An efficient numerical method for the small-signal AC analysis of MOS capacitors

Abstract

A numerical method for the small-signal ac analysis of MOS capacitors is presented. The equations describing device operation, which comprise a boundary value problem, are formulated as an initial value problem and are solved by a shooting method. This results in a numerically stable and efficient algorithm for their solution. The recognized ill-conditioning of the boundary value problem, manifesting itself in numerical instabilities in the conductance-voltage characteristics of MOS capacitors is addressed. Calculated small-signal ac admittance as a function of gate bias for homogeneously doped and ion-implanted devices is shown. The high- "and low-frequency" positional dependence of convection and displacement current densities is determined.