Computational technique for coupled Poisson-Schrodinger equation with mixed boundary conditions in nano scale semiconductor devices using iterative finite difference schemes
Resumo
Accurate and effective solutions of coupled Poisson-Schrodinger equations are sought to enable higher degree of accuracy in nanoscale semiconductor device simulations. This is due to the fact that the system accounts for quantum confinement effects that surface in nanoscale devices and induces significant alterations in the device characteristics. In this article, we formulate and analyze a novel and efficient computational technique which besides deriving self-consistent solutions also attends to the singularly perturbed nature of the Schrodinger equation. The coupled system with appropriate boundary conditions is investigated using singular perturbation approach applying iterative finite difference schemes on various layer adapted meshes. A meticulous convergence analysis of an iterative scheme on the coupled system comprising of singularly perturbed reaction diffusion equation subjected to Robin boundary conditions is the first of its kind. The desired efficacy of the proposed numerical technique is confirmed by presenting computational findings.
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