complementary nMOS/pMOS logic blocks. Cell design can be split into two tasks: transistor placement and interconnect routing. Real estate budgets often have priority status, so that some thought may be required to fit the subsystem into the allocated area. The main limitations are usually due to design rule spacings and the complexity to the interconnect topolgy. Other considerations which may come into play include the shape of the allocated area, location of input and output lines relative to neighboring logic units, and clock distribution. Some of the more interesting designs are based on the complementary placement of opposite polarity MOSFETs. Consider a NOR2 gate. This circuit uses 2 nMOS transistors in parallel and 2 pMOS transistors in series. Fig. 5.28 shows how the complementary arrangement can be implemented by using similar transistor arrays with different interconnect patterning. Reversing the transistors in the NOR2 gate in Fig. 5.28(a) directly yields the NAND2 gate shown in Fig. 5.28(b). Although some layouts are based on the schematic patterning, these do not generally yield minimum-area circuits. Thoughtful use of transistor arrays and interconnect routing is usually

VLSI

Design Course

5-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout

required; intelligent CAD/CAE tools may also prove helpful.

Figure 5.28: Complement Static Gates

5.4.6

Transistor-Gate-Based Logic

The Layout of transmission-gate logic circuits is complicated by the transmission gate itself. The switch uses parallel-connected nMOS and a pMOS transistors which reside in oppositepolarity backgrounds. Consider, for example, a pwell process. The p-channel transistor is

VLSI

Design Course

5-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Basic Layout

located on the n-substrate, while the nMOS is in a p-well region. Two extreme layout philosophies are (a) use a p-well for every transmission gate, or, (b) use a single p-well for all transmission gates in the circuit. These are illustrated in Fig. 5.29. Approach (a) reduces integration density due to the p-well spacing requirement, but is easy to replicate on a CAD systems; (b) on the other hand, may provide higher logic density, but has a larger capacitance from the extra interconnect. Although both are used in practice, minimizing the number of wells is ussually the preferred strategy. Since each well requires a connection to either VDD or VSS , this also aids in power distribution. A critical aspect of high-speed CMOS layout is control of the parasitic capacitance values.

Figure 5.29: Transmission Gate Layout

VLSI

Design Course

5-33

Darmstadt University of Technology Institute of Microelectronic Systems

0

Layout Examples 5.5

Layout Examples

Figure 5.30: Layout of an inverter

VLSI

Design Course

5-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

Layout Examples

Figure 5.31: Layout of a 2-input nand gate

Figure 5.32: Layout of a 2-input nor gate

VLSI

Design Course

5-35

Darmstadt University of Technology Institute of Microelectronic Systems

0

Layout Examples

Figure 5.33: Layout of an exor gate

Figure 5.34: Layout of a ram cell

VLSI

Design Course

5-36

Darmstadt University of Technology Institute of Microelectronic Systems

0

Layout Examples

Figure 5.35: Layout of a pad

Figure 5.36: Layout of a RS-latch

VLSI

Design Course

5-37

Darmstadt University of Technology Institute of Microelectronic Systems

0

Layout Examples

Figure 5.37: Layout of a D-latch

Figure 5.38: Layout of a comparator

VLSI

Design Course

5-38

Darmstadt University of Technology Institute of Microelectronic Systems

0

Layout Examples

Figure 5.39: Layout of a 1-bit fulladder

VLSI

Design Course

5-39

Darmstadt University of Technology Institute of Microelectronic Systems

0

Introduction

Chapter 6

VLSI Device Packaging 6.1

Introduction

Packaging affects significantly or in some cases dominates the overall chip costs ([22]). The increase of packaging costs for a increasing number of gates on is different for memory and logic/microprocessor devices: Memory devices: Due to multiplexing techniques on the chip, the I/O requirements remain essentially constant Logic and microprocessor devices: The number of required I/O terminals increases in proportion to the number of gates on the chip. An empirical estimation for the number of I/O-terminals needed for logic devices is known as Rent’s Rule: #I/O = α(#Gates )β (6.1) Package design has to provide: • good heat dissipation • good electricial performance • high reliability • package must be easy to inspect after assembly • package must be compatible with a variety of assembly, test and handling systems

VLSI

Design Course

6-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Introduction

Figure 6.1: Continuous growth in DRAM complexity and size places little demand on package size and number of I/Os

VLSI

Design Course

6-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Introduction

Figure 6.2: Comparison of I/O requirements for DRAM, logic and microprocessor devices

VLSI

Design Course

6-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Types 6.2

Package Types

Principally there are two types of mounting devices to printed wiring boards (PWB): 1. through-hole (TH) mounting: • Dual-in-line packages (DIP) • Pin-grid-array (PGA) (available in hermetic plastic and ceramic types) (pitches: 2.54, 1.78 and 1.27 mm) 2. surface mounting (SM) • up to 48 terminals: – small outline (SO) (available in plastic only): SOP: small outline package SSOP: shrinked small outline package – quad types: chip carriers (CC) and flatpacks (available in ceramic and plastic) • above 48 terminals: quad types only – leaded plastic (PLCC) – leaded ceramic (LDCC) – leadless ceramic (LLCC) (pitches: 1.37 or 0.635 mm)

VLSI

Design Course

6-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Types

Figure 6.3: Examples for packages and PWB mounting techniques: (a) TH: Dual-in-line (DIL) package. (b) TH: Pin-grid-array (PGA) package. (c) SM: ”J”-leaded packages, leaded chip carrier or smalloutline. (d) SM: Gull-wing-leaded packages, chip-carrier or small-outline. (e) SM: Butt-leaded package, small-outline dualin-line type. (f) Leadless type, ceramic chip carrier mounted to a matching ceramic substrate

Figure 6.4: IC package types as a function of I/Os and attachment type

VLSI

Design Course

6-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Types 6.2.1

24-pin Packaging Evolution

Figure 6.5: Package history

Figure 6.6: Comparison: 24-pin SO package and 48-pin SSO package

VLSI

Design Course

6-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Considerations 6.3

Design Considerations

6.3.1

VLSI Design Rules

Figure 6.7: Bonding-pad pitch versus chip lead count for several chip sizes

Figure 6.8: Arrangement of staggered bonding pads: → lower pitch than with single line of bonding pads. (a) Bonding pads size and spacing. (b) Maximum wire angle with respect to die edge

VLSI

Design Course

6-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Considerations

Figure 6.9: CAD template for positioning bonding pads (assures that wire span length meets the design rules)

Figure 6.10: CAD template for checking adherence to wire-span guidelines. The template also provides an extended zone (beyond the optimum shown in Fig. 6.9) for cases where location in optimum zone is not compatible with the device layout.

VLSI

Design Course

6-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Considerations

Figure 6.11: CAD template for checking the maximum distance that wire spans over silicon. Here: violation of the guidelines. The circle must be at minimum tangent to the step-and-repeat centerline (case of maximum distance) or cross it

VLSI

Design Course

6-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Considerations 6.3.2

Thermal Considerations

• Objective: keep temperature of silicon die low enough to prevent failure rate • Conductive thermal resistance: function of package materials, geometry and orientation.

6.3.3

Electricial Considerations

Increased operation speed and reduced noise margins demand a more careful consideration of package design. Performance criterions: • low ground resistance (minimum power-supply voltage drop) • short signal leads (minimum self-inductance) • minimum power supply spiking due to signal lines simultaneously switching • short parallel signal runs (cross talk) • short-length signal length near a ground plane (minimum capacitive loading)

Figure 6.12: Lead inductances for various package sizes The inductances of SM packages are significantly lower than the inductances of TH packages due to their shorter lead traces. Most important problem: noise reduction. The noise induced in the ground line when one line is switching is given by di Vi = Lg (6.2) dt

VLSI

Design Course

6-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Considerations

where Lg is the inductance of the ground lead. If j lines are switching: Vi = Lg

X dij j

(6.3)

dt

If m ground leads are used, the total inductance is approximately Lg /m. In practical designs often up to 25% of the leads have to be grounded in order to keep noise in desired limits (also usage of large-area power and ground planes within the package).

6.3.4

Mechanical Design Considerations

• Ideally: prefer to use materials that are matched in physical properties, especially which have the same TCE (Themal Coefficient of Expansion)

Figure 6.13: TCE of materials for semiconductor devices, (◦ C)

• Tradeoff between TCE, thermal conductivity and elastic modulus

VLSI

Design Course

6-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Considerations

Figure 6.14: Plastic package: composite structure consisting of silicon chip, metal leadframe and plastic moulding compound

VLSI

Design Course

6-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Assembly Technologies 6.4

Assembly Technologies

Figure 6.15: Generic assembly sequence for plastic and ceramic packages

6.4.1

Wafer Preparation

• Wafer sawing with diamant blade technology • In some cases: wafer thinning down using highly automated backgrinding processes • The sawed wafer is still mounted on a tape frame-fixture (to which it has been attached before sawing and which is not destroyed by the sawing step) and loaded into an automatic die bonder that picks only the good chips from the tape

6.4.2

Die Bonding

The back of the die is mechanically attached to a mount medium, such as ceramic substrate, multilayer-ceramic-package-piece part or metal leadframe. This attachment sometimes enables electricial connection to the back of the die to be made. Two common Methods of die bonding:

VLSI

Design Course

6-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Assembly Technologies

1. Eutectic die bonding 2. Epoxy die bonding Eutectic Die Bonding (Hard solders)

Figure 6.16: Eutectic die bonding

• The die is metallurgically attached to a substrate material • Substrate material: metal leadframe made of Alloy 42 or ceramic material (usually 90. . .95% Al2 O3 ) • Melting preform: thin sheet of the appropriate solder-bonding Alloy • Substrate: Metallization with Ag (leadframes) or Au (leadframes or ceramic) ◦

• Bonding temperature: about 400 C

VLSI

Design Course

6-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Assembly Technologies

Epoxy Die Bonding

Figure 6.17: Epoxy die bonding

• Bond material: silver-filled adhesives • Advantage: less expensive than the high-gold-content hard soldiers and easy to process

6.4.3

Wire Bonding

Typically gold-wire is ball-wedge bonded (thermosonic or thermocompression). • ball-bonding to the chip bond pad (typically Al) • wedge-bonding to the package substrate (typically Ag or Au) Description of the bonding cycle s.pdf as seen in Fig. 6.18: (a) targeting the capillary on the die’s bond pad (b) the capillary presses the ball on the pad. In a thermosonic system ultrasonic vibration is then applied (c) the clamp opens and the capillary rises (d) the lead of the device is positioned under the capillary, which is then lowered on the lead (e) the capillary deforms the wire against the lead. In a thermosonic system ultrasonic vibration is applied

VLSI

Design Course

6-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Assembly Technologies

Figure 6.18: Tailless ball-and-wedge bonding cycle

VLSI

Design Course

6-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Technologies

(f) the capillary rises and the wire clamp closes at a predefined height (g) a new ball is formed using a hydrogen flame or an electronic spark

Figure 6.19: Thermosonic ball wire bonds on a gate array VLSI chip

6.5

Package Technologies

6.5.1

Ceramic Package Technology

• very effective for constructing complex packages with many signal, power, ground, bonding and sealing layers

VLSI

Design Course

6-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Technologies

Figure 6.20: Process sequence to create a laminated refractory-ceramic product from a ceramic slurry

Figure 6.21: Cross-sectional sketches of several package types

VLSI

Design Course

6-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Technologies 6.5.2

Glass-Sealed Refractory Technology

Figure 6.22: Structures of CERDIP and quad CERPAC Lower cost ceramic technology applicable to single-chip DIPs and quad CERPACs. This technology relies on glass-sealing a leadframe between two pressed ceramic units.

VLSI

Design Course

6-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Technologies 6.5.3

Plastic Molding Technology

Figure 6.23: Ball-and-wedge-bonded silicon die in a plastic DIP

Postmolding • low cost • state-of-the-art plastic package technology • thermosetting epoxy resins are molded around the leadframe-chip subassembly after the chip being wire-bonded to the leadframe Premolding • avoids exposure of die and wire bond to viscous molding material • package is molded first and then chip-leadframe compound is added

VLSI

Design Course

6-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Package Technologies 6.5.4

Molding Process

Figure 6.24: Molding processing system → the preheated molding compound flows under pressure to fill the cavities containing leadframe strips with their attached ICs.

VLSI

Design Course

6-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

IC Package Market Share 6.6

IC Package Market Share

Figure 6.25: IC package market share

Figure 6.26: Worldwide IC package market share by material

VLSI

Design Course

6-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Packaging Trends 6.7

Packaging Trends

Figure 6.27: Pin count versus usable gates

6.7.1

MultiChip Modules

• multiple dies are mounted on multilayer ceramic packages • increasing performance by reducing the inter-die line length

VLSI

Design Course

6-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Packaging Trends

Figure 6.28: Plastic IC package material costs

VLSI

Design Course

6-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Packaging Trends

Figure 6.29: Ceramic IC package material costs

VLSI

Design Course

6-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Packaging Trends

Figure 6.30: MCM: microprocessor performance

VLSI

Design Course

6-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Packaging Trends 6.7.2

Comparison of Packaging Alternatives

Packaging Approach Single Chip Package (SCP)

MultiChip Modules (MCM)

Chip-on-Board (COB)

Monolithic Wafer Scale Integration (MWSI)

VLSI

Design Course

Features • Mature • Reliable • Low risk

• • • • • • • • • • •

Limitations Low density Speed: <30MHz Increased PWB complexity Low PWA producibility Requires automated assembly equipment • Cost • Test and burn-in of bare chips required • • • • •

Increased density Speed: 30 . . . 100MHz Average PWB complexity Good PWA producibility Good ’middle ground’ between MCMs and MWSI High density Speed: GHz range Extreme density Speed: High GHz range Potential for low cost Simplicity (once fabrication processes are fully developed)

6-27

• Environmental protection of bare die • TCE effects of coatings and/or PWBs • Difficult repairability • Available 1995 - 1999 • Defect density of wafers require redundancy • Thermal management • TCE effects • Vibration/shock environments • No repairability

Darmstadt University of Technology Institute of Microelectronic Systems

0

CAD Tools

Chapter 7

Computer Aided Design of Integrated Circuits 7.1

CAD Tools

The following list shows some important CAD tools used for the design of integrated circuits: • graphics editor (drawing schematic diagrams, physical layout, stick layout diagrams, . . . , used for displaying results from simulations, layout verifications (like design rule checks), placement and routing, . . . ) • language based circuit capture tools (for hardware description languages like VHDL, Verilog, EDIF, . . . ) • physical design verification tools (design rule checker, extractor, LVS, schematic and electrical rule checker, . . . ) • simulation tools (analog simulation: circuit level; digital simulations: circuit level, switch level, logic level, register transfer level, architectural level, behavioural level; thermal simulation: displaying heat dissipation on chip) • layout compilers (stick2layout, macrocell generators, datapath compilers) • layout synthesizer, layout compactor • logic optimizer • database interfaces (file input / output from / to standardized interchange formats) • database management (to keep different versions (current, backup1, backupn) and views of a design object [schematic, simulation netlist, stick diagram, physical layout, . . . ]) in the design database)

VLSI

Design Course

7-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Full Custom Design 7.2

Full Custom Design

With Full Custom Design techniques, the designer is able to individually specify the geometrical layout of the integrated circuit (transistor size [channel length, channel width, shape, . . . ], transistor placement, wire width, . . . ). The designer has the option to manually optimize the layout → the most dense layouts can be generated using the full custom design styles. Hand Crafted Layout • The layout is drawn in form of rectangles and polygons on different layers using a graphics editor. • The designer has to know a large set of process dependent design rules. • The mask layout is generated as drawn on the screen → direct influence to component placement, to important parameters as W and L of transistors, wire widths, .... Stick Diagram • The layout is drawn in form of lines and polygons on different layers using a graphics editor. A stick–to–layout converter together with a compactor and a description of the process design rules is then used to generate the rectangle based layout. • The designer can draw almost process and design rule independent symbolic layouts. Process adaption is done by the converter/compactor. • Converter constraints (cell dimensions, channel widths / lengths of transistors, . . . ) can be specified. Geometrical Specification Language • The layout is specified in textual form giving either the position and layer of rectangles (similar to hand crafted layout) or lines (as in stick diagrams). • Since programming language constructs like parameterized macros (to be used for layout segments as cells, . . . ), loops (while, repeat, for, . . . ), and conditional statements (if, case, . . . ) may be available, parameterized layouts (e. g. generic transistor with W and L as parameters, cells for different bit–widths, . . . ) can be described using geometrical specification languages. • Used in a large number of macrocell compilers.

VLSI

Design Course

7-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Full Custom Design

B x y dx dy Ln Mn E Cnxym Q

Box with length dx, width dy, and lower left hand corner placed at (x, y). Layout level (layer) for the box definitions that follow Start of macro definition n End of macro definition Call for macro number n with translation x, y and orientation m. End layout file. Table 7.1: Simplified geometrical specification language Layer 1 2 3 4 5 8 9

CMOS n-diffusion p-diffusion polysilicon metal contact n-well overglass

NMOS n-diffusion ion implant polysilicon metal contact — overglass

Table 7.2: MOS layer definitions

Figure 7.1: Cell orientations Orientation 1 2 3 4 5 6 7 8

Description no rotation rotate 90o counterclockwise rotate 180o counterclockwise rotate 270o counterclockwise mirror about y-axis rotate 90o counterclockwise and mirror about y-axis rotate 180o counterclockwise and mirror about y-axis rotate 270o counterclockwise and mirror about y-axis Table 7.3: Rotations of geometry

VLSI

Design Course

7-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Full Custom Design

Figure 7.2: Full custom layout (hand crafted or generated out of a stick diagram resp. a layout description)

VLSI

Design Course

Figure 7.3: Corresponding geometrical specification file and schematic diagram

7-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Full Custom Design

Figure 7.4: Memory cell schematic and corresponding stick diagram

VLSI

Design Course

7-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Full Custom Design

Stick Diagram

Symbol Generation

Editor

6 ?

stick2layout Converter Compactor

?

Schematic Entry

?

?

Simulation Netlist Extraction

Layout Editor

Block Layout ?

Circuit Simulation ?

Floorplanning Timing Analysis Placement

6

Routing Design Analysis ?

Mask Layout Data

DRC ERC Circuit Extraction LVS

-

?

Fabrication



Fabrication Test Pattern Figure 7.5: Full Custom Design Flow

VLSI

Design Course

7-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Cell Based Design 7.3

Cell Based Design

The Cell Based Design approaches rely on layout components predefined and provided by the silicon foundry. Several implementation styles can be distinguished: Gate Array • pre-fabricated diffusion and poly layers (regular structures e. g. transistors) • customized interconnect structures (wires in metal 1 and metal 2) • fixed size interconnect areas (channels) Sea of Gate Array • pre-fabricated diffusion and poly layers (regular structures e. g. transistors) • customized interconnect structures (wires in metal 1 and metal 2) • variable size interconnect areas (channels) over unused transistors Standard Cell • layout blocks predefined by silicon foundry • full process sequence for chip fabrication required

VLSI

Design Course

7-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Cell Based Design

Macrocell Symbol Generation

Specification / Compilation

6

Compiled Macrocell ?

Graphical -

Schematic Entry

Data Cell

?

Simulation Netlist Extraction

-

Simulation Models ?

Library

?

Logic Simulation

Placement LayoutData

Macrocells IO-Cells Standard-Cells

Fault Simulation



Timing Analysis 6

Parasitic Wire Capacitances /

?

Delay Backannotation

Routing

Channel Generation  Global Routing Detailed Routing P & R – Optimization Design Analysis

?

Mask Layout Data

-

DRC Parasitics Extraction

?

Fabrication



Fabrication Test Pattern

Figure 7.6: Standard Cell Design Flow

VLSI

Design Course

7-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Verification 7.4

Design Verification

7.4.1

Physical Design Rule Check

Physical design rule checks (DRCs) are performed to guarantee the conformity of a layout design to the silicon vendor’s set of design rules. Design rules are defined between objects on the same layer (minimum width, minimum spacing) as well as for objects on different layers (minimum spacing, overlapping, extension). Minimum width Minimum spacing Overlapping Extension Design rule violations are usually reported in the physical layout using a graphics editor. Sometimes, also a tabular form indicating the location and type of design rule violation can be generated.

7.4.2

Extraction

Circuit Level Extraction: can be used to create a netlist for circuit level simulations (e. g. SPICE, . . . ). The netlist consists of MOS transistors (including geometrical parameters as W / L, parasitic capacitances), resistors, capacitances, diodes, . . . . Switch Level Extraction: can be used to create a netlist which can be processed by a switch level simulator. The resulting netlist consists of MOS transistors and parasitic capacitances (to model storage effects in MOS circuits). Parasitics Extraction: is used in conjunction with cell based design techniques. Since wire delay is dependent on the parasitic capacitance of a wire, parasitic capacitances of nets and input capacitances of other gates connected to an output can be used to estimate the extrinsic delays (Note: intrinsic delays [i. e. the delay of unloaded gates] are fetched from the cell library’s simulation model data).

Schematic Extraction: is executed to generate the connectivity data out of a graphical representation (schematic diagram) of a circuit module. The connectivity data is forwarded to a netlister which provides the information required e. g. by simulation tools (the simulators cannot operate on graphical data, they require netlists in a textual format). This kind of extraction is usually required in pre-layout design specification phases.

VLSI

Design Course

7-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Verification

Figure 7.7: Example of a design rules set checked during design verification

VLSI

Design Course

7-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Verification 7.4.3

LVS

The layout–versus–schematic (LVS) comparison tool checks the equivalence of the layout and its schematic. The tool can be used to find wrong connections or parameter mismatch (as W / L of transistors, . . . ) between a schematic and its physical layout representation.

7.4.4

Schematic / Electrical Rule Check (SRC / ERC)

To verify schematics used e. g. in cell based designs, a schematic rule checker can find schematic rule violations (like the following examples): Warnings: • unconnected (floating) wire segments • open outputs • exceeded fanout Errors: • open inputs (undefined input value!) • number of bits differ for 2 buses connected together • number of input/output pins in a schematic differs from its symbol representation (→ pins are not accessible / not present at higher levels of schematic hierarchy) • more than one active driver connected to a net at the same time

VLSI

Design Course

7-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Simulation 7.5

Simulation

7.5.1

Goal of Simulation

• Validation of the system, logic timing, and electricial behaviour • Verify testability aspects • Software development

7.5.2

7.5.3

Simulator Classification Level

Primitives

observable Values

Timing Model

RT

registers, user coded primitives, busses, etc.

bit strings, vectors

discrete time set

Gate

gates

bits

continuous or discrete

Switch

transistors, capacitators

bits

continuous or discrete

Electricial

capacitators, resistors, inductors, diodes etc.

real values

continuous time set

Signal Modelling

• values which exist in real circuits (0, 1, high impedance, oscillation, . . .) • values which exist only in the simulator (unknown, tranistion, . . .) • boolean logic set not sufficient

7.5.4

Signal States

3-valued logic: log. zero log. one unknown

= = =

0 1 U

1 0 1 U

U 0 U U

Example: AND 0 1 U

0 0 0 0

4-valued logic: additional state Z (= high impedance) is introduced

VLSI

Design Course

7-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Simulation

Problems: • Pessimism of U-value (for example: circuit initialisation, spikes) • logic values are often not sufficient (value strength needed)

7.5.5

Circuit and Delay Modelling

• Circuit is built up by simulator primitives • Modelling of the timing/delay behaviour:

x

HH d 

τ (n)

y

y t = x t−τ (n)

∆

:

basic time unit

τ (n) = n · ∆

:

delay of the gate

t1 , t 2 , t 3 , . . .

:

clock time of synchronous circuit

(tν+1 − tν

= ∆t = m · ∆)

Timing models: • Zero-Delay: ∆ = 0 • Unit-Delay: τ (n) = constant • Nominal-Delay: τ (n) = user specified

VLSI

Design Course

7-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Simulation 7.5.6

Advanced Logic Simulators

• Introduction of signal strength additional to logic values for driver and bus modelling A P S X Y Z

: : : : : :

active, e.g. low impedance driver passive, e.g. high impedance driver (depletion load) storing, e.g. capacitive stored state active indeterminate (e.g. active or storing) passive indeterminate (e.g. passive or storing) high impedance

• Instead of simple logical values signals are used for simulation. A signal consists of a logical value and a strength. • Logical Values = {0,1,X} • 16 states Overview on Signal Combinations A0 A0

A0 A1 AX P0 P1 PX S0 S1 SX X0 X1 XX Y0 Y1 YX ZZ

A1 AX A1

AX AX A1 AX

P0 A0 A1 AX P0

P1 A0 A1 AX PX P1

PX A0 A1 AX PX PX PX

S0 A0 A1 AX P0 P1 PX S0

S1 A0 A1 AX P0 P1 PX SX S1

SX A0 A1 AX P0 P1 PX SX SX SX

X0 A0 AX AX X0 XX XX X0 XX XX X0

X1 AX A1 AX XX X1 XX XX X1 XX XX X1

XX AX AX AX XX XX XX XX XX XX XX XX XX

Y0 A0 A1 AX P0 PX PX Y0 YX YX X0 X1 XX Y0

Y1 A0 A1 AX PX P1 PX YX Y1 YX X0 XX XX YX Y1

YX A0 A1 AX PX PX PX YX YX YX XX XX XX YX YX YX

ZZ A0 A1 AX P0 P1 PX S0 S1 SX X0 X1 XX Y0 Y1 YX ZZ

Example: Driver Modelling

7.5.7

Simulation Techniques

• Compiler driven technique Problems: – – – –

Feedbacks Sorting of gate netlist Zero delay model Entire circuit is simulated

• Event driven simulation . . .

VLSI

Design Course

7-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Simulation

HH HH H A1 A H  

HH HH H P0 B H  

HH HH H A1 A H  

HH H A1 - H HH C  

HH HH H S1 B H  



HH HH H A0 B H  

A stronger than B

HH HH HH P0 A  

HH H AX- H H C H 

Short circuit

HH HH H X1 A H  

HH H P0 - H HH C  

HH HH H P0 B H  

P stronger than S

HH H XX- H H C H  

short circuit possible

Figure 7.8: Competing drivers at a bus

7.5.8

Switch Level Simulation

• well suited to simulate digital MOS circuits

VLSI

Design Course

7-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Simulation

Figure 7.9: Example: compiler driven simulation • no fixed direction of signal flow • transistor modeled as a switch with three states: open, closed, unknown • algebraic or RC models

VLSI

Design Course

7-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Simulation

MOS Transistor Model Ideal Switch Transistor Model

Drain d

Gate 

-\ \ \ d

Logic (Gate) 1 0 X

n-Channel Enhancement Closed Open Unknown

p-Channel Enhancement Open Closed Unknown

Depletion Weak Weak Weak

Source

remarks:

• Switch transition time is assumed to be zero or some nominal value. • Unknown states can cause problems.

Linear Switch Tranistor Model

Drain d

Gate 

-\ \ \ ... .......

REF F

XX  X X  X X  X X .......

Logic (Gate) 1 0 X

n-Channel Enhancement REF F ∞ [REF F , ∞]

p-Channel Enhancement ∞ REF F [REF F , ∞]

Depletion REF F REF F REF F

....

d

Source

remarks:

• In the linear model, node capacitance and devices resistance are used to compute output logic levels and transition times. • Ratio errors can be detected.

VLSI

Design Course

7-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL 7.6

Hardware Description with VHDL

VLSI

Design Course

7-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-33

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-35

Darmstadt University of Technology Institute of Microelectronic Systems

0

Hardware Description with VHDL

VLSI

Design Course

7-36

Darmstadt University of Technology Institute of Microelectronic Systems

0

Weinberger Structuring

Chapter 8

Digital Subsystem Design 8.1

Weinberger Structuring

Weinberger structuring is a structured approach that simplifies physical layout and improves layout density. The method has been presented by Weinberger in 1967. Weinberger Arrays • are created by placing transistors on the chip in a geometrically regular manner. Horizontal and vertical interconnect patterns are used to wire the devices together. • using one type of gate; for example, NOR gates form a complete logic set for nMOS circuits • regularity of Weinberger Arrays is very suitable for automatically layout generation

VLSI

Design Course

8-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Weinberger Structuring

Example: F = (A + B + C) = A B C

(8.1)

Figure 8.1: NOR gate reduction for Weinberger structuring • empty squares denote input connections • filled squares denote output connections

VLSI

Design Course

8-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Weinberger Structuring

Example: 3-to-8 decoder

Figure 8.2: Weinberger structuring for 3-to-8 decoder

VLSI

Design Course

8-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Weinberger Structuring

Figure 8.3: Weinberger structuring for 3-to-8 decoder (continued)

VLSI

Design Course

8-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Weinberger Structuring

Example: Z =U +V +W +X +Y

(8.2)

U V Z W X Y

Figure 8.4: Function representation in random logic b

b

b b

b

b

b

b

b

b b b

b

b

b

U V

b

b

b b

b

b b

b

b b

b

b

b

b

b

W

b VDD

b

X

Y

Z

Figure 8.5: Weinberger NOR array representation

b b

U V

..b .. .. . b ....c .. ..b .. .. .. .. .. .............. .. b ... .. .. .............. .. .. .. b ....b .. .. .. .. .. .. .. .. .. .. .. .. .. ..b .. .. .. ..

b

..b .. .. . b ....c .. ..b .. .. .. .. .. ........ ... .. .. b ....b .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..b .. .. .. ..

W

b

X

..b .. .. . b ....c .. ..b .. .. .. .. .. ........ ... .. .. b ....b .. .. .. .. ........ .. .. .. .. b .... ............. .. .. .. b ... .. .. .. .. .. .. ..b .. .. .. ..

b

..b .. .. . b ....c .. ..b .. .. .. .. .. ........ ... .. .. b .... .. .. .. .. ........ .. .. .. .. b .... .. .. .. .. .. .. .. .. .. .. .. .. .. ..b .. .. .. ..

Y

b VDD

Z

Figure 8.6: Weinberger stick diagram

VLSI

Design Course

8-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Weinberger Structuring

Figure 8.7: Weinberger array structure: (a) schematic (b) layout

VLSI

Design Course

8-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Matrix Layout 8.2

Gate Matrix Layout

Gate matrix layout is a character based layout style for custom CMOS circuitry. It is a regular design style, employing a matrix of intersecting transistor diffusion rows and polysilicon columns such that intersections are potential transistor sites.

8.2.1

Creating a Gate Matrix

Representational line drawing or stick figure using the levels of interconnections available (e.g. polysilicon gate technology: polysilicon, metal, diffusion) • immediately draw series of parallel poly lines corresponding to the number of inputs to the circuit (may become more if an output is chosen to be polysilicon) • subsequent transistor placements will be determined by two factors, i.e. input column and serial or parallel association among transistors. • after row definition, further interconnections may be done with horizontal and vertical metal interconnection tracks • final improvements

VLSI

Design Course

8-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Matrix Layout

Figure 8.8: Gate matrix layout: (a) schematic (b) layout (c) optimized layout of n part

VLSI

Design Course

8-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Matrix Layout 8.2.2

Example: Half-Adder

A

C HA

B

S

A

C

B

A

S

B

Figure 8.9: Half adder NAND/INV representation

C = AB = AB

(8.3)

S = AB + AB = (A + B) B + (A + B) A = (A B) B + (A B) A = (A B B) (A B A)

VLSI

Design Course

8-9

Darmstadt University of Technology Institute of Microelectronic Systems

(8.4)

0

Gate Matrix Layout

Figure 8.10: Half adder realizations: (a) standard cell (b) gate matrix

8.2.3 N P + ∗ | ! : –

Character Definitions for Symbolic Layout

n-channel transistor p-channel transistor metal-poly or metal-diffusion crossover contact polysilicon or n-diffusion wire p-diffusion wire vertical metal horizontal metal

VLSI

Design Course

8-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Matrix Layout

Figure 8.11: Typical gate matrix layout

VLSI

Design Course

8-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Matrix Layout

The following rules summarise the gate-matrix technique: 1. Polysilicon runs only in one direction and is of constant width and pitch. 2. Diffusion wires (of constant width) may run vertically between polysilicon columns. 3. Metal may run horizontally and vertically. Any pitch departures from a minimum (e.g. power rails) are manually specified. 4. Transistors can only exist on polysilicon columns. Wide transistors may be specified by abutting two or more N or P symbols.

Figure 8.12: Gate matrix row and column spacings

VLSI

Design Course

8-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Matrix Layout 8.2.4

Summary of Gate Matrix Properties

+ regular design style + technology updatable + modularity is encouraged by the block nature of the layout style + circuit extraction may done at the symbolic level or at the mask level by conventional circuit extractions – character symbolic description is not hierarchical ⇒ modules must be assembled in their entirety and ”pasted” together at the mask level – no freedom to locally optimize geometry, e.g. transistor size

VLSI

Design Course

8-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout 8.3

Optimal CMOS Complex Gate Layout

In MOS circuit design advantage can be taken by the application of complex functional cells in order to achieve better performance. In this section the implementation of a random logic function on an array of CMOS transistors will be discussed. The method has been presented by Uehara and van Cleemput in 1981. A graph theoretical approach for systematic and efficient layout generation minimizes the required chip area.

⇓ optimal

Figure 8.13: (a) CMOS complex gate schematic and (b) corresponding layout

VLSI

Design Course

8-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout 8.3.1

CMOS Functional Cells

Figure 8.14: Implementation of an EXOR function: (a) Logic diagram. (b) Circuit. (c) Layout Advantages of complex gate approach: + better performance

VLSI

Design Course

8-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.15: Example of row-based layout scheme + smaller size In the following, the consideration is limited to AND/OR networks realized in complex gate CMOS by means of series/parallel connections of transistors. The topology of the nMOS network and the pMOS network are assumed to be dual. The delay of a complex CMOS cell mainly depends on the maximum number of series transistors between VDD or VSS and the cell output, which is called level of the complex cell. This quantity has a direct influence on the charging or discharging resistance of the cell. Generally cells with less than four levels are desirable. The number of cells with parallel/serial topology is given by the following table: number of levels 1 2 3 4

number of cells 1 6 80 3434

So it’s reasonable to use mainly cells with three levels and only sometimes cells with four levels in order to get a sufficient performance.

VLSI

Design Course

8-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.16: Alternative complex gate implementation of EXOR function: (a) Logic diagram. (b) Circuit. (c) Layout

VLSI

Design Course

8-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout 8.3.2

Basic Layout Strategy

Figure 8.17: Basic layout of the functional cell: (a) Logic diagram. (b) Circuit. (c) Graph model. (d) Layout

VLSI

Design Course

8-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Layout properties (from Fig. 8.17(d)): • two rows of transistors, implementing the pMOS and nMOS part of the circuit • equal number of transistors in both rows

Figure 8.18: Layout optimization: (a) Diffusion connection of adjacent transistors. (b) Optimal arrangement (reordered input lines) Fig. 8.18 shows layout improvements for the circuit in Fig. 8.17. If the metal connections between adjacent transistors are replaced by diffusion (designer should be careful in doing this for high-speed circuits) the layout of Fig. 8.18(a) is achieved. An even more sophisticated layout arrangement which reduces the required area is shown in Fig. 8.18(b). The best layout is achieved by the transistor arrangement of Fig. 8.19, which is logically equivalent to the previous figures.

VLSI

Design Course

8-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.19: Alternative optimal circuit layout: (a) Logic diagram. (b) Circuit. (c) Graph model. (d) Optimal Layout.

VLSI

Design Course

8-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Generally the area costs of a functional cell can be calculated by area

=

width ∗ height

(8.5)

height = const.

(8.6)

width = basic grid size ∗ (#inputs + #separations + 1)

(8.7)

with and

A separation is required when there is no connection between physically adjacent transistors. An optimal layout is obtained by reducing the number of separations.

8.3.3

Graph Theoretical Algorithm

The p-side and the n-side of the circuit can be formulated as graphs which can be defined as follows: GP

= (VP , EP )

p − side network

(8.8)

GN

= (VN , EN )

n − side network

(8.9)

Graph properties: • the graphs are series/parallel graphs (CMOS complex gate property/assumption) • every source/drain potential is represented by a vertex V • every transistor is represented by an edge E, connectiong the vertices representing source and drain • edges are labeled by the corresponding transistor gate input signal • GP and GN are dual If two edges Ei and Ej are adjacent in the graph model, then it is possible to place the corresponding gates in a physically adjacent position of an array and hence, connect them by a diffusion area. In order to minimize the number of separations a set of minimum size paths has to be found, which corresponds to chains of transistors in the array. Definition 1 An Euler path is a closed path on a graph, that covers every edge of the graph exactly once If there exist Euler paths for GN and GP then all transistors can be chained by diffusion areas. Otherwise the graphs have to be partitioned into subgraphs which have Euler graphs. It’s necessary to find a pair of paths for GP and GN with the same sequence of labels, because p- and n-type transistors corresponding to the same input have to be positioned at the same horizontal position (poly line).

VLSI

Design Course

8-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

General algorithm: 1. enumerate all possible decompositions of the graph model to find the minimum number of Euler paths that cover the graph 2. chain the gates by means of a diffusion area according to the order of the edges in each Euler path and 3. if more than two Euler paths are necessary to cover the graph model, then provide a separation area between each pair of chains =⇒ Search of minimal number of Euler paths is NP-complete

8.3.4

Problem Reduction

An odd number of series or parallel edges can be reduced to a single edge:

Figure 8.20: Reduction of odd numbers of edges Definition 2 The reduced graph is obtained by iteratively replacing an odd number of series (parallel) edges by a single edge, until no further reduction is possible. Theorem 1 If there is an Euler path in the reduced Graph then there exists an Euler path in the original graph. Proof: It is possible to reconstruct an Euler path in the original graph by replacing each edge of the Euler path in the reduced graph by a sequence of the original odd number of edges.

Theorem 2 If the number of inputs to every AND/OR element is odd, then 1. the corresponding graph model has a single Euler path 2. there exists a graph model such that the sequence of edges on an Euler path corresponds to the vertical order of inputs on a planar representation of the logic diagramm. If there are gates in the logic diagramm with an even number of inputs, additional “pseudo” inputs have to be introduced in order to guarantee an odd number of inputs. It is guaranteed by the second previously given theorem, that there exists an Euler path for this modified problem. But the pseudo edges in the Euler path have to be removed afterwards and then they can cause diffusion separations. An algorithm for minimizing separations caused by pseudo edges is given in the next section (⇒ minimal interlace of normal and pseudo inputs). The heuristic algorithm for generating an Euler path is given by:

VLSI

Design Course

8-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.21: Application of reduction rule: (a) Logic Diagram. (b) Graph model and its reduction. (c) Reconstruction of an Euler path 1. To every gate with an even number of inputs a “pseudo” input is added 2. Add this new input to the gate such that the planar representation of the logic diagram shows a minimal interlace of “pseudo” and real inputs. It should be noted that a “pseudo” input at the top or at the bottom of the logic diagram does not contribute to the separation areas as shown in Fig. 8.22(b) and (c). 3. Construct the graph model such that the sequence of edges corresponds to the vertical order of inputs on the planar logic diagram. 4. Chain together the gates by means of diffusion areas, as indicated by the sequence of edges on the Euler path. “Pseudo” edges indicate separation areas. 5. The final circuit topology can be derived by deleting “pseudo” edges in parallel with other edges and by contracting “pseudo” edges in series with other edges.

VLSI

Design Course

8-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

This heuristic algorithm does not necessarily give the optimal layout, but if the resulting sequence has no separations areas, it is the real optimal solution.

Figure 8.22: Application of the heuristic algorithm: (a) New inputs p1 and p2 are added. (b) Optimal sequence of inputs without the interlace of p1 or p2. (c) Circuit with the dual path {p1,2,3,1,4,5,p2}

8.3.5

VLSI

Algorithm for Calculating Minimal Interlace

Design Course

8-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.23: Minimal interlace algorithm

VLSI

Design Course

8-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.24: Application example for minimal interlace algorithm

VLSI

Design Course

8-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout 8.3.6

Examples

Figure 8.25: Carry look-ahead circuit (this representation has no Euler path)

VLSI

Design Course

8-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.26: Alternative topology for carry look-ahead circuit (with possibility of constructing an Euler path)

VLSI

Design Course

8-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Optimal CMOS Complex Gate Layout

Figure 8.27: Comparison of space: (a) Functional cell realization. (b) Conventional NAND realization

VLSI

Design Course

8-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Standard Cell Layout 8.4

Standard Cell Layout

Figure 8.28: Standard cell architecture

Figure 8.29: Synchronous counter schematic

VLSI

Design Course

8-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Standard Cell Layout

Figure 8.30: Synchronous counter floorplan using standard cells

VLSI

Design Course

8-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays 8.5

Programmable Logic Arrays

A programmable logic array (PLA) maps a set of Boolean functions in cannonical, two-level sum-of-product form into a geometrical structure. A PLA consists of an AND-plane and an OR-plane. For every input variable in the Boolean equations, there is an input signal to

Figure 8.31: AND-OR-PLA the AND-plane. The AND plane produces a set of product terms by performing an AND operation. The OR-plane generates output signals by performing an OR operation on the product terms fed by the AND-plane. PLA: AND array and OR array programmable product term sharing: every product term of the AND array can be connected to any of the OR output gates PAL: AND array is programmable and OR array has fixed connection points (OR gates) PROM: AND array hardwired, OR array programmable (→ the set of all possible product terms is realized)

VLSI

Design Course

8-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Figure 8.32: Programmable logic approaches

VLSI

Design Course

8-33

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Example:

x0 0 0 0 0 1 1 1 1

x1 0 0 1 1 0 0 1 1

x2 0 1 0 1 0 1 0 1

z0 1 1 0 0 0 0 1 0

z1 1 1 0 0 0 0 0 1

z0 = x0 x1 x2 + x0 x1 x2 + x0 x1 x2 = x0 x1 + x0 x1 x2

(8.10)

z1 = x0 x1 x2 + x0 x1 x2 + x0 x1 x2 = x0 x1 + x0 x1 x2

(8.11) (8.12)

here: • PROM implementation realizes all of the 8 product terms • PLA implementation needs only 3 terms

AND

OR

0

0 X

-

1

1

1

1

0

-

1

0

1

1

1

-

0

1

? ? ?

x0 x1 x2

? ?

z0 z1

Figure 8.33: PLA realization for given example

VLSI

Design Course

8-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays 8.5.1

Floor Plan for PLA

Figure 8.34: PLA generic floor plan A O AO IN OUT LA RO BL BM BR TL TA TM TO TR

VLSI

Design Course

AND plane programming cell OR plane programming cell AND-OR communication cell AND plane input cell OR plane output cell Left AND plane cell Right OR plane cell Bottom left cell Bottom middle cell Bottom right cell Top left cell Top AND cell Top middle cell Top OR cell Top right cell

8-35

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays 8.5.2

Static nMOS and Pseudo-nMOS PLA

nMOS PLA: Pull-up network realized by single nMOS depletion transistor Pseudo nMOS PLA: Pull-up by high resistance pMOS transistor with permanently grounded gate input Since the AND-OR structure is not suited to MOS circuit technology both AND and OR planes are implemented using distributed NOR or NAND gate structures based on deMorgans law: 1. INV-NOR-NOR-INV structure:

a b + c d = (a + b) + (c + d)          = (|{z} a +b) + (c + d) | {z }     INV  NOR | {z }

(8.13)

NOR

|

{z

}

INV

Example: z0 = xo x1 + x0 x1 x2 = =

h

i

(x0 x1 + x0 x1 x2 )



(x0 + x1 ) + x0 + x1 + x2

(8.14) 

(8.15) Properties:

Figure 8.35: NOR-NOR PLA structure • high static power dissipation • small area

VLSI

Design Course

8-36

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Figure 8.36: Pseudo nMOS NOR-NOR PLA circuit

Figure 8.37: PLA implementation in pseudo nMOS logic

VLSI

Design Course

8-37

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Figure 8.38: Stick diagram of nMOS PLA • useful if high speed is not required 2. NAND-NAND structure:

ab + cd = ab + cd = (a b) (c d)

(8.16)

Example: z0 = xo x1 + x0 x1 x2 =





(x0 x1 ) (x0 x1 x2 )

(8.17) (8.18)

Properties: • NAND-NAND approach not recommended: • decreasing performance at increasing number of inputs (because of series connection of nMOS transistors) • high static power dissipation

VLSI

Design Course

8-38

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays 8.5.3

Static CMOS PLA

NOR gates with a large number of inputs should be avoided in CMOS, because the p-channel devices are in series. Static CMOS PLA are usually realized with NAND-INV-INV-NAND structure in order to avoid long chains of pMOS transistors. Properties:

Figure 8.39: PLA NAND-INV-INV-NAND implementation

• no static power dissipation • area increase becomes unacceptable for large PLA’s • working fast

8.5.4

Dynamic CMOS PLA

• less size than static CMOS • fast • 2-phase clocking • states of φ1 :

VLSI

Design Course

8-39

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Figure 8.40: CMOS PLA layout φ1 = 1: – no path to ground – inputs change – both NOR planes are precharged φ1 = 0: – first NOR plane discharges – dummy: worst case discharge (prevents second NOR plane to discharge) – after first NOR plane, the second NOR plane evaluates

VLSI

Design Course

8-40

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Figure 8.41: Dynamic 2-phase PLA circuit • φ2 is used to latch the second stage → intermediate clock is required to precharge OR plane: this is – as mentioned above – generated by the cells TL, TA and TM. This uses a dummy product row that discharges at the worst case rate according to the loading of the and array

8.5.5

Noise in PLAs

• in dynamic PLAs noise problems on switched supply lines • discharging current is generating transients in the power supply bus • to reduce noise: locally grounding the PLA; use of metal lines for power supply whenever possible (reduced impedance)

8.5.6

Optimization of PLAs

Logic Minimization • optimizations (minimizations) of boolean equations in order to reduce the number of minterms or literals

VLSI

Design Course

8-41

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Figure 8.42: Noise problem in dynamic PLAs • if a term is needed both positive and negative sometimes a reduction can be achieved using negative logic Example: 0

0

0

0

z = x1 + x0 x1 x2 + x0 x1 x2 =⇒ 3 minterms z

0

0

0

0

0

0

= (x1 + x0 x1 x2 + x0 x1 x2 ) 0

0

0

0

0

0

0

= x1 (x0 x1 x2 ) (x0 x1 x2 ) 0

0

0

= x1 (x0 + x1 + x2 ) (x0 + x1 + x2 ) 0

0

0

0

= (x1 x0 + x1 x2 ) (x0 + x1 + x2 ) 0

0

0

0

= x0 x1 x2 + x0 x1 x2 =⇒ 2 minterms • decoder in front of the AND plane to generate combined input variables

VLSI

Design Course

8-42

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Multiple Sided Access

Figure 8.43: Multiple sided input/output access

Folding

Figure 8.44: PLA before folding

Figure 8.45: Row-folded PLA An advantage of multiple-sided access and folding is the decreased layout area, but the layout structure has changed and the wiring is more difficult.

VLSI

Design Course

8-43

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Figure 8.46: Column-folded PLA

8.5.7

Timing and Power Dissipation of a Static PLA

Delay is determined by • (W/L) of the AND/OR load • (W/L) of the AND/OR cells Minimum Delay: • large load current Iload • (W/L)ORplane = e · (W/L)ANDplane Limitations: • Iload limited by: – the total power of the PLA !

– the internal logical ’0’: (I · RnMOS = ’0’) < VT • the stage sizing factor e for successive stages can not always be realized due to the floorplan

VLSI

Design Course

8-44

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays 8.5.8

Automatic PLA Layout Generation Input: boolean equations

JJ

logical optimization A
A


truth table = matrix Cells: A
input/output buffer A
HH  clock driver  floorplanner HH VDD/VSS cells Schmittrigger ...

structure of PLA

A
A


Output: layout with mask data Figure 8.47: Automatic PLA layout generation Example: PLA generator input file PLA adderpla; INPUT: I1,I2,I3; OUTPUT: O1,O2; PRODUCT: P1,P2,P3,P4,P5,P6,P7; AND_BEGIN P1 := I1 * I2; P2 := I1 * I3; P3 := I2 * I3; P4 := I1 * I2’ * I3’; P5 := I1’ * I2 * I3’; P6 := I1’ * I2’ * I3; P7 := I1 * I2 * I3; END_END OR_BEGIN O1 := P1 + P2 + P3; O2 := P4 + P5 + P6 + P7; OR_END

VLSI

Design Course

8-45

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Arrays

Truth table matrix: optimized intermediate result 11X 1X1 X11 100 010 001 111

VLSI

10 10 10 01 01 01 01

Design Course

8-46

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine 8.6

Finite-State Machine

A typical digital circuit architecture for computation intensive applications consists of a datapath and a controller. The data-path is formed by a number of arithmetic units like adders, ALUs, multipliers etc. connected through a network of connections, busses, multiplexors and registers. Registers are required to separate computational stages from each other (to synchronize computations) or to feed back data for further arithmetic operations (to break up circuit loops). However, no circuit can be realized through a data-path only since this circuit part has to be controlled to perform actual computations. Signals are required to select e.g. the functionality of an ALU, to steer data through multiplexors to a dedicated input of an arithmetic unit or to control the reading of values into registers. Those signals are provided through a control unit or short controller. To support a hierarchical design approach data-path and controller are always regarded separately as shown in figure 8.48. The control section provides some control

Figure 8.48: Datapath and controller block signals required for datapath control and on the other hand reads status information as e.g. overflow flags or comparator results (to control loop execution etc). A typical control task example is the instruction set execution of standard microprocessors. Simplified the controller can work in the following way: step 1: step 2: step 3:

initialize processor fetch instruction (address) decode instruction

instr 1(add) step step step step

VLSI

4: 5: 6: 7:

load operand 1 load operand 2 add op1 op2 store result

Design Course

instr 2 (move)

instr 3

step 4: load operand step 5: store operand

8-47

. . .

. . .

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

step n: address = address + 1 step n+1: goto step 2 Different steps are required to fetch, decode and execute an instruction. Depending on the decoding of the instruction a dedicated sequence of steps will be executed. During each step an output vector will be produced to control the datapath (e.g. switch a multiplexor to select a certain operand or determine ALU-operation to be performed on operands). In this example the controller is also receiving signals from the datapath as e.g. instruction decoding information in step 3 to be able to branch into the corresponding instruction execution sequence. The question arises now, how such a controller can be specified and designed. Combinational circuit specification through boolean equations provides a good model for the behaviour of memoryless digital circuits. However, it is quite obvious that a controller realization cannot be memoryless. This is due to the fact that one is passing through a sequence of steps which generally will be influenced through signals to be read from the datapath. During each step an output vector has to be produced to control/steer the datapath. Therefore, a controller can be regarded as a black box with an input and output vector, where the values of the output vector depend on the current step. A certain step is reached through a sequence of preceding steps which finally means, that the value of an output vector depends on the history of the circuit. Such a behaviour is only possible when memory is available. Synchronous digital circuits which comprise memory elements are called sequential circuits since the results produced at the primary outputs generally depend on the values at the primary inputs and the history of the circuit. History in this context means the values of all registers in the current step (or state) which received those values before the actual clock cycle (in the past). Therefore, during its operation the circuit will run through a sequence of states represented through the register contents. Each sequential circuit can be represented in a way as depicted for the controller on the left side of figure 8.48 if all registers are collected into the state register, all combinational logic producing the contents of the registers into the next state logic and all combinational logic producing the primary output values into the output function. Due to the existence of memory, combinational circuit theory is no well suited model for the description of controllers or any other sequential logic. Since a controller can be regarded as a special case of sequential logic application (and one is interested in a general approach to cope with all sequential logic circuits) the more general term sequential logic will be investigated in the remaining section. Figure 8.49 shows a small example of a sequential circuit. Despite it is principally possible to replace the registers through the corresponding combinational circuits and to open the feedback loop such that combinational circuit theory can be applied, a more abstract behaviour description would be desirable. This is especially true for complex controllers where a designer does not want to be concerned with too much circuit details. Fortunately, the theory of finite state machines provides an abstract basis for the modelling of sequential logic.

VLSI

Design Course

8-48

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

Figure 8.49: Sequential circuit example

8.6.1

Introduction into Finite State Machines

In this section we will show how a sequential circuit can be seen as one of several possible implementations of a particular finite state machine (FSM). Each FSM has a finite set of discrete states as well as a finite set of digital inputs and outputs and a set of digital rules that govern its behaviour. An FSM operates in discrete time why its behaviour can be characterized as a sequence of steps that occur at regular intervals (all registers are synchronously clocked). An FSM’s inputs, outputs, and state are assumed to be constant during each interval, changing only at the boundaries between consecutive intervals (the registers are triggered with rising or falling clock edge). Summarizing an FSM is defined in the following way: A finite state machine is a digital device having • a finite set of states S1 , S2 , ..., Sk (where k is the number of states). Optionally one of these, SI is distinguished as the initial state of the FSM • a finite number of binary inputs I1 , I2 , ..., Im (where m is the number of inputs) • a finite number of binary outputs O1 , O2 , ..., On (where n is the number of outputs) • a set of state-transition rules specifying, for each choice of current state SS and input values I1 , I2 , ..., Im , a next state SS 0 • a set of output rules specifying, for each choice of current state SS and input values I1 , I2 , ..., Im , the binary value at each output One distinguishes between two types of finite state machines, namely the Moore machine and the Mealy machine. Both types of machine differ in the last of the topics mentioned above. In the case of Moore type machines the output rules are such that the outputs of a Moore FSM are functions of the current state only. In figure 8.48 this would mean that control inputs are only going into the next-state function block and not into the output function block. The alternative Mealy machine model allows outputs to reflect current inputs as well as current state. Therefore, figure 8.48 represents a Mealy machine. The behaviour of every FSM can be described using either model, although the number of states and timing details will generally differ. The Moore machine has some advantages for theoretical reasoning and is therefore generally used in proving, however, the Mealy machine type is preferred in actual circuit implementations since it generally requires less states (which means less logic for its realization) and

VLSI

Design Course

8-49

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

it can respond immediately upon changes of the input vector (a Moore machine first has to branch into a new state since output values only depend on the state information). Practical FSM implementations typically have a reset input, which returns the FSM to a well defined initial state such that the automata can be reset before a new input sequence is applied (e.g. when the system containing the FSM is turned on). Returning to the circuit of figure 8.49, one can identify the discrete states by tabulating combinations of values for its state variables. If q0 and q1 are used to denote the values of the state variables in the current state, and n0 and n1 to denote the values in the succeeding state, the following equations will describe this circuit: n0 = in · q¯1 n1 = q 0 out = q1 · q0 The state-transition and output rules are shown in the truth table of table 8.1, which lists all possible combinations of current state and input variables on the left side, and the next Current state q1 q0 00 00 01 01 10 10 11 11

Input 0 1 0 1 0 1 0 1

Next state n1 n0 00 01 10 11 00 00 10 10

Output 0 0 0 0 0 0 1 1

Table 8.1: State-transition truth table state which the machine should enter on the right side along with the corresponding output. These tables can be easily obtained from the implementation of the FSM. For example, if in the circuit above, q1 = 0, q0 = 0, and in = 0, then the next state that results is q1 = 0, q0 = 0. If in = 1, the next state will be q1 = 0, q0 = 1. The state-transition table immediately suggests a ROM implementation of the FSM, the lefthand side of the table being the address of the ROM and the right-hand columns being data outputs. The final and most abstract representation for a finite-state machine is a state-transition diagram. In such a diagram, states are shown as circles. Outputs associated with the state are given inside the circle. Transitions between states are represented as directed arcs from one circle to another. The input combination that causes a given transition is written along the arc. Since we are dealing with clocked sequential machines, transitions only occur on clock edges, and for this reason the clock is not explicitly shown on state-transition diagrams. Figure 8.50 gives the state-transition diagram for the FSM discussed above.

VLSI

Design Course

8-50

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

Figure 8.50: State-transition diagram

8.6.2

Realization of Finite-State Machines

The realization of clocked sequential circuits is a fairly straightforward processing having four main steps. First step is to draw a state-transition diagram for the FSM. This is often a very difficult step since it requires thinking very precisely about what the FSM is supposed to do. Next, determine the number of state variables (and therefore registers) from the number of states in the state-transition diagram and assign a binary encoding to each state. This assignment can be done arbitrarily, however, this might result in an inefficient solution. An optimal state assignment is of major importance for the amount of combinational circuitry required to implement the FSM. Unfortunately this problem is NP-hard which means that it is suspected to require exponentially growing computation time if the problem size is increasing. The importance of an appropriate state encoding will be illustrated at the end of this subsection. Then, based on the state-transition diagram, a state-transition table has to be built. It is important that the table covers all possible input combinations for each possible state (if a combination does not occur don’t cares should be inserted which can be exploited during combinational logic minimization). From the table, the circuit can be directly implemented with ROMs. If another implementation is required (logic gates, for example), Karnaugh maps from the state-transition table for each next-state variable have to be developed. Finally, a reduced sum-of-products expression has to be found for each which can be implemented through appropriate combinational logic. To illustrate those steps consider the design of a simple FSM whose one output goes high every five clock times and remains high for one clock period. The frequency of the output pulses is one-fifth that of the clock. This type of circuit is called a divide-by-5 counter. This machine has no external inputs. Its state-transition diagram is shown in figure 8.51. A state assignment and a state-transition table for this counter are given in table 8.2. Please note that the number of 3 bits for state encoding as well as the actual encoding of each state had been done arbitrarily. A larger number of bits or another encoding could have been selected! The table can now be realized through e.g. ROMs or using explicit combinational logic (realized as two/multilevel gates, PLA etc). Figure 8.52 shows another example which in the following will be used to illustrate the im-

VLSI

Design Course

8-51

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

Figure 8.51: State-transition diagram for the divide-by-5 counter Transition table Current Current state state A 000 B 001 C 010 D 011 E 100

Output table Next State Output 001 0 010 0 011 0 100 0 000 1

Table 8.2: State-transition table for divide-by-5 counter

Figure 8.52: State-transition diagram of an arbitrary FSM portance of state-encoding. The behaviour of the FSM is given represented in transition table 8.3. State encoding is the process of assigning a unanimous bit vector to each state of the FSM, e.g. the following two encodings can be selected:

VLSI

Design Course

8-52

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine Current state q1 q0 S0 S0 S1 S1 S2 S2

Input 0 1 0 1 0 1

Next state n1 n0 S0 S1 S2 S1 S0 S1

Output 0 0 0 0 0 1

Table 8.3: State-transition truth table Encoding 1 S0 = 00 S1 = 01 S2 = 11

Encoding 2 S0 = 00 S1 = 11 S2 = 01

There are s possible encodings with s=

k! (k − m)!

with k = 2n (n is the number of selected state bits) and m being the number of states to be encoded. Typically n is chosen as n = dlg2 (m)e. However, other values are possible for n, e.g. one bit per state! In the example above: k = 22 = 4 and m = 3. With these constraints the number of 4! = 24. Each corresponding encoding results in different complex possible encodings is (4−3)! realizations. The first state encoding had been S0 = 00, S1 = 01, S2 = 11 The corresponding output function is out = abc resulting in the state transition functions y1 = a ¯¯bc y2 = a¯b + ¯bc + ac The number of product terms is 5 and that of the literals 12. A resulting hardware implementation using combinational logic is shown in figure 8.53 The second encoding had been S0 = 00, S1 = 11, S2 = 01 The corresponding output function is out = a ¯bc

VLSI

Design Course

8-53

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

Figure 8.53: FSM-realization for first encoding scheme and the transfer functions y1 = a¯b y2 = a¯b + bc The number of related product terms and literals is now 4 resp. 9. Figure 8.54 shows a corresponding realization. As one can see state encoding is crucial for efficiency of the final solution. Unfortunately there is no way to find an optimal assignment with an algorithm whose complexity is bound by a polynomial expression. A good heuristic is to simply select an encoding where only one bit is changing when sequencing from state to state (gray code). Another good approach can be one-hot encoding (where a single bit represents each state) which is certainly restricted to a small number of states.

8.6.3

Synchronous FSM Circuit Models

Although it is possible to base FSM realizations on self-timed or other timing disciplines, most FSM implementations are based on a synchronous, single-clock scheme. As already mentioned in connection with figure 8.48 a general sketch of an implementation strategy using the Moore

VLSI

Design Course

8-54

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

Figure 8.54: FSM-realization for second encoding scheme machine model (outputs are functions only of current state, independently of current inputs) is shown in figure 8.55. One should note the use of a clocked register to hold the current state

Figure 8.55: FSM (Moore automata) implementation information. All other blocks are combinational logic components which can be realized in different ways (PLA, ROM, dedicated logic circuits etc). Timing of the inputs of such a circuit has to be synchronous with the FSM’s clock because all signal outputs of the next-state logic have to be settled down before the values are loaded into the registers during rising clock. In the case of asynchronous transitions nonsense might be loaded or meta-stable states of the registers might be activated. Asynchronous inputs can be treated as shown in figure 8.56. The synchronisation through additional clocked registers guarantees that the inputs to the state register are stable at each active clock edge, assuming of course that the propagation delay along the combinational

VLSI

Design Course

8-55

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

Figure 8.56: Treatment of asynchronous inputs in a Moore machine path through the logic is shorter than the clock period (plus setup-time of state registers). Moreover, although meta-stable behaviour of the input register remains a possibility, it has a clock period (minus the next-state propagation delay) to become valid before it corrupts the contents of the state register. Thus, for sufficiently long clock periods, this latter design should be arbitrarily reliable. It is important to recognize that the implementations of figures 8.55 and 8.56 behave slightly differently, owing to the extra clock delay in the inputs of figure 8.56. Given identical nextstate logic, identical input sequences will yield output sequences delayed by one clock cycle in the second approach.

8.6.4

States and Bits

Most real digital systems are finite-state machines, yet the view and techniques introduced in this chapter are not appropriate in every circumstance. The binary encoding of an FSM’s state allows at most 2k states to be represented in k bits of state variables, and in general about k flip-flops are required to hold the state of a 2k -state machine. Adding a single flip-flop to a machine potentially doubles its number of states. This exponential relationship between the number of states and the amount of physical hardware in a sequential circuit leads the FSM model to become awkward in dealing with sequential circuits having more than a few bits of storage. A 10-bit register, for example, would be quite difficult to characterize by a state-transition diagram; the number of states of a supercomputer is inconceivably large. Typically, such systems are viewed in terms of memory cells and registers, partitioning the enormous state into more tractable units. It is important to recognize that sequential circuits may be viewed either in state or in bit terms, that the two are exponentially related, and that it is often useful to change between these views. Therefore, the reader should be aware that it makes no sense to apply the FSM-model to each type of sequential circuit. However, the FSM-model is very well suited to support the design of controllers since the number of states is reasonably small.

VLSI

Design Course

8-56

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine 8.6.5

Equivalence of FSMs

The input/output behaviour of two FSM’s may be identical even though the machines have different transition and output rules or even different numbers of states. As a degenerate example, one consider two single-input FSMs whose output remains constant, independent of their state. From external observations it is impossible to distinguish between the states of such machines – one might have one state and the other nine, yet the machines are externally indistinguishable. We call FSMs equivalent if they are indistinguishable; for all practical purposes, equivalent FSMs are interchangeable. Therefore, the equivalence of FSMs is important for their construction since the designer is interested to transform an initial FSM specification to an equivalent machine which can be realized most efficiently on silicon meeting all required constraints. It is therefore useful to develop the notion of equivalence together with engineering tools for reducing a specified FSM to a simpler equivalent. The terms state equivalence and FSM equivalence are defined in the following way: State equivalence: Let s1 and s2 be particular states of FSMs M1 and M2 . State s1 of M1 is equivalent to state s2 of M2 if and only if for every finite sequence of inputs, the outputs resulting from the application of that sequence to M1 in s1 are identical to the outputs resulting from the application of the same sequence to M2 in s2 . Thus two states are not equivalent only if there exists a finite input sequence that leads them to produce distinct outputs. The notation M : s will be used to specify state s of machine M . FSM equivalence: Let s1 and s2 be initial states of FSMs M1 and M2 . Then the machines M1 and M2 are equivalent if and only if M1 : s1 is equivalent to M2 : s2 . Given an FSM that solves some practical problem, one is often interested in finding the smallest equivalent FSM in order to minimize costs. While several measures of ‘smallest’ might be proposed, a natural candidate (and usual choice) is the number of FSM states. Thus one seeks to perform a state reduction on a given FSM M1 to yield and equivalent M2 having fewer states. In general, this may be done by detecting and merging equivalent states within M1 . For example one can look for pairs M1 : si and M2 : sj that are equivalent. When such a pair is found, they simply can be combined into a single state, yielding an equivalent FSM with one fewer state. This process of looking for equivalent states can be continued in the new FSM and terminates when a pair of equivalent states can no longer be found. This is an example of a relaxation algorithm, in which a set of reduction rules is repeatedly applied to reduce a structure until it can be reduced no more. It begins with a pessimistic but working model of the desired FSM and iteratively improves the cost while maintaining equivalence. This approach has the disadvantage that the equivalence of two states can be difficult to detect. Rather than incrementally improving an initial pessimistic model, the optimistic relaxation approach begins with the assumption that all of the states of M1 are equivalent (yielding a one-state machine). The relaxation iteratively discovers pairs of presumed equivalent states that cannot in fact be equivalent and grudgingly splits them into their components. This scheme is based on the detection of state none-equivalence through the following two rules: • If states si and sj have different outputs, then they are nonequivalent • If, for some input combination v1 , v2 , ..., vm state si1 goes to state Si2 and state sj1 goes

VLSI

Design Course

8-57

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

to state Sj2 , where Si2 and Sj2 are nonequivalent, then si1 and sj1 are nonequivalent Beginning with the unrealistic assumption that all states are equivalent, iteration of the above rules will uncover more and more nonequivalent pairs of states until every pair that has not been shown nonequivalent is in fact equivalent. Consider e.g. the FSM diagrammed in figure 8.57. The search for a reduced equivalent starts

Figure 8.57: Five-state FSM by constructing a truth table for output and transition rules for a one-state equivalent:

New state S0 = S1 = S2 = S3 = S 4

Output X

Transitions 0 1

In the course of building the table, it has to be checked that each output and next-state value for a merged state is consistent with each of the component states from the original FSM. In this first step, an inconsistency will be detected immediately: It is impossible to put a value into the output column for the single combined state that is consistent with all five component states. Thus the aggregate state has to be split into two new states for the next iteration, with output values of 0 and 1. One partitions the five-state aggregate into one state corresponding to the original S0 and S3 states with a 1 output, and a second state corresponding to the original states with a 0 output. Then it has to be attempted to fill out the truth table:

New state S0 = S3 S1 = S2 = S 4

Output 1 0

Transitions 0 1 S1 = S4 S0 S2 X

This time the table could be nearly completed. A single inconsistency is encountered when trying to assign a transition for the S1 = S2 = S4 state on a 1 input: In the original machine, S1 and S4 both go to S3 in this case, while S2 goes to S4 . Since the respective next states S3 and S4 are not equivalent, S2 has to be split into a separate state. This results in:

VLSI

Design Course

8-58

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

New state S0 = S3 S1 = S4 S2

Output 1 0 0

Transitions 0 1 S1 = S4 S0 S2 S3 S2 S4

The corresponding state-transition diagram is shown in figure 8.58. The reader might verify

Figure 8.58: Reduced equivalent FSM that this reduced FSM is equivalent to the original. While simple optimistic relaxation gives optimal reductions in the case of completely specified FSMs, optimal solutions to interesting variations of the FSM reduction problem are known to be computationally intractable. For example, optimal reduction of an incompletely specified FSM (don’t cares are available), in the sense that any values are acceptable for certain outputs and/or transitions, is NP-hard. The development of good heuristic approaches to this and related optimization problems remains a topic of research.

8.6.6

Regular Expressions and Nondeterministic FSMs

Regular expressions are a commonly used notation for describing simple classes of strings and symbols. For the purpose of this subsection the following regular-expression syntax for describing stings of uppercase letters will be used: 1. Finite strings of symbols (letters), including the empty string (which will be written as ), are regular expressions. Thus, A,  and ABCAABCAAABB are valid regular expressions, each denoting a set containing only the specified string of zero or more letters 2. If p and q are regular expressions, then pq is a regular expression denoting the set of strings formed by concatenating a string from p with a string from q 3. If p and q are regular expressions, then p | q is a regular expression denoting the set of strings that includes both the strings denoted by p and the strings denoted by q. Thus A | B is a regular expression defining a set containing the strings A and B 4. If p is a regular expression, then (p) is a regular expression denoting the same set of strings; parentheses are used to disambiguate – for example, to distinguish (AB) | C from A(B | C)

VLSI

Design Course

8-59

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine 5. If p is a regular expression, then p∗ is a regular expression denoting all strings that are concatenations of finitely many (zero or more) strings denoted by p. Thus A∗ denotes the set of strings containing the empty string as well as every string consisting of finitely many As; A(A | B)∗ B denotes the set of all strings of As and Bs that begin with A and end with B An interesting property of regular expressions is that each regular expression defines a set of strings that can be recognized by a finite state machine. It is assumed that the input to the FSM is a sequence of symbols (in this case, encoded uppercase letters) and that each consecutive input symbol can cause a transition from the current FSM state to a new state. At any time when the sequence of input symbols corresponds to a string to be recognized, the FSM is in a distinguished state marked R; it is allowed to mark several states in this way. The starting state will be marked S. The FSM of figure 8.59, for example, recognizes the strings

Figure 8.59: Example FSM B(AB)∗ . Note that transitions corresponding to input strings that are not recognized (such as those containing the letter C) are omitted. The selected convention is that such strings cause implicit transitions to a BAD state, which causes the entire input sequence to be rejected. Although every regular expression denotes a set of strings recognizable by an FSM, the systematic derivation of an FSM recognizer from a regular expression is not entirely trivial. A useful conceptual tool in dealing with regular expressions is the nondeterministic FSM (NFSM), whose state-transition diagram is ambiguous in the sense that it may indicate several possible transitions on a given input symbol. The simple NFSM in figure 8.60 recognizes the strings

Figure 8.60: Nondeterministic FSM A | (AB). One can view the NFSM as being in several states simultaneously. Its behaviour can be emulated by hand, using tokens that are moved about on the state-transition diagram to record active states. One begins with a token on the starting state. At each input symbol,

VLSI

Design Course

8-60

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine

tokens are placed on each state at the arrow end of a transition from a marked state and the previous tokens have to be removed. Note that at most one token has to be placed in each state. Whenever one or more states marked R contains a token, the input string is accepted (recognized) by the NFSM. It is possible to construct a deterministic FSM that recognizes any regular expression, but the construction becomes cumbersome when an expression of the form α | β is encountered. In effect, the FSM under construction must entertain the two alternative forms α and β as possible inputs until some input symbol rules one or both forms out; this may require a number of states, each corresponding to some combination of a tentative parse of form α or an alternative parse of form β. In contrast, the NFSM provides direct accommodation for alternative input forms by means of ambiguous transitions. The dual paths between the S and R states of figure 8.60, for example, correspond directly to the alternative input forms A and AB. As a further convenience in the construction of NFSMs from regular expression, the use of transitions on the empty input string is allowed; such transitions are taken spontaneously by the NFSM. In the token model, whenever there is an empty transition from a state marked by a token, the target of the empty transition will be marked as well. Figure 8.61 shows how one might use empty transitions, designated by , to convert the A | (AB) NFSM, for example, to

Figure 8.61: NFSM that recognizes strings of form (A | (AB))∗ recognize (A | (AB))∗ . Nondeterministic FSMs are, in an important sense, no more powerful than deterministic FSMs: The same set of strings (the ones that can be described by regular expressions) can be recognized by each. NFSMs, however, provide a primitive model for parallelism because of their ability to model several discrete states simultaneously. While NFSMs and FSMs perform the same computations, a deterministic FSM may require exponentially many states compared to the equivalent NFSM. The nondeterministic FSM, although not directly realizable in hardware, can be an important tool in the synthesis of realizable deterministic FSMs that perform useful computations. The synthesis of an FSM to recognize strings described by the regular expression (A | (AB))∗ , for example, might be approached by the straightforward synthesis of the NFSM of figure 8.61 followed by the derivation of an equivalent (but less intuitive) deterministic FSM using a computer-based algorithm.

VLSI

Design Course

8-61

Darmstadt University of Technology Institute of Microelectronic Systems

0

Finite-State Machine 8.6.7

Context

Finite-state machines are simultaneously a mathematical abstraction that has received considerable attention from theorists and a practical engineering tool of enormous consequence to the designer of digital systems. These roles are not independent; the formal study of FSMs has significantly enriched the repertoire of optimizations and techniques available to the engineer, while their practical significance stimulates continued attention by theorists.

VLSI

Design Course

8-62

Darmstadt University of Technology Institute of Microelectronic Systems

0

ASIC Design Process

Chapter 9

ASIC Design Concepts 9.1

ASIC Design Process

9.1.1

VLSI

The VLSI Design Process as a Transformation from Higher to Lower Descriptive Levels

Design Course

9-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

ASIC Design Process 9.1.2

VLSI

Phases of Electronic System Design

Design Course

9-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

ASIC Design Process 9.1.3

Application Architectural Properties

Data path oriented: • Microprocessors, DSP’s and Co-Processors • Data operation by a number of functional units interconnected by a wordsized datapath • Functional units: ALU, Multiplier, . . . Control-dominated: • Sequencers, Protocol Engines • no arithmetic structures • no or small data path • decentralized • set of coupled controllers

9.1.4

Synthesis S.pdf

1. Architectural Synthesis (= Behavioural Synthesis) • translation of a source description into a data flow graph • scheduling the events in the flow graph • allocation of functional units in the machine • binding the functional units to real components in a specific technology 2. Logic Synthesis • translation of a register-transfer level description of a circuit into combinational logic and registers • finite state machine synthesis • technology-independent logic optimization • mapping the result on a suitable target technology (Gate Arrays, Standard Cells, Sea of Gates, . . .) • circuit retiming to meet performance requirements 3. Layout Synthesis • module generators generate automatically a dense layout of specific modules • typical modules: functional units of data paths (ALU, register, shifter, adder, . . .) • greatest leverage for data path oriented design • PLA-generators for control logic • most useful in the design of application specific DSPs and generic components such as microprocessors

VLSI

Design Course

9-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

ASIC Design Styles 9.2

ASIC Design Styles

9.2.1

ASIC Technology Tree

VLSI

Design Course

9-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

ASIC Design Styles

VLSI

Design Course

9-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays 9.3

Gate Arrays

9.3.1

Introduction to Gate Arrays

Gate Arrays (Masterslices): • Prefabricated active elements (master) • Construction of logic functions by personalization (wiring macros from a cell library, intra-cell routing) • Connection of functional blocks by inter-cell routing in 1 . . . 3 layers + contact/via layers • Arrangement of gate arrays: – Row Structure – Island Structure – Matrix of structures (= sea of gates) • Mixed analog/digital gate arrays

Figure 9.1: Gate array floorplan with row structure

VLSI

Design Course

9-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays

Figure 9.2: Floorplan for a sea of gates array

VLSI

Design Course

9-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays 9.3.2

IMI Grid Structure

Figure 9.3: IMI gate array structure Fig. 9.3 principally shows the structure of gate arrays of International Microcircuits Inc. (IMI) (single metal layer). The real circuit has 1440 cells. In the Figure a reduced number of 40 cells is drawn in order to improve the clearity of the representation. The gate array consists of the following elements: • Pad (connection to outside world) • Buffer devices (drive out-chip load capacitances) • Distributed power and ground buses • Underpasses to cross under the power and ground buses without contacting them • Each point represents a contact (potential interconnection point) From Fig. 9.4 the following features can be seen:

VLSI

Design Course

9-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays

Figure 9.4: Corner of IMI gate array die • Cells containing transistors are clustered around the VDD and VSS buses. • In each cell four horizontal bars (crossing VDD and VSS ) can be seen. The thick bar represents a poly underpass while the the three thin bars are common poly input lines to an nMOS/pMOS transistor pair • Between cell columns a column of short horizontal poly underpasses is placed

VLSI

Design Course

9-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays

Figure 9.5: Grid representation of IMI gate array

VLSI

Design Course

9-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays

Figure 9.6: Explanations of grid: (a) basic cell. (b) internal interconnects. (c) basic cell and crossover (poly) block. (d) XR = transistor. (e) crossover block interconnects In Fig. 9.6 (b) the internal gate (long horizontal poly lines) and internal diffusion (short horizontal diffusion lines) are shown. From Fig. 9.6 (d) it can be seen that adjacent nMOS or pMOS transistors have a common drain/source connection. Contacts for the nMOS source and drain connections are at both sides of the VSS bus (same for pMOS transistors and VDD bus.

VLSI

Design Course

9-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays

Figure 9.7: Symbolic IMI cell structure representation

Figure 9.8: CMOS matrixcell

VLSI

Design Course

9-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays 9.3.3

CDI Grid Structure

Figure 9.9: CDI single metal layer gate array structure

VLSI

Design Course

9-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays 9.3.4

Gate Array Design Flow

Figure 9.10: Gate array design flow

VLSI

Design Course

9-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays 9.3.5

Personalization Examples for IMI and CDI Gate Array

Figure 9.11: Personalization for inverter: (a) schematic. (b),(c) IMI layout. (d) CDI layout

VLSI

Design Course

9-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays

Figure 9.12: NOR gate on IMI

Figure 9.13: Layout of transmission gates: (a) single TG. (b) pair of TGs with common output

VLSI

Design Course

9-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays 9.3.6

Qualification of Gate Array Design Style

Advantages: • Lower number of individual masks needed • Higher number of pieces for uncustomized master (cost reduction) • Many others for masters, second source fabrication, libraries and design systems Disadvantages: • Area overhead (by unused transistor cells) • Overdimensioned routing channels • Larger cell size =⇒ Advantages dominate for smaller production volumes

VLSI

Design Course

9-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gate Arrays 9.3.7

Gate Array Market

Figure 9.14: Gate array market by process technology

Figure 9.15: Worldwide gate array market by user sector

VLSI

Design Course

9-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Standard Cell Design 9.4

Standard Cell Design

9.4.1

Introduction to Standard Cells

Figure 9.16: Circuit and corresponding standard cell

VLSI

Design Course

9-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Standard Cell Design

Figure 9.17: Standard cell scheme

Figure 9.18: Standard cell floorplan

VLSI

Design Course

9-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Standard Cell Design

Standard Cells: • No prefabrication: all cell layouts from a system library • Cells in rows: VDD /VSS - lines connected by cell abutment, uniform cell height, variable width: I/O - connections top and bottom • Cell rows alternating with routing channels • Width of routing channel adaptable to design needs • Crossing of Cells possible: feed-through cells, electricially equivalent pins

9.4.2

Qualification of Standard Cell Design Style

Advantages: • substantial saving of chip area compared to Gate Arrays (typically 40%) • thereby reduction of fabrication costs per chip • higher flexibility in cell design Disadvantages: • all masks individually (high initial cost and turn-around time) • very complex or large-area functional blocks like RAM, ROM or PLA cannot be inserted =⇒ Advantages dominate with a higher number of pieces (> 10000)

VLSI

Design Course

9-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Standard Cell Design 9.4.3

Standard Cell Market

Figure 9.19: Standard cell market by process technology

Figure 9.20: Standard cell market by application

VLSI

Design Course

9-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Macro Cell Concept 9.5

Macro Cell Concept

9.5.1

Introduction to the Macro Cell Concept

• Rectangular cells, any form and size • Free cell arrangement • Wiring channels between the cells • Width of wiring channels according to routing needs • Power/ground routing not separated from signal routing

Figure 9.21: Floor plan for macro cell design style (= building block approach

VLSI

Design Course

9-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Mixed Design Styles 9.6

Mixed Design Styles

9.6.1

Introduction: Mixed Design Styles

Figure 9.22: Mixed design style structures

9.6.2

Features of Mixed-Mode ASICs

• Mixed analog/digital macros • EEPROM cells • Power components: – High-current analog buffer – Power MOSFET driver • ASIC-Hybrid combinations • Subsystem Cells: 555 Timer, 4046 PLL, . . . • SC-Filter • Biquad units • Temperature sensors

VLSI

Design Course

9-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices 9.7

Programmable Logic Devices

9.7.1

Classical PLD Devices

• PROM (Programmable Read Only Memory) Device with fixed AND array and a programmable OR array 1. mask programmable + superior speed performance due to internal connections hardwired during manufacture + cheap at high volumes – can only be programmed by manufacturer – development cycle = weeks or months 2. field programmable + immediately programmable + at low volumes less expensive than mask-programmable devices – resistance of programmable routing switches lowers signal performance • EPROM (Erasable Programmable Read-Only Memory) • EEPROM (Electricially Erasable Programmable Read-Only Memory) =⇒ additional advantage to be erasable and re-programmable =⇒ structures of PROMs are best suited for the implementation of memories • PLA AND array and OR array programmable product term sharing: every product term of the AND array can be connected to any of the OR output gates • PAL AND array is programmable and OR array has fixed connection points – combinational PAL devices used for implementation of logic functions – sequential PAL devices used for implementation of sequential logic (finite state machines) – arithmetic PAL devices sum of product terms may be combined by EXOR gates at the input of the macrocell D flip-flop

VLSI

Design Course

9-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices

Figure 9.23: Combinational PAL devices: AMD 16L2

VLSI

Design Course

9-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices

Figure 9.24: Sequential PAL devices: AMD PAL16R4

VLSI

Design Course

9-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices

Figure 9.25: Arithmetic PAL devices: AMD PAL16A4

VLSI

Design Course

9-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices 9.7.2

Advanced PLD Devices

• EPLD (Erasable Programmable Logic Devices) • EEPLD (Electricially Erasable Programmable Logic Devices) =⇒ these devices use EPROM cells or EEPROM cells instead of fuses as programmable connections =⇒ tendency: instead of large global logic planes a blockoriented architecture with local logic blocks and macrocells and an interconnection network between the blocks is used Example: Altera EP1800

Figure 9.26: Advanced PLD devices: Altera EP1800

VLSI

Design Course

9-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices

Figure 9.27: Local macro cell

Figure 9.28: Global macro cell

• each EP1800 quadrant contains 12 macrocells and has a local bus with 24 lines (for normal and inverted macrocell outputs) and a local clock • the global bus has 64 lines and runs through all of the four quadrants (true and complement signals of 12 inputs (= 24 lines) + true and complement of 4 clocks (= 8 lines) + true and complement of I/O-pins of the 4 global macro cells in each quadrant (= 32 lines) • macrocells: combinational or registered data output; the flip-flop is configurable: D, T, JK or SR)

VLSI

Design Course

9-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices

Figure 9.29: Synchronous clock, output enabled by product term

Figure 9.30: Asynchronous clock, output permanently enabled

VLSI

Design Course

9-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices

Example: Altera MAX7000 Family

Figure 9.31: Block diagram of MAX7000 family

VLSI

Design Course

9-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Programmable Logic Devices

Figure 9.32: MAX7000 macrocell

9.7.3

PLA-based Device Properties

1. Easy to map Espresso/MIS style logic into sum of products 2. Easy to route, very fast turnaround 3. Performance independent of netlist 4. Wide designer acceptance 5. Relatively mature technology, but some innovation still ongoing

VLSI

Design Course

9-33

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays 9.8

Field Programmable Gate Arrays

9.8.1

The FPGA Concept

Figure 9.33: Principal FPGA structure • Logic blocks • Routing resources that can connect the logic blocks The routing resources are both the greatest strength and weakness of FPGA’s

VLSI

Design Course

9-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays 9.8.2

FPGA Categories

1. Block organized, SRAM based (internal block structure not restricted to AND–OR) • Xilinx • Altera (FLEX) • Plessey • AT&T • ... 2. Cell organized, anti-fuse based • Actel • Quicklogic • ...

Figure 9.34: Four classes of commercially available FPGAs

VLSI

Design Course

9-35

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays 9.8.3

Programming Technologies

Static SRAM Programming Technology • connection elements are controlled by SRAM cells

Figure 9.35: SRAM programming technology Basic Technology Issues: SRAM

1. Function unit and routing are controlled by SRAM cells 2. These cells are located adjacent to the logic they control (not in a separate chip) 3. SRAM cells are configured at power-up and potentially reconfigured during operation 4. Configuration is a non-destructive process 5. SRAM cells are large (5 transistors), require connection to power, ground, data and select lines 6. . . . but they can be intimately intermixed with CMOS logic 7. SRAM memory design is highly refined Anti-Fuse Programming Technology • Anti-fuses are made with a modified CMOS process involving an extra step • This step creates a very thin insulating layer that separates two conducting layers • This insulator is penetrated by applying a high voltage to the to conducting layers (this process is not reversible) • The programming voltage must be much higher than the logic threshold, otherwise the chip would program itself under operation • Such high voltages can be destructive for CMOS logic circuitry • Large isolation devices may be required to protect logic gates from the programming voltage

VLSI

Design Course

9-36

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays

Actel PLICE Anti-Fuse Programming Technology

Figure 9.36: Actel PLICE anti-fuse structure • Actel PLICE anti-fuses can be programmed by placing a relatively high voltage (18V) across the anti-fuse terminals, heat and melt the dielectric by a driving current of about 5 mA and form a conductive link between poly-Si and n+ diffusion • bottom and top layer of the anti-fuse are connected to metal, the over all resistance of a programmed anti-fuse (from metal to metal) is about 300Ω – 500Ω • manufactured by 3 additional masks to a normal CMOS process Quicklogic ViaLink Anti-Fuse Programming Technology

Figure 9.37: Quicklogic ViaLink Anti-Fuse • amorphous silicon antifuse • a low resistance path (80Ω) between two metal wires is created by a 10V programming voltage at the terminals of the anti-fuse

VLSI

Design Course

9-37

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays

EEPROM Programming Technology

Figure 9.38: EEPROM programming technology • used in FPGAs (PLDs) manufactured by Altera and Plus Logic • static charge on floating gate turns the transistor permanently off • EPROM transistors are used to pull bit lines to ground • disadvantage of EPROM technology: static power dissipation

9.8.4

Overview: Commercially Available FPGAs Company Xilinx Actel Altera Plessey Plus AMD Quicklogic

VLSI

General Architecture Symmetrical Array Row-based

Algotronix

Hierarchical PLD Sea-of-gates Hierarchical PLD Hierarchial PLD Symmetrical Array Sea-of-gates

Concurrent

Sea-of-gates

Crosspoint

Row-based

Design Course

9-38

Logic Block Type Look-up Table MultiplexerBased PLD Block NAND-gate PLD Block PLD Block MultiplexerBased Multiplexers and Basic Gates Multiplexers and Basic Gates Transistor Pairs and Multiplexers

Programming Technology Static RAM Anti-Fuse EPROM/SRAM Static RAM EPROM EEPROM Anti-Fuse Static RAM Static RAM Anti-Fuse

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays 9.8.5

Xilinx Architecture

Figure 9.39: General architecture of XILINX FPGAs Series XC2000 XC3000 XC4000

Number of CLBs 64 . . . 100 64 . . . 320 64 . . . 900

Equivalent Gates 1200 . . . 1800 2000 . . . 9000 2000 . . . 20000

Figure 9.40: Xilinx XC4000 CLB • two stage look-up tables, two functions of 4 variables or one function of five variable can be implemented

VLSI

Design Course

9-39

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays

Figure 9.41: Xilinx XC4000 single length lines • XC4000 routing architecture: Single-length Lines and Double-length lines • high CLB connectivity to wiring segments

Figure 9.42: Xilinx XC4000 double length lines and long lines

VLSI

Design Course

9-40

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays 9.8.6

Actel Architecture

Figure 9.43: General architecture of Actel FPGAs Series Act-1 Act-2

Number of LMs 295 . . . 546 430 . . . 1232

Equivalent Gates 1200 . . . 2000 6250 . . . 20000

• rows of programmable Logic Modules (LM) • horizontal routing channels between rows

Figure 9.44: Act-1 logic module

VLSI

Design Course

9-41

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays

Figure 9.45: Act-1 programmable interconnection architecture

VLSI

Design Course

9-42

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays

Figure 9.46: Act-2 logic cells

VLSI

Design Course

9-43

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays 9.8.7

CAD for FPGAs

Figure 9.47: FPGA CAD

VLSI

Design Course

9-44

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays

Figure 9.48: The Xilinx design flow

VLSI

Design Course

9-45

Darmstadt University of Technology Institute of Microelectronic Systems

0

Field Programmable Gate Arrays 9.8.8

Economical Considerations

Figure 9.49: Cost per Chip (Dollars) Economics and Performance of FPGAs compared to MPGAs: FPGA: + no overhead cost ⇒ less cost intensive for low volumes + short turnaround time ⇒ short time to market + high designers flexibility (short turnaround time), low redesign costs – relatively low speed of operation caused by the resistance and capacitance of programmable switches in the routing network – decreased logical density, programmable switches and configuration network require chip area MPGA: + low per chip costs at high volumes + fabrication hardwired metal connection layers ⇒ fast operation + high logic density – very high costs for low volumes (for example prototypes) – no redesign flexibility

VLSI

Design Course

9-46

Darmstadt University of Technology Institute of Microelectronic Systems

0

Overview on Logic Design Alternatives 9.9

Overview on Logic Design Alternatives

Figure 9.50: Logic design alternatives

VLSI

Design Course

9-47

Darmstadt University of Technology Institute of Microelectronic Systems

0

Overview on Logic Design Alternatives

Figure 9.51: Relative merits of various ASIC implementation styles

VLSI

Design Course

9-48

Darmstadt University of Technology Institute of Microelectronic Systems

0

Adders / Subtracters

Chapter 10

Arithmetic Units In the following chapter, basic arithmetic units like adders, subtracters, or multipliers are discussed. These components are widely used in VLSI circuits e. g. for the digital signal processing application domain. More detailed descriptions on arithmetic units can be found e. g. in [13] or [3].

10.1

Adders / Subtracters

10.1.1

Basic Adder Cells

Half Adder The circuit realizing the function C = A1 A2

(10.1)

S = A1 ⊕ A2

(10.2)

is called half–adder and can be used to calculate the sum S of two bits A1 and A0 . A possible carry is set at the C output. Full Adder For adding binary numbers having a bitwidth of more than one single bit, the concept of the half–adder has to be extended. The carry output of less significant bits in the addition process have to be taken into account in the more significant bits. For that, a new circuit structure called full–adder is used which is based on the following functional equations: Cout = Cin (A1 + A2 ) + A1 A2

(10.3)

Sout = A1 ⊕ A2 ⊕ Cin

(10.4)

These equations can be realized either by logic gates (AND, OR, XOR) or by two half–adders and an OR gate.

10.1.2

Adders / Subtracters for Binary Coded Integers

The following section introduces the basic arithmetic components used in VLSI designs. First, adder and subtracter architectures are discussed. Since addition and subtraction for binary

VLSI

Design Course

10-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Adders / Subtracters numbers can be calculated by almost the same hardware (by selecting the appropriate complement representation first), the term “adder” is used as synonym for both adder and subtracter in the following section. Serial Adders The principle of serial adders is shown in Fig. 10.1: Carry Register n

..... ....

Operand A

?

Cout

Shift Register n

..... ....

X

Operand B

? Shift Register

-

+

S

Y

6Cin Full-Adder

-

Shift Register n

..... ....

?Sum

?Cout

Figure 10.1: Serial adder principle At the beginning of the operation, the two n–bit operands A and B are loaded to the shift registers. The carry register is cleared resp. set to the value of the carry input. During the next n clock cycles (if a wordlength of n bits for each operand is assumed), the operands are added bitwise in the full–adder and stored in the sum register. For that, the operand shift registers apply the least significant bit to the full–adder inputs whereas the sum shift register reads the current sum output of the full–adder at the serial input and and shift the contents by one bit to the right each clock cycle. The carry output of an addition is stored in the carry register for use in the next clock cycle. The n-bit sum and the carry output are available after (n+1) clock cycles [1 operand load, n calculation]. The serial adder has the smallest hardware complexity which is wordlength independent (if the shift registers are not considered) but requires the highest computation time of all adder implementations. Parallel Adders Ripple Carry Adder Chained full–adders which form an adder of the required wordlength are called ripple carry adder since during addition the carry “ripples” through the whole chain from the least significant to the most significant bit as shown in Fig. 10.2: The addition time is therefore dependent on the wordlength of the operands. Carry Lookahead Adder To speed up the addition process, lookahead methods can be applied to reduce the time associated with carry propagation. The carry input of a stage i is calculated directly from the input of the preceding stages i − 1, i − 2, . . . i − k rather

VLSI

Design Course

10-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Adders / Subtracters A[n-1] B[n-1] ?

+

Full-Adders

A[0] B[0]

A[1] B[1] ?

? 

. .Cout[1] . 

? ? CoutSum[n-1]

? 

+

? Cout[0]

+

? Sum[1]

? 

Cin

? Sum[0]

Figure 10.2: Ripple carry adder principle than allowing carries to ripple from stage to stage. To perform that task, the cout of ordinary full–adders are substituted by the generate and propagate signals defined by gi = ai bi

(10.5)

pi = ai + bi .

(10.6)

The carry input signal of stage i + 1 is defined by the equation cini+1 = ci = gi + pi ci−1

(10.7)

and by recursive substitution in an example of a 4 bit adder c0 = cin1 = g0 + p0 cin

(10.8)

c1 = cin2 = g1 + p1 g0 + p1 p0 cin

(10.9)

c2 = cin3 = g2 + p2 g1 + p2 p1 g0 + p2 p1 p0 cin

(10.10)

c3 = cout = g3 + p3 g2 + p3 p2 g1 + p3 p2 p1 g0 + p3 p2 p1 p0 cin .

(10.11)

As can be seen in the equations above, the carry lookahead logic circuits can be realized by a two level logic implementation, that means the whole addition is performed in constant time (without influence of wordlength). The implementation of the carry lookahead corresponding to the above equations is shown in Fig. 10.3. A[3] B[3]

A[2] B[2]

? ? Cin[3] + 

g[3]

A[0] B[0]

? ? + Cin[1]

?

?

?

?

Sum[3]

Sum[2]

Sum[1]

Sum[0]

p[3]

??

A[1] B[1]

? ? + Cin[2]

g[2]

p[2]

??

g[1]

p[1]

??

Carry Lookahead Circuit

? ? Cin[0] + 

g[0]

Cin

p[0]

?? 

? Cout

Figure 10.3: Carry lookahead adder for 4 bits The number of gate inputs is restricted due to technological constraints. That means, the wordlength of a carry lookahead cannot increase above any number. Due to that reason, adders for a big wordlength are split into smaller groups processed by single carry lookahead adders with reasonable wordlengths as shown in Fig. 10.4.

VLSI

Design Course

10-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Adders / Subtracters A[15:12]

B[15:12] A[11:8]

? ? 4 bit

C[15]

+

B[11:8]

? ? 4 bit

C[11]

+

A[7:4]

B[7:4]

? ? 4 bit

 C[7]

+

A[3:0]

B[3:0]

? ? 4 bit

 C[3]

+



CLA-Add

CLA-Add

CLA-Add

CLA-Add

? ? Cout Sum[15:12]

? Sum[11:8]

? Sum[7:4]

? Sum[3:0]

Cin

Figure 10.4: Clustered carry lookahead adder for 16 bits The carry signal produced by a group is forwarded to the next group so that, if the group is considered as a single block, the carry ripples through different blocks as in the carry ripple adder. Alternatively, a hierarchical approach might be chosen in a way, that for each group a group-generate as well as a group-propagate signal are generated which are evaluated by a second level carry lookahead circuit. Carry Select Adder In the following adder type, the wordlength of the operands is again subdivided into clusters (see Fig. 10.5). The cluster subwordlength is chosen to balance the time required for intra-cluster carry ripple additions and carry calculation of the preceding clusters. The additions are all performed in parallel assuming the following two cases: carry in of a cluster are ’0’ and are ’1’. The results (cluster carry out and partial sum C/Sum[i : j]) are forwarded to multiplexors which select the appropriate value depending on the carry output of the preceding stages. Since the time to switch a multiplexor is almost negligible compared to the time required for the carry ripple additions, the overall addition time is almost independent of the wordlength. A[15:12]

B[15:12] A[11:8]

? ? 4 bit + 

A[15:12]

? ? 4 bit + 

0

CR-Adder

B[11:8]

A[7:4]

B[7:4]

? ? 4 bit + 

0

CR-Adder

A[3:0]

0

CR-Adder

C/Sum0[11:8]

C/Sum0[7:4]

B[15:12] A[11:8]

B[11:8]

B[7:4]

? ? 4 bit + 

? ? 4 bit + 

1

CR-Adder

CR-Adder

C/Sum1[15:12]

? H1?  0  H H ? ? Cout

? ? 4 bit + 

1

C/Sum1[11:8]

C[11]

?

Cin

C/Sum[3:0]

1

CR-Adder

C/Sum1[7:4]

? H1?  0  H H

Sum[15:12]

? ? 4 bit + 

CR-Adder

C/Sum0[15:12]

A[7:4]

B[3:0]

? H1?  0 C[3] H H C[7]

Sum[11:8]

?

?

Sum[7:0]

Sum[3:0]

Figure 10.5: Carry select adder for 16 bits Since the carry select adder requires two carry ripple adder chains for each cluster (except in the least significant), the hardware amount is almost twice that of a simple ripple carry adder. It is slower than a carry lookahead adder but compared to that type it has a higher regularity and is for that reason better suited for VLSI implementation.

VLSI

Design Course

10-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Adders / Subtracters Carry Save Adder For the addition of very many addends (e. g. in parallel multipliers), the time required for full carry propagation even in the case of use of carry lookahead adders might be to high for some applications. To achieve constant addition time complexity, the propagation of computed carry results is avoided in the same stage and both, the S and the Cout vectors are connected to the correct adder in the succeeding stage. This concept requires a final addition to merge the sum and the carry vector of the final stage into a single sum vector which can be realized using any of the adders discussed above (in Fig. 10.6 a carry ripple adder has been chosen for simplicity). In a carry save adder, the adder delay is increased by one full-adder delay if it is extended by an additional operand. X[n-1]

Full-Adders

Y[n-1]

X[2]

?? + . ..... ....

. . W[n-1]



 .



? ?

+ 

Full-Adders

. .... ....

?? + 

Full-Adders

Full-Adders

? + 

0

Y[2]

X[1]

?? +

. .

V[n-1]
? ?

+ 



 .


. . .



.... .....

.... .....

?? + 

# # ?? + 

?

?

#

Y[1]

X[0]

?? +




. ..... ....

. ..... ....



W[2]
? ?

+ 


W[1]
? ?

+ 


. .... ....






. .... ....

? ?

+  .... .....

.... .....

.... ... Cin

. ..... .... W[0]

?? + 




V[1]
? ?

+ 

V[2]

Y[0]

?? + 

Carry Save Adder Array

0

. .... .... V[0]

?? + 

0

... ....... ...

?? ??  +  Cout[1] + 

. Cout[2] . .

0 ... ....

? ?

Cout Sum[n+1] .... ...

Sum[n]

?

Sum[n-1]

Sum[2]

?

Sum[1]

Final Carry Propagation

?

Sum[0]

.. ....

Stages required to evaluate the carry outputs of preceeding stages

Figure 10.6: Carry save adder for summation of 4 operands (V, W, X, Y)

VLSI

Design Course

10-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Multipliers 10.2

Multipliers

Shift and Add Multiplier The most common multiplier is the Shift and Add Multiplier (SAA Mult.). Two binary unsigned integer words X and Y of bit-size Nx and Ny , respectively, can be written using their binary representation:

X=

NX x −1

Ny −1

xi 2i

Y =

i=0

X

yj 2j

(10.12)

j=0

The product Z = X ∗ Y can now be computed:

Z=

NX x −1

xi Y 2i = (...((xNx −1 Y )2 + xNx −2 Y )2 + ...)2 + x0 Y

(10.13)

i=0

The following recurrence can be derived from formula 10.13: D0 = 0

Di+1 = Di 2−1 + xi Y

Z = DNx 2Nx −1

(10.14)

In each step of the recurrence one bit of X is multiplied (a simple AND-operation) with Y and added to the intermediate result Di which is shifted one bit. Figure 10.7 shows the general structure of the Shift and Add multiplier with bit-sizes Nx and Ny .

Figure 10.7: Structure of SAA multipliers For this multiplier type it takes Nx clock cycles to complete the multiplication, since one bit of X is processed each step. The delay of the combinatorical circuit (which determines the maximum clock frequency) is approximately: Ny δF A (δF A is the delay of a full adder, the register delays are not considered). The cost of a Shift and Add Multiplier is (3Ny + 2Nx )γF A (the cost of a full adder γF A is assumed to be equal to the cost of a register). Carry Save Multiplier In opposite to the SAA-Multiplier, the Carry Save Multiplier (CSM) calculates the result in one step. Every bit of the first argument is multiplied with every bit of the second argument concurrently. The results are added up according to the position of the source bits.

VLSI

Design Course

10-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Multipliers

The CSM consists of combinatorial logic only. The multiplication of two 4-bit binary numbers can be written as X3 X2 X1 X0 Y3 Y2 Y1 Y0 ————————– P30 P20 P10 P00 P31 P21 P11 P01 P32 P22 P12 P02 P33 P23 P13 P03 ————————————————— Z7 Z6 Z5 Z4 Z3 Z2 Z1 Z0

where Pij = Xi ∧ Yj . The addition of all Pij terms can be done in an array of full adders. Figure 10.8 shows the general structure of a Carry Save Multiplier assuming Nx ≥ Ny . Part II is omitted in case of same size for Nx and Ny . The Carry In of the full adder is supplied in the upper right corner. Not every full adder needs a Carry In, for some position half adders are sufficient. The adder Carry Out is depicted in the lower left corner.

Figure 10.8: Structure of CSM multipliers The delay of this type of multipliers is (Nx + Ny − 2)δF A . The cost is (Nx − 1)Ny γF A plus (2Ny + 2Nx )γF A , if X, Y and the Z-register are accounted as in the shift and add case above. Block Multiplier A combination of the fully parallel Carry Save Multiplier and the serial Shift and Add Multiplier leads to a flexible architecture which can be configured from working fully serial to working fully parallel. Many combinations in between are possible, thus allowing the adaptation to given specifications and restrictions.

VLSI

Design Course

10-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Multipliers

The basic idea of the block multiplication is to divide each argument into blocks of the same size. Each block of the first argument is multiplied with each block of the second argument in a fast Carry Save Multiplier. All calculated block products are added up taking into account the positions of the current argument blocks. Therefore, as in the Shift and Add Multiplier, the arguments and the intermediate result have to be shifted in an appropriate way. . . .

. ....... .

. . .

X register

Y register

nx



AA

.

..........

ny

.... ... ..

Carry Save Multiplier

XX XX nx+ n y

( ( nx+ n y

..... ..... ..........

..... ..... ..........

Adder

( ( nx+ n y ........ ..

Controller

..... ..... ..........

. ....... .

. . .

Z register

Figure 10.9: Architecture of the block multiplier Figure 10.9 shows the architecture of the block multiplier. The argument registers and the Carry Hold Register are simple shift registers. The intermediate result has to be shifted in both directions, thus requiring a bidirectional shift register. Signals for controlling the shift directions are generated by a controller, which can be realized using a simple counter. The multiplier can be configured by varying the block sizes of the arguments. With increasing block sizes the multiplier becomes more parallel, thus reducing the number of clock cycles needed to perform a multiplication. Larger block sizes, however, require a larger Carry Save Multiplier, which increases the area needed to realize the multiplier. Assuming that the first argument is separated in kx Blocks of size nx and the second argument in ky blocks of size ny , the multiplier needs kx ∗ ky clock cycles to perform a multiplication. The delay of the multiplier is determined by the size of the ripple carry adder, which has a width of nx + ny bits.

VLSI

Design Course

10-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Microarchitectures

Chapter 11

Microarchitectures The term microarchitecture describes the domain between the macroarchitecture (the lowestlevel hardware visible to the user) and the implementation technology (MOS VLSI) [27]. For better analysis, microarchitectures are usually divided into 3 parts: the data path which performs the data manipulations and calculations, the control path is used to apply correct sequences of control signals to the data path, and the input/output unit providing access from/to the external world (see Fig. 11.1) 

Control .. .. .....

Signals Data

Control

Path

Path Status .. ... ....

-

Flags ... .....

6 ?

Input / Output ..... ....

6 ?

External I/O Data

Figure 11.1: Microarchitecture blocks The control path which can be interpreted as a more or less complex finite state machine (FSM) can be either hardwired (used in fixed applications like a controller for the serial adder in Fig. 10.1) or programmable (microprocessor with downloadable microcode). The microarchitecture scheme as shown in Fig. 11.1 can represent quite simple circuits (like a traffic light controller) as well as complex microprocessors.

VLSI

Design Course

11-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Datapath Design 11.1

Datapath Design

In the datapath of a microarchitecture, the operations and data manipulations are performed. For that, control signals are generated by the control path depending on the operation(s) to be executed. By forwarding information about the status of the data path (e. g. exceptional conditions, underflow, overflow, division by zero, . . . ), the control path is able to react in a correct way to the actual needs. The state signals (flags) can be used to enable conditional branching depending on the state of the data path. Data processing is usually performed by typical components like ALUs, shifters, register files, . . . . The following section shows how datapath structures are usually implemented in larger VLSI designs. For that, we assume the following simple datapath structure:

Control Signals Clock

OP-Sel

Sel

Shift

Clock

Cin .......... .

?

Inputs

Ain

? P -PP

.......... .

? ? -@ @ -

..... . .....

?

.......... .

?

-

6

-

- Rout

Output

? Bin

-

-

 

? Status Flags

Status Signals Figure 11.2: Datapath example The datapath consists of 2 input registers for the input operands Ain and Bin, an arithmeticlogic unit (ALU), a multiplexor to select between the Cin input and the ALU output, a shifter unit, and an output register. The datapath structure could be implemented based on standard cells, where basic library cells (like gates, muxes, registers, . . . ) are selected and interconnected, or, if a datapath compiler is used, based on a set of several layout tiles as shown in Fig. 11.3. A datapath compiler creates a regular layout depending on the wordlength of the operands by stacking the appropriate number of tiles in the layout. The horizontal structure consisting of a set of tiles performing all functions for a single bit is called bit slice. If we apply vertical cuts to the layout structure, the whole layout will be subdivided in layout blocks corresponding to a single function implemented. These layout stripes are called functional slices.

11.1.1

Bit-slice ALU AMD 2901

As an example for a discrete datapath implementation the 2901 bit-slice will be discussed in the following section (→ [10]). The 2901 integrated circuit contains besides of a 16 word register set, a Q register (used

VLSI

Design Course

11-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Datapath Design

AReg BReg

ALU

MUX

Shifter

RReg Control Signal Buffers ..... ..... .

Bit[0] Bit[1]

Bit Slices . ..... ....

Bit[n-1]

Status Buffers ..... ..... .

. .... .....

Functional Slices

Figure 11.3: Corresponding layout scheme

Figure 11.4: 2901 4-bit ALU slice

VLSI

Design Course

11-4

Figure 11.5: 2901 µ-OPs

Darmstadt University of Technology Institute of Microelectronic Systems

0

Datapath Design

within add-shift multiplications or divisions) an arithmetic-logic unit (ALU), a shifter, and an instruction decoder (see Fig. 11.4). All operations and the registers are designed for 4 bit operands. The set of instructions which can be executed by the 2901 IC is also shown in Fig. 11.5. The instructions are encoded in a 9 bit I vector which is provided by an external microcode controller. The first of these tables shows the selection of the sources for both ALU inputs (R and S), the second mentions the ALU functions, whereas the third indicates the destination of the ALU results. To form an ALU for wordlengths with multiples of 4 bits, the 2901 ICs can be cascaded as shown in Fig. 11.6. In the example, a simple carry propagation scheme has been selected. As an additional option, carry-lookahead circuits (AMD 2902) could be used to enhance the speed for carry propagation.

Figure 11.6: 16-bit bit-sliced ALU The 2901 IC has been widely used for applications in digital signal processing and for minicomputers. It is available as stand-alone IC and some silicon manufacturers also provide macrocells with the functionality of the 2901 (for different wordlengths) that might be included to ASIC designs.

VLSI

Design Course

11-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Controller Implementations 11.2

Controller Implementations

Controllers are used to apply a sequence of control signals to the datapath components. These control signals are chosen to perform the desired operation(s) within the datapath. The datapath is able to interact with the controller unit by sending appropriate status signals (e. g. overflow flag when an addition is performed, equal flag as a result of a comparison, . . . ). The controller can be designed to change the sequence of control signals depending on these flags (used e. g. in microprocessors to perform conditional branches). The general structure of such a controller can be found in Fig. 11.7. Environmental Inputs

?

?

Combinational Logic

? State Register

? Control Outputs

Figure 11.7: Basic controller structure It consists of a combinational logic block and a register. The combinational logic block generates out of the input signals (which can be e. g. an instruction word defining the sequence of control signals to be generated, state flags, . . . ) and parts of the previous register content the control output signals as well as the information which step in the sequence of control signals is to be executed in the next cycle. The controller can be seen as a realization of the abstract model of a finite state machine. To get a high level of regularity in the design of a controller, very often regular layout structures (like ROMs or PLAs) are used to implement the combinational logic block rather than directly implement the logic functions in separate gates (random logic). The random logic approach was chosen in the control unit of many early microprocessors (≤ 8 bit) and in RISC (Reduced Instruction Set Computer) processors whereas the regular layout structures are used in CISC (Complex Instruction Set Computer) processors to simplify their controller design. Regular structures simplify the design process due to the fact that if modifications in the control sequences are required only the contents of a PLA resp. a ROM has to be redefined instead of designing a whole combinational gate network. Since the design process for the latter approach can be compared with programming a memory contents instead of circuit design, that approach is called microprogramming and will be considered in detail in the sequel.

VLSI

Design Course

11-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Controller Implementations 11.2.1

Microprogrammed Controllers

Microprogrammed controllers mainly consist of a control memory and a microinstruction register. The control memory is implemented using ROM (Fig. 11.8) or PLA (Fig. 11.9) structures. For special applications, also RAM based control memories are used if e. g. the instruction set of a processor has to be changed for special purposes. That flexibility is not available when using hardwired logic. On the other hand, extra hardware cost compared to random logic due to address decoding (in the ROM based controller) and sparse control matrices and a performance penalty due to larger internal delays in the PLA or ROM could be the prize for that flexibility. The control memory contains both the control signals to be forwarded through the microinstruction register to the datapath and some sequencing information giving the address (NA next address) of the subsequent microinstruction. The concatenation of the control signals and the next address is called microinstruction. Address @ @ Decoder 

ROM

? Control NA 6 6 ? Control Outputs

Environmental Inputs

Figure 11.8: ROM based controller . . . . . . . . . . . . . . .P . .L. .A. . . . . . . .  . OR A . . . . ......................

...... . . . . . ND . . . . . .6 .....

? Control NA 6 6 ? Control Outputs

Environmental Inputs

Figure 11.9: PLA based controller Depending on the generation of the control signals, two types of microinstructions can be distinguished:

VLSI

Design Course

11-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Controller Implementations

Horizontal Microinstructions. The control word from the microinstruction register is directly applied to the circuit which is to be controlled (see Fig. 11.10). Each elementary control point has a corresponding entry in the control word. That results in a very long control word and therefore big control memories. On the other hand, very specific encoding and a high degree of parallelism in the operations is possible. Vertical Microinstructions. That type of microinstructions is based on a different approach: since in a n-bit control word 2n configurations would be possible which are hardly used by the controller, the wordlength of the control word in the control memory is reduced by encoding the smaller number of, let’s say M , used control vectors into a vector of dlog2 M e bits. In a second step, the n-bit control word is fetched from a secondary memory used as control vector decoder (implemented e. g. as ROM or PLA) and forwarded to the datapath (see Fig. 11.11). It is also possible to use encoding of the control vector in groups for different hardware units (one group for ALU control, the next for shifter control, . . . ) which are decoded group by group instead of using a single and large control vector decoder. Control Bits in the Microinstruction

? ? ? ? ? ? ? ? ? ? ? ? . ..... ....

..... ..... .

Control Lines

Figure 11.10: Horizontal microinstruction Control Bits in the Microinstruction

? @ @ Control Bit Decoder

? ? ? ? ? ? ? ? ? ? ? ? ..... .....

..... ..... .

Control Lines

Figure 11.11: Vertical microinstruction In controller design, one can proceed one step further: if a microinstruction itself can be represented as a sequence of ‘sub’microinstructions (so called nanoinstructions, the structure shown in Fig. 11.12 can be used. The most simple approach, which already has been mentioned under vertical microcode, is a single step ‘sequence’ of nanoinstructions, namely the decoding of the control outputs out of an encoded control vector from the microcode control memory.

VLSI

Design Course

11-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Controller Implementations

If feedback is introduced in the decoder PLA (via the NNA [nanocode next address] register), control sequences can be generated by the nanocode PLA. As long as a nanocode sequence is running, the MNA [microcode next address] register is halted. In the case that many microinstructions use the same nanocode sequences, significant savings in implementation area for the whole controller can be reached. . . . . . . . .Microcode . . . . . . . . .PLA ..... . . . . .  . OR A . . . . ......................

...... . . . . . ND . . . . . .6 .....

? MNA 6 6 Environmental Inputs . . . . . . . . Nanocode . . . . . . . . .PLA .......... . ? . . . . . AND OR . . . . . . . . . . ....6 ...................... ... .... ... ? .... .. ... NNA ... ... Control .... . ..................................... ?

. . . . . . . . . . . .

Control Outputs

Figure 11.12: A microcode/nanocode controller

VLSI

Design Course

11-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Introduction

Chapter 12

ASIC Design Guidelines 12.1

Introduction

The following design guidelines have been adapted from [5]. These recommendations are useful in order to avoid functional faults and get the desired functionality.

12.2

Synchronous Circuits

• all data storage elements are clocked • the same active edge of a single clock is applied at precisely the same time to all storage elements

12.2.1

Non-Recommended Circuits

Figure 12.1: Flip-flop driving clock input of another Flip-flop

→ The clock-input of the second FF is skewed by the clock-to-q delay of the first FF and not activated at every activation clock edge (e.g. ripple counter)

VLSI

Design Course

12-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Synchronous Circuits

Figure 12.2: Gated clock line

→ Clock skew caused by gating the clock line (e.g. multiplexer in clock line)

Figure 12.3: Double-edged clocking

→ FFs are clocked on the opposite edges of the clock signal → Insertion of scan-path impossible → Difficulties in determing critical path lengths

Figure 12.4: Flip-flop driving asynchronous reset of another Flip-flop

→ Synchronous design principle, that all FFs change state at exactly the same time is not fulfilled

VLSI

Design Course

12-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clock Buffering 12.2.2

Recommended Circuits

Recommended circuits for synchronous circuit design are described in the subsequent sections.

12.3

Clock Buffering

12.3.1

Non-Recommended Circuits

Figure 12.5: Unequal depth of clock buffering

→ Clock skew

VLSI

Design Course

12-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clock Buffering

Figure 12.6: Unbalanced fanout of clock buffers

→ Clock skew by different load-dependent delays → Excessive clock fanouts should be avoided (slow edges)

VLSI

Design Course

12-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clock Buffering 12.3.2

Recommended Circuits

Figure 12.7: Balanced clock tree buffering

→ Same depth of buffering → Same fanout → Limited fanout in order to achieve sharp clock edges

VLSI

Design Course

12-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Clock Buffering

Figure 12.8: Combined geometric/tree buffering

→ Using intermediate buffer of suitable strength at each fanout point

VLSI

Design Course

12-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Gated Clocks 12.4

Gated Clocks

12.4.1

Non-Recommended Circuits

Figure 12.9: Multiplexer on clock line

→ Signal change at multiplexer input can cause a glitch at the clk input (FF captures invalid data) → Gating the clock line introduces clock skew

12.4.2

Recommended Circuits

Figure 12.10: Enabled (E-type) flip-flop

Figure 12.11: Toggle (T-type) flip-flop

VLSI

Design Course

12-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Double-edged Clocking 12.5

Double-edged Clocking

12.5.1

Non-Recommended Circuit

Figure 12.12: Pipelined logic with double-edged clocking

→ Not recommended in context with scan-path methods

12.5.2

Recommended Circuit

Figure 12.13: Pipelined logic with single-edged clocking

VLSI

Design Course

12-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Asynchronous Resets 12.6

Asynchronous Resets

12.6.1

Non-Recommended Circuit

Figure 12.14: Flip-flop driving asynchronous reset of another flip-flop

12.6.2

Recommended Circuits

Figure 12.15: Global asynchronous reset by external signal

Figure 12.16: Flip-flop driving synchronous reset of flip-flop

VLSI

Design Course

12-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Shift-Registers 12.7

Shift-Registers

12.7.1

Non-recommended Circuits

Shift register with forward or reverse chain of clock buffers:

Figure 12.17: Shift register with forward chain of clock buffers

→ Internal clock skew can cause data fallthrough

12.7.2

Recommended Circuits

Figure 12.18: Shift register with balanced tree of clock buffers

VLSI

Design Course

12-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Asynchronous Inputs 12.8

Asynchronous Inputs

12.8.1

Non-Recommended Circuits

→ Circuits with complicated feedback loops to capture asynchronous inputs (very sensitive to noise and functionality can be influenced by placement and routing delays

12.8.2

Recommended Circuits

1. Chain of two or more D-type registers (reducing the probability of metastability) 2. Use of 4-bit register as shift register 3. Asynchronous handshake circuit

Figure 12.19: Series D-type flip-flops for capturing asynchronous input

→ The probability of propagating metastable state is decreased with increasing number of register stages

Figure 12.20: 4-bit register used as shift register to capture an asynchronous input

VLSI

Design Course

12-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Asynchronous Inputs

Figure 12.21: Asynchronous handshake circuit

VLSI

Design Course

12-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Asynchronous Inputs

The asynchronous handshake ciruit works as follows: • the first flip-flop is reset asynchronously when the r input is zero or when the qb outputs of the second and the third FF both have the value 0 • the q-output of the first FF is asynchronously set to high, when a positive edge arises at its ck-input • the high output of the first FF is propagated through the second and the third FF in the two following cycles. The q-outputs of these FFs are set to zero and the reset logic for the first FF is activated. Now the first FF is ready to receive another edge at its input. • Three cases of metastability caused by simultaneously rising edges of the asynchronous input and the system clock: 1. the second FF stabilizes to q=1 before the next rising clock edge (circuit works as desired) 2. the second FF settles to q=0 and the third FF remains in its state. Since the output q of the first FF is high, the propagation of this output works correctly, but it needs one cycle more than in the first case. 3. The metastable state of the second FF is still there at the next rising edge of the clock signal. Then the third FF also becomes metastable. The probability of receiving a metastable d (internal) signal can be reduced by increasing the length of the register chain.

Figure 12.22: Operation of asynchronous handshake circuit

VLSI

Design Course

12-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Delay Lines and Monostables 12.9

Delay Lines and Monostables

12.9.1

Non-Recommended Circuits

In general it can not be recommended to build circuits, which functionality relies on delays.

Figure 12.23: Monostable pulse generator

Figure 12.24: Pulse generator using flip-flop

Figure 12.25: Multivibrator

12.9.2

Recommended Circuits

→ Usage of higher clock speed and build synchronous pulse generator → Minimum time resolution is given by clock cycle

12.10

Bistable Elements

12.10.1

Non-Recommended Circuits

→ Cross-coupled flip-flops and RS flip-flops

VLSI

Design Course

12-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Bistable Elements

Figure 12.26: Synchronous pulse generator

Figure 12.27:

Bistable storing element formed by cross-coupled NAND gates

Figure 12.28: Bistable storing element formed by cross-coupled NOR gates

VLSI

Design Course

12-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Bistable Elements

Figure 12.29: Asynchronous RS flip-flop

12.10.2

Recommended Circuits

→ Use D-types with set/reset → Use latch configured as RS flip-flop

Figure 12.30: Latch configured as RS flip-flop

VLSI

Design Course

12-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

RAMs and ROMs in Synchronous Circuits 12.11

RAMs and ROMs in Synchronous Circuits

Problem: RAMs are double-edge triggered. The address is latched on the opposite edge to the data

Figure 12.31: ME and WEbar RAM/DPRAM timing scheme

12.11.1

Recommended Circuits

Figure 12.32: Interfacing RAM into synchronous circuit: ME and WEbar generation

VLSI

Design Course

12-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

RAMs and ROMs in Synchronous Circuits

Figure 12.33: Using flip-flop for WEbar generation: timing schene

Figure 12.34: Avoiding floating RAM/DPRAM output propagation

VLSI

Design Course

12-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Tristates 12.12

Tristates

12.12.1

Non-Recommended Circuit

Figure 12.35: Tristate bus with non-central enable control

VLSI

Design Course

12-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Tristates 12.12.2

Recommended Circuits

Figure 12.36: Tristate bus with central control of tristate enables and additional driver activated on non-controlled states

12.12.3

Multiplexer ↔ Tristates

Disadvantages of Tristates: • large area • limited buffering • large routing load, → slow Advantages of Multiplexers: • small area • efficient routing Control decoding expense is the same for tristates and multiplexers.

VLSI

Design Course

12-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Parallel Signals 12.13

Parallel Signals

12.13.1

Non-Recommended Circuits

Figure 12.37: Wired-OR part used to create higher fanout

12.13.2

Recommended Circuit

Figure 12.38: High-fanout buffer replacing wired OR part

VLSI

Design Course

12-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fanout 12.14

Fanout

12.14.1

Non-Recommended Circuit

Figure 12.39: Excessive fanout on control signal

VLSI

Design Course

12-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fanout 12.14.2

Recommended Circuits

Figure 12.40: Geometric buffering on control signal

VLSI

Design Course

12-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fanout

Figure 12.41: Tree buffering on control signal

VLSI

Design Course

12-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Speed 12.15

Design for Speed

1. Use a maximum of 2 inputs on all combinational logic gates

Figure 12.42: 4-input AND gate and 2-input NAND/NOR equivalent

2. Use AOI logic (complex cells from standard cell library) where possible

Figure 12.43: Multiplexer using AOI logic

3. Feed late changing inputs late into combinational logic

Figure 12.44: Late changing input fed late into combinational logic

VLSI

Design Course

12-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Speed

4. Use shift (Johnson) counters instead of binary counters

Figure 12.45: 4-stage Johnson counter

q0 0 1 1 1 1 0 0 0 0

q1 0 0 1 1 1 1 0 0 0

q2 0 0 0 1 1 1 1 0 0

q3 0 0 0 0 1 1 1 1 0

5. Use duplicate logic to reduce fanout

Figure 12.46: Using duplicate logic for reducing fanout 6. Use fast library cells where available 7. Reduce length of critical signal paths 8. Use Schmitt trigger inputs in noisy environments

VLSI

Design Course

12-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability 12.16

Design for Testability

Testability: 1. Controllability 2. Observability

12.16.1

Non-Recommended Circuits

Figure 12.47: Circuit with inaccessible internal logic: only first block is controllable and only last block is directly observable

Figure 12.48: Chain of counters: first counter is not directly observable and second counter is not directly controllable

VLSI

Design Course

12-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Figure 12.49: Counter with closed feedback loop: initial state not known

VLSI

Design Course

12-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability 12.16.2

Recommended Circuits

1. Insert test inputs and outputs

Figure 12.50: Circuit with test inputs and outputs

2. Break long counter/shift register chains

Figure 12.51: Chain of counters broken by test input and output signals

VLSI

Design Course

12-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

3. Open feedback loops

Figure 12.52: Counter with feedback loop opened by test control and output signals

4. Use BIST (Built-In Self Test) with compiled megacells

Figure 12.53: Compiled megacell with compiled inputs/outputs

VLSI

Design Course

12-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

5. Scan path testing

Figure 12.54: E-type scan path flip-flop

Figure 12.55: Circuit with scan path

VLSI

Design Course

12-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

6. Use of JTAG boundary scan path

Figure 12.56: JTAG test circuitry

VLSI

Design Course

12-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Motivation

Chapter 13

Testing and Design for Testability 13.1

Motivation

• Stable chip manufacturing costs • Increasing testing costs: – Increasing number of gates/device – Limited number of pins → Increasing number of internal states → Increasing logical and sequential depth Example: Testing of a combinational circuit with n inputs (10 MHz, one test per cycle) n 25 30 40 50 60

time for test 3 s 107 s 1 day 3.5 years 3656 years

• Testability has to be considered in all phases of design

VLSI

Design Course

13-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Economical Considerations 13.2

Economical Considerations

13.2.1

Average Quality Level (AQL)

aql =

VLSI

Design Course

#DefectiveParts #AcceptedParts

13-2

Darmstadt University of Technology Institute of Microelectronic Systems

(13.1)

0

Economical Considerations 13.2.2

Correlation: Fault Coverage and Defective Parts

• DL(= AQL): Number of defective circuits which have been classified as correct working (testing with T ) • Y: yield • T: fault coverage DL = 1 − Y 1−T

VLSI

Design Course

13-3

(13.2)

Darmstadt University of Technology Institute of Microelectronic Systems

0

Economical Considerations

Figure 13.1: Defect level as function of yield and fault coverage

VLSI

Design Course

13-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design Flow: Testing 13.3

Design Flow: Testing

Figure 13.2: A typical synthesis flow

VLSI

Design Course

13-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fundamental Definitions 13.3.1

Chip Test after Manufacturing Manufacturing Process ↓ Parametric Test (current/power dissipation) (erroneous chips are marked with color points and removed after sawing)

↓ Chip Test on Tester

13.4

Fundamental Definitions

Figure 13.3: Relationship between faults, errors and failures

• fault: physical defect, imperfection or flaw which occurs in an hardware or software component • error: manifestation of a fault (erroneous information on an hardware line or in a program, caused by a fault) • failure: malfunction of a system

Figure 13.4: Three-universe model of a system

VLSI

Design Course

13-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Models 13.5

Fault Models

Basis: physical phenomena • Oxide defects • Missing implants • Lithographic defects • Junction defects • Metal shorts & opens • Moisture accumulation • Impurities/Contaminants • Static discharge

Figure 13.5: Examples for physical faults

VLSI

Design Course

13-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Models

VLSI

Design Course

13-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Models

VLSI

Design Course

13-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Models

VLSI

Design Course

13-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Models

VLSI

Design Course

13-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Tolerant Design 13.6

Fault Tolerant Design

Fault tolerance achieved by redundancy techniques: • Duplication with Complementary Logic

Figure 13.6: Fault detection by duplication with complementary logic • Self-Checking Logic • Reconfigurable Array Structures

VLSI

Design Course

13-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Tolerant Design

Figure 13.7: 4-by-4 array with one spare column

VLSI

Design Course

13-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Tolerant Design

Figure 13.8: Reconfigured array

VLSI

Design Course

13-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation 13.7

Test Pattern Generation

• manually • pseudo random (leads up to 60% fault coverage) • algorithmic • special test patterns for RAMs

? fault coverage sufficient ? ⇒ fault simulation

13.7.1

The D-Algorithm

Every test generation procedure has to solve the following problems 1. Creation of a change at the faulty line 2. Propagation of the change to the primary output line In the D-Algorithm the symbols D and D are used to refer to the changes. D and D are used as follows: D: used if a line has the value 1 in absence of a fault and the value 0 in case of a fault ocurrance D: used if a line has the value 0 if no fault occurs and otherwise the value 1 The D-algorithm method for path sensitization consists of two principal phases: 1. forward drive (propagation) of an D-value to an primary output 2. backward trace (consistency operation) These two s.pdf are iterated for different propagation paths for the D-value from one dedicated internal point i to one dedicated primary output point o until the backward trace phase is finished without any contradiction (a test vector for a fault at i has been found) or until all possible paths from i to o have been examined.

VLSI

Design Course

13-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation

Figure 13.9: Basic concept of D-algorithm 1. A primitive D-cube of a failure is a D-cube associated with a fault l/α on the output line l of a gate G. This produces the value D or D on l and the input lines have values which would produce α in the fault-free case.

Figure 13.10: Primitive D-cube of fault (pdcf) for two-input NAND gate

VLSI

Design Course

13-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation

2. A propagation D-cube of a failure specifies the propagation of changes at one (or more) inputs of a gate G to its output l.

Figure 13.11: Propagation-D-cube (pdc) for two-input NAND gate 3. A singular cover of a gate G is a {0,1,X} truth table representation of G

Figure 13.12: Singular cover for two-input NAND gate

VLSI

Design Course

13-17

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation

Figure 13.13: Singular covers for several basic logic gates

VLSI

Design Course

13-18

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation

Figure 13.14: Construction the singular cover of an logic module

VLSI

Design Course

13-19

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation

In the following the D-algorithm is illustrated for the given example from fig. 13.15

Figure 13.15: Example circuit illustrating D-algorithm

Table 13.1: Propagation D-cube table

Table 13.2: Singular cover table

VLSI

Design Course

13-20

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation

Table 13.3: D-cube intersection table

VLSI

Design Course

13-21

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation

Running the D-algorithm for generating a test for line 5/0: 1. Start with D-cube for the fault 5/0:

2. The D of line 5 is automatically propagated to line 6 and 7 by cube j. 3. Now the propagation along path 6 → 9 → 11 is considered: D on line 6 is propagated to line 9 by cube d. Combining d and k yields cube l:

4. If cube i is used with D instead of D, the propagation to the output can be done:

5. Now the consistency phase is started and a value for line 4 has to be found. From the singular cover table can be seen that a 0 on line 10 implies both line 7 and line 8 to be 1. In cube m line 7 is a D (and also line 5 which is connected to 7 by j) and this D must now be set to 1 which is a contradiction which disables the path sensitization 5 → 6/7 → 9 → 11. ⇒ Start test vector generation using another path 6. Starting the propagation along 5 → 7 → 10 → 11 leads to the following cube:

7. From the singular cover table we get the information that a 1 on line 8 is the same as a 0 on line 4. Additionally it can be seen that the 0 on line 9 can be obtained by a 1 on line 1. 8. This yields the final cube 1110DDD10DD

VLSI

Design Course

13-22

Darmstadt University of Technology Institute of Microelectronic Systems

0

Test Pattern Generation 9. ⇒ a test vector for line 5/0 is given by 1110

VLSI

Design Course

13-23

Darmstadt University of Technology Institute of Microelectronic Systems

0

Fault Simulation 13.8

Fault Simulation

13.8.1

Algorithms: Serial Fault Simulation

Figure 13.16: Serial fault simulation

13.8.2

Improved Algorithms

• Parallel Fault Simulation • Concurrent Fault Simulation ⇒ discussed in CAD lecture

VLSI

Design Course

13-24

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability 13.9

Design for Testability

• Circuit level: restriction of physically possible faults • Logic level: restrict possibilities of realizations • System level: restrict size of components and number of states Testability: • controllability • observability • → additional chip area required • → shorter design cycle Methods to improve controllability and observability: • ad-hoc techniques • structured approaches

Figure 13.17: Design for testability: complex gate (a) not testable with stuck-at model. (b) fully testable with stuck-at model

13.9.1

Ad-Hoc Techniques

• developed for special design • less silicon area • design automation almost impossible • partitioning (test of circuit components by use of dedicated multiplexers)

VLSI

Design Course

13-25

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Figure 13.18: Testability: ad-hoc techniques (partitioning for testability)

VLSI

Design Course

13-26

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Figure 13.19: Testability: ad-hoc techniques (a) insertion of register in order to limit logic depth to a given maximum value. (b) test shift registers for PLA test (increasing PLA area).

VLSI

Design Course

13-27

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability 13.9.2

Scan-Path Methods

Scan-Path: • Main idea: test of sequential network is reduced to test of combinational network • for circuits consisting of logic with some feedbacks • can be realized by reconfiguration of latches as shift registers (two mode of use)

Figure 13.20: Feedback logic with scanpath Test scan-path/register function first: • Flush test (0 . . . 010 . . . 0) or • shift test (00110011 . . .) (each register transfer is tested by this combination: 0 → 0, 0 → 1, 1 → 1 and 1 → 0). Cycle for testing combinational logic function: 1. Scan mode: Preload Y and set PI 2. System operation mode: Wait until inputs of Y are steady. Clock new state into Y. 3. Shift state out. Compare PO and state values with expected responses

VLSI

Design Course

13-28

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Advantages: • Testability of clocked circuits is improved and guaranteed at design stage • Consistent with good VLSI design practice (rules, abstraction, modularity . . .) • Does not require special CAD Disadvantages: • Wastes silicon • Constrains designer to design according given conditions • Additional Complexity Overhead ' 2% for a fundamentally ’structured’ design ' 30% for ’wild’ logic

13.9.3

Built-In Tests

• System generates test vectors by its own • Analyse and evaluation of test vectors is also automatically done • Compromise: silicon ↔ testability Test Pattern Generators • Test patterns are generated inside the circuit to be tested • Short testing time, simple test programs, self-test • Example: Test pattern memories, deterministic generators, counter

VLSI

Design Course

13-29

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Figure 13.21: Examples for built-in test pattern generators

VLSI

Design Course

13-30

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Pseudo Random Number Generators

Figure 13.22: Pseudo random pattern generator

VLSI

Design Course

13-31

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Example:

Figure 13.23: Example for pseudo random pattern generator

VLSI

Design Course

13-32

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability 13.9.4

Evaluation of Testing Data

• Evaluation of testing results inside the circuit • Counting techniques, signature analyse Example: Counting Techniques

Figure 13.24: Counting techniques for test data evaluation

VLSI

Design Course

13-33

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Signature Analyse • Communication technique: coding theory • Code words: data stream D, polynom P(x), division modulo 2 R D =Q+ P P → Evaluation of testing data

Figure 13.25: Test data evaluation by signature analyse

VLSI

Design Course

13-34

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Signature Analyse: Degree of Fault Recognition 1. Length of sequence: m bit → 2m sequences possible 2. One sequence contains no faults → number of erroneous sequences is 2m − 1

3. Length of signature register: n bit → 2n signatures 4. 2m sequences are mapped on 2n signatures → number of nondetectable faults: 2m − 1 = 2m−n − 1 2n

5. Possibility for nondetection of erroneous sequence: number of nondetectable faults divided by number of possible faults: N=

2m−n − 1 2m − 1

6. ⇒ Fault detection rate:

VLSI

Design Course

2m−n − 1 2m − 1

F

= 1−

F

≈ 1 − 2n

13-35

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability

Interpretation: • all faults recognized if m < n (trivial) • long sequences: n is important only • n = 16 bit −→ F = 99,99985% Parallel Signature Register with k Inputs

Figure 13.26: Parallel signature register Fault recognition rate: F =1−

VLSI

Design Course

13-36

2mk−n − 1 2mk − 1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability 13.9.5

Built-In Logic Block Observation

A BILBO register is a universal element for use in either a scanpath environment or a self-test (signature analysis) environment.

Figure 13.27: BILBO registers: 1. full circuit 2. normal use 3. scan-path use 4. signature analysis Advantages: • Versatility – Normal operation – Scan-path test: enhances testability – Test vector generation via LFSR – Data compression via LFSR – Combined scan-path/self-test using same LFSRs Disadvantages: • Silicon area – BILBO latch can be ' 50% larger than ordinary latch

VLSI

Design Course

13-37

Darmstadt University of Technology Institute of Microelectronic Systems

0

Design for Testability 13.9.6

Example: Self-testing Circuit

Figure 13.28: Example: self-testing circuit

VLSI

Design Course

13-38

Darmstadt University of Technology Institute of Microelectronic Systems

0

Chapter 14

Boundary-Scan Architecture – JTAG Standard • miniaturization of electronic components, multilayer and surface mount techniques make test of boards more complicate ⇒ requirement of design-integrated test structures

• 1985 first meeting of small group from European electronics companies • later North American companies joined the group (→ Joint Test Action Group = JTAG) • results: IEEE Standard Test Access Port and Boundary-Scan Architecture

VLSI

Design Course

14-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Classical Board Test Approaches 14.1

Classical Board Test Approaches

Figure 14.1: In-circuit test using bed-of-nails

Figure 14.2: Functional test using board connector

VLSI

Design Course

14-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Classical Board Test Approaches

Figure 14.3: Combined use of in-circuit and functional test Disadvantages of classical approach: • high costs for test hardware • increased density • not suited for surface mount technology • modern chip testing techniques as – scan path techniques – built-in self-test techniques (BIST)/BILBO are not exploited well

VLSI

Design Course

14-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Introduction to Boundary Scan 14.2

Introduction to Boundary Scan

Scan-testing at the board-level: • permits use of automatic test pattern generation tools • simplification of the hardware of the test equipment

Figure 14.4: Scan design at the board level

VLSI

Design Course

14-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Introduction to Boundary Scan

Figure 14.5: Testing for interconnection faults

Input x1x1x0xxxxxx x0x0x1xxxxxx

VLSI

Design Course

Output Expected Actual xxxxxxxx01x1 xxxxxxxx11x0 xxxxxxxx10x0 xxxxxxxx11x0

14-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Introduction to Boundary Scan

Figure 14.6: Testing on-chip logic

Input x10xxxxx x01xxxxx x11xxxxx

Expected Output xxxxx1xx xxxxx1xx xxxxx0xx

Boundary scan application properties and limitations • each test vector has to be shifted into scan path ⇒ not very suitable for testing the chips themselves because of reduced test rate compared to stand-alone chip testing • well suited for interconnection testing • testing of dynamic behaviour impossible • self-testing ICs: boundary scan can be used to trigger the self-test procedure

VLSI

Design Course

14-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1 14.3

The IEEE Standard 1149.1

14.3.1

IEEE Std 1149.1 Architecture

Figure 14.7: IEEE Std 1149.1 test logic

• TAP Controller: responds to the control sequences supplied through the test access port (TAP) and generates the clocks an control signals required for the operation of the other circuit blocks • Instruction Register: shift register which is serially loaded with instruction for test • Test Data Registers: Bank of shift registers. The stimuli values required for a test are serially loaded into a test register selected by the current instruction. After execution the results can be shifted out for examination

VLSI

Design Course

14-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1

Figure 14.8: Test data registers

14.3.2

Test Access Port

• Test Clock Input (TCK): independent of the system clock; used for synchronization of test operations between various chips on a board • Test Mode Select Input (TMS): Input for controlling the test logic • Test Data Input (TDI): Serial input for instruction and test register data • Test Data Output (TDO): Serial output of instruction or test register data (source selected by TMS code) • Optional Test Reset Input (TRST∗): For test initialization

VLSI

Design Course

14-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1

Figure 14.9: Serial connection of IEEE Std 1149.1-compatible ICs

Figure 14.10: Parallel connection of IEEE Std 1149.1-compatible ICs

VLSI

Design Course

14-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1

Control of the test signals • by external automatic test equipment (ATE) or • by on-board bus master chip

Figure 14.11: Use of bus master chip to control IEEE Std 1149.1 chips

14.3.3

TAP-Controller

• 16-state FSM which controls data register (DR) and instruction register (IR) operations • input signals: – TRST∗ – TCK – TMS – last state (stored in internal FFs)

VLSI

Design Course

14-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1 • output signals: – Reset* – Select – Enable – ShiftIR – ClockIR – UpdateIR – ShiftDR – ClockDR – UpdateDR

14.3.4

The Instruction Register

Figure 14.12: Daisy-chain connection of instruction registers

Figure 14.13: Instruction register

VLSI

Design Course

14-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1

Figure 14.14: An example instruction register cell (stage)

VLSI

Design Course

14-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1 14.3.5

Test Data Registers

Test data registers: • bypass register (mandatory) • boundary scan register (mandatory) • device identification register (optional) Bypass Register

Figure 14.15: Example design for bypass register

Figure 14.16: Use of bypass register

VLSI

Design Course

14-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1

Basic Boundary Cells

Figure 14.17: Provision of boundary-scan cells

VLSI

Design Course

14-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

The IEEE Standard 1149.1

Figure 14.18: Basic boundary-scan cell for input pin

Figure 14.19: Basic boundary scan cell for output pin

VLSI

Design Course

14-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog Signal Processing

Chapter 15

Analog VLSI systems 15.1

Analog Signal Processing

Typical signal processing applications require mixed analog/digital implementations. These mainly consist of • Preprocessing of the signals, e.g. filtering and A/D conversion • Digital signal processing, e.g. digital filtering, calculation of FFT • Postprocessing, e.g. D/A conversion as shown in Fig.15.1 The aim of development is to integrate all these functions on a single chip.

Figure 15.1: Block diagram of a typical signal processing system

VLSI

Design Course

15-1

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog Signal Processing 15.1.1

Signal Bandwidths in Analog VLSI

Figure 15.2: Bandwidths of signals used in signal processing applications

Figure 15.3: Signal bandwidths that can be processed by present day (1989) technologies

VLSI

Design Course

15-2

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog Signal Processing 15.1.2

A/D and D/A Conversion in Signal Processing Systems

Fig. ?? illustrates how analog-to-digital (A/D) and digital-to-analog (D/A) converters are used in data systems. In general, an A/D conversion process will convert a sampled and held analog signal to a digital word that is a representative of the analog signal. The D/A conversion process is essentially the inverse of the A/D process. Digital words are applied to the input of the D/A converter to create from a reference voltage an analog output signal that is a representative of the digital word.

Figure 15.4: Converters in signal processing systems: (a) A/D, (b) D/A

VLSI

Design Course

15-3

Darmstadt University of Technology Institute of Microelectronic Systems

0

Digital-To-Analog Converters 15.2

Digital-To-Analog Converters

Input to D/A converters are (a) a digital word of N bits (b1 , b2 , b3 , . . . , bN ) (b) a reference Voltage Vref The output voltage can be expressed as VOU T = KVref D

(15.1)

where K is a scaling factor and D is given as D=

b1 b2 b3 bN + 2 + 3 + ... + N 1 2 2 2 2

(15.2)

Thus, the output of a D/A converter can be expressed by VOU T = KVref

N X

bi 2−i

(15.3)

i=1

Figure 15.5: (a) Conceptual block diagram of a D/A converter, (b) Clocked D/A converter In most cases, the digital input of the D/A converter is synchronously clocked. It is therefore necessary to provide a latch to hold the word for conversion and a sample-and-hold circuit at the output, as shown in Fig. ??(b). The basic architecture of the D/A converter without an output sample-and-hold circuit is shown in Fig. ??. Fig. ?? shows the ideal input-output characteristics for such a D/A converter.

15.2.1

Current Scaling D/A Converters

The output Voltage of a current-scaling D/A converter as shown in Fig. ?? can be expressed as   R R b1 b2 b3 bN Vout = − I0 = − + + + . . . + N −1 Vref (15.4) 2 2 R 2R 4R 2 R = −Vref (b1 2−1 + b2 2−2 + b3 2−3 + . . . + bN 2−N ) (15.5)

VLSI

Design Course

15-4

Darmstadt University of Technology Institute of Microelectronic Systems

0

Digital-To-Analog Converters

Figure 15.6: (a) Sample-and-hold circuit, (b) Waveforms illustrating the operation of the sample-and-hold circuit

Figure 15.7: Block diagram of a D/A converter

VLSI

Design Course

15-5

Darmstadt University of Technology Institute of Microelectronic Systems

0

Digital-To-Analog Converters

Figure 15.8: Ideal input-output characteristics for a 3-bit D/A converter

The major disadvantage of this approach is the large ratio of component values. For example, the ratio of the resistor for the MSB to the resistor for the LSB is given by RM SB 1 = N −1 RLSB 2

(15.6)

For a 8-bit converter, this gives a ratio of 1/128. An alternative to this approach is the use of a R-2R ladder as shown in Fig. ??. Using the fact that the resistance to the right of any of the vertical 2R resistors is 2R, we see that the currents I1 , I2 , I3 , . . . , IN are binary-weighted and given as I1 = 2I2 = 4I3 = . . . = 2N −1 IN

(15.7)

Thus, the output voltage of the R-2R D/A converter is given by Eq. ??.

VLSI

Design Course

15-6

Darmstadt University of Technology Institute of Microelectronic Systems

0

Digital-To-Analog Converters

Figure 15.9: (a) Conceptual illustration of a current-scaling D/A converter, (b) Implementation of (a)

Figure 15.10: A current-scaling D/A converter using an R-2R ladder

VLSI

Design Course

15-7

Darmstadt University of Technology Institute of Microelectronic Systems

0

Digital-To-Analog Converters 15.2.2

Voltage Scaling D/A Converters

A voltage-scaling D/A converter is shown in Fig. ??. Its output voltage at any tap i can be expressed as Vref Vi = (i − 0.5) (15.8) 8 The output voltage of the D/A converter is then determined by the values of the inputs b1 , b2 and b3 .

Figure 15.11: Illustration of a voltage-scaling D/A converter The structure of this voltage-scaling D/A converter is very regular and thus well suited for MOS technology. A problem with this type of D/A converters is the accuracy requirements of the resistors used. This makes it difficult to build D/A converters of this type with more than 8 bit resolution.

VLSI

Design Course

15-8

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters 15.3

Analog-To-Digital Converters

The objective of an A/D converter is the determination of the digital word corresponding to the analog input signal. Usually a sample-and-hold circuit (see Fig. ??) is required at the input of the A/D converter because it is not possible to convert a changing analog signal. A block diagram of a general A/D converter is shown in Fig. ??. The ideal input-output characteristics for a A/D converter are shown in Fig. ??.

Figure 15.12: Block diagram of a general analog-to-digital converter

Figure 15.13: Ideal input-output characteristics for a 3-bit A/D converter

VLSI

Design Course

15-9

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters 15.3.1

Serial A/D Converters

Two possible implementations of serial A/D converters are single-slope and dual-slope A/D converters. Both will not be discussed in detail here. The main advantages of these converters is their simplicity, their main disadvantage is the long conversion time required.

15.3.2

Successive Approximation A/D Converters

This type of A/D converters converts an analog input into an N-bit digital word in N clock cycles. Consequently, the conversion time is less than for the serial converters without much increase in the complexity of the circuit. Fig. ?? shows an example of a successive approximation A/D converter architecture.

Figure 15.14: Example of a successive approximation A/D converter architecture The successive approximation process is shown in Fig. ??.

VLSI

Design Course

15-10

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters

Figure 15.15: The successive approximation process

15.3.3

Parallel A/D Converters

In many applications, it is necessary to have a smaller conversion time than is possible with the previously described A/D converter architectures. Parallel A/D converters, also known as flash A/D converters, typically require down to one clock cycle for conversion. An architecture of a 3-bit parallel A/D converter is shown in Fig. ??. Parallel A/D converters can reach typically up to 20 MHz for CMOS technology. The sampleand-hold time may though be larger than 50 ns and could prevent this conversion time from being realised. Another problem is that the number of comparators required is 2N −1 . For N greater than 8, too much area is required. One method of achieving small system conversion times is to use slower A/D converters in parallel, which is called time-interleaving and is shown in Fig. ??. Here M successive approximation A/D converters are used in parallel to complete the N -bit conversion of one analog signal per clock cycle. The sample-and-hold circuits consecutively sample and apply the input analog signal to their respective A/D converters. N clock cycles later, the A/D converter provides a digital word output. If M = N , then a digital word is given out every clock cycle. If one examines the chip area for an N -bit A/D converter using the parallel A/D converter architecture (M = 1) compared with the time-interleaved architecture for M = N , the minimum area will occur for a value of M between 1 and N .

VLSI

Design Course

15-11

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters

Figure 15.16: A 3-bit parallel A/D converter

VLSI

Design Course

15-12

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters

Figure 15.17: A time-interleaved A/D converter array

VLSI

Design Course

15-13

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters 15.3.4

Sigma-Delta A/D Converter

Introduction The basic structure of a sigma-delta converter is shown in Fig. ??. The sigma-delta converter can be referred to as an oversampling converter, although oversampling is just one of the techniques contributing to the performance of a sigma-delta converter. The sigma-delta converter shown in Fig. ?? quantizes an analog signal with very low resolution (1 bit) and a very high sampling rate (2 MHz). With the use of oversampling techniques and digital filtering, the sampling rate is reduced (8 kHz) and the resolution is increased (16 bits).

Figure 15.18: Basic structure of a sigma-delta converter A more detailed block diagram of the sigma-delta modulator is shown in Fig. ??. It consists of an integrator, a quantizer (comparator for 1 bit) and a feedback loop with a D/A converter (switch for 1 bit). The output of the sigma-delta modulator is shown in Fig.?? for a sine wave input. The single-bit conversion will result in an output which is either ’1’ or ’0’. When the signal is near plus full scale, the output is positive during most of the clock cycles. The opposite is true for near minus full scale signals. When the output is followed by a digital filter as shown in Fig. ?? which can perform sophisticated averaging functions, the 1-bit sequence is transformed into a much more meaningful signal.

Figure 15.19: First-order sigma-delta modulator block diagram

Noise Shaping One feature that makes the sigma-delta converter so powerful is its noise shaping capability. To understand how this works, the analysis of the sigma-delta modulator in the frequency domain is appropriate. Fig.?? shows the frequency domain linearized model of a sigma-delta modulator.

VLSI

Design Course

15-14

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters

Figure 15.20: Output of first-order sigma-delta modulator

Figure 15.21: Frequency domain linearized model of a sigma-delta modulator

VLSI

Design Course

15-15

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters

The integrator is represented as a analog filter. For an integrator, the transfer function has an amplitude which is inversly proportional to the input frequency ( f1 relationship). The quantizer is modelled as a gain stage followed by the addition of quantization noise. Thus, the output y of the sigma-delta converter can be expressed by y = (x − y)

1 +q f

(15.9)

where (x − y) is the difference signal from the summing node at the input and q is the quantization noise. Applying some algebraic rearrangement yields y = 

1 1+ y = f 

y = y =

x y − +q f f x +q f x f

1+

1 f

+

q 1+

1 f

x qf + f +1 f +1

(15.10)

At a frequency f = 0, the output signal equals x with no noise element q. At higher frequencies, the value of x is reduced and the influence of q increases. In essence, the sigma-delta modulator has a low pass effect on the signal and a high pass effect on the noise. As a result of this, the modulator can be thought of as a noise shaping filter where noise in the signal pass band is reduced and noise energy is pushed into the higher frequency region. The effect of this procedure on normally equally distributed (white) quantization noise is shown in Fig. ??.

Figure 15.22: Noise-shaping filter function

VLSI

Design Course

15-16

Darmstadt University of Technology Institute of Microelectronic Systems

0

Analog-To-Digital Converters

Digital Filtering The sigma-delta modulator described so far produces a stream of single-bit digital values at a very high rate. The modulator’s output bit stream is fed into the converter’s digital filter, which performs several different functions. All of these functions, however, are integrated into a single filter implementation. The functions of the filter are: • sophisticated averaging (low pass filtering) • removing high frequency noise (quantization noise) • reducing sampling rate The sampling rate reduction is done by averaging over a sample of cycles of the input bit stream and produces an output data stream that is reduced in sampling rate, but increased in resolution (i.e. number of bits per sample). Advantages of Sigma-Delta Converters The advantages of the sigma-delta converter technology are • Sigma-delta converters are a complete conversion and filtering system, additional digital filtering functions may easily be implemented in the digital output filter of the converter • Very low-cost and high-performance conversion ist possible as the analog part of the converter is very simple and need not be as accurate as in other A/D converters. The main part of the converter is the digital filter which can be integrated more easily in MOS technology. • excellent signal-to-noise performance, therefore high resolution converters possible • no sample-and-hold circuit preceeding the converter is neccessary as sampling rates are very high

VLSI

Design Course

15-17

Darmstadt University of Technology Institute of Microelectronic Systems

0