A NEW SIMPLIFIED 2-DIMENSIONAL MODEL FOR THE THRESHOLD VOLTAGE OF MOSFETS WITH NONUNIFORMLY DOPED SUBSTRATE

Abstract

A new simplified two-dimensional model for the threshold voltage of MOSFET's is derived in terms of simple characteristic functions. These characteristic functions are transformed from the exact series solution of the two-dimensional Poisson's equation, in which the effects of a nonuniformly doped substrate and a finite graded source-drain junction depth have been included. The attractive features of the developed model are: 1) charge-screening effects are proposed to account for the weak dependence of the threshold voltage on the substrate bias for short-channel MOSFET's, and 2) exact source and drain boundary potentials can be approximated by their equivalent power functions. The accuracy of the simplified 2-D model has been verified by 2-D numerical analysis. Moreover, comparisons between the simplified 2-D model and the experimental results have been made, and good agreement has been obtained for wide ranges of channel lengths, applied substrate, and drain biases.