197
Compact Models for Small Geometry MOSFETs
5.3.2 Subthreshold Region Drain Current Model
The subthreshold current model is the same as derived for the long channel
devices in Chapter 4 with minor change for improving the accuracy of data
fitting and is given by [27,28]
I
I e
e
V
V
ds
s
V V V
n v
V v
gs
th
gs
th
OFF
k T
ds kT
=
−
<
− −
(
)
−(
)
0
1
;
(5.64)
where V OFF is the model parameter to account for the difference between
V th in the strong inversion and the subthreshold region and I s0 is given by
(see Equation 4.118)
I
W L C v
s
s
eff
eff
d kT
0
2
= (
)
µ
(5.65)
In Chapter 4 (Equation 4.127), we have shown that the subthreshold slope is
given by
S
nv kT
= 2 3
.
(5.66)
where the ideality factor is given by
n
C
C
C
C
d
ox
IT
ox
= +
+
1
(5.67)
In BSIM [27,28] compact models, a parameter called NFACTOR is introduced
to ensure accurate calculation of C d and is extracted from the measured data.
Again, in short channel devices the surface potential in the channel is determined by both V gs and V ds through the coupling of C ox and C dsc as shown in
Figure 5.10. The coupling capacitance C dsc (L) is an exponential function of L.
Therefore, in BSIM4 the parameter n is modeled as
n
NFACTOR
C
C
C
C
C
C
V C
V
d
ox
IT
ox
DSC
D SCD ds
D SCB bseff
= +
+
+
+
+
(
)
1
0 5
.
.
. /co osh(
. / )
DVT L l
C
eff t
ox
1
1
−
(
)
(5.68)
where:
C DSC , C DSCD , and C DSCB are the model parameters that describe the coupling
between the channel and the drain
C DSCD and C DSCB represent the drain bias and body bias dependence of
channel/drain coupling, respectively
5.3.3 Linear Region Drain Current Model
The high lateral electric field along the channel due to the applied V ds significantly effects device performance. As we observe from Figure 5.11 that
for electrons in silicon, the drift velocity v d saturates near E ~ 10 4 V cm −1 .
Compact Models for Small Geometry MOSFETs
5.3.2 Subthreshold Region Drain Current Model
The subthreshold current model is the same as derived for the long channel
devices in Chapter 4 with minor change for improving the accuracy of data
fitting and is given by [27,28]
I
I e
e
V
V
ds
s
V V V
n v
V v
gs
th
gs
th
OFF
k T
ds kT
=
−
<
− −
(
)
−(
)
0
1
;
(5.64)
where V OFF is the model parameter to account for the difference between
V th in the strong inversion and the subthreshold region and I s0 is given by
(see Equation 4.118)
I
W L C v
s
s
eff
eff
d kT
0
2
= (
)
µ
(5.65)
In Chapter 4 (Equation 4.127), we have shown that the subthreshold slope is
given by
S
nv kT
= 2 3
.
(5.66)
where the ideality factor is given by
n
C
C
C
C
d
ox
IT
ox
= +
+
1
(5.67)
In BSIM [27,28] compact models, a parameter called NFACTOR is introduced
to ensure accurate calculation of C d and is extracted from the measured data.
Again, in short channel devices the surface potential in the channel is determined by both V gs and V ds through the coupling of C ox and C dsc as shown in
Figure 5.10. The coupling capacitance C dsc (L) is an exponential function of L.
Therefore, in BSIM4 the parameter n is modeled as
n
NFACTOR
C
C
C
C
C
C
V C
V
d
ox
IT
ox
DSC
D SCD ds
D SCB bseff
= +
+
+
+
+
(
)
1
0 5
.
.
. /co osh(
. / )
DVT L l
C
eff t
ox
1
1
−
(
)
(5.68)
where:
C DSC , C DSCD , and C DSCB are the model parameters that describe the coupling
between the channel and the drain
C DSCD and C DSCB represent the drain bias and body bias dependence of
channel/drain coupling, respectively
5.3.3 Linear Region Drain Current Model
The high lateral electric field along the channel due to the applied V ds significantly effects device performance. As we observe from Figure 5.11 that
for electrons in silicon, the drift velocity v d saturates near E ~ 10 4 V cm −1 .