Self-consistent solution of 2D-Poisson and Schrodinger wave equation for nano-metric MOSFET modeling for VLSI/ULSI purposes

A numerical solution of two-dimensional Poisson's equation and Schrodinger wave equation of a deep sub-micron and nano-meter MOSFET has been obtained to gather information about the charge and the potential distribution in the depletion region. The quantum as well as classical charge has been computed. The quantum charge is a direct function of Density of States (DOS). The classical charge can be found out by simply solving the two-dimensional Poisson equation under specific boundary conditions governed by the physics of the device. The channel voltage profile has also been presented. It is seen that the classical model underestimates the channel voltage and the longitudinal electric field in the channel as compared to that obtained through Quantum Mechanical (QM) approach.