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VLSI Design
Volume 6 (1998), Issue 1-4, Pages 239-242

An Efficient Solution Scheme for the Spherical-Harmonics Expansion of the Boltzmann Transport Equation Applied to Two-Dimensional Devices

1Dipartimento di Elettronica, Informatica e Sistemistica, Università di Bologna, Viale Risorgimento 2, Bologna 40136, Italy
2Universität Kaiserslautern, FB Mathematik, Erwin Schrödingerstraβe, Kaiserslautern 67653, Germany

Copyright © 1998 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.


This paper presents a novel numerical scheme applicable to the solution of the Boltzmann transport equation by means of a spherical-harmonics expansion. This scheme improves the solution at low energies, keeping the desired accuracy in the calculation of the mean quantities while saving a significant amount of CPU time. This is important in view of the applications of the method, since the typical number of nodes to be used in the combined space-energy domain is in the range of 104–105.