Calculation of threshold voltage in nonuniformly doped MOSFET's

A simple algorithm is presented that is based on a semi-empirical modification of a closed form expression for the inversion charge, to allow the calculation of the so-called extrapolated threshold voltage versus source-substrate bias in nonuniformly doped MOSFET's. This algorithm is suitable for incorporation into process simulation computer programs like SUPREM. It is demonstrated, by comparison to exact calculations and to measurements, that the algorithm gives accurate values of extrapolated threshold voltage even for cases where junctions are present in the MOSFET substrate under the gate.