Multiple polynomial regression for modeling a MOSFET in saturation to validate the Early voltage

Early voltage is indeed a very simple form of calculation for mathematical ease. But Channel Length Modulation is not actually linear. The non-linear Channel Length Modulation is in fact tells nothing strict about the Early voltage conception of MOSFET. For very short channel devices or thin oxide insulation, there arises lots of parameters which must be considered. The simulators uses lot more difficult equations to calculate the quantities. This paper deals with HSPICE, that uses hundreds of parameters to return the real world situation as it considers lots of non-ideal effects like- Non-uniform doping, Short channel DIBL effects, Narrow-width effect, Gate to substrate leakage, Bulk charge effect, Velocity saturation of intrinsic and extrinsic case, Drain induced threshold shift by pocket implant, Velocity overshoot, Flicker noise, Temperature dependence and a lot more complexities [1]. This paper describes the numerical approach to show whether the existing Early voltage approximation is valid for BSIM3 or BSIM4 MOSFET Model equations of HSPICE as they almost predict the real world situation. The most significant contribution of this paper is to propose a multiple polynomial regression method that can best approximate the Early voltage as well as the MOSFET characteristics in saturation.