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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 12 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 
B
BB
nC
x
neD
J
0
 
 
   
4
1319
10
1059.220106.1

 
 
 or 
 828.0nCJ A/cm 2 
 Assuming a long collector 
 









t
BC
C
nOC
pC
V
V
L
peD
J exp 
 where 
 
  4
16
2102
1025.2
10
105.1



C
i
cO
N
n
p cm 3 
 and 
   710215  COCC DL  
 
310732.1  cm 
 Then 
 
   
3
419
10732.1
1025.215106.1




pCJ 
 






0259.0
6.0
exp 
 or 
 359.0pCJ A/cm 2 
 The collector current is 
   AJJI pCnCC  
   310359.0828.0  
 or 
 19.1CI mA 
 The emitter current is 
   310828.0  AJI nCE 
 or 
 828.0EI mA 
_______________________________________ 
 
12.27 
 (a) 
 
 BB
T
Lxcosh
1
 and 
T
T





1
 
 
BB Lx T  
0.01 
0.10 
1.0 
10.0 
0.99995 
0.995 
0.648 
0.0000908 
19,999 
199 
1.84 
0 
 
 
 
 
 (b) For BE DD  , BE LL  , BE xx  , we 
 have 
 
   EBBOEO NNnp 



1
1
1
1
 
 and 





1
 
 
EB NN   
0.01 
0.10 
1.0 
10.0 
0.990 
0.909 
0.50 
0.0909 
99 
9.99 
1.0 
0.10 
 
 (c) For 10.0BB Lx , the value of  is 
 unreasonably large, which means that the 
 base transport factor is not the limiting factor. 
 For 0.1BB Lx , the value of  is very 
 small, which means that the base transport 
 factor will probably be the limiting factor. 
 
 If 01.0EB NN , the emitter injection 
 efficiency is probably not the limiting factor. 
 If, however, 01.0EB NN , then the current 
 gain is small and the emitter injection 
 efficiency is probably the limiting factor. 
_______________________________________ 
 
12.28 
 We have 
 
 BBB
BOB
sO
LxL
neD
J
tanh
 
 Now 
 
  3
17
2102
1025.2
10
105.1



B
i
BO
N
n
n cm 3 
 and 
   71025  BOBB DL  
 
4108.15  cm 
 Then 
 
   
   8.157.0tanh108.15
1025.225106.1
4
319




sOJ 
 or 
 1010287.1 sOJ A/cm 2 
 Now