This document discusses the calculation of the built-in potential in a p-n junction. It covers determining the equilibrium electron and hole concentrations using the Fermi-Dirac distribution and relates them to the built-in potential. It also examines how the extrinsic Fermi level remains constant throughout the p-n junction under equilibrium conditions.

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
=