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Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
8/19/2020 1Arpan Deyasi, RCCIIT, India
Topic: Junction
Calculation of built-in potential
EF
EV
EC
EFI
qΦFp
qΦFn
Vbi
8/19/2020 2Arpan Deyasi, RCCIIT, India
Calculation of built-in potential
Equilibrium electron concentration
0 exp F FI
i
E E
n n
kT
− 
=  
 
0 exp Fn
i
q
n n
kT
φ 
=  
 
8/19/2020 3Arpan Deyasi, RCCIIT, India
0
lnFn
i
nkT
q n
φ
 
=  
 
Calculation of built-in potential
ln D
Fn
i
kT N
q n
φ
 
=  
 
8/19/2020 4Arpan Deyasi, RCCIIT, India
Calculation of built-in potential
Equilibrium hole concentration
0 exp FI F
i
E E
p n
kT
− 
=  
 
0 exp
Fp
i
q
p n
kT
φ 
=  
 
8/19/2020 5Arpan Deyasi, RCCIIT, India
Calculation of built-in potential
0
lnFp
i
pkT
q n
φ
 
=  
 
ln A
Fp
i
kT N
q n
φ
 
=  
 
8/19/2020 6Arpan Deyasi, RCCIIT, India
Calculation of built-in potential
bi Fn FpV φ φ= +
ln lnD A
bi
i i
kT N kT N
V
q n q n
   
+   
   
8/19/2020 7Arpan Deyasi, RCCIIT, India
ln lnD A
bi
i i
kT N N
V
q n n
    
+    
    
Calculation of built-in potential
2
ln D A
bi
i
kT N N
V
q n
  
=   
   
8/19/2020 8Arpan Deyasi, RCCIIT, India
Extrinsic Fermi Level is constant
8/19/2020 9Arpan Deyasi, RCCIIT, India
We consider p-n junction under external bias
0pJ =
Under equilibrium
0
0 0p z p
dp
qp E qD
dz
µ − =
8/19/2020 10Arpan Deyasi, RCCIIT, India
0
0 p z p
dp
p E D
dz
µ =
Extrinsic Fermi Level is constant
0
0
p
z
p
D dp
p E
dzµ
=
8/19/2020 Arpan Deyasi, RCCIIT, India 11
Extrinsic Fermi Level is constant
0
0 z
dpkT
p E
q dz
=
0 exp FI F
i
E E
p n
kT
− 
=  
 
8/19/2020 Arpan Deyasi, RCCIIT, India 12
0
expi FI F
FI F
dp n E E
dz kT kT
dE dE
dz dz
 −  
=   
  
 
× − 
 
Extrinsic Fermi Level is constant
0
0 z
dpkT
p E
q dz
=
8/19/2020 Arpan Deyasi, RCCIIT, India 13
Extrinsic Fermi Level is constant
z
dV
E
dz
= −
FI
z
d E
E
dz q
 
=− − 
 
1 FI
z
dE
E
q dz
=
0
0 z
dpkT
p E
q dz
=
8/19/2020 Arpan Deyasi, RCCIIT, India 14
Extrinsic Fermi Level is constant
1
exp
exp
FI F FI
i
i FI F FI F
E E dE
n
kT q dz
nkT E E dE dE
q kT kT dz dz
− 
× = 
 
 −    
× × −    
    
8/19/2020 Arpan Deyasi, RCCIIT, India 15
FI FI FdE dE dE
dz dz dz
 
= − 
 
Extrinsic Fermi Level is constant
0FdE
dz
=

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p-n junction: built-in potential and constant Fermi level

  • 1. Course: Electronic Devices paper code: EC301 Course Coordinator: Arpan Deyasi Department of Electronics and Communication Engineering RCC Institute of Information Technology Kolkata, India 8/19/2020 1Arpan Deyasi, RCCIIT, India Topic: Junction
  • 2. Calculation of built-in potential EF EV EC EFI qΦFp qΦFn Vbi 8/19/2020 2Arpan Deyasi, RCCIIT, India
  • 3. Calculation of built-in potential Equilibrium electron concentration 0 exp F FI i E E n n kT −  =     0 exp Fn i q n n kT φ  =     8/19/2020 3Arpan Deyasi, RCCIIT, India
  • 4. 0 lnFn i nkT q n φ   =     Calculation of built-in potential ln D Fn i kT N q n φ   =     8/19/2020 4Arpan Deyasi, RCCIIT, India
  • 5. Calculation of built-in potential Equilibrium hole concentration 0 exp FI F i E E p n kT −  =     0 exp Fp i q p n kT φ  =     8/19/2020 5Arpan Deyasi, RCCIIT, India
  • 6. Calculation of built-in potential 0 lnFp i pkT q n φ   =     ln A Fp i kT N q n φ   =     8/19/2020 6Arpan Deyasi, RCCIIT, India
  • 7. Calculation of built-in potential bi Fn FpV φ φ= + ln lnD A bi i i kT N kT N V q n q n     +        8/19/2020 7Arpan Deyasi, RCCIIT, India
  • 8. ln lnD A bi i i kT N N V q n n      +          Calculation of built-in potential 2 ln D A bi i kT N N V q n    =        8/19/2020 8Arpan Deyasi, RCCIIT, India
  • 9. Extrinsic Fermi Level is constant 8/19/2020 9Arpan Deyasi, RCCIIT, India We consider p-n junction under external bias 0pJ = Under equilibrium 0 0 0p z p dp qp E qD dz µ − =
  • 10. 8/19/2020 10Arpan Deyasi, RCCIIT, India 0 0 p z p dp p E D dz µ = Extrinsic Fermi Level is constant 0 0 p z p D dp p E dzµ =
  • 11. 8/19/2020 Arpan Deyasi, RCCIIT, India 11 Extrinsic Fermi Level is constant 0 0 z dpkT p E q dz = 0 exp FI F i E E p n kT −  =    
  • 12. 8/19/2020 Arpan Deyasi, RCCIIT, India 12 0 expi FI F FI F dp n E E dz kT kT dE dE dz dz  −   =         × −    Extrinsic Fermi Level is constant 0 0 z dpkT p E q dz =
  • 13. 8/19/2020 Arpan Deyasi, RCCIIT, India 13 Extrinsic Fermi Level is constant z dV E dz = − FI z d E E dz q   =− −    1 FI z dE E q dz = 0 0 z dpkT p E q dz =
  • 14. 8/19/2020 Arpan Deyasi, RCCIIT, India 14 Extrinsic Fermi Level is constant 1 exp exp FI F FI i i FI F FI F E E dE n kT q dz nkT E E dE dE q kT kT dz dz −  × =     −     × × −         
  • 15. 8/19/2020 Arpan Deyasi, RCCIIT, India 15 FI FI FdE dE dE dz dz dz   = −    Extrinsic Fermi Level is constant 0FdE dz =