Soluções de Problemas em Física de Semicondutores

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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 12 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 
 
EO
B
EO
B
N
N
K
N
N
K
A
B



1
2
1


 
 
















EO
B
EO
B
N
N
K
N
N
K 1
2
1 
 
EO
B
EO
B
N
N
K
N
N
K 
2
1 
 
EO
B
N
N
K
2
1  
 or 
 
 
  E
B
B
E
EO
B
x
x
D
D
N
N
A
B

2
1


 
 (ii) Now 
 
E
B
E
B x
x
K
x
x
K


 1
1
1
 
 Then 
 
 
 
 
EO
B
EO
B
x
x
K
x
x
K
A
C



1
2
1


 
 
















EO
B
EO
B
x
x
K
x
x
K 1
2
1 
 
EO
B
EO
B
x
x
K
x
x
K  21 
 
EO
B
x
x
K 1 
 or finally 
 
 
  EO
B
B
E
E
B
x
x
D
D
N
N
A
C
1


 
 (b) We have 
 
2
2
1
1 








B
B
T
L
x
 
 (i) 
 
 
 
1
A
B
T
T


 
 (ii) 
 
 
 
1
A
C
T
T


 
 
 
 
 
 
 (c) Neglect any change in space charge width. 
 







 


t
BE
sO
rO
V
V
J
J
2
exp1
1
 
 
sO
sO
J
K
J
K


 1
1
1
 
 (i) 
 
 
  



















sOAsOB
sOA
sOB
J
K
J
K
J
K
J
K
A
B
11
1
1


 
 
sOAsOB J
K
J
K
 1 
 Now 
 
EE
sO
xN
J
1
 
 so 
 
 
 
   EOEO NKNK
A
B
 21


 
 or 
 
 
  EONK
A
B
1


 
 Recombination factor decreases 
 (ii) We have 
 
 
 
 EO
EO xK
x
K
A
C







2
1


 
 or 
 
 
  EOxK
A
C

2
1
1


 
 Recombination factor increases 
_______________________________________ 
 
12.26 
 (b) 
 
  3
17
2102
1025.2
10
105.1



B
i
BO
N
n
n cm 3 
 Then 
   








t
BC
BOB
V
V
nn exp0 
   






0259.0
6.0
exp1025.2 3 
 
131059.2  cm 3 
 Now