3/27/2015phy 752 spring 2015 -- lecture 251 phy 752 solid state physics 11-11:50 am mwf olin 107...
TRANSCRIPT
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
PHY 752 Spring 2015 -- Lecture 25 163/27/2015
Semiconductor junction
PHY 752 Spring 2015 -- Lecture 25 173/27/2015
Simplified model:
Semiconductor junction
PHY 752 Spring 2015 -- Lecture 25 183/27/2015
Semiconductor junction
PHY 752 Spring 2015 -- Lecture 25 193/27/2015
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