12
Compact Models for Integrated Circuit Design
It has been reported that the symmetric linearization approach is not
particularly sensitive to the details of the velocity saturation model,
which enabled the merger of the best features of the SP and MM11 models to create PSP model. In addition to charge linearization relative to
the source causing violation of the Gummel symmetry test, the singular nature of the popular velocity saturation model [79,94] is a critical
problem. The problem can be solved using different techniques such as
adopting a V ds -dependent critical field [38,62,72]. When combined with
the symmetric linearization method, this technique automatically solves
the singularity issue [85,94]. Some of the specific features of SP include
its unique symmetric linearization method, completely noniterative formulation, nonregional description from accumulation to strong inversion,
inclusion of all relevant short-channel and thin-oxide effects, bias-dependent
effective doping to deal with halo effects, physical description of the overlap regions and of the inner-fringing effects, and the comprehensive and
accurate NQS model based on the spline collocation method [93]. The
latter has been recently extended to include the accumulation region [92]
and the small-geometry effects [95]. Finally, it has been reported [96,97]
that when combined with the general one-flux theory of the nonabsorbing barrier, SP model is capable of reproducing the quasi-ballistic effects
using the one-flux method [98].
The new f s –based PSP model is obtained by merging and developing the
best features of SP (developed at the Pennsylvania State University) and
MM11 (developed at Philips) models. The first version of the compact MOS
model PSP, Level 100, has been released to the public domain in April 2005.
In December 2005, CMC elected PSP as the new industrial standard model
for compact MOSFET modeling [48].
1.2.2.3 Charge-Based Compact MOSFET Modeling
During the late 1980s, the charge-based compact models emerged as a viable alternative to widely used V th -based compact models due the increasing
complexities of V th -based modeling for scaled MOSFET devices and computationally demanding solution techniques for f s -based modeling. In 1987,
Maher and Mead reported a drain current expression in terms of the inversion charge density (Q i ) at the source and the drain ends [99]. Subsequently,
a unified charge control model (UCCM) relating charge densities in terms of
terminal voltages was reported in the early 1990s [100,101]. In 1995, Cunha
et al. derived expressions for the total charges and small signal parameters
as a function of the source and drain channel charge densities [102]. In 2001,
Gummel et al. derived a charge equation and reported a charge-based model,
referred to as USIM [103]. In 2003, He et al. reported an alternative derivation
of charge [104] using gradual channel [26] and charge-sheet [23] approximations and linearization of the bulk and inversion charges with respect to the
Compact Models for Integrated Circuit Design
It has been reported that the symmetric linearization approach is not
particularly sensitive to the details of the velocity saturation model,
which enabled the merger of the best features of the SP and MM11 models to create PSP model. In addition to charge linearization relative to
the source causing violation of the Gummel symmetry test, the singular nature of the popular velocity saturation model [79,94] is a critical
problem. The problem can be solved using different techniques such as
adopting a V ds -dependent critical field [38,62,72]. When combined with
the symmetric linearization method, this technique automatically solves
the singularity issue [85,94]. Some of the specific features of SP include
its unique symmetric linearization method, completely noniterative formulation, nonregional description from accumulation to strong inversion,
inclusion of all relevant short-channel and thin-oxide effects, bias-dependent
effective doping to deal with halo effects, physical description of the overlap regions and of the inner-fringing effects, and the comprehensive and
accurate NQS model based on the spline collocation method [93]. The
latter has been recently extended to include the accumulation region [92]
and the small-geometry effects [95]. Finally, it has been reported [96,97]
that when combined with the general one-flux theory of the nonabsorbing barrier, SP model is capable of reproducing the quasi-ballistic effects
using the one-flux method [98].
The new f s –based PSP model is obtained by merging and developing the
best features of SP (developed at the Pennsylvania State University) and
MM11 (developed at Philips) models. The first version of the compact MOS
model PSP, Level 100, has been released to the public domain in April 2005.
In December 2005, CMC elected PSP as the new industrial standard model
for compact MOSFET modeling [48].
1.2.2.3 Charge-Based Compact MOSFET Modeling
During the late 1980s, the charge-based compact models emerged as a viable alternative to widely used V th -based compact models due the increasing
complexities of V th -based modeling for scaled MOSFET devices and computationally demanding solution techniques for f s -based modeling. In 1987,
Maher and Mead reported a drain current expression in terms of the inversion charge density (Q i ) at the source and the drain ends [99]. Subsequently,
a unified charge control model (UCCM) relating charge densities in terms of
terminal voltages was reported in the early 1990s [100,101]. In 1995, Cunha
et al. derived expressions for the total charges and small signal parameters
as a function of the source and drain channel charge densities [102]. In 2001,
Gummel et al. derived a charge equation and reported a charge-based model,
referred to as USIM [103]. In 2003, He et al. reported an alternative derivation
of charge [104] using gradual channel [26] and charge-sheet [23] approximations and linearization of the bulk and inversion charges with respect to the