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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 13 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 Also 
 
s
d
PO
Nea
V


2
2
 
 
    
  14
162419
1085.87.112
104105.0106.1




 
 or 
 726.7POV V 
 Then 
    









726.7
8915.0
3136.121 satI D
 
 













726.7
8915.0
3
2
1 
 or 
   05.91 satI D mA 
_______________________________________ 
 
13.30 
 (a) If 1L m, then saturation will occur 
 when 
    110110 44  LVDS V 
 We find 
 
 
2/1
2
2





 

d
GSDSbis
sat
eN
VVV
hh 
 We have 8915.0biV V and for 0GSV , we 
 obtain 
 
   
  
2/1
1619
14
104106.1
18915.01085.87.112











sath 
 or 
 410247.0 sath cm 247.0 m 
 Then 
    WhaeNsatI satsatdD  1 
    71619 10104106.1   
    44 103010247.050.0   
 or 
   86.41 satI D mA 
 If velocity saturation did not occur, then from 
 the previous problem, we would have 
     1.18
1
2
05.91 





satI D mA 
 (b) If velocity saturation occurs, then the 
 relation    LsatI D 11  does not apply. 
_______________________________________ 
 
 
 
 
13.31 
 (a) 
    73 1041058000  n cm/s 
 Then 
 12
7
4
105
104
102 






L
td s 
 or 
 5dt ps 
 (b) Assume 710 sat cm/s 
 Then 
 11
7
4
102
10
102 




sat
d
L
t

s 
 or 
 20dt ps 
_______________________________________ 
 
13.32 
 (a) 
    74 10101000  n cm/s 
 Then 
 11
7
4
102
10
102 





L
td s 
 or 
 20dt ps 
 (b) For 710 sat cm/s 
 11
7
4
102
10
102 




sat
d
L
t

s 
 or 
 20dt ps 
_______________________________________ 
 
13.33 
 The reverse-bias current is dominated by the 
 generation current. We have 
 PObiP VVV  
 We find 
  
  
  










210
1618
105.1
103105
ln0259.0biV 
 or 
 884.0biV V 
 Also 
s
d
PO
Nea
V


2
2
 
 
    
   












14
162419
1085.87.112
103103.0106.1