201
Compact Models for Small Geometry MOSFETs
v(y) = v sat at E y = E c , in Equation 5.71, we get the saturation region (V ds ≥ V dsat )
drain current as
I
W C V V A V
v
ds
eff ox
g s
t h
b ulk dsat
sat
=
−
−
(
)
(5.76)
Using the expression for v sat from Equation 5.70, we get from Equation
5.76 an alternate expression for drain current in the saturation region of
MOSFETs as
I
W
C V V A V
E
ds
eff eff ox
gs
th
bulk dsat
c
=
−
−
(
)
1
2
µ
(5.77)
Again, Equations 5.76 and 5.77 are valid when R ds = 0 and must be modified
for R ds > 0.
In order to derive the expression for saturation drain voltage V dsat , we recognize that I ds given by Equations 5.74 and 5.77 must be continuous at V ds = V dsat ;
therefore, equating Equation 5.74 to Equation 5.77, we get
W
L
V L E
C V V
A V
eff
eff
d sat
eff c
eff ox
g s
t h
b ulk dsat
1
1
2
+ (
)
−
−
µ
=
−
−
(
)
+
−
1
2
2
W
C V V A V E
E L
V
V
eff eff ox
gs
th
bulk dsat
c
c eff
dsat
gs
µ
or
V V
A V
V
V V A V
th
bulk dsat
dsat
gs
th
bulk dsat
−
=
−
−
(
)
1
2
(5.78)
After simplification of Equation 5.78, we can show
V
E L V V
A E L
V V
dsat
c eff
gs
th
bulk c eff
gs
th
=
−
(
)
+
−
(
)
(5.79)
For R ds > 0, V dsat is higher than that given by Equation 5.79 and can be calculated from Equations 5.75 and 5.77 with two model parameters, A1 and A2, to
account for the nonsaturating effect of I–V characteristics [28,41].
The I dsat model described in Equations 5.76 and 5.77 must be corrected for
output resistance, R out , due to (1) CLM, (2) DIBL, and (3) substrate current–
induced body effect (SCBE).
5.3.5 Bulk-Charge Effect
When V ds is large and/or when the channel length is long, the depletion
region thickness of the channel is not uniform along the channel length.
This will cause V th to vary along the channel. This effect is called the
Compact Models for Small Geometry MOSFETs
v(y) = v sat at E y = E c , in Equation 5.71, we get the saturation region (V ds ≥ V dsat )
drain current as
I
W C V V A V
v
ds
eff ox
g s
t h
b ulk dsat
sat
=
−
−
(
)
(5.76)
Using the expression for v sat from Equation 5.70, we get from Equation
5.76 an alternate expression for drain current in the saturation region of
MOSFETs as
I
W
C V V A V
E
ds
eff eff ox
gs
th
bulk dsat
c
=
−
−
(
)
1
2
µ
(5.77)
Again, Equations 5.76 and 5.77 are valid when R ds = 0 and must be modified
for R ds > 0.
In order to derive the expression for saturation drain voltage V dsat , we recognize that I ds given by Equations 5.74 and 5.77 must be continuous at V ds = V dsat ;
therefore, equating Equation 5.74 to Equation 5.77, we get
W
L
V L E
C V V
A V
eff
eff
d sat
eff c
eff ox
g s
t h
b ulk dsat
1
1
2
+ (
)
−
−
µ
=
−
−
(
)
+
−
1
2
2
W
C V V A V E
E L
V
V
eff eff ox
gs
th
bulk dsat
c
c eff
dsat
gs
µ
or
V V
A V
V
V V A V
th
bulk dsat
dsat
gs
th
bulk dsat
−
=
−
−
(
)
1
2
(5.78)
After simplification of Equation 5.78, we can show
V
E L V V
A E L
V V
dsat
c eff
gs
th
bulk c eff
gs
th
=
−
(
)
+
−
(
)
(5.79)
For R ds > 0, V dsat is higher than that given by Equation 5.79 and can be calculated from Equations 5.75 and 5.77 with two model parameters, A1 and A2, to
account for the nonsaturating effect of I–V characteristics [28,41].
The I dsat model described in Equations 5.76 and 5.77 must be corrected for
output resistance, R out , due to (1) CLM, (2) DIBL, and (3) substrate current–
induced body effect (SCBE).
5.3.5 Bulk-Charge Effect
When V ds is large and/or when the channel length is long, the depletion
region thickness of the channel is not uniform along the channel length.
This will cause V th to vary along the channel. This effect is called the