The effect of quantum confinement and discrete dopants in nanoscale 50 nm n-MOSFETs: a three-dimensional simulation

Abstract In this paper, we investigate the effects of quantum confinement at the Si–SiO2 interface on the properties of MOSFETs with a channel length of 50 nm. To this end, we have developed a three-dimensional Poisson–Schrödinger solver, based on an approximation which allows us to decouple the Schrödinger equation into an equation in the direction perpendicular to the channel and an equation in the plane of the channel. This code is able to provide the MOSFET transport properties for very small drain-to-source voltage. We have also evaluated the effects of the discrete distribution of dopants on the dispersion of threshold voltage, by simulating a large number of devices with uniform nominal doping profile but with different actual ‘atomistic’ distributions of impurities.