Rf Mos Transistor Models For Substrate Coupling

Christian Enz [email protected]

Swiss Center for Electronics and Microtechnology

RF MOS TRANSISTOR MODELING FOR SUBSTRATE COUPLING

INTRODUCTION Strong demand for low-cost, small form-factor and low-power transceivers vDeep submicron CMOS well suited for wireless v

High ft and good RF noise performance 4High integration capabilities 4

Design of RF ICs remains a challenge vCrucial to accurately predict performance of RF ICs vRequires accurate MOST models valid for all bias from dc to RF and for a large range of geometries v

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

2

OUTLINE v

MOST Transistor Modeling at RF Equivalent circuit at RF 4Approximate Y-parameters analysis 4

v

Effect of Intra-Device Substrate Coupling Output admittance 4Thermal noise 4

v

Conclusion

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

3

TYPICAL RF MULTIFINGER DEVICE RF MOS Transistors are usually large devices vImplemented as multi-finger devices due to limited width v

Wf

D S G

© C. Enz, Aug. 2001

Lf

Nf : # of fingers

D

Wf : width of a single finger

S

Lf : length of a single finger

D

Weff=Nf·Wf : total width

RF MOS Transistor Modeling for Substrate Coupling

4

MOST EQUIVALENT CIRCUIT B

G (G) Drain S (S) Gate D (D) Substrate (B) Substrate (B) Source

G Rg

gi

Cgbo S

Cgso Rs Dsb bi

Rsb

si

Cgdo Mi Rdsb

di

Rd

Ddb db

Rdb

B © C. Enz, Aug. 2001

D

intrinsic part of compact model

B RF MOS Transistor Modeling for Substrate Coupling

5

QUASI-STATIC SMALL-SIGNAL MODEL (in saturation)

G

I1

Rg Cgb

S

gi Cgs Rs si Ims

V1

Cgd di Rd

I2

D

gds Csb bi Rsb

B

C gs = C gsi + C gso C gd = C gdi + C gdo C gb = C gbi + C gbo © C. Enz, Aug. 2001

Im

Bulk referenced model:

Rdsb

Cdb db

V2

Rdb B

Csb = Csbi + C jsb Cdb = Cdbi + C jdb

I m = Ym ⋅ (V (gi ) − V (bi )) I ms = Yms ⋅ (V (si ) − V (bi )) Ym = g m − jωCm Yms = n ⋅ Ym = g ms − jωCms Ym = g m ⋅ (1 − jωτ qs ) Yms = g ms ⋅ (1 − jωτ qs )

τ qs =

RF MOS Transistor Modeling for Substrate Coupling

Cm Cms = g m g ms 6

APPROXIMATE Y-PARAMETERS v

Assuming ωRgCgg << 1 and neglecting substrate resistances 2 Y11 ≅ ω 2 Rg C gg + jω C gg

Y12 ≅ −ω 2 Rg C gg C gd − jω C gd

Y21 ≅ g m − ω 2 Rg C gg ⋅ (Cm + C gd )− jω ⋅ (Cm + C gd )

Y22 ≅ g ds + ω 2 Rg C gg ⋅ (Cbd + C gd )+ jω ⋅ (Cbd + C gd ) C gg ≡ C gs + C gd + C gb v

Can be used for direct extraction

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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MEASURED VERSUS ANALYTICAL Y-PARAMETERS N-channel, Nf = 10, Wf = 12 µm, Lf = 0.36 µm, VG = 1 V, VD = 1 V 1

measured analytical

Re{y11} 0.5 [mA/V] Re{y12} [mA/V]

0 0 0.2

2

4

6

8

10

0

-0.2 0 2 4 30 Re{y21} 20 [mA/V] 10 Substrate 0 coupling 0 2 4 effect 2.0

6

8

10

6

8

10

6

8

10

Re{y22} [mA/V] 1.0 0

© C. Enz, Aug. 2001

0

2

4

Frequency [GHz]

15 Im{y11} 10 [mA/V] 5 0 0 0 Im{y12} -1 [mA/V] -2 -3 0 0 Im{y21} -2 -4 [mA/V] -6 -8 0 8 Im{y22} 6 4 [mA/V] 2 0 0

RF MOS Transistor Modeling for Substrate Coupling

2

4

6

8

10

2

4

6

8

10 Cm=0

2

4

6

8

10

2

4

6

8

10

Without transcapacitance

Frequency [GHz]

8

INTRA-DEVICE SUBSTRATE COUPLING B

S

D

G

D sb Ddb (Cjsb ) Rdsb (C jdb ) Eliminate to save 1 node

R sb

G

[Liu, IEDM 97] Rg

sb

gi

Cgbo S

Rs

Cgso si

Dsb

sb

B

Rsb © C. Enz, Aug. 2001

bi

Cgdo R Mi di d D Rdsb

[Tiemeijer, ESSDERC 98]

db

sb

B

B

bi

db

B

B

[Tin, CICC 99]

Ddb db

Rdb

bi

R db

sb

B

bi

B RF MOS Transistor Modeling for Substrate Coupling

sb

db

B

bi

db

B

B 9

SUBSTRATE RESISTANCES SCALING Symmetric substrate contacts

G

“Horse-shoe” substrate contacts

B

B

S

S

D

D

S D

1 Rdb ∝ Wf

G

1 Ns

S D

S

S

B

B

1 Rsb ∝ Wf © C. Enz, Aug. 2001

Rsb ∝

RF MOS Transistor Modeling for Substrate Coupling

Rdb ∝

1 Nd 10

SUBSTRATE NETWORK EXTRACTION (1/2) deembedding Rg and Rd

′ Y22    → Y22

Y22

v

′ Y22

Assuming Rs << Rds simplifies schematic

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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SUBSTRATE NETWORK EXTRACTION (2/2) deembeddin g C gd and Rds

′    → Ysub Y22

1 ′ − ≅ Y22 − jωC gd Rds

′ Y22

Ysub

gmb estimated from gm v g extracted from Re{Y’ } at low-frequency m 21 v R ≈R , R sb db dsb, Csb and Cdb extracted by local optimization v

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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EXTRACTED Ysub N-channel, Nf = 20, Wf = 10 µm, Lf = 0.5 µm, VG = 1.18 V, VD = 1 V, VS = 0 V

Re{Ysub} and Im{Ysub} [A/V]

6.0x10

-3

Cgb + Csb=334 fF Cdb=114 fF Rdsb=19 Ω Rsb=Rdb=180 Ω

5.0 4.0

Im{Ysub}

3.0

Re{Ysub}

2.0

meas. sim.

1.0 0.0

0

2

4

6

8

10

Frequency [GHz] © C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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Y-PARAMETERS VERSUS FREQUENCY N-channel, Nf = 10, Wf = 12 µm, Lf = 0.36 µm, VG = 1 V, VD = 1 V , EKV v2.6 1

measured analytical simulation

Re{y11} 0.5 [mA/V] 0 0 0.2

Re{y12} [mA/V]

2

4

6

8

10

2

4

6

8

10

2

4

6

8

10

2

4

6

8

10

0

-0.2 0 30 Re{y21} 20 [mA/V] 10 0 0

Re{y22} 2.0 [mA/V] 1.0 0

© C. Enz, Aug. 2001

0

Frequency [GHz]

15 Im{y11} 10 [mA/V] 5 0 0 0 Im{y12} -1 [mA/V] -2 -3 0 0 Im{y21} -2 -4 [mA/V] -6 -8 0 8 Im{y22} 6 4 [mA/V] 2 0 0

RF MOS Transistor Modeling for Substrate Coupling

2

4

6

8

10

2

4

6

8

10

2

4

6

8

10

2

4

6

8

10

Frequency [GHz]

14

Y-PARAMETERS VERSUS FREQUENCY N-channel, Nf = 10, Wf = 12 µm, Lf = 0.36 µm, VG = 1 V, VD = 1 V -3

0.5 6

8

10

-1 0.03

0

2

0.02

6

8

10

8

10

measured ekv ekv (scalable) bsim3 (scalable)

0.01

0 0 x10 2.5 2.0 1.5 1.0 0.5 0 0

4

2

2

4

6

4 6 8 Frequency [GHz]

10

0.015

0.01 0.005 0

0

2

4

6

8

10

-3

0

2

4

6

8

10

-3

0

2

4

6

8

10

0

2

4 6 8 Frequency [GHz]

10

-3

x10

0

-1 -2 -3 x10

Im{y21} [A/V]

Re{y21} [A/V] Re{y12} [A/V]

4

0

-3

Re{y22} [A/V]

2

Im{y12} [A/V]

0 0 x10 1 -4

© C. Enz, Aug. 2001

Im{y11} [A/V]

1

Im{y22} [A/V]

Re{y11} [A/V]

x10

0 -2 -4 -6 -8

x10 8

6 4 2 0

RF MOS Transistor Modeling for Substrate Coupling

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Y-PARAMETERS VERSUS BIAS N-channel, Nf = 10, Wf = 12 µm, Lf = 0.36 µm, f = 1 GHz, VD = 0.5, 1, 1.5 V, EKV v2.6 20

Re{y11} [µA/V] 10 Re{y12} [µA/V]

Im{y11} [mA/V]

0 10

1 0 0

Im{y12} -0.5 [mA/V]

0

-10 30 Re{y21} measured 20 simulation [mA/V] 10 0 -1 10-2 Re{y22} 10-3 [A/V] 10-4 10-5 10 -2 -1 0 1 2 3 10 10 10 10 10 10

-1 0

Im{y21} -0.5 [mA/V] Im{y22} [mA/V]

ID / Ispec

© C. Enz, Aug. 2001

2

RF MOS Transistor Modeling for Substrate Coupling

-1 2 1 0 -2 -1 0 1 2 3 10 10 10 10 10 10

ID / Ispec

16

NOISE MODEL IN SATURATION Channel thermal noise: Sind = 4kT ⋅ Gnch Gnch = α sat ⋅ g m

α sat = n ⋅ γ sat

2 = n ≅ 0 .9 3

Induced gate noise: Sing = 4kT ⋅ Gng

Gng = β sat

β sat © C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

(ωCgs )2

gm δ 4 = = ≅ 0 .2 5n 15n 17

NOISY TWO-PORT Noisy two-port

Ys V1

V1

in

I2 Noiseless two-port

V2

S v ( f ) ≡ 4kT ⋅ Rv ( f ) Si ( f ) ≡ 4kT ⋅ Gi ( f )

Ys ≡ Gs + jBs v

I1 vn

INout

I1

Noise sources vn and in are usually correlated Gi =

Giu {

+

uncorrelated

Gic {

= Giu +

correlated

Yc ≡ Gc + jBc = © C. Enz, Aug. 2001

Yc 2 {

⋅ Rv

correlation admittance

in ⋅ v*n vn2

RF MOS Transistor Modeling for Substrate Coupling

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NOISE FACTOR & NOISE PARAMETERS F = Fmin

[

Rv 2 2 ( ) ( ) + ⋅ Gs − Gopt + Bs − Bopt Gs

]

Fmin, Rv, Gopt and Bopt (or Γopt) are the four noise parameters extracted from noise measurements vF=F min for Gs=Gopt AND Bs=Bopt (noise matching) vThe circuit parameters G , G and B are given by i c c v

(

2

)

2 2 Gi = Yopt ⋅ Rv = Gopt + Bopt ⋅ Rv

Gc = © C. Enz, Aug. 2001

Fmin − 2 RvGopt − 1 2 Rv RF MOS Transistor Modeling for Substrate Coupling

Bc = − Bopt 19

SIMPLE MOST NOISE ANALYSIS (1/3) I1 Rg

gate resistance noise

V1

I2 ing Cgs

Vgsi

gm·Vgsi

gmb·Vbsi

ind Vbsi

Rsub

inrsub V2

substrate noise

induced gate noise

© C. Enz, Aug. 2001

channel noise

Rg = 3 Ω

gm = 17 mA/V

αsat = 0.87

Rsub = 120 Ω

gmb = 5.1 mA/V

βsat = 0.2

Cgs = 180 fF

ft ≈ 15 GHz

cg = 0.4

RF MOS Transistor Modeling for Substrate Coupling

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SIMPLE MOST NOISE ANALYSIS (2/3) Dc ≅ 1 + α g + α sub

α sat Rv = ⋅ Dc gm Gopt Bopt

αg =

Dc ⋅ψ − χ 2 ≅ ωC gs ⋅ Dc

χ = − Bc ≅ −ωC gs ⋅ Dc

Fmin ≅ 1 + 2 ⋅ Rv ⋅ Gopt © C. Enz, Aug. 2001

g m ⋅ Rg

α sub ≡

α sat

≅ 0.05

g 2mb ⋅ Rsub

α sat ⋅ g m ψ ≅ 1.621 + α sub χ ≅ 1.192 + α sub

≅ 0 .2

ω ≅ 1 + ⋅ 2α sat ⋅ Dc ⋅ψ − χ 2 ωt

RF MOS Transistor Modeling for Substrate Coupling

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SIMPLE MOST NOISE ANALYSIS (3/3) α sat Rv = ⋅ (1 + α g + α sub ) gm Gopt ≅ ωC gs ⋅ 0.45 ⋅

1 + 8α g + 1.184α sub 1 + α g + α sub

≅ ωC gs ⋅ 0.47

Bopt

1 + 0.834α sub = − Bc ≅ −ωC gs ⋅ 1.192 ⋅ ≅ −ωC gs ⋅ 1.1 1 + α g + α sub

Fmin

ω ω ≅ 1 + ⋅ α sat ⋅ 0.9 ⋅ 1 + 8α g + 1.184α sub ≅ 1 + ωt ωt

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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1.4

1.2

1.2

1) ft / f

1.4 1.0 0.8 0.6 0.4

without Rsub with Rsub

0.2 0.0 0

0.1

0.2

0.3

0.4

0.5

(Fmin

Rv / Ro

RELATIVE CONTRIBUTION OF Rsub (1/2) 1.0 0.8 0.6 0.4

without Rsub with Rsub approx

0.2 0.0 0

f / ft

0.1

0.2

0.3

0.4

0.5

f / ft

Rsub contributes to about 20% of Rv which is dominated by channel noise vF min is therefore also slightly influenced by Rsub v

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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RELATIVE CONTRIBUTION OF Rsub (2/2) 1.2

0.4 0.3 0.2 0.1 0.0 0

without Rsub with Rsub

0.1

0.2

0.3

0.4

0.5

Bopt Ro ft / f

Gopt Ro ft / f

0.5

1.0 0.8 0.6 0.4 0.2 0.0

without Rsub with Rsub

0

0.1

0.2

f / ft

v

0.3

0.4

0.5

f / ft

Gopt and Bopt are almost insensitive to Rsub

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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MEAS. AND SIM. NOISE PARAMETERS 2

2.5

1.5

2 1.5

1 0.5

0.1 0.15 0.125 0.1 0.075 0.05 0.025 0 0.1

© C. Enz, Aug. 2001

0.2 0.3

f / ft

0.2 0.3

f / ft

1

αg=0 and αsub=0

0.5

measure simulation (with ing) analytic

0.4 0.5

0 0.1

0.2

0.4 0.5

0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 0.1

0.2

Bopt·Zo [-]

0

Gopt·Zo [-]

Rv / Zo [-]

NFmin [dB]

N-channel, Nf = 10, Wf = 10 µm, Lf = 0.36 µm, VG = 0.743 V, VD = 1 V, VS = 0 V EKV v2.6, Z0 = 50 Ω, ID = 1.038 mA, ft = 12.5 GHz

RF MOS Transistor Modeling for Substrate Coupling

0.3

0.4 0.5

0.3

0.4 0.5

f / ft

f / ft

25

CONCLUSION v

Intra-device substrate coupling mainly affects: Output admittance 4RF noise parameters (mainly R and F v min) 4

This effect has been modeled by adding a resistive substrate network vThe scalable RF MOST model has been validated up to 10 GHz, from moderate to strong inversion and for several geometries v

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

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ACKNOWLEDGMENTS F. Pengg from CSEM vA.-S. Porret, T. Melly and J.-M. Sallese from EPFL and my former colleagues from Conexant vY. Cheng, M. Matloubian, M. Schroter, V. Dellatorre as well as vD. Pehlke, J. Chen and L. Tocci v

© C. Enz, Aug. 2001

RF MOS Transistor Modeling for Substrate Coupling

27

INDUCED GATE NOISE (IGN) (in saturation)

noisy piece of channel

G

ing

induced gate noise

G

noiseless

ing S

S

D

vn

Sing = 4kT ⋅ Gng (ω ) with Gng

ind

ind

drain noise

( ωC gs )2 (ω ) = δ ⋅ =β

For long-channel in saturation © C. Enz, Aug. 2001

D

5g ms

4 δ= and 3

RF MOS Transistor Modeling for Substrate Coupling

sat

β sat

( ωC gs )2 ⋅ gm

δ ≡ 5n 28

CORRELATION FACTOR OF IGN Watch sign! ing X=0

L ind

M1 ing

vn

Cgd1

(linear region)

Correlation coefficient

Rch1 +j

vn

Rch2

0

source © C. Enz, Aug. 2001

D

c≡

Sing ,ind Sing ⋅ Sind

ind nd

 0 c= + jc g

linear region (VDS = 0) saturation

Watch sign!

0 –j

noiseless

ing S

M2

Cgs2 i

G

x

L

For long-channel

c g ≅ 0.4

drain RF MOS Transistor Modeling for Substrate Coupling

29