196
Compact Models for Integrated Circuit Design
The mobility Equations 5.58 through 5.60 have been derived assuming
strong inversion condition. In the strong inversion regime, the inversion
carrier mobility is a function of gate bias. In the subthreshold region the
accuracy of the mobility is not critical since Q inv varies with V gs and cannot
be modeled accurately. Therefore, in subthreshold regime, the mobility is
usually modeled as a constant concentration dependent mobility.
To ensure the continuity of the mobility model, BSIM mobility model
is modified based on the V gsteff expression to obtain the basic empirical
models as [28]
µ eff
A
C bseff
g steff
t h
O X
B
gsteff
t
U
U U V
V
V T
U V
V
=
+
+
(
)
+
(
)
+
+
0
1
2
2
.
h h
O X
T
(
)
2
(5.61)
or
µ eff
A
g steff
t h
O X
B
gsteff
th
OX
U
U
V
V T
U V
V T
=
+
⋅
+
(
)
+
+
(
)
0
2
1
2
2
+
(
)
1 U V
C bseff
(5.62)
where:
V bseff is the effective value of body bias to set the upper limit of computation
as defined earlier
The BSIM4 model parameter set for the basic mobility model is {U 0 , U A , U B ,
U C } and is extracted from the I ds − V gs characteristics at low V ds with body
bias. Different options of Equation 5.59 have been implemented in BSIM4
model and readers are encouraged to look at the users’ manual to use the
appropriate model and extract the appropriate model parameters for circuit CAD [28]. It can be observed from the earlier defined mobility models that μ eff approaches a constant value of U 0 for V gs < V th as used in the
subthreshold regime.
The expression for V gsteff is obtained by equating the channel charge of
weak and strong inversions at the transition point for model continuity in
the entire range of device operation and can be shown as [28]
V
nv
m V V nv
m nC
q K N
gsteff
kT
gs
th
kT
ox
s
s i
C
=
+
−
(
)
{
}
+
ln
exp *
*
1
2
0
φ
ε
H H
g s
t h
o ff
kT
m V V V
nv
exp
*
− −
(
) − −
(
)
{
}
1
2
(5.63)
It should be pointed out that all of the mobility models given earlier account
for only the influence of the vertical electrical field due to V gs at low lateral
electric field and often referred to as the low-field mobility model. The influence of the lateral electric field due to the applied V ds on device performance is
modeled in drain current by considering the velocity saturation in MOSFET
devices under high lateral electric field.
Compact Models for Integrated Circuit Design
The mobility Equations 5.58 through 5.60 have been derived assuming
strong inversion condition. In the strong inversion regime, the inversion
carrier mobility is a function of gate bias. In the subthreshold region the
accuracy of the mobility is not critical since Q inv varies with V gs and cannot
be modeled accurately. Therefore, in subthreshold regime, the mobility is
usually modeled as a constant concentration dependent mobility.
To ensure the continuity of the mobility model, BSIM mobility model
is modified based on the V gsteff expression to obtain the basic empirical
models as [28]
µ eff
A
C bseff
g steff
t h
O X
B
gsteff
t
U
U U V
V
V T
U V
V
=
+
+
(
)
+
(
)
+
+
0
1
2
2
.
h h
O X
T
(
)
2
(5.61)
or
µ eff
A
g steff
t h
O X
B
gsteff
th
OX
U
U
V
V T
U V
V T
=
+
⋅
+
(
)
+
+
(
)
0
2
1
2
2
+
(
)
1 U V
C bseff
(5.62)
where:
V bseff is the effective value of body bias to set the upper limit of computation
as defined earlier
The BSIM4 model parameter set for the basic mobility model is {U 0 , U A , U B ,
U C } and is extracted from the I ds − V gs characteristics at low V ds with body
bias. Different options of Equation 5.59 have been implemented in BSIM4
model and readers are encouraged to look at the users’ manual to use the
appropriate model and extract the appropriate model parameters for circuit CAD [28]. It can be observed from the earlier defined mobility models that μ eff approaches a constant value of U 0 for V gs < V th as used in the
subthreshold regime.
The expression for V gsteff is obtained by equating the channel charge of
weak and strong inversions at the transition point for model continuity in
the entire range of device operation and can be shown as [28]
V
nv
m V V nv
m nC
q K N
gsteff
kT
gs
th
kT
ox
s
s i
C
=
+
−
(
)
{
}
+
ln
exp *
*
1
2
0
φ
ε
H H
g s
t h
o ff
kT
m V V V
nv
exp
*
− −
(
) − −
(
)
{
}
1
2
(5.63)
It should be pointed out that all of the mobility models given earlier account
for only the influence of the vertical electrical field due to V gs at low lateral
electric field and often referred to as the low-field mobility model. The influence of the lateral electric field due to the applied V ds on device performance is
modeled in drain current by considering the velocity saturation in MOSFET
devices under high lateral electric field.