ABSTRACT
The first model for MOS transistors that was used in SPICE2 was the model that was proposed by Shichman and Hodges [1]. The authors of this model used the equations that were previously developed by Wallmark and Johnson [2] and created a simple model to represent a metal gated NMOS and PMOS device. They neglected the subthreshold conduction completely, but did take into account the body effect and channel length modulation. These authors were more concerned about the simulation of switching circuits and therefore were able to neglect some of the more advanced effects in MOSFET device but still get simulation results that were very close to measurement results. This is the model that is referred to as MOSFET Level 1 Model in most circuit simulators such as HSPICE, Spectre, and so forth. The model equations for the Level 1 Model as implemented in most simulators can be summarized as below:
IDS = µ0Cox (
W
L
)[ (VGS − Vth)VDS −
] if VGS > Vth in linear region (19.1)
IDS = µ0Cox (
W
2L
) (VGS − Vth)2 if VGS > Vth in saturation region (19.2)
IDS = 0 if VGS < Vth (19.3)
And the threshold voltage is modeled using the familiar form below, in which ϕ is the surface potential and γ is the body factor.
