Semi Con

VIEW OF AN INTEGRATED CIRCUIT • Scanning electron microscope images of an IC: Al

Lecture 12

(a)

(d)

Si (doped)

45 µm

0.5 mm

• A dot map showing location of Si (a semiconductor): --Si shows up as light regions.

ELECTRICAL PROPERTIES

(b)

• A dot map showing location of Al (a conductor): --Al shows up as light regions.

(c)

3

ELECTRICAL PROPERTIES

What is Electrical Current? Transport, or flow, of electrical charge (charged species) in the material

• How are electrical conductance and resistance characterized?

V = Usually Electrons

• What are the physical phenomena that distinguish conductors, semiconductors, and insulators? • For metals, how is conductivity affected by imperfections, T, and deformation? • For semiconductors, how is conductivity affected by impurities (doping) and T?

I

Define Electrical Current: I = J*Area (Amount of Charge per second, or C/s = A = Amps = Amperes)

Flux of Charge = Current Density

J= 2

Charge  C  A =  2 = 2 Time * Area s*m  m 4

ELECTRICAL CONDUCTION ?=

J=

V L

I A

§

§

Where E is the electric field created by a potential V is applied to a material of length L:

V

J is the current density or flux, flow of charge per unit area A.

L

ELECTRICAL CONDUCTION • Resistivity, r and Conductivity, s : --geometry-independent forms of Ohm's Law

I

A

E: electric field intensity

∆V I = ρ L A

resistivity (Ohm -m) J: current density

V ρ=R

A L

ρ=

§

• Resistance: And ? is the resistivity or resistance per unit distance (?·m).

= =

ELECTRICAL CONDUCTION

R=

=

Property of a Specific Piece of Material

=

ρL L = A Aσ

Resistive Properties of x t he Material

Dimensions of the Specific Piece

7

What Determines the Resistivity? § The quantity R depends on the shape and size of a material that is

§ When a potential V is applied across a material, it induces a flow of

experimentally measured

charge: the current I (number of charge per second) that depends on the resistance R.

§ The physical property of the material r is define for a certain type of

∆V = I R

material regardless of its size and shape.

§ The conductivity s is the inverse of the resistivity and how many charges

resistance (Ohms)

will flow through an area A per unit time under an applied electric field E and has units of (?·m)-1.

conductivity e-

L

L

5

current (amps)

I

V

 V 1 E  m V  m m = = = Ω  σ J  A 2 A    m

• Ohm's Law: voltage drop (volts)

=

I

σ=

I ρ

current density

J= σ E

§Charged Particles (usually electrons) Moving Through the Material V §Can be: Ions or “holes” Charge  C  A J= =  s m2  = m2 Time * Area   *

∆V

I 6

8

What Determines the Resistivity?

Band structure: metallic conductors § Due to the delocalized nature of valence electrons in the metallic bond, all

Then, the current density in the material is given by:

{

J=nev

A

m2

=

metals are conductors. n = Number of charged particles (“carriers” per unit volume v = Average (“drift”) velocity of the electrons e = Charge of one electron

# of carriers

C

*

m3

carrier

m

§ This implies that all metals must have a partially filled energy band. § There are two types of band structures for metallic conductors.

C

§ Metals with a partially filled s,

* s = m 2s

p, or d band.

§ Metals with overlapping full and empty bands which generate an overall partially filled energy band.

And the conductivity is then

J v σ = =ne E E

{

µ=

v E

 m2   Vs

Carriermobility, 

n=Carrierdensity,

(m ) -3

9

11

Band structure: metallic conductors

BAND STRUCTURE AND CONDUCTIVITY IN SOLIDS § The band structure describes the energy bands of a solids material. § The structure of the energy bands determine the properties of electrical

§ Metallic elements with a full s or d orbital such as

conductivity of a solids material.

§ The band structure is defined by the type of bonding in the solid. § There are three types of band structures. § Conductors have §

§

one partially filled band. Insulator have two bands separated by a large band gap that electrons can not cross. Semiconductors have two bands separated by a small band gap that some electrons can cross. 10

§

Mg12 : [Ne 10] 1s2 or Zn30 : [Ar 18]4s2 3d 10 can still form a partially filled energy band by overlapping s, p and d bands. Metallic elements with a ½ filled s orbital such as alkali or with a partially filled p or d orbital such as Al13 : [Ne 10]3s2 p1 or Ti22 : [Ar 18]3d2 4s2 will generate a partially filled s, p or d band.

12

Band structure: ionic solids

Band structure: ionic solids

§ Ionic solids by definition are composed of atoms of very different

§ The large difference in energy between the two bands result in a large band

electronegativity. This induces charge transfer and ions formation.

gap Eg.

§ Hence ionic solids are insulators. § The valence band is full and can not contribute to the conductivity.

§ To obtain the band structure we can describe the ionic bond in terms of molecular orbitals.

§ The band gap Eg is too big for electrons to

§ We combine the valence electrons of §

§

§

Na:[Ne]3s1with the valence electron of Cl:[Ne]3s2p5. Because of the large difference in electronegativity, the energy of the Na 3s orbitals are much higher in energy than the Cl 3p orbitals which are tightly bound to the nucleus and stabilized in energy. The result is that the two orbitals do not interact significantly and the antibonding has mostly the Na character while the bonding has mostly the Cl character. This is why the e- from Na is transferred to Cl

access the conduction band which stays empty and cannot contribute to the conductivity either.

Conduction band empty

Valence band full

13

15

Band structure: ionic solids

Band structure: covalent solids

§ We can extend that MO diagram to the solid by combining many atomic

§ Semiconductors are covalent solids and form directional bonds in

orbitals and obtain the energy band structure.

tetrahedral lattices.

§ Due to the difference in energy the Na and Cl form two separate bands § The high energy band formed by the Na 3s is empty as the Na e- are §

transferred to the Cl. It is called the conduction band. The low energy band is formed from the Cl 3p orbitals which are filled with the Na e- (Cl-: 3p6). It is called the valence band.

§ Elements from group IV (Si, Ge) are well known semiconductors. They have § §

§ Na 3s band

(empty) Conduction band

§

4 valence electrons and form 4 covalent bonds in a tetrahedral configuration (diamond lattice). Compound semiconductors also have a total average of 4 valence electrons and form a similar tetrahedral structure (Zinc Blend) Binary semiconductors such as ZnS (2e- provided by Zn and 6e- by S) and GaAs (3e- provided by Ga and 5e- by As) have an average of 4 valence electrons per atom. There are also ternary semiconductors such as CuAlSe2 and AgGaTe 2.

§ Cl 3p band (full) Valence band 14

16

Band structure: covalent solids

Band structure: covalent solids

§ Elements forming semiconductors combine the s and px, py, pz orbitals to

§ The antibonding is then empty and correspond to the conduction band of

form 4 equivalent sp3 hybrid orbitals.

Þ

the semiconductor.

§ The energy gap between the bands is narrow and a few electrons can be promoted into the conduction band and contribute to conductivity.

§ A material with a band gap below 4 eV is consider a semiconductor. § The bonding band correspond to the valence band and is therefore full since each atom provide two electrons to the covalent bond.

§ The four sp3 hybrid orbitals have the same shape and energy and adopt a

§ Semiconductors have intermediary

tetrahedral configuration.

conduction between metals and insulators

§ The tetrahedral geometry of the sp3 hybrids give rise to the diamond structure of semiconductors.

Antibonding Conduction

Bonding Valence

17

Band structure: covalent solids

19

Band structure: The case of semimetals:

§ We can build the MO diagram for the interaction of these sp3 orbitals and extend that concept to the solid by combining many sp3 orbitals and obtain the band structure. § Hybridization gives 4 equivalent orbitals § Initially there are s and p orbitals. § Two sp3 combine into a bonding and antibonding orbitals § Combining many sp3 generate a antibonding band and a bonding band. § These two bands are separated by a small gap Eg.. 18

§ In some solids such as graphite and bismuth, the two bands that are barely overlapping. At T=0 K a few electrons are in the upper band and the lower band is not entirely filled. This generates conductivity intermediary between metals and semiconductors.

Electronic levels at T=0 K

20

Mobility: m

CONDUCTIVITY IN SOLIDS

§ § §

σ=neµ

§

n is the number of charge carriers (electrons) per unit volume (m-3).

§

e is the charge of the electron (1.6x10-19C).

§

µ is the mobility of the electron.

§ µ is the proportionality constant between the electric field and the

§

velocityacquired by the electron in that field: v= µ·E. (µ has unit of m2V-1s-1)

§

The path of the electron throughout the crystalline lattice is limited by collisions with impurities lattice imperfections and lattice vibration (phonon) induced by thermal energy. At low temperature vibrations have small amplitude and the mobility is dominated by the lattice defects. At higher temperature the decrease in mobility is dominated by increasing lattice vibrations which scatters the moving electrons. Since thermal vibrations increase with temperature the conductivity of metals decrease with increasing temperature.

s then has units of m -3Cm2V-1s-1=(VsC-1)-1m-1or W -1m-1. Typically:

§ § §

Metals: large n, low µ Semiconductors: large µ, low n Insulators: n=0 21

23

Mobility: m § § §

§

§ §

Mobility: m §

An electron under an electric field E should keep gaining energy and accelerating. An electron under an electric field E should keep gaining energy and accelerating. This scattering phenomenon is manifested as a resistance to the passage of an electric current and electrons moving through solids therefore reach an average constant mobility µ. An electron moving through a solid constantly collides with defects in the crystalline structure as well as vibrating atoms. The electrons are randomly scattered in any direction. This is why materials have a finite resistance R.

§ § §

§

§ 22

In metals: the mobility of electrons in metals is fairly low due to the large quantity of lattice defects. However n is very large and sis high. Plastic deformation of metals increases the density of defects and therefore decreases the mobility and conductivity. Similarly, alloying increase the number of impurities scattering center and also decreases the mobility and conductivity. In semiconductors: the strong and rigid covalent network limits vibrations, the electron mobility is therefore higher, however the carrier concentrations n are very low and the overall conductivity is lower. In general: Heavier atoms vibrate more slowly with lower amplitude and therefore induce less scattering events. Hence, compounds with higher atomic weigh typically exhibit higher mobility.

24

Carrier concentration: n § § §

§

Carrier distribution in semiconductors

In metals, n is essentially the total number of valence electrons, hence the conductivity of metals is larger by many orders of magnitude. The charge carriers are the free electrons that can be promoted to a higher energy level under application of an electric field and can therefore contribute to the electrical conductivity. In insulator n=0 as there are no free electrons.

In semiconductors, n correspond to the number of electrons thermally promoted in the conduction band and therefore n increase with temperature. 25

§

The electron gaining enough energy to jump over the band gap are called intrinsic carriers.

§

According to Fermi statistics, the number of intrinsic carriers at temperature T is given by:

§

Nc is considered constant at Nc=5x1025m-3. It is the maximum value of n when the exponential term tend to 1 at high T. Nc is the density of electrons at the top of the valence band from which the electrons are promoted into the conduction band.

§

27

Carrier distribution in semiconductors

Conductivity in semiconductors

§

In semiconductors at temperature T=0°K no electron have enough energy to cross the band gap. Hence at T=0°K, n=0 and the conductivity is zero.

§

As the material gets hotter the thermal energy E=kT becomes sufficient to promote electrons in the conduction band.

§ § §

§

§

As T and E=kT increases, more and more electrons are excited in the upper band and can contribute to the electrical conductivity, the number of charge carrier n increase with increasing temperature. Hence the conductivity of semiconductors increases with increasing temperature. At very high temperature, n reaches a maximum and eventually the vibration amplitudes start to dominate the mobility just as in metals and the conductivity ultimately decreases 26

These electron can jump into a empty state, leaving their own state empty which will be filled by another electron. The net results of this motion is much easier to describe in term of an empty state or hole moving in the opposite directions of the electrons. These holes correspond to a missing electron hence have positive charge. In semiconductors the electrons excited in the conduction band leave empty levels or holes in the valence band. Hence some electron from the valence band can also contribute to the conductivity by changing their energy in response to the electric field.

§ The total conductivity of a semiconductor must then be expressed as the contribution of both charge carriers, electrons and holes. The mobility of holes is always lower than electrons and their contribution can be minimal but must be accounted for. 28

Conductivity in semiconductors § § §

EX: CONDUCTIVITY PROBLEM

In pure semiconductors ne=nh however µe> µh. Note the hole mobility is always lower than electrons mobility and that mobility generally increase with atomic weigh. Compounds such as GaAs which have much higher mobility than silicon gain importance for semiconductor device application as they can increase device speed and minimize device heating from electron friction during scattering events.

• Problem 12.2, p. 524, Callister 2e: 100m e-

Cu wire -

I = 2.5A

+

∆V

What is the minimum diameter (D) of the wire so that ∆V < 1.5V? 100m < 1.5V

R= πD2 4

L ∆V = Aσ I

2.5A 7

6.07 x 10 (Ohm-m)

-1

Solve to get D > 1.88 mm 29

CONDUCTIVITY: COMPARISON

semiconductors

• Metals: CERAMICS Soda-lime glass 10 Concrete 10 Aluminum oxide <10

-- Thermal energy puts many electrons into a higher energy state.

-10 -9 -13

POLYMERS -14 Polystyrene <10 -15 -10 -17 Polyethylene 10 insulators

• Energy States:

Energy

-- the cases below for metals show that nearby energy states are accessible by thermal fluctuations.

empty band

+ net e - flow

Energy empty band

GAP partly filled valence band

filled band 30

-

filled states

SEMICONDUCTORS Silicon 4 x 10 -4 Germanium 2 x 10 0 GaAs 10 -6

CONDUCTION & ELECTRON TRANSPORT

-1

filled states

• Room T values (Ohm-m) METALS conductors Silver 6.8 x 10 7 Copper 6.0 x 10 7 Iron 1.0 x 10 7

31

filled valence band filled band 32

EX: ESTIMATING CONDUCTIVITY

ENERGY STATES: INSULATORS AND SEMICONDUCTORS

• Question: --Estimate the electrical conductivity of a Cu-Ni alloy that has a yield strength of 125MPa.

• Semiconductors:

--Higher energy states not accessible due to gap.

Energy

Yield strength (MPa)

--Higher energy states separated by a smaller gap.

Energy empty band

filled valence band

GAP filled states

filled states

empty band

?

GAP

filled band

filled valence band

180 160 140 120 10 0 21 wt%Ni 80 60 0 10 20 3 0 4 0 5 0 wt. %Ni, (Concentration C)

Resistivity, ρ (10 -8 Ohm-m)

• Insulators:

50 40 30 20 10 0 0 10 20 30 4 0 50 wt. %Ni, (Concentration C)

ρ = 30x10 −8 Ohm − m

σ=

filled band

1 = 3.3x10 6 (Ohm − m) −1 ρ

33

35

METALS: RESISTIVITY VS T, IMPURITIES

SEMICONDUCTORS §

• Imperfections increase resistivity --grain boundaries --dislocations --impurity atoms --vacancies (10 -8 Ohm-m)

Resistivity,

ρ

6 5 4 3 2 1 0

These act to scatter electrons so that they take a less direct path.

Ni at% 3.32 i i t%N .16 a 2 at%N 2 + 1 . 1 Cu + d Cu i rme at%N defo 1.12 Cu + u e” C “Pur Cu +

-200

-100

0

T (°C)

§ §

• Resistivity

§

increases with:

§

--temperature --wt% impurity --%CW

Pure semiconductors are elements from group IV: Ge, Si with 4 electrons on the outer shell Si14 :[Ne10]2s2 2p 2. They form tetrahedral sp3 hybrid orbitals each populated with one electron. Following the octet rule each sp3 will share an electron with an adjacent atom and form 4 covalent bonds in tetrahedral configuration. Si and Ge semiconductor crystals therefore adopt the tetrahedral structure of diamond. This covalent network generates a full bonding band (valence) and a empty antibonding band (conduction) separated by a small energy gap (Eg) which produce semiconducting properties.

ρ = ρthermal +ρ thermal +ρdef 34

36

Semiconductivity §

SEMICONDUCTOR DEVICES: DEVICES: N-type doping §

Some electrons get thermally excited across the band gap into the conduction band. The population of conducting electrons therefore increase with temperature.

§ § §

§

Addition of group V element is therefore termed N-type doping because it donate negatively charged mobile carriers (electrons). In terms of band structure, the additional electron generates a donor state within the band gap at about 0.05 eVbelow the conduction band. This electron can then be easily excited in the conduction band (ionization of dopant) and contribute to the conductivity of silicon. Essentially all donor levels are ionized at ambient temperature.

Excited electrons leave empty levels (holes) in the valence band which also contribute to the conductivity .

§

The total conductivity must be expressed as the contribution of both charge carriers. 37

39

SEMICONDUCTOR DEVICES: DEVICES: N-type doping § §

§ §

SEMICONDUCTOR DEVICES: DEVICES: P-type doping

Doping of semiconductors consist in introducing a small amount of substitutional impurities in the materials. Usually one in 1012 atoms. N-type doping correspond to introduction of impurities from Group V such as P and As.

Group V elements have 5 valence electrons, 4 of which are involved in the covalent bonds and one extra bound around the dopant atoms Hence group V elements are called donor impurities. With a small amount of energy the impurity is ionized and the electron become free to contribute to the conductivity. 38

§

In contrast, P-type doping corresponds to the substitution of minute amount of group III elements such as B and Al into the Silattice.

§

The migration of the holes generates a net charge movement which also contribute to the conductivity. Holes migrate in the direction opposite to electrons. This generates a hole in the electronic structure which can be filled with a neighboring electron, hence group III elements are called Group III elements have only three valence electrons hence one electron is missing in the covalent bond structure. acceptor impurities.

§ §

40

CONDUCTION IN TERMS OF ELECTRON AND HOLE MIGRATION

SEMICONDUCTOR DEVICES: DEVICES: P-type doping § § § §

Addition of group III elements is therefore termed P-type doping because it contribute positively charged mobile carriers (holes). In the band structure model the missing electron generates an acceptor state within the band gap at about 0.1 eV above the valence band. However electrons from the valence band can get thermally excited into the acceptor state and the hole thus created in the valence band are mobile and can contribute to the conductivity. The hole on the acceptor state is not mobile (lightly bound to dopant).

• Concept of electrons and holes: valence electron

+ no applied electric field

electron hole pair migration

electron hole pair creation

Si atom

- + applied electric field

applied electric field

• Electrical Conductivity given by:

# holes/m 3

σ = ne µ e + p e µ h # electrons/m 3

hole mobility

electron mobility

41

43

INTRINSIC VS EXTRINSIC CONDUCTION

PURE SEMICONDUCTORS: CONDUCTIVITY VS T • Data for Pure Silicon: --σ increases with T --opposite to metals electrical conductivity, (Ohm-m) -1

σ

GAP

filled states

pure (undoped)

1000 T(K)

§

In a intrinsic semiconductor there is no dopant and the conductivity is due to the electron excited across the band gap and the holes created in the valence band:

§

At ambient T the number of holes and electrons is 1.5×1016m-3 for Si.

empty band

?

10 2 10 1

10 -2 50 10 0

# electrons = # holes (n = p) --case for pure Si

Energy

10 4 10 3

10 0 10 -1

σundoped ∝ e

• Intrinsic Intrinsic:

−Egap / kT

filled valence band

electrons can cross gap at higher T

filled band

material Si Ge GaP CdS

band gap (eV) 1.11 0.67 2.25 2.40 42

44

INTRINSIC VS EXTRINSIC CONDUCTION

INTRINSIC VS EXTRINSIC CONDUCTION §

• Extrinsic Extrinsic:: --n ? p --occurs when impurities are added with a different # valence electrons than the host (e.g., Si atoms)

The number of extrinsic carrier is: Where Eb is the gap between the band and the defect state and ND is the number of dopant atom. The number of intrinsic carrier is: where Eg is the band gap.

§

§

In an extrinsic semiconductor the number of charge carriers depends primarily on dopant concentration since essentially all dopants are ionized at room temperature. A typical level of dopant is 1022m-3.

§ §

Hence for N-type semiconductors

(major carriers: electrons).

And for P-type semiconductors

(major carriers: holes).

At low T, kT>Eb and nex @ ND.

§ § §

Eg>Eb hence at moderate T: n ex @ ND and n ex>>n in At high T, kT>Eg and nin>> nex

45

INTRINSIC VS EXTRINSIC CONDUCTION

DOPED SEMICON: CONDUCTIVITY VS T

Boron atom hole

4+ 4+ 4+ 4+ no applied electric field

conduction electron valence electron Si atom

4+ 4+ 4+ 4+ 4+ 3+ 4+ 4+

σ ≈ p e µh

4+ 4+ 4+ 4+

σ

4+ 5+ 4+ 4+

electrical conductivity, (Ohm-m) -1

4+ 4+ 4+ 4+

σ ≈ n e µe

no applied electric field

46

10 4 10 3 10 2 10 1 10 0

0.0052at%B doped 0.0013at%B

pure (undoped)

10 -1 10 -2 50 10 0

1 000 T(K)

intrinsic vs extrinsic conduction... --extrinsic doping level:1021/m 3 of a ntype donor impurity (such as P). --for T < 100K: "freeze-out“ thermal energy insufficient to excite electrons. --for 150K < T < 450K: "extrinsic" --for T >> 450K: "intrinsic"

doped undoped

3 2 1

in trinsic

Phosphorus atom

• Comparison:

extrinsic

-- s increases doping --reason: imperfection sites lower the activation energy to produce mobile electrons.

freeze-out

• Data for Doped Silicon: • P-type Extrinsic: (p >> n)

conduction electron concentration (10 21 /m 3 )

• Extrinsic: Extrinsic : • N-type Extrinsic: (n >> p)

47

0 0

2 00 4 00 600 T(K)48

P- N RECTIFYING JUNCTION

DOPED SEMICON: CONDUCTIVITY VS T § § § §

In intrinsic semiconductors, charge carriers are thermally excited across the band gap and are generated according to Boltzman statistics. In extrinsic semiconductors most carriers are free at room temperature and the number of carriers is constant in the intrinsic region. In the upper T limit, electrons get thermally promoted across the band gap and the semiconductor reverts to intrinsic behavior. In the freeze out region, T is too low to ionize the defects.

• Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current. • Processing: diffuse P into one side of a B-doped crystal. • Results:

+ p -type+ + + +

--No applied potential: no net current flow. --Forward bias: carrier flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows. --Reverse bias: carrier flow away from p-n junction; carrier conc. greatly reduced at junction; little current flow.

p -type

n -type

-

-

-

-

-

+ - n-type ++- - +-

+

+

-

+p -type+ + + +

n -type

-

-

-

+

-

49

SUMMARY

DOPED SEMICON: CONDUCTIVITY VS T § § §

51

The conductivity of an intrinsic semiconductor changes with T and the slope of lns vs 1/T give Eg. In contrast the conductivity of an extrinsic semiconductor stabilizes at the temperature where nin @ nex=ND. For higher concentration of dopant, ND is higher and the switch from intrinsic to extrinsic takes place at higher T.

• Electrical conductivity and resistivity are: --material parameters. --geometry independent.

• Electrical resistance is: --a geometry and material dependent parameter.

• Conductors, semiconductors, and insulators... --different in whether there are accessible energy states for conductance electrons.

• For metals, conductivity is increased by --reducing deformation --reducing imperfections --decreasing temperature.

• For pure semiconductors, conductivity is increased by --increasing temperature --doping (e.g., adding B to Si (p-type) or P to Si (n-type). 50

52