1 (88)

Prévia do material em texto

Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 7 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
7.32 
 Plot 
_______________________________________ 
 
7.33 
(a) 









2
ln
i
dOaO
tbi
n
NN
VV 
 (c) p-region 
 
 
s
aO
s
eNx
dx
d




 
 
 or 
 1C
xeN
s
aO 

 
 We have 
 0 at 
s
paO
p
xeN
Cxx

 1 
 Then for 0 xx p 
  p
s
aO xx
eN


 
 n-region, Oxx 0 
 
 
s
dO
s
eNx
dx
d





2
1 
 
 or 
 21
2
C
xeN
s
dO 

 
 n-region, nO xxx  
 
 
s
dO
s
eNx
dx
d




 2
 
 or 
 32 C
xeN
s
dO 

 
 We have 02  at nxx  
 
s
ndO xeN
C

 3 
 so that for nO xxx  , we have 
  xx
eN
n
s
dO 

 2 
 We also have 12  at Oxx  
 Then 
  On
s
dO
s
OdO xx
eN
C
xeN




2
2
 
 which gives 
 








2
2
O
n
s
dO x
x
eN
C 
 
 Then for Oxx 0 we have 
 










22
1
O
n
s
dO
s
dO x
x
eNxeN
 
_______________________________________ 
 
7.34 
 (a)
     
dx
xdx
dx
xd
s





2
2
 
 For 12  x m,   deNx  
 So 
 1C
xeNeN
dx
d
s
d
s
d 





 
 At 2x m Ox , 0 
 So 
 
s
Od xeN
C

1 
 Then 
  O
s
d xx
eN


 
 At 0x ,    10  x , so 
     410210 


s
deN
 
 
  
  
 4
14
1519
101
1085.87.11
105106.1 





 
 or 
   410726.70  V/cm 
 (c) Magnitude of potential difference is 
  dx  dxxx
eN
O
s
d
 

 
 2
2
2
Cxx
xeN
O
s
d 









 
 Let 0 at Oxx  , then 
 
s
Od
O
O
s
d xeN
CCx
xeN













22
0
2
22
2
2
 
 Then we can write 
  2
2
O
s
d xx
eN


 
 At 1x m 
 
  
  
  24
14
1519
1 1021
1085.87.112
105106.1 





 
 or 
 863.31  V 
 Potential difference across the intrinsic region