Chapter 7, PN Junction
22 and 24 February 2016
Carrier Transport at the PN Junction
P-type
P-type
N-type
N-type
Depletion region
2
Formation of Depletion Region
• Space charge region=depletion region= region depleted of charge carries (electrons or holes)
• Space charges: ionized acceptor atoms in the p-side and ionized donor atoms in the n- side.
Space charges cannot move.
3
PN Junction Under Equilibrium Condition
— band diagram
Features under equilibrium condition (zero bias):
• The Fermi-level is flat throughout the whole junction
• The diffusion force is balanced by the internal E-field built by the space charges (this
is why the depletion region is limited)
4
Band Bending and Built-in Potential
E-field in the Depletion Region
8
Built-in Potential
Vbi   ( x  xn )   ( x   x p ) 
1 e
N d xn2  N a x 2p 
2 x
Band bending:
E Fi , p  E Fi ,n  eVbi
Solution for Vbi from Fermi-functions
eVbi  e Fn  e Fp
 Na Nd
 kT ln  2
 ni
kT  N a N d
Vbi 
ln  2
e  ni






Width of Depletion Region
xp
xn
W
1 e
N d xn2  N a x 2p 
Vbi 
2 x
Vbi 
kT  N a N d
ln 
e  ni2




xn 
2 sVbi
e
 Na 

1
 

N
N

N
d 
 d  a
xp 
2 sVbi
e
 Nd 

1
 

N
N

N
d 
 a  a
N a x p  N d xn
W  xn  x p 
2 sVbi  N a  N d 


e  Na Nd 
12