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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 13 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
13.17 
 n-channel MESFET - GaAs 
 (a) We want 10.0TV V 
 Then 
 POnBnPObiT VVVV   
 so 
 
s
d
d
c
tT
Nea
N
N
VV










2
ln89.010.0
2
 
 which can be written as 
   






 
dN
17107.4
ln0259.0 
 
  
  
10.089.0
1085.81.132
1035.0106.1
14
2419






dN
 
 or 
   






 
dN
17107.4
ln0259.0 
   79.010453.8 17  
dN 
 By trial and error, 
 15101.8 dN cm 3 
 (b) At 400T K 
 
 
 
54.1
300
400
300
400
2/3







c
c
N
N
 
 Then 
     54.1107.4400 17cN 
 
171024.7  cm 3 
 Also 
   03453.0
300
400
0259.0 





tV 
 Then 
   










15
17
101.8
1024.7
ln03453.089.0TV 
   1517 101.810453.8   
 which becomes 
 050.0TV V 
_______________________________________ 
 
13.18 
(a) 
2/1
2





 

d
pOs
eN
V
a 
 
   
  
2/1
1619
14
102106.1
5.11085.81.132










 
 
51030.3  cm 330.0 m 
 
 
(b) 
pObiT VVV  
 We find 
   


















16
17
102
107.4
ln0259.0ln
d
c
tn
N
N
V 
 0818.0 V 
 788.00818.087.0  nBnbiV  V 
 Then 
 712.05.1788.0 TV V 
(c) 
 
2/1
2
2





 

d
GSDSbis
eN
VVV
h 
 
   
  
2/1
1619
14
102106.1
1085.81.132













GSDSbi VVV
 
 (i)     2/110
2 4.00788.010246.7  h 
 
510677.1  cm 1677.0 m 
 1623.01677.0330.02  ha m 
(ii)
    2/110
2 4.00.1788.010246.7  h 
 
510171.3  cm 3171.0 m 
 0129.03171.0330.02  ha m 
 (iii) 
    2/110
2 4.00.4788.010246.7  h 
 
51064.5  cm 564.0 m 
 022  haah 
_______________________________________ 
 
13.19 
(a) 
s
d
pO
Nea
V


2
2
 
 
    
  14
152419
1085.81.132
1051050.0106.1




 
 8626.0 V 
 We find 
   










15
17
105
107.4
ln0259.0n 
 1177.0 V 
 1177.087.0  nBnbiV  
 7523.0 V 
 8626.07523.0  pObiT VVV 
 1103.0 V