304
Compact Models for Integrated Circuit Design
8.5.3.2 Variance of the Global Process Variability- Sensitive
Compact Model Parameters
For Monte Carlo (MC) statistical modeling, M global is described by normal distribution N M M global
0 , σ
(
) , around its mean (TT) value M 0 . The global variance σM global is obtained from the statistical distribution of ET data for each
M measured from multiple die, wafers, and lots over a period of time [1,9].
However, for the next-generation technology, the ET data are scarcely available for statistical analysis. In this case, the numerical simulation data can
be used for the computation of σM global and generate rev0 compact model for
circuit analysis of the target technology [51–55]. Typically, n M global
σ
is used to
model global process variability with 3 ≤ n ≤ 6.
8.5.4 Formulation of Compact Model for Process
Variability-Aware Circuit Design
As described in Section 8.4.1, the TT model for circuit CAD consists of a set of
parameters {M 0 } that models the device and circuit performance of centerline
process of the target technology node. The set M 0
{ } represents the nominal device specifications of the target technology. The local and global components of the variability-sensitive compact model parameter are included
in the nominal set M 0
{ } to generate compact variability model library for
circuit CAD. The final model library includes the nominal parameters with
the components of process variability. Thus, a process variability-sensitive
model parameter M including both local and global process variability components is given by
M M
M
n M
mismatch
g lobal
=
+
+
0
σ
σ
(8.21)
Equation 8.21 is used to build the compact model of the target technology
for process variability-aware circuit analysis. Thus, for the compact model
parameter V TH , Equation 8.21 yields
V
V
V
nV
TH
TH
TH mismatch
T H global
=
+
+
0
0
0
σ
σ
,
,
(8.22)
Equation 8.22 is used to build statistical corner model for realistic analysis
of process variability in scaled MOSFETs. Table 8.3 shows FF and SS corner
limit of a set of process variability-sensitive model parameters obtained by
analytical approach discussed in Section 8.5.2.2.
For MC statistical compact modeling, the probability distribution function
(PDF) of the mismatch component of M for HSPICE (see Section 1.2.2.1) [56]
circuit CAD is obtained using 1-σ variation between paired transistors
PDF M
M
a gauss
mismatch
mismatch
σ
σ
(
)= (
)
( , , )
0 1 1
(8.23)
Compact Models for Integrated Circuit Design
8.5.3.2 Variance of the Global Process Variability- Sensitive
Compact Model Parameters
For Monte Carlo (MC) statistical modeling, M global is described by normal distribution N M M global
0 , σ
(
) , around its mean (TT) value M 0 . The global variance σM global is obtained from the statistical distribution of ET data for each
M measured from multiple die, wafers, and lots over a period of time [1,9].
However, for the next-generation technology, the ET data are scarcely available for statistical analysis. In this case, the numerical simulation data can
be used for the computation of σM global and generate rev0 compact model for
circuit analysis of the target technology [51–55]. Typically, n M global
σ
is used to
model global process variability with 3 ≤ n ≤ 6.
8.5.4 Formulation of Compact Model for Process
Variability-Aware Circuit Design
As described in Section 8.4.1, the TT model for circuit CAD consists of a set of
parameters {M 0 } that models the device and circuit performance of centerline
process of the target technology node. The set M 0
{ } represents the nominal device specifications of the target technology. The local and global components of the variability-sensitive compact model parameter are included
in the nominal set M 0
{ } to generate compact variability model library for
circuit CAD. The final model library includes the nominal parameters with
the components of process variability. Thus, a process variability-sensitive
model parameter M including both local and global process variability components is given by
M M
M
n M
mismatch
g lobal
=
+
+
0
σ
σ
(8.21)
Equation 8.21 is used to build the compact model of the target technology
for process variability-aware circuit analysis. Thus, for the compact model
parameter V TH , Equation 8.21 yields
V
V
V
nV
TH
TH
TH mismatch
T H global
=
+
+
0
0
0
σ
σ
,
,
(8.22)
Equation 8.22 is used to build statistical corner model for realistic analysis
of process variability in scaled MOSFETs. Table 8.3 shows FF and SS corner
limit of a set of process variability-sensitive model parameters obtained by
analytical approach discussed in Section 8.5.2.2.
For MC statistical compact modeling, the probability distribution function
(PDF) of the mismatch component of M for HSPICE (see Section 1.2.2.1) [56]
circuit CAD is obtained using 1-σ variation between paired transistors
PDF M
M
a gauss
mismatch
mismatch
σ
σ
(
)= (
)
( , , )
0 1 1
(8.23)