Diode Introduction
•
A diode is formed by
interfacing an
n
-type
semiconductor with a
p
-type
semiconductor.
•
A
pn
junction
is the
interface between
n
and
p
regions.
Diode symbol
Carrier Diffusion
Carriers diffuse from high
concentration to low
concentration.
Drift Currents
•
Diffusion currents lead to localized charge density (
ρ
) variations near
the
pn
junction.
•
Gauss’ law predicts an electric field due to the charge distribution:
•
Assuming constant permittivity (
ε
S
),
•
Resulting electric field gives rise to a drift current.
With no external
circuit connections, drift and diffusion currents cancel.
There is no
actual current, since this would imply power dissipation, rather the
electric field cancels the diffusion current ‘tendency.’
∇⋅
E
=
ρ
c
ε
s
E
(
x
)
=
1
ε
s
ρ
(
x
)
dx
∫
(Change in electric field is proportional to net charge per unit volume.)
Space Charge Region Formation
at the
pn
Junction
Potential across the Junction
Charge Density
Electric Field
(define
E
=0 in neutral region)
Potential
(define
φ
=0 at
junction)
φ
j
= −
E
(
x
)
dx
∫
=
V
T
ln
N
A
N
D
n
i
2
⎛
⎝
⎜
⎞
⎠
⎟
,
V
T
=
kT
q
Width of Depletion Region
w
d
0
=
(
x
n
+
x
p
)
=
2
ε
s
q
1
N
A
+
1
N
D
⎛
⎝
⎜
⎞
⎠
⎟
φ
j
Combining the previous expressions, we can form an expression
for the width of the space-charge region, or depletion region.
It
is called the depletion region since the excess holes and electrons
are depleted from the dopant atoms on either side of the junction.
The 0 subscript indicates that no voltage is applied to diode terminals.

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