A numerical iterative method for solving Schrödinger and Poisson equations in nanoscale single, double and surrounding gate metal-oxide-semiconductor structures

Numerical solution of the Schrödinger and Poisson equations (SPEs) plays an important role in semiconductor simulation. We in this paper present a robust iterative method to compute the self-consistent solution of the SPEs in nanoscale metal-oxide-semiconductor (MOS) structures. Based on the global convergence of the monotone iterative (MI) method in solving the quantum corrected nonlinear Poisson equation (PE), this iterative method is successfully implemented and tested on the single-, double-, and surrounding-gate (SG, DG, and AG) MOS structures. Compared with other approaches, various numerical simulations are demonstrated to show the accuracy and efficiency of the method.