Níveis Quase-Fermi em Semicondutores

Prévia do material em texto

Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 6 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 Quasi-Fermi level for holes: we have 
 






 

i
o
FpFi
n
pp
kTEE

ln 
 We have 1610op cm 3 and pn   . 
 We find 
 x (  m) (
FpFi EE  ) (eV) 
 0 
 50 
+0.58115 
+0.58140 
_______________________________________ 
 
6.36 
(a) We can write 
 








i
o
FFi
n
p
kTEE ln 
 and 
 






 

i
o
FpFi
n
pp
kTEE

ln 
 so that 
     FpFFFiFpFi EEEEEE  
 














 

i
o
i
o
n
p
kT
n
pp
kT lnln

 
 or 
  kT
p
pp
kTEE
o
o
FpF 01.0ln 






 


 
 Then 
   010.101.0exp 

o
o
p
pp 
 
 or 
  010.0
op
p
low injection, so that 
 12105p cm 3 
 (b) 
 








i
FiFn
n
p
kTEE

ln 
   










10
12
105.1
105
ln0259.0 
 or 
 1505.0 FiFn EE eV 
_______________________________________ 
 
6.37 
 Plot 
_______________________________________ 
 
 
6.38 
(a) 








i
FpFi
n
p
kTEE

ln 
   







10105.1
ln0259.0
p
 
 1110p cm 3 , 04914.0 FpFi EE eV 
 1210 10877.0 
 1310 16841.0 
 1410 0.22805 
 1510 0.28768 
(b) 






 

i
o
FiFn
n
nn
kTEE

ln 
   










10
16
105.1
102
ln0259.0
n
 
 1110n cm 3 , 365273.0 FiFn EE eV 
 
1210 0.365274 
 
1310 0.365286 
 
1410 0.365402 
 
1510 0.366536 
_______________________________________ 
 
6.39 
 (a) 
 
 
   ppCnnC
nnpNCC
R
pn
itpn



2
 
 
 
   ppnn
nnp
nOpO
i




2
 
 Let inpn  . For 0 pn 
 
nOpO
i
inOipO
i n
nn
n
R
 





2
 
(b) We had defined the net generation rate as 
  RRggRg oo
 
 where oo Rg  since these are the thermal 
 equilibrium generation and recombination 
 rates. 
 If 0g , then RRg  and 
 
nOpO
in
R
 

 
 so that 
nOpO
in
Rg
 
 
 Thus a negative recombination rate implies a 
 net positive generation rate. 
_______________________________________