13
Introduction to Compact Models
surface potential at a fixed gate bias. Since there is no Q i in the accumulation
region, different approaches used include an equation for the accumulation
charge similar to that for Q i or accumulation surface potential.
In charge-based models, an implicit function is evaluated to find the
charge density for each set of biasing voltages in SPICE iterations similar to
f s calculation. Note that the current is an exponential function of f s whereas
a linear or quadratic function of Q i . Therefore, the accuracy of calculation
of the Q i is not as high as that of f s calculation. Some of the widely referred
charge-based compact MOSFET models include ACM [102], EKV [16], and
BSIM6 [4] as described below.
In 1995, Cunha et al. reported a charge-based compact model, called
the advanced compact MOSFET or ACM model [102]. The basic formulation of the ACM model is based on the charge-sheet model [23], inversion
charge versus current relationship [99], UCCM [100,101], and symmetrical
MOSFET model [105]. Explicit expressions for the current, charges, transconductances, and the 16 capacitive coefficients are shown to be valid in
the weak, moderate, and strong inversion regions. In 1997, the ACM model
was implemented in a circuit simulator [106] and emerged out of the necessity of modeling MOS capacitor for analog design in digital CMOS technology. In order to model the weak nonlinearities of an MOS capacitor in the
accumulation and moderate as well as strong inversion regimes, Behr et al.
reported an improved capacitive model of the MOSFET gate in 1992 [107]. A
link between the charge model by Cunha et al. [102] and the current-based
model of Enz et al. [16] was established by Galup-Montoro et al. [105] and
Cunha et al. [108]. The models for DC, AC, and NQS behaviors were developed [105,106]. In 1999, UCCM [100,101] was revisited [109,110] to enhance the
basic ACM model [102].
The ACM model has been reported to have a hierarchical structure facilitating the inclusion of different physical phenomena into the model [111].
Because of its very simple expression for the derivative of the channel
charge density, ACM has been reported to offer simple explicit expressions for all intrinsic capacitive coefficients even when SCEs are taken into
account [111]. The parameters of the ACM can be easily extracted [108,110].
Recently, ACM has been reported to include unified 1/f noise and mismatch models [112,113].
In 1995, Enz et al. reported an analytical compact MOSFET model, referred
to as the EKV model, by referencing all the terminal voltages to the substrate [16]. The primary objective of the EKV model was low-power analog IC
CAD using an analytical model that is valid in all modes of device operation
with accurate modeling of weak inversion regime [114,115]. The model uses
the linearization of Q i with respect to the channel voltage to derive I ds based
on the continuous g m /I ds characteristics. In 2003, a rigorous derivation of the
charge-based EKV model along with the detailed technique of Q i linearization was reported using the existing charge-based models [99,103,116,117].
Introduction to Compact Models
surface potential at a fixed gate bias. Since there is no Q i in the accumulation
region, different approaches used include an equation for the accumulation
charge similar to that for Q i or accumulation surface potential.
In charge-based models, an implicit function is evaluated to find the
charge density for each set of biasing voltages in SPICE iterations similar to
f s calculation. Note that the current is an exponential function of f s whereas
a linear or quadratic function of Q i . Therefore, the accuracy of calculation
of the Q i is not as high as that of f s calculation. Some of the widely referred
charge-based compact MOSFET models include ACM [102], EKV [16], and
BSIM6 [4] as described below.
In 1995, Cunha et al. reported a charge-based compact model, called
the advanced compact MOSFET or ACM model [102]. The basic formulation of the ACM model is based on the charge-sheet model [23], inversion
charge versus current relationship [99], UCCM [100,101], and symmetrical
MOSFET model [105]. Explicit expressions for the current, charges, transconductances, and the 16 capacitive coefficients are shown to be valid in
the weak, moderate, and strong inversion regions. In 1997, the ACM model
was implemented in a circuit simulator [106] and emerged out of the necessity of modeling MOS capacitor for analog design in digital CMOS technology. In order to model the weak nonlinearities of an MOS capacitor in the
accumulation and moderate as well as strong inversion regimes, Behr et al.
reported an improved capacitive model of the MOSFET gate in 1992 [107]. A
link between the charge model by Cunha et al. [102] and the current-based
model of Enz et al. [16] was established by Galup-Montoro et al. [105] and
Cunha et al. [108]. The models for DC, AC, and NQS behaviors were developed [105,106]. In 1999, UCCM [100,101] was revisited [109,110] to enhance the
basic ACM model [102].
The ACM model has been reported to have a hierarchical structure facilitating the inclusion of different physical phenomena into the model [111].
Because of its very simple expression for the derivative of the channel
charge density, ACM has been reported to offer simple explicit expressions for all intrinsic capacitive coefficients even when SCEs are taken into
account [111]. The parameters of the ACM can be easily extracted [108,110].
Recently, ACM has been reported to include unified 1/f noise and mismatch models [112,113].
In 1995, Enz et al. reported an analytical compact MOSFET model, referred
to as the EKV model, by referencing all the terminal voltages to the substrate [16]. The primary objective of the EKV model was low-power analog IC
CAD using an analytical model that is valid in all modes of device operation
with accurate modeling of weak inversion regime [114,115]. The model uses
the linearization of Q i with respect to the channel voltage to derive I ds based
on the continuous g m /I ds characteristics. In 2003, a rigorous derivation of the
charge-based EKV model along with the detailed technique of Q i linearization was reported using the existing charge-based models [99,103,116,117].