3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107...
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Transcript of 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107...
![Page 1: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/1.jpg)
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
![Page 2: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/2.jpg)
PHY 752 Spring 2015 -- Lecture 25 23/27/2015
![Page 3: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/3.jpg)
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
![Page 4: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/4.jpg)
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
![Page 5: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/5.jpg)
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
![Page 6: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/6.jpg)
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
![Page 7: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/7.jpg)
PHY 752 Spring 2015 -- Lecture 25 73/27/2015
Semiconductor properties
Population of electrons (n) and holes (p) in a pure semiconductor
m
![Page 8: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/8.jpg)
PHY 752 Spring 2015 -- Lecture 25 83/27/2015
Semiconductor properties -- continued
For:
![Page 9: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/9.jpg)
PHY 752 Spring 2015 -- Lecture 25 93/27/2015
Semiconductor properties -- continued
multiplicity of conduction band minima
![Page 10: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/10.jpg)
PHY 752 Spring 2015 -- Lecture 25 103/27/2015
Semiconductor properties -- continued
For intrinsic semiconductor, n=p=ni
![Page 11: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/11.jpg)
PHY 752 Spring 2015 -- Lecture 25 113/27/2015
Semiconductor properties -- continued
Effects of impurities:
Intrinsic carriers:
![Page 12: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/12.jpg)
PHY 752 Spring 2015 -- Lecture 25 123/27/2015
Semiconductor properties – continued
Typically, the ionized impurities dominate the carrier concentrations
![Page 13: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/13.jpg)
PHY 752 Spring 2015 -- Lecture 25 133/27/2015
Semiconductor properties – continued
For primarily donor doping: For primarily acceptor doping:
![Page 14: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/14.jpg)
PHY 752 Spring 2015 -- Lecture 25 143/27/2015
Semiconductor junction
Before equilibration
After equilibration
Junction potential
![Page 15: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/15.jpg)
PHY 752 Spring 2015 -- Lecture 25 153/27/2015
Semiconductor junction
![Page 16: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/16.jpg)
PHY 752 Spring 2015 -- Lecture 25 163/27/2015
Semiconductor junction
![Page 17: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/17.jpg)
PHY 752 Spring 2015 -- Lecture 25 173/27/2015
Simplified model:
Semiconductor junction
![Page 18: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/18.jpg)
PHY 752 Spring 2015 -- Lecture 25 183/27/2015
Semiconductor junction
![Page 19: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/19.jpg)
PHY 752 Spring 2015 -- Lecture 25 193/27/2015
Behavior of ideal diode
![Page 20: 3/27/2015PHY 752 Spring 2015 -- Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25: Chap. 18 & 19 in Marder Impurity.](https://reader036.fdocuments.net/reader036/viewer/2022070414/5697c0031a28abf838cc3967/html5/thumbnails/20.jpg)
PHY 752 Spring 2015 -- Lecture 25 203/27/2015
Behavior of ideal diode – continued
Diffusion of electrons and holes:
where
: '
'
n
p
n
p