PHY 752 Spring 2015 -- Lecture 25 13/27/2015

PHY 752 Solid State Physics11-11:50 AM MWF Olin 107

Plan for Lecture 25:

Chap. 18 & 19 in Marder Impurity states Properties of semiconductors

Some of the lecture materials are from slides prepared by Marder

PHY 752 Spring 2015 -- Lecture 25 23/27/2015

PHY 752 Spring 2015 -- Lecture 25 33/27/2015

Impurity states due to point defects

0

0Unperturbed Hamiltonian: n n n

V EH

H

k k kò

' '' '

Expand

Equation for expansion

as a superposition of Blo

coefficients:

ch waves:

' '

n nn

n n n nn

C

C n V n C EC

k kk

k k k kk

k kò

PHY 752 Spring 2015 -- Lecture 25 43/27/2015

Impurity states due to point defects -- continued

3

Define:

( )

( () )( )

in n

in n

F e

d

C

sF e

k rk

k

k sk

k

r

r sr

2 2

*

2 2

*

Suppose that for impurity states near the conduction

band edge: 2

Suppose that for impurity states near the valence

band edge: 2

n cc

n v

v

k

m

k

m

k

k

ò ò

ò ò

PHY 752 Spring 2015 -- Lecture 25 53/27/2015

Impurity states due to point defects -- continued

2

( ) effZVr

er

òDielectric constant

valence charge of impurity relative to that of host lattice

22 2 2 2 2 2

* * *

22 2 2 2 2 2

* * *

Equation for wavepacket amplitudes

( ) ( ) 2 2 2

( ) ( ) 2 2 2

eff

e

n c c cc c c

n v v v

v v

ff

v

Z eF EF

m m m

Z eF EF

m m m

k

r

k

r

k

k

r r

r r

ò ò ò òò

ò ò ò òò

PHY 752 Spring 2015 -- Lecture 25 63/27/2015

Impurity states due to point defects -- continued

cò

vò

* 2 4

2 2 2

Electron impurity:

2c eff

c

Zm e

nE

ò

ò

* 2 4

2 2 2

Hole impurity:

2v eff

v

m eZ

nE

ò

ò

PHY 752 Spring 2015 -- Lecture 25 73/27/2015

Semiconductor properties

Population of electrons (n) and holes (p) in a pure semiconductor

m

PHY 752 Spring 2015 -- Lecture 25 83/27/2015

Semiconductor properties -- continued

For:

PHY 752 Spring 2015 -- Lecture 25 93/27/2015

Semiconductor properties -- continued

multiplicity of conduction band minima

PHY 752 Spring 2015 -- Lecture 25 103/27/2015

Semiconductor properties -- continued

For intrinsic semiconductor, n=p=ni

PHY 752 Spring 2015 -- Lecture 25 113/27/2015

Semiconductor properties -- continued

Effects of impurities:

Intrinsic carriers:

PHY 752 Spring 2015 -- Lecture 25 123/27/2015

Semiconductor properties – continued

Typically, the ionized impurities dominate the carrier concentrations

PHY 752 Spring 2015 -- Lecture 25 133/27/2015

Semiconductor properties – continued

For primarily donor doping: For primarily acceptor doping:

PHY 752 Spring 2015 -- Lecture 25 143/27/2015

Semiconductor junction

Before equilibration

After equilibration

Junction potential

PHY 752 Spring 2015 -- Lecture 25 153/27/2015

Semiconductor junction

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Semiconductor junction

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Simplified model:

Semiconductor junction

PHY 752 Spring 2015 -- Lecture 25 183/27/2015

Semiconductor junction

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Behavior of ideal diode

PHY 752 Spring 2015 -- Lecture 25 203/27/2015

Behavior of ideal diode – continued

Diffusion of electrons and holes:

where

: '

'

n

p

n

p