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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 7 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 
   








19
14
106.1
7305.01085.87.112
 
 
2/1
161616
16
102102
1
102
102




















 
 or 
 410154.0 nx cm 154.0 m 
 By symmetry 
 
410154.0 px cm 154.0 m 
 Now 
 
s
nd xeN

max 
 
   
  14
41619
1085.87.11
101537.0102106.1




 
 or 
 
4
max 1075.4  V/cm 
_______________________________________ 
 
7.6 
 (b) 




 

kT
EE
nN FiF
id exp 
   






0259.0
365.0
exp105.1 10 
 or dN
161098.1  cm 3 
 




 

kT
EE
nN FFi
ia exp 
   






0259.0
330.0
exp105.1 10 
 or aN
151012.5  cm 3 
 (c) 
  
  
  










210
1615
105.1
1098.11012.5
ln0259.0biV 
 695.0 V 
_______________________________________ 
 
7.7 
 200 K; 017267.0kT ; 38.1in cm 3 
 300 K; 0259.0kT ; 
6108.1 in cm 3 
 400 K; 034533.0kT ; 91028.3 in cm 3 
 For 200 K; 
  
  
  






 

2
1615
38.1
104102
ln017267.0biV 
 257.1 V 
 
 For 300 K; 
  
  
  










26
1615
108.1
104102
ln0259.0biV 
 157.1 V 
 For 400 K; 
  
  
  










29
1615
1028.3
104102
ln034533.0biV 
 023.1 V 
_______________________________________ 
 
7.8 
  pnn xxWx  25.025.0 
 pn xx 25.075.0  3
n
p
x
x
 
 apdn NxNx  3
n
p
a
d
x
x
N
N
 
 So ad NN 3 
(a)  
  









210105.1
ln0259.0 da
bi
NN
V 
  
  









210
2
105.1
3
ln0259.0710.0 aN
 
 or   






0259.0
710.0
exp105.13
2102
aN 
 which yields 1510766.7 aN cm 3 
 161033.2 dN cm 3 
 
2/1
12

























dad
abis
n
NNN
N
e
V
x 
 
   








19
14
106.1
710.01085.87.112
 
 
 
2/1
1510766.74
1
3
1

















 
 
61093.9  nx cm 
 or 0993.0nx m 
   








19
14
106.1
710.01085.87.112
px 
 
 
2/1
1510766.74
1
1
3

















 
 
510979.2  cm 
 or 2979.0px m