A quantum correction Poisson equation for metal–oxide–semiconductor structure simulation

Abstract

In this paper, we present a quantum correction Poisson equation for metal–oxide–semiconductor (MOS) structures under inversion conditions. Based on the numerical solution of Schrödinger–Poisson (SP) equations, the new Poisson equation developed is optimized with respect to (1) the position of the charge concentration peak, (2) the maximum of the charge concentration, (3) the total inversion charge sheet density Q, and (4) the average inversion charge depth X. Instead of solving a set of coupled SP equations, this physically-based Poisson equation characterizes the quantum confinement effects of the MOS structure from the interface of silicon and oxide (Si/SiO2) with the silicon substrate. It successfully predicts distribution of the electron density in inversion layers for MOS structures with various oxide thicknesses Tox and applied gate voltages VG. Compared to SP results, the prediction of the proposed equation is within 3% accuracy. Application of this equation to the capacitance–voltage measurement of an n-type metal–oxide–semiconductor field effect transistor (MOSFET) produces an excellent agreement. This quantum correction Poisson equation can be solved together with transport equations, such as drift-diffusion, hydrodynamic and Boltzmann transport equations without encountering numerical difficulties. It is feasible for nanoscale MOSFET simulation.