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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 8 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 (ii) 








t
a
sD
V
V
II exp 
   





 
0259.0
6.0
exp1050.1 22 
 1210726.1  A 
 (iii)   





 
0259.0
8.0
exp1050.1 22
DI 
 910896.3  A 
 (iv)   





 
0259.0
0.1
exp1050.1 22
DI 
 
610795.8  A 
(b)
02
WAen
I i
gen  
  
  
  










26
1616
108.1
107107
ln0259.0biV 
 263.1 V 
 
   








19
14
106.1
3263.11085.81.132
W 
 
  
2/1
1616
1616
107107
107107












 
 
510201.4  cm 
(i)Then 
    
 8
56194
1022
10201.4108.1106.1102




genI
 
1410049.6  A 
 (ii) 








t
a
rorec
V
V
II
2
exp 
  
 






 
0259.02
6.0
exp106 14 
 
910436.6  A 
(iii)  
 






 
0259.02
8.0
exp106 14
recI 
 
710058.3  A 
 (iv)  
 






 
0259.02
0.1
exp106 14
recI 
 
510453.1  A 
_______________________________________ 
 
 
 
 
 
 
8.31 
 Using results from Problem 8.30, we find 
 4.0aV V, 161064.7 dI A, 
 101035.1 recI A, 101035.1 TI A 
 6.0aV V, 121073.1 dI A 
 91044.6 recI A, 91044.6 TI A 
 8.0aV V, 91090.3 dI A 
 71006.3 recI A, 71010.3 TI A 
 0.1aV V, 61080.8 dI A 
 51045.1 recI A, 51033.2 TI A 
 2.1aV V. 21099.1 dI A 
 41090.6 recI A, 21006.2 TI A 
_______________________________________ 
 
8.32 
 Plot 
_______________________________________ 
 
8.33 
 Plot 
_______________________________________ 
 
8.34 
 We have that 
 
   ppnn
nnp
R
nOpO
i




2
 
 Let OnOpO   and inpn  
 We can write 
 




 

kT
EE
nn FiFn
i exp 
 and 
 







 

kT
EE
np
FpFi
i exp 
 We also have 
     aFpFiFiFn eVEEEE  
 so that 
    FiFnaFpFi EEeVEE  
 Then 
 
 





 

kT
EEeV
np FiFna
i exp 
 
 





 







kT
EE
kT
eV
n FiFna
i expexp