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VLSI Design
Volume 13 (2001), Issue 1-4, Pages 341-347

Three-dimensional Spectral Solution of Schrödinger Equation

1lntel Corporation, RA1-305, 2501 NW 229th Ave, Hillsboro, OR 97124, USA
23255 Beckman Institute, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a fast and robust method for the full-band solution of Schrödinger's equation on a grid, with the goal of achieving a 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.