Formula Sheet MOSFET & MOS Capacitor - Electronic Devices - Electronics

 Page 1


MOSFET & MOS Capacitor F orm ula Sheet for
GA TE (Electronics Devices)
MOS Capacitor
• Capacitance of MOS Structure : Oxide capacitance p er unit area.
C
o x
=
?
o x
t
o x
(Units: Fm
-2
)
where ?
o x
is the p ermittivit y of the o xide (Fm
-1
), t
o x
is the o xide thic kness (m ).
• Flat-Band V oltage : V oltage at whic h there is no band b ending.
V
FB
=?
ms
-
Q
ss
C
o x
where ?
ms
is the metal-semiconductor w ork function difference ( V ), Q
ss
is the fixed
o xide c harge (Cm
-2
).
• Threshold V oltage : V oltage required to form an in v ersion la y er.
V
T
=V
FB
+2?
F
+
v
4?
s
qN
A
?
F
C
o x
where ?
F
is the F ermi p oten tial (V ), ?
s
is the p ermittivit y of the semiconductor, q is
the electron c harge (16e-19C ), N
A
is the substrate doping concen tration (m
-3
).
• Op erating Regions :
– A ccum ulation: V
G
<V
FB
– Depletion: V
FB
<V
G
<V
T
– In v ersion: V
G
>V
T
MOSFET (n-MOSFET)
• Threshold V oltage : Similar to MOS capacitor, adjusted for MOSFET.
V
T
=V
FB
+2?
F
+
v
2?
s
qN
A
(2?
F
+V
SB
)
C
o x
where V
SB
is the source-b o dy v oltage (V ).
• Op erating Regions :
– Cut-off : V
GS
<V
T
, I
D
˜ 0 .
– Linear/T rio de : V
GS
>V
T
, V
DS
<V
GS
-V
T
.
I
D
=µ
n
C
o x
W
L
[
(V
GS
-V
T
)V
DS
-
V
2
DS
2
]
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Page 2


MOSFET & MOS Capacitor F orm ula Sheet for
GA TE (Electronics Devices)
MOS Capacitor
• Capacitance of MOS Structure : Oxide capacitance p er unit area.
C
o x
=
?
o x
t
o x
(Units: Fm
-2
)
where ?
o x
is the p ermittivit y of the o xide (Fm
-1
), t
o x
is the o xide thic kness (m ).
• Flat-Band V oltage : V oltage at whic h there is no band b ending.
V
FB
=?
ms
-
Q
ss
C
o x
where ?
ms
is the metal-semiconductor w ork function difference ( V ), Q
ss
is the fixed
o xide c harge (Cm
-2
).
• Threshold V oltage : V oltage required to form an in v ersion la y er.
V
T
=V
FB
+2?
F
+
v
4?
s
qN
A
?
F
C
o x
where ?
F
is the F ermi p oten tial (V ), ?
s
is the p ermittivit y of the semiconductor, q is
the electron c harge (16e-19C ), N
A
is the substrate doping concen tration (m
-3
).
• Op erating Regions :
– A ccum ulation: V
G
<V
FB
– Depletion: V
FB
<V
G
<V
T
– In v ersion: V
G
>V
T
MOSFET (n-MOSFET)
• Threshold V oltage : Similar to MOS capacitor, adjusted for MOSFET.
V
T
=V
FB
+2?
F
+
v
2?
s
qN
A
(2?
F
+V
SB
)
C
o x
where V
SB
is the source-b o dy v oltage (V ).
• Op erating Regions :
– Cut-off : V
GS
<V
T
, I
D
˜ 0 .
– Linear/T rio de : V
GS
>V
T
, V
DS
<V
GS
-V
T
.
I
D
=µ
n
C
o x
W
L
[
(V
GS
-V
T
)V
DS
-
V
2
DS
2
]
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– Saturation : V
GS
>V
T
, V
DS
=V
GS
-V
T
.
I
D
=
1
2
µ
n
C
o x
W
L
(V
GS
-V
T
)
2
where µ
n
is electron mobilit y (m
2
V
-1
s
-1
), W/L is the width-to-length ratio of the
c hannel, V
GS
is gate-source v oltage, V
DS
is drain-source v oltage.
• Bo dy Effect : Increase in threshold v oltage due to source-b o dy bias.
?V
T
=?
(
v
2?
F
+V
SB
-
v
2?
F
)
where ? =
v
2?sqN
A
C o x
is the b o dy effect co e?icien t.
• Channel Length Mo dulation : Effect in saturation region.
I
D
=
1
2
µ
n
C
o x
W
L
(V
GS
-V
T
)
2
(1+?V
DS
)
where ? is the c hannel length mo dulation parameter (V
-1
).
• Small-Signal T ransconductance : In saturation region.
g
m
=µ
n
C
o x
W
L
(V
GS
-V
T
)
Key P arameters
• P ermittivit y of silicon dio xide: ?
o x
= 3.9?
0
, where ?
0
= 8.854×10
-12
Fm
-1
.
• P ermittivit y of silicon: ?
s
= 11.7?
0
.
• Electron c harge: q = 1.6×10
-19
C .
• F ermi p oten tial: ?
F
=
kT
q
ln
(
N
A
n
i
)
, where n
i
˜ 1× 10
10
cm
-3
for silicon at ro om
temp erature.
Key N otes
• Use SI units for GA TE calculations.
• F or p-MOSFET, replace µ
n
with µ
p
, and adjust v oltage p olarities (e.g., V
GS
<-V
T
for conduction).
• Ensure consisten t units for W , L , and t
o x
(t ypically µm or m ).
• F or n umerical problems, c hec k for b o dy effect and c hannel length mo dulation if sp ec-
ified.
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