Formula Sheet: Semiconductors in Electronic Devices

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Semiconductors in Electronic Devices F orm ula S heet
for GA TE
Semiconductor Basics
• Energy Band Gap : Energy difference b et w een conduction and v alence bands.
E
g
( e.g., Si: 1.12eV, Ge: 0.67eV, GaAs: 1.43eV)
• In trinsic Carrier Concen tration : Num b er of c harge carriers in in trinsic semicon-
ductor.
n
i
=
v
N
c
N
v
exp
(
-
E
g
2kT
)
where N
c
, N
v
are effectiv e densities of states in conduction and v alence bands, k is
Boltzmann constan t (8.617×10
-5
eVK
-1
), T is temp erature (K ).
• F ermi Lev el in In trinsic Semiconductor : Lies appro ximately at the middle of the
band gap.
E
Fi
˜
E
c
+E
v
2
Extrinsic Semiconductors
• Carrier Concen tration (n-t yp e) : Electron concen tration in n-t yp e semiconductor.
n˜N
D
, p˜
n
2
i
N
D
where N
D
is donor concen tration.
• Carrier Concen tration (p-t yp e) : Hole concen tration in p-t yp e semiconductor.
p˜N
A
, n˜
n
2
i
N
A
where N
A
is a cceptor concen tration.
• Mass A ction La w : Pro duct of electron and hole concen trations.
np =n
2
i
PN Junction and Dio de Equations
• Built-in P oten tial : P oten tial across the depletion region.
V
bi
=
kT
q
ln
(
N
A
N
D
n
2
i
)
where q is electron c harge (1.602×10
-19
C ).
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Page 2


Semiconductors in Electronic Devices F orm ula S heet
for GA TE
Semiconductor Basics
• Energy Band Gap : Energy difference b et w een conduction and v alence bands.
E
g
( e.g., Si: 1.12eV, Ge: 0.67eV, GaAs: 1.43eV)
• In trinsic Carrier Concen tration : Num b er of c harge carriers in in trinsic semicon-
ductor.
n
i
=
v
N
c
N
v
exp
(
-
E
g
2kT
)
where N
c
, N
v
are effectiv e densities of states in conduction and v alence bands, k is
Boltzmann constan t (8.617×10
-5
eVK
-1
), T is temp erature (K ).
• F ermi Lev el in In trinsic Semiconductor : Lies appro ximately at the middle of the
band gap.
E
Fi
˜
E
c
+E
v
2
Extrinsic Semiconductors
• Carrier Concen tration (n-t yp e) : Electron concen tration in n-t yp e semiconductor.
n˜N
D
, p˜
n
2
i
N
D
where N
D
is donor concen tration.
• Carrier Concen tration (p-t yp e) : Hole concen tration in p-t yp e semiconductor.
p˜N
A
, n˜
n
2
i
N
A
where N
A
is a cceptor concen tration.
• Mass A ction La w : Pro duct of electron and hole concen trations.
np =n
2
i
PN Junction and Dio de Equations
• Built-in P oten tial : P oten tial across the depletion region.
V
bi
=
kT
q
ln
(
N
A
N
D
n
2
i
)
where q is electron c harge (1.602×10
-19
C ).
1
• Depletion Width : 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 semic onductor, V is applied v oltage.
• Dio de Curren t : Curren t through a PN junction dio de.
I =I
S
(
exp
(
qV
kT
)
-1
)
where I
S
is rev erse saturation c urren t.
• 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,D
p
,D
n
are diffusion co e?icien ts, L
p
,L
n
are diffusion lengths.
Semiconductor Prop erties
• Mobilit y : Electron and hole mobilit y .
µ
n
,µ
p
( Units: m
2
V
-1
s
-1
)
• Conductivit y : Conductivit y of a semiconductor.
s =q(nµ
n
+pµ
p
)
• Einstein Relation : Relates diffusion co e?icien t to mobilit y .
D
n
=
kT
q
µ
n
, D
p
=
kT
q
µ
p
Key Notes
• Standard v alues: k = 8.617×10
-5
eVK
-1
, q = 1.602×10
-19
C , n
i
˜ 1.5×10
10
cm
-3
for Si at 300K .
• Ensure consisten t units (SI preferred for GA TE).
• F or dio des, consider idealit y factor (? ) in some problems:
qV
?kT
.
• T emp erature dep endence: n
i
increases with temp erature.
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