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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 4 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
Chapter 4 
 
4.1 
 







 

kT
E
NNn
g
ci exp2
 
 







 







kT
ET
NN
g
OcO exp
300
3
 
 
where cON and ON are the values at 300 K. 
 
 (a) Silicon 
T (K) kT (eV) in (cm 3 ) 
200 
400 
600 
01727.0 
03453.0 
0518.0 
41068.7  
121038.2  
141074.9  
 
 (b) Germanium (c) GaAs 
T (K) 
in (cm 3 ) in (cm 3 ) 
200 
400 
600 
101016.2  
141060.8  
161082.3  
38.1 
91028.3  
121072.5  
 
_______________________________________ 
 
4.2 
 Plot 
_______________________________________ 
 
4.3 
(a) 







 

kT
E
NNn
g
ci exp2
 
     
3
1919211
300
1004.1108.2105 






T
 
 
  



 

3000259.0
12.1
exp
T
 
  
3
3823
300
10912.2105.2 






T
 
 
  
   





T0259.0
30012.1
exp 
By trial and error, 5.367T K 
 
 
 
 
 
 
(b) 
   252122 105.2105 in 
     
   











T
T
0259.0
30012.1
exp
300
10912.2
3
38 
By trial and error, 5.417T K 
_______________________________________ 
 
4.4 
 At 200T K,   






300
200
0259.0kT 
 017267.0 eV 
 At 400T K,   






300
400
0259.0kT 
 034533.0 eV 
 
 
 
 
 
17
22
210
2
2
10025.3
1040.1
1070.7
200
400




i
i
n
n
 
 





 





 














017267.0
exp
034533.0
exp
300
200
300
400
3
3
g
g
E
E
 
 






034533.0017267.0
exp8
gg EE
 
   9578.289139.57exp810025.3 17  gE 
 or 
   1714.38
8
10025.3
ln9561.28
17







 
gE 
 or 318.1gE eV 
 
 Now 
  
3
210
300
400
1070.7 





 oco NN  
 




 

034533.0
318.1
exp 
   1721 10658.2370.210929.5  oco NN  
 so 371041.9 oco NN  cm 6 
_______________________________________