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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 12 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
(b)   








t
EB
BB
V
V
pp exp0 0
 
   






0259.0
615.0
exp1025.2 4 
 141062.4  cm 3 
   








t
EB
EE
V
V
nn exp0 0
 
   






0259.0
615.0
exp105.4 2 
 121024.9  cm 3 
_______________________________________ 
 
12.11 
(a) 
 
16
2102
0
102
105.1



B
i
B
N
n
n 
 410125.1  cm 3 
 Now 
      151021.00  BB Nn cm 3 
 









t
BE
B
V
V
n exp0 
 Then   










4
15
10125.1
102
ln0259.0BEV 
 6709.0 V 
(b) 
 
17
2102
0
108
105.1



E
i
E
N
n
p 
 
2108125.2  cm 3 
   








t
BE
EE
V
V
pp exp0 0
+ 
   






0259.0
6709.0
exp108125.2 2 
 
13100.5  cm 3 
_______________________________________ 
 
12.12 
 We have 
 
 




























 1exp
sinh
t
BE
B
B
BOB
V
V
L
x
n
dx
nd 
 
 



















 







 

BBB
B
B L
x
LL
xx
L
cosh
1
cosh
1
 
 
 
 
At 0x , 
 
 































1exp
sinh
0 t
BE
B
B
B
BO
x
B
V
V
L
x
L
n
dx
nd 
 
 












 1cosh
B
B
L
x
 
 At Bxx  , 
 
 































1exp
sinh
t
BE
B
B
B
BO
xx
B
V
V
L
x
L
n
dx
nd
B

 
 













B
B
L
x
cosh 
 Taking the ratio 
 
 
 
0

x
B
xx
B
dx
nd
dx
nd
B


 
1cosh1exp
cosh1exp



















































B
B
t
BE
B
B
t
BE
L
x
V
V
L
x
V
V
 
 









B
B
L
x
cosh
1
 
 (a) For  1.0
B
B
L
x
Ratio 9950.0 
 (b) For  0.1
B
B
L
x
Ratio 648.0 
 (c) For 10
B
B
L
x
Ratio 
51008.9  
_______________________________________ 
 
12.13 
 In the base of the transistor, we have 
 
    
0
2
2

BO
BB
B
xn
dx
xnd
D


 
 or 
 
    
0
22
2

B
BB
L
xn
dx
xnd 
 
 where BOBB DL 