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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 9 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
  60.0230.012.1 e 
     1419 1085.87.11106.12
1  


itD
 
    2/116 164.060.0105  
 
 
 
  60.001.475.4
1020
1085.8
8
14






itD
 
 We then find 
 111097.4 itD cm 2 eV 1 
_______________________________________ 
 
9.14 
(a)   224.0
105
108.2
ln0259.0
15
19










n V 
(b) 666.0224.089.0  nBnbiV  V 
(c) 




 
 
kT
e
TAJ Bn
sT

exp2 
    




 

0259.0
89.0
exp300120
2
 
 81029.1 sTJ A/cm 2 
(d) 
   















81029.1
5
ln0259.0ln
sT
ta
J
J
VV 
 512.0aV V 
_______________________________________ 
 
9.15 
(a) 63.00 B V 
    




 

0259.0
63.0
exp300120
2
sTJ 
 
410948.2  A/cm 2 
    844 10948.210948.210  sTI A 
 (i) 








sT
ta
I
I
VV ln 
   












8
6
10948.2
1010
ln0259.0 
 151.0 V 
 (ii)   












8
6
10948.2
10100
ln0259.0aV 
 211.0 V 
 (iii)   











8
3
10948.2
10
ln0259.0aV 
 270.0 V 
 
(b)   030217.0
300
350
0259.0 





kT eV 
     




 
 
030217.0
63.0
exp35012010
24
sTI 
 610296.1  A 
 (i) 
















 1exp
t
a
sT
V
V
II 
  














1
10296.1
1010
ln030217.0
6
6
aV 
 0654.0 V 
 (ii)   











1
10296.1
10100
ln030217.0
6
6
aV 
 1317.0 V 
 (iii)   











6
3
10296.1
10
ln030217.0aV 
 201.0 V 
_______________________________________ 
 
9.16 
(a) 88.0Bn V 
(b)    




 

0259.0
88.0
exp30012.1
2
sTJ 
 
1010768.1  A/cm 2 
(c)   







1010768.1
10
ln0259.0aV 
 641.0 V 
(d)      2ln0259.02ln  ta VV 
 0180.0 V 
_______________________________________ 
 
9.17 
 Plot 
_______________________________________ 
 
9.18 
 From the figure, 68.0Bn V 
 






 







 

tt
Bn
ST
VV
TAJ

expexp2* 
    






 





 

tV

exp
0259.0
68.0
exp300120
2
 
 or 
 






 
 
t
ST
V
J

exp10277.4 5