This document discusses the position of the Fermi level in intrinsic and extrinsic semiconductors. It begins by defining the intrinsic Fermi level position in an intrinsic semiconductor. It then describes how the Fermi level shifts in n-type and p-type extrinsic semiconductors due to the introduction of donor and acceptor dopants. Equations are provided for calculating the intrinsic carrier concentration and extrinsic carrier concentrations in n-type and p-type materials.

1. Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
8/4/2020 1Arpan Deyasi, RCCIIT
Topic: Fermi Level (Intrinsic and Extrinsic)

2. 8/4/2020 Arpan Deyasi, RCCIIT 2
Position of Fermi level
In intrinsic semiconductor
0 0n p=
exp
exp
C FI
C
FI V
V
E E
N
kT
E E
N
kT
 −  
−  
  
 −  
−  
  
F FIE E=

3. 8/4/2020 Arpan Deyasi, RCCIIT 3
Position of Fermi level
2
expC C V FI
V
N E E E
N kT
 + −  
=   
  
1 1
( ) ln
2 2
V
FI C V
C
N
E E E kT
N
 
= + +  
 

4. 8/4/2020 Arpan Deyasi, RCCIIT 4
Position of Fermi level
3/2*
*
C e
V h
N m
N m
 
=  
 
3/2
2
2 *
2 e
C
m kT
N
h
π 
=  
 
3/2
2
2 *
2 h
V
m kT
N
h
π 
=  
 

5. 8/4/2020 Arpan Deyasi, RCCIIT 5
Position of Fermi level
*
*
1 3
( ) ln
2 4
h
FI C V
e
m
E E E kT
m
 
= + +  
 
1
( )
2
FI C VE E E α= + +
* *
h em m>

6. 8/4/2020 Arpan Deyasi, RCCIIT 6
Position of Fermi level
EC
EV
EFI
EFI
α
Intrinsic Fermi level is not at the middle of forbidden region
(EC+EV)/2
(EC+EV)/2
1
( )
2
FI C VE E E α= + +

7. 8/4/2020 Arpan Deyasi, RCCIIT 7
Intrinsic Carrier Concentration
2
0 0in n p=
2
exp
exp
C FI
i C
FI V
V
E E
n N
kT
E E
N
kT
 −  
= −  
  
 −  
× −  
  

8. 8/4/2020 Arpan Deyasi, RCCIIT 8
Intrinsic Carrier Concentration
2
exp C V
i C V
E E
n N N
kT
 −  
−  
  
2
exp g
i C V
E
n N N
kT
  
= −  
  

9. 8/4/2020 Arpan Deyasi, RCCIIT 9
Intrinsic Carrier Concentration
exp
2
g
i C V
E
n N N
kT
  
−  
  
* *
( , , )i e h gn f m m E=

10. 8/4/2020 Arpan Deyasi, RCCIIT 10
Extrinsic Carrier Concentration (n-type)
Consider n-type semiconductor
ND: Donor concentration
0exp C F
C D
E E
N n N
kT
 −  
− ==  
  
exp C F
C D
E E
N N
kT
 −  
=   
  

11. 8/4/2020 Arpan Deyasi, RCCIIT 11
exp C FI
C i
E E
N n
kT
 −  
− =  
  
Extrinsic Carrier Concentration (n-type)
exp C FI
C i
E E
N n
kT
 −  
=   
  

12. 8/4/2020 Arpan Deyasi, RCCIIT 12
Extrinsic Carrier Concentration (n-type)
exp F FI
i D
E E
n N
kT
 −  
=  
  
exp expC FI C F
i D
E E E E
n N
kT kT
 −   −    
=      
      

13. 8/4/2020 Arpan Deyasi, RCCIIT 13
Extrinsic Carrier Concentration (n-type)
ln D
F FI
i
N
E E kT
n
 
= +  
 
ND
EF
EFI
ni=ND
EC

14. 8/4/2020 Arpan Deyasi, RCCIIT 14
Extrinsic Carrier Concentration (p-type)
Consider p-type semiconductor
NA: Acceptor concentration
0exp F V
V A
E E
N p N
kT
 −  
− ==  
  
exp F V
V A
E E
N N
kT
 −  
=   
  

15. 8/4/2020 Arpan Deyasi, RCCIIT 15
Extrinsic Carrier Concentration (p-type)
exp FI V
V i
E E
N n
kT
 −  
− =  
  
exp FI V
V i
E E
N n
kT
 −  
=   
  

16. 8/4/2020 Arpan Deyasi, RCCIIT 16
Extrinsic Carrier Concentration (p-type)
exp expFI V F V
i A
E E E E
n N
kT kT
 −   −    
=      
      
exp FI F
i A
E E
n N
kT
 −  
=  
  

17. 8/4/2020 Arpan Deyasi, RCCIIT 17
Extrinsic Carrier Concentration (p-type)
ln A
F FI
i
N
E E kT
n
 
= −  
 
NA
EF
EFI
ni=NA
EV