A Piecewise Approximation for Short-Channel "Extrinsic" MOSFET Drain Current Dependence on Drain-to-Source Bias Including Linear Triode, Linear Saturation and Asymptotic Saturation Regimes

Abstract

Previously, we transformed the linear drain bias asymptote equation for the MOSFET drain current in the saturation regime from the “intrinsic” case into “extrinsic” case with accounting for the velocity saturation effect. We obtained the equation for the drain current that yielded the nonlinear dependence on the “extrinsic” drain bias in saturation regime in an implicit form. We derived the equation for the differential conductance of the MOSFET at the “saturation point” and proposed a linear approximation for the dependence of the drain current on the “extrinsic” drain bias in the saturation regime for not very high drain bias when nonlinear effects can be neglected. In this paper, we investigate the asymptotic behavior of the implicit equation for the drain current in case when “extrinsic” drain bias tends to infinity. We propose the nonlinear approximation for the drain current asymptotic that describes a slow current rise to its limiting value when the “extrinsic” drain bias tends to infinity. This approximation is based on analytical solution of quartic equation that can be solved easily enough using Ferrari's method.