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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 7 
By D. A. Neamen Problem Solutions 
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Chapter 7 
 
7.1 
 









2
ln
i
da
tbi
n
NN
VV 
 (a) 
 (i)  
  
  










210
1515
105.1
102102
ln0259.0biV 
 611.0 V 
 (ii)  
  
  










210
1615
105.1
102102
ln0259.0biV 
 671.0 V 
 (iii)  
  
  










210
1715
105.1
102102
ln0259.0biV 
 731.0 V 
 (b) 
 (i)  
  
  










210
1517
105.1
102102
ln0259.0biV 
 731.0 V 
 (ii)  
  
  










210
1617
105.1
102102
ln0259.0biV 
 790.0 V 
 (iii)  
  
  










210
1717
105.1
102102
ln0259.0biV 
 850.0 V 
_______________________________________ 
 
7.2 
 Si: 10105.1 in cm 3 
 Ge: 13104.2 in cm 3 
 GaAs: 6108.1 in cm 3 
 
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2
ln
i
da
tbi
n
NN
VV and 0259.0tV V 
 (a) 1410dN cm 3 , 1710aN cm 3 ' 
 Then Si: 635.0biV V 
 Ge: 253.0biV V 
 GaAs: 10.1biV V 
 
 
 
 
 
 (b) 16105dN cm 3 , 16105aN cm 3 
 Si: 778.0biV V 
 Ge: 396.0biV V 
 GaAs: 25.1biV V 
 (c) 1710dN cm 3 , 1710aN cm 3 
 Si: 814.0biV V 
 Ge: 432.0biV V 
 GaAs: 28.1biV V 
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7.3 
(a) Silicon ( 300T K) 
  
  









210105.1
ln0259.0 da
bi
NN
V 
 For 1410 da NN cm 3 ; 4561.0biV V 
 1510 ; 5754.0 V 
 1610 ; 6946.0 V 
 1710 ; 8139.0 V 
(b) GaAs ( 300T K) 
  
  









26108.1
ln0259.0 da
bi
NN
V 
 For 1410 da NN cm 3 ; 9237.0biV V 
 
1510 ; 043.1 V 
 
1610 ; 162.1 V 
 
1710 ; 282.1 V 
(c) Silicon (400 K), 034533.0kT 
 121038.2 in cm 3 
 For 1410 da NN cm 3 ; 2582.0biV V 
 
1510 ; 4172.0 V 
 
1610 ; 5762.0 V 
 
1710 ; 7353.0 V 
 GaAs(400 K), 91029.3 in cm 3 
 For 1410 da NN cm 3 ; 7129.0biV V 
 
1510 ; 8719.0 V 
 
1610 ; 031.1 V 
 
1710 ; 190.1 V 
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