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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 7 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 (i) For 0RV , 
 
   








19
14
106.1
6767.01085.87.112
W 
 
  
2/1
1516
1516
10105
10105












 
 510452.9  cm 
 or 9452.0W m 
 (ii) For 5RV V, 
 
   








19
14
106.1
56767.01085.87.112
W 
 
  
2/1
1516
1516
10105
10105












 
 
410738.2  cm 
 or 738.2W m 
(c) 
 
W
VV Rbi 
2
max 
 (i)For 0RV , 
 
  4
4max 1043.1
109452.0
6767.02




V/cm 
 (ii)For 5RV V, 
 
  4
4max 1015.4
10738.2
56767.02





V/cm 
_______________________________________ 
 
7.17 
(a)  
  
  










210
1617
105.1
104102
ln0259.0biV 
 8081.0 V 
(b) 
 
 
2/1
12


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




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










dad
aRbis
n
NNN
N
e
VV
x 
 
   








19
14
106.1
5.28081.01085.87.112
 
 
2/1
161716
17
104102
1
104
102




















 
 
4102987.0  cm 
 or 2987.0nx m 
 
 
2/1
12








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
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













daa
dRbis
p
NNN
N
e
VV
x 
 
 
 
 
   








19
14
106.1
5.28081.01085.87.112
 
 
2/1
161717
16
104102
1
102
104




















 
 61097.5  cm 
 or 0597.0px m 
 
 
2/1
2















 

da
daRbis
NN
NN
e
VV
W 
 
   








19
14
106.1
5.28081.01085.87.112
 
 
  
2/1
1617
1617
104102
104102












 
 4103584.0  cm 
 or 3584.0W m 
 Also 3584.0 pn xxW m 
(c) 
   
4max
103584.0
5.28081.022





W
VV Rbi
 
 
51085.1  V/cm 
(d) 
  
2/1
2 








daRbi
das
NNVV
NNe
AC 
      
 







5.28081.02
1085.87.11106.1
102
1419
4 
 
  
2/1
1617
1617
104102
104102












 
 
121078.5  F 
 or 78.5C pF 
_______________________________________ 
 
7.18 
(a) 









2
ln
i
da
tbi
n
NN
VV 
 









2
280
ln
i
d
t
n
N
V 
 We find 
 








t
bi
id
V
V
nN exp80 22 
   






0259.0
740.0
exp105.1
210 
 
3210762.5 