11
Introduction to Compact Models
modeling [72] of advanced ICs using analytical solution of surface potential.
The implicit f s equation is modified to include polysilicon depletion effect by
including a potential across the depletion layer due to polysilicon depletion
and an empirical parameter to account for SCEs. In order to obtain efficient
expressions for model outputs, several approximations were made, mainly
based on the linearization of the inversion charge as a function of f s . In
MM11, a linearization is performed around the average of source and drain
potentials given by φ
φ
φ
s
s
sL
=
+
(
)
1 2 0
[72]. This linearization technique was
shown to yield simpler and accurate expressions for f s keeping model symmetry with respect to source-drain interchange. This linearization approach
offers an easy implementation of well-known physical phenomena such as
thermal noise [73], induced gate noise [73], and gate leakage [74] in f s -based
models.
In MM11, an accurate description of mobility effects and conductance
effects has been added with a special emphasis on distortion modeling. For
an accurate description of distortion, MM11 model is shown to accurately
describe the drain current and its higher-order derivatives (up to at least
the 3rd order). Thus, MM11 models reported contain improved expressions
for mobility reduction [75], velocity saturation, and various conductance
effects [76]. The distortion modeling of MM11 has been rigorously tested
on various MOSFET technologies [77], and is shown to offer an accurate
description of modern CMOS technologies. MM11 model is shown to preserve the source-drain interchange symmetry in model expressions [75,78]
and thus eliminates the discontinuities in the high-order derivatives of
channel current at V ds = 0 [79]. MM11 incorporates an accurate description
of all-important physical effects, such as polydepletion [80], the effect of
pocket implants [81], gate tunneling current [66,80], bias-dependent overlap
capacitances [80,82], GIDL, and noise [68,83] and therefore offers an accurate
description of advanced MOSFETs in circuit operation.
In the early 1990s, the development of f s –based model, called SP model,
started at the Pennsylvania State University by the research group led by
Gildenblat. The modeling algorithm has been developed over the years
[84–90]. In SP, SCE is modeled using the reported [91] bias and geometrydependent lateral gradient factor while the geometry-dependent technique
was used in HiSIM [68]. To overcome the inherent complexities of f s -based
compact model, especially the expressions for the intrinsic charges [38,92,93],
various approximations were developed based, primarily, on the linearization of the inversion charge as a function of f s . It is observed that this linearization technique [79] is a critical step to preserving the Gummel symmetry
test and to avoid difficulties in the simulation of passive mixers and related
circuits [94]. The symmetric linearization method developed in SP [85,87,93]
preserves the Gummel symmetry and produces expressions for both the
drain current and the terminal charges that are as simple as those in V th -
based or Q i -based models and are numerically indistinguishable from the
original charge-sheet model equations [85,94].
Introduction to Compact Models
modeling [72] of advanced ICs using analytical solution of surface potential.
The implicit f s equation is modified to include polysilicon depletion effect by
including a potential across the depletion layer due to polysilicon depletion
and an empirical parameter to account for SCEs. In order to obtain efficient
expressions for model outputs, several approximations were made, mainly
based on the linearization of the inversion charge as a function of f s . In
MM11, a linearization is performed around the average of source and drain
potentials given by φ
φ
φ
s
s
sL
=
+
(
)
1 2 0
[72]. This linearization technique was
shown to yield simpler and accurate expressions for f s keeping model symmetry with respect to source-drain interchange. This linearization approach
offers an easy implementation of well-known physical phenomena such as
thermal noise [73], induced gate noise [73], and gate leakage [74] in f s -based
models.
In MM11, an accurate description of mobility effects and conductance
effects has been added with a special emphasis on distortion modeling. For
an accurate description of distortion, MM11 model is shown to accurately
describe the drain current and its higher-order derivatives (up to at least
the 3rd order). Thus, MM11 models reported contain improved expressions
for mobility reduction [75], velocity saturation, and various conductance
effects [76]. The distortion modeling of MM11 has been rigorously tested
on various MOSFET technologies [77], and is shown to offer an accurate
description of modern CMOS technologies. MM11 model is shown to preserve the source-drain interchange symmetry in model expressions [75,78]
and thus eliminates the discontinuities in the high-order derivatives of
channel current at V ds = 0 [79]. MM11 incorporates an accurate description
of all-important physical effects, such as polydepletion [80], the effect of
pocket implants [81], gate tunneling current [66,80], bias-dependent overlap
capacitances [80,82], GIDL, and noise [68,83] and therefore offers an accurate
description of advanced MOSFETs in circuit operation.
In the early 1990s, the development of f s –based model, called SP model,
started at the Pennsylvania State University by the research group led by
Gildenblat. The modeling algorithm has been developed over the years
[84–90]. In SP, SCE is modeled using the reported [91] bias and geometrydependent lateral gradient factor while the geometry-dependent technique
was used in HiSIM [68]. To overcome the inherent complexities of f s -based
compact model, especially the expressions for the intrinsic charges [38,92,93],
various approximations were developed based, primarily, on the linearization of the inversion charge as a function of f s . It is observed that this linearization technique [79] is a critical step to preserving the Gummel symmetry
test and to avoid difficulties in the simulation of passive mixers and related
circuits [94]. The symmetric linearization method developed in SP [85,87,93]
preserves the Gummel symmetry and produces expressions for both the
drain current and the terminal charges that are as simple as those in V th -
based or Q i -based models and are numerically indistinguishable from the
original charge-sheet model equations [85,94].