NNSE 618
Lecture #20
1
Lecture
contents
•
P-n junction
–
Current : Shockley model
–
Generation-recombination current
–
High injection

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NNSE 618
Lecture #20
2
First we will use Shockley approximation:
•
Drift-diffusion current
•
Abrupt depletion layer approximation
•
Non-degenerate = Boltzman statistics
•
Low injection = Fermi level do not change in the depletion
layer = minority carrier densities << majority carrier
densities
= majority carrier density equals to doping
concentration
•
No generation/recombination in the depletion layer
Let’ apply bias and calculate current through the p
-n junction
Currents in p-n junction
From Sze, 1981

NNSE 618
Lecture #20
3
Currents through p-n junction: Shockley model
Minority carrier current
Majority carrier current
Total current
is constant
throughout
the device
Recombination region
Recombination region

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NNSE 618
Lecture #20
4
Definitions of quasi-Fermi levels:
Potential across the junction:
Currents in p-n junction: Shockley theory
Minority carrier concentrations at
the edges of the depletion region
(will serve as boundary conditions):
From Sze, 1981
t
a
V
V
a
i
p
p
e
N
n
x
n
2
)
(
a
i
V
q
t
a
V
V
d
i
n
n
e
N
n
x
p
2
)
(
kT
E
E
N
kT
E
E
n
n
c
Fn
c
i
Fn
i
exp
exp
kT
E
E
N
kT
E
E
n
p
Fp
v
v
Fp
i
i
exp
exp
Fn
Fp
a
E
E
qV