1 (71)

Prévia do material em texto

Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 6 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
(b) 






 

i
o
FiFn
n
nn
kTEE

ln 
   










10
1415
105.1
102105
ln0259.0 
 33038.0 eV 
(c) 









i
FpFi
n
p
kTEE

ln 
   










10
14
105.1
102
ln0259.0 
 2460.0 eV 
_______________________________________ 
 
6.33 
(a) 








i
FiFn
n
n
kTEE

ln 
 or 




 

kT
EE
nn FiFn
i exp 
   






0259.0
270.0
exp105.1 10 
 
141005.5  cm 3 
(b) 






 

i
o
FpFi
n
pp
kTEE

ln 
   










10
1415
105.1
1005.5106
ln0259.0 
 33618.0 eV 
(c) (i)    FFiFpFiFpF EEEEEE  
 














 

i
o
i
o
n
p
kT
n
pp
kT lnln

 
 






 

o
o
p
pp
kT

ln 
 (ii) FpF EE  
   










15
1415
106
1005.5106
ln0259.0 
 
310093.2  eV 
 or 093.2 meV 
_______________________________________ 
 
 
 
 
 
 
 
 
6.34 
(a) (i) 






 

i
o
FiFn
n
nn
kTEE ln 
  
  










6
16
108.1
1002.1
ln0259.0 
 58166.0 eV 
 (ii) 









i
FpFi
n
p
kTEE

ln 
   










6
16
108.1
1002.0
ln0259.0 
 47982.0 eV 
(b) (i)   










6
16
108.1
101.1
ln0259.0FiFn EE 
 58361.0 eV 
 (ii)   










6
16
108.1
101.0
ln0259.0FpFi EE 
 52151.0 eV 
_______________________________________ 
 
6.35 
 Quasi-Fermi level for minority carrier 
 electrons: 
 






 

i
o
FiFn
n
nn
kTEE

ln 
 
  4
16
262
1024.3
10
108.1 


o
i
o
p
n
n cm 3 
 We have 
   






50
1014 x
n 
 Then 
 
 










6
144
108.1
50101024.3
ln
x
kTEE FiFn 
 We find 
 x (  m) ( FiFn EE  ) (eV) 
 0 
 1 
 2 
 10 
 20 
 50 
-0.581 
+0.361 
+0.379 
+0.420 
+0.438 
+0.462