189
Compact Models for Small Geometry MOSFETs
where we have used the effective channel length (L eff ) and effective channel
width (W eff ) in Equation 5.34. Equation 5.34 shows the overall V th expression
for MOSFET devices to accurately model geometry and substrate doping
dependence on device performance. In real CAD implementation the following modifications are made [28].
1. Electrical oxide thickness, TOXE dependence is introduced in model
parameters K1 and K2 to improve scalability of V th model over TOXE as
K
K
K
K
ox
ox
1
2
1
2
=
=
.
.
TOXE
TOXM
and
TOXE
TOXM
(5.35)
where:
TOXM is the model parameter required to fit device characteristics
2. In order to set a lower bound for the body bias during circuit simulations to prevent occurrence of unreasonable values during iterations
in CAD environment, V bs is implemented as [28]
V
V
V V
V V
V
bseff
b c
b s
b c
b s
b c
b c
=
+ ⋅
−
−
(
)+
−
−
(
)− ⋅

 

 
1
2
4
1
1
2
1
δ
δ
δ
(5.36)
where δ 1  = 1 mV and V bc is the maximum allowable V bs and found
from dV dV
th
bs = 0 to be
V
K
K
bc
s
=
−






0 9
1
4 2
2
2
. φ
(5.37)
For positive V bs , there is need to set an upper bound for the body bias
as [28]
V
V
V
bseff
s
s
b seff
s
bseff
=
− ⋅
− ′ −
(
) +
− ′ −
(
) −
0 95
1
2
0 95
0 95
1
1
2
.
.
.
φ
φ
δ
φ
δ
4 4 0 95
1
δ
φ
⋅

 

 
.
s
(5.38)
Effective Channel Length and Width: The effective channel length (L eff ) and
width (W eff ) used in Equation 5.34 are given by
L
L
L
eff
d rawn
=
−2∆
(5.39)
W
W
W
eff
d rawn
=
−2∆
(5.40)
where ΔL and ΔW are model parameters that include S/D overlap under
the gate and poly overlap along the width direction, respectively, and are
given by