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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 7 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 
   








19
14
106.1
5574.01085.87.112
 
 
2/1
151414
15
10510
1
10
105

















 
 
 or 
 41066.2 nx cm 
(c) For 30nx m, we have 
 
   










19
14
4
106.1
1085.87.112
1030 Rbi VV
 
 
2/1
151414
15
10510
1
10
105

















 
 
 which becomes 
  Rbi VV   76 10269.1109 
 We find 
 4.70RV V 
_______________________________________ 
 
7.29 
 An pn  junction with 1410aN cm 3 , 
(a) A one-sided junction and assume 
 biR VV  . Then 
 
2/1
2





 

a
Rs
p
eN
V
x 
 or 
     
  1419
14
24
10106.1
1085.87.112
1050





 RV
 
 which yields 
 193RV V 
 (b) 
 








d
a
pn
a
d
n
p
N
N
xx
N
N
x
x
 
 so 
   







 
16
14
4
10
10
1050nx 
 
41050.0  cm 50.0 m 
 (c) 
 
 
4max
105.50
15.19322


W
VR 
 or 
 
4
max 1065.7  V/cm 
_______________________________________ 
 
 
 
7.30 
(a)  
  
  










210
1517
105.1
102102
ln0259.0biV 
 7305.0 V 
(b) 
 
2/1
2









Rbi
ds
VV
Ne
ACAC 
     
 



 

Rbi VV2
106.1
10
19
5 
     2/11514 1021085.87.11   
 
Rbi VV
C



1310287.1
 
 (i) For 1RV V, 
1410783.9 C F 
 (ii) For 3RV V, 
1410663.6 C F 
 (iii) For 5RV V, 
1410376.5 C F 
_______________________________________ 
 
7.31 
(a)  
 
  










26
16
108.1
108
ln0259.0 d
bi
N
V 20.1 
     






0259.0
20.1
exp108.1108
2616
dN 
 151036.5  dN cm 3 
(b) 
  
2/1
2 








daRbi
das
NNVV
NNe
ACAC 
 
 
 







0.120.12
106.1
1010.1
19
12 A 
    
 
2/1
1516
151614
1036.5108
1036.51081085.81.13







 
 
51056.7  A cm 2 
(c)    
 







Rbi VV2
106.1
1056.71080.0
19
512 
 
    
 
2/1
1516
151614
1036.5108
1036.51081085.81.13







 
 
Rbi VV 




8
8 101585.2
100582.1 
 RRbi VVV  20.1161.4 
 96.2RV V 
_______________________________________