We present a fast and robust method for the full-band solution of Schrödinger's equation on a grid, with the goal of achieving more complete description of high energy states and realistic temperatures. Using Fast Fourier Transforms, Schrödinger's equation in the one band approximation can be expressed as an iterative eigenvalue problem for arbitrary shapes of the conduction band. The resulting eigenvalue problem can then be solved using Krylov subspace methods as Arnoldi iteration. We demonstrate the algorithm by presenting an example concerning non-parabolic effects in an ultra-small Metal-Oxide-Semiconductor quantum cavity at room-temperature. For this structure, we show that the non-parabolicity of the conduction band results in a significant lowering of high-energy electronic states.
- Full band
- Quantum dot
ASJC Scopus subject areas
- Hardware and Architecture
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering