Formula Sheet: P-N Junction & Diodes

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P-N Junction & Dio des F orm ula Sheet for GA TE
P-N Junction Characteristics
• Built-in P oten tial : P oten tial across the depletion region of a P-N junction.
V
bi
=
kT
q
ln
(
N
A
N
D
n
2
i
)
where k is Boltzmann constan t (8.617×10
-5
eVK
-1
), T is temp erature (K ), q is elec-
tron c harge (1.602×10
-19
C ),N
A
is acceptor c oncen tration,N
D
is donor concen tration,
n
i
is in trinsic carrier concen tration.
• Depletion Width : T otal width of the depletion region.
W =
v
2?
s
(V
bi
-V)
q
(
N
A
+N
D
N
A
N
D
)
where ?
s
is p ermittivit y of the semiconductor (Fm
-1
), V is applied v oltage (p ositiv e
for forw ard bias, negativ e for rev erse).
• Depletion Width on P-side and N-side :
W
p
=W
N
D
N
A
+N
D
, W
n
=W
N
A
N
A
+N
D
• Electric Field in Depletion Region : Maxim um electric field at the junction.
E
max
=
qN
D
W
n
?
s
=
qN
A
W
p
?
s
Dio de Curren t
• Dio de Curren t Equation : Curren t through a P-N junction dio de.
I =I
S
(
exp
(
qV
?kT
)
-1
)
where I
S
is rev erse saturation curren t, ? is idealit y factor (1 for ideal dio des, 1–2 for
real dio des), V is applied v oltage.
• Rev erse Saturation Curren t :
I
S
=Aqn
2
i
(
D
p
L
p
N
D
+
D
n
L
n
N
A
)
whereA is junction area (m
2
),D
p
,D
n
are diffusion co e?icien ts for holes and electrons,
L
p
, L
n
are diffusion lengths.
• Small-Signal Resistance : Dynamic resistance of the dio de.
r
d
=
?kT
qI
where I is the DC bias curren t .
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