A Novel Parallel Approach for Numerical Solution of the Schrödinger and Poisson Equations in Semiconductor Devices

A new parallel implementation of quantum confinement effects simulations for semiconductor devices is presented. In this simulation, a set of self-consistent Schrödinger and Poisson (SP) equations is solved with parallel divide and conquer and monotone iterative algorithms on a Linux-cluster with message-passing interface (MPI) library. To solve the Schrödinger equation, instead of the conventional large-scale approach for eigenvalue problem, a novel parallel divide and conquer scheme is developed to find all the corresponding wave functions and energy levels. Moreover, the nonlinear Poisson equation is solved with monotone iterative method instead of the Newton’s iterative method. The parallel implementation shows that a well-designed simulation can reduce the execution time up to many orders of magnitude. Compared with the measured data and classical results, numerical simulations on a realistic metal-oxide-semiconductor (MOS) device are presented to show the accuracy and efficiency of the method. Key-Words: Schrödinger and Poisson Equations, Parallel Divide and Conquer, Monotone Iterative Technique, Semiconductor Device Simulation, Quantum Confinement Effects