Three-dimensional Spectral Solution of Schrödinger Equation

We present a fast and robust method for the full-band solution of Schrödinger'sequation on a grid, with the goal of achieving a more complete description of highenergy states and realistic temperatures. Using Fast Fourier Transforms, Schrödinger'sequation in the one band approximation can be expressed as an iterative eigenvalueproblem for arbitrary shapes of the conduction band. The resulting eigenvalue problemcan then be solved using Krylov subspace methods as Arnoldi iteration. We demonstratethe algorithm by presenting an example concerning non-parabolic effects in anultra-small Metal-Oxide-Semiconductor quantum cavity at room-temperature. Forthis structure, we show that the non-parabolicity of the conduction band results in asignificant lowering of high-energy electronic states