434
Compact Models for Integrated Circuit Design
Let us define sigvtp_svtp as the mismatch in V th of svt PMOS devices, cvtp is
the mismatch coefficient, and 1/ WL is the geometrical factor (geo_fac); then
the V th mismatch is modeled by
sigvtp svtp cvtp svtp geo fac mismatchflag
_
_
_
= (
)⋅(
)⋅
(12.4)
where
cvtp_svtp = ‘avtp/1.414214’;
lef = ‘l-5.6E-09’; wef = ‘w/n_fingers+0E-09’; and geo_fac = ‘1/ sqrt(multi*n_
fingers*lef*wef)’ with
lef and wef are used to define the effective channel length and width (w),
respectively, n_fingers represents the number of gate geometries in
the layout of a transistor, and multi is a number.
Again, the mismatchflag is used to turn on and off the model in circuit analysis.
In corner simulation, only geometry dependent fixed mismatch can be
modeled by using a flag to appropriately call the model if desired without
MC simulation use
‘
_
_
_
sigvtp vtp cvtp svtp geo fac globalsigmavtflag
= (
)⋅(
)⋅
(12.5)
For MC statistical model the mismatch is modeled by one-sigma variation of
the parameter in space
‘
_
_
_
, ,
sigvtp svtp cvtp svtp geo fac agaus
mismatchfl
= (
)⋅(
)⋅
(
)⋅
0 1 1
a ag (12.6)
where the mismatch parameter, avtp, for p-channel devices is extracted from
the sigma(delta_vt) versus 1/ WL plots. The expressions given in Equations
12.4 through 12.6 are used in generating compact model cards in the examples shown at the end of this chapter.
12.2.4.3 Generate Model Card
Finally, use the above formulations to develop a compact model card for circuit
CAD. In reality, the corner files, header files, and other files can be kept separate in the model library and a simple script file can be used to call the relevant
models for circuit analysis. In this chapter all the relevant files are integrated
into a single comprehensive compact model card. To illustrate the basic procedure, a compact MOSFET model card ex1mod0p1.l and an SRAM model card
sram127hp.l are presented at the end of this chapter. Note that due to continuous
updates of compact model formulations and CAD environment, appropriate
changes in the parameters of the model library may be needed to use the model
for circuit CAD. Again, the model cards represent BSIM4 model for HSPICE circuit CAD tool. The model parameters are defined in BSIM4 user’s manual [2–4].
The model card ex1mod0p1.l is a statistical model that can be used for corner
analysis of a VLSI circuit as well as MC statistical analysis of the circuit by
Compact Models for Integrated Circuit Design
Let us define sigvtp_svtp as the mismatch in V th of svt PMOS devices, cvtp is
the mismatch coefficient, and 1/ WL is the geometrical factor (geo_fac); then
the V th mismatch is modeled by
sigvtp svtp cvtp svtp geo fac mismatchflag
_
_
_
= (
)⋅(
)⋅
(12.4)
where
cvtp_svtp = ‘avtp/1.414214’;
lef = ‘l-5.6E-09’; wef = ‘w/n_fingers+0E-09’; and geo_fac = ‘1/ sqrt(multi*n_
fingers*lef*wef)’ with
lef and wef are used to define the effective channel length and width (w),
respectively, n_fingers represents the number of gate geometries in
the layout of a transistor, and multi is a number.
Again, the mismatchflag is used to turn on and off the model in circuit analysis.
In corner simulation, only geometry dependent fixed mismatch can be
modeled by using a flag to appropriately call the model if desired without
MC simulation use
‘
_
_
_
sigvtp vtp cvtp svtp geo fac globalsigmavtflag
= (
)⋅(
)⋅
(12.5)
For MC statistical model the mismatch is modeled by one-sigma variation of
the parameter in space
‘
_
_
_
, ,
sigvtp svtp cvtp svtp geo fac agaus
mismatchfl
= (
)⋅(
)⋅
(
)⋅
0 1 1
a ag (12.6)
where the mismatch parameter, avtp, for p-channel devices is extracted from
the sigma(delta_vt) versus 1/ WL plots. The expressions given in Equations
12.4 through 12.6 are used in generating compact model cards in the examples shown at the end of this chapter.
12.2.4.3 Generate Model Card
Finally, use the above formulations to develop a compact model card for circuit
CAD. In reality, the corner files, header files, and other files can be kept separate in the model library and a simple script file can be used to call the relevant
models for circuit analysis. In this chapter all the relevant files are integrated
into a single comprehensive compact model card. To illustrate the basic procedure, a compact MOSFET model card ex1mod0p1.l and an SRAM model card
sram127hp.l are presented at the end of this chapter. Note that due to continuous
updates of compact model formulations and CAD environment, appropriate
changes in the parameters of the model library may be needed to use the model
for circuit CAD. Again, the model cards represent BSIM4 model for HSPICE circuit CAD tool. The model parameters are defined in BSIM4 user’s manual [2–4].
The model card ex1mod0p1.l is a statistical model that can be used for corner
analysis of a VLSI circuit as well as MC statistical analysis of the circuit by