A new simplified threshold-voltage model for n-MOSFETs with nonuniformly doped substrate and its application to MOSFET´s miniaturization

The formulation, verification, and application of a new simplified 2-D threshold voltage model for n-MOSFETs with nonuniformly doped substrate profile are provided, in which the averaged normal field at the Si/SiO₂ interface in the active channel is quoted from a simplified solution of two-dimensional Poisson equation using the Green function technique. Starting with the expression of this average normal field, a simple threshold-voltage model for short-channel n-MOSFETs with nonuniformly doped substrate profile is explicitly expressed in terms of device structures and terminal voltages by considering parabolic source-drain boundary potentials. Moreover, the effects of the junction depth on the threshold voltage are examined in detail. It is shown that the DIBL effect cannot be completely eliminated by simply increasing the substrate doping concentration. Comparisons among developed model, 2-D numerical analysis, and experimental data have been made and the accuracy of the developed analytical model has been verified. In addition, a direct extension of our model to the case of uniformly doped substrates leads to a new constraint equation for device miniaturization.