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Numerical study of the systematic errorin Monte Carlo schemes for semiconductors

Published online by Cambridge University Press:  26 August 2010

Orazio Muscato ,
Wolfgang Wagner  and
Vincenza Di Stefano
Orazio Muscato
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, Italy. muscato@dmi.unict.it
Wolfgang Wagner
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany. wagner@wias-berlin.de
Vincenza Di Stefano
Affiliation:
Dipartimento di Matematica, Università degli Studi di Messina, Contrada Papardo 31, 98166 Messina, Italy. vdistefano@dmi.unict.it
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Abstract

The paper studies the convergence behavior ofMonte Carlo schemes for semiconductors.A detailed analysis of the systematic error with respect to numerical parameters is performed.Different sources of systematic error are pointed out andillustrated in a spatially one-dimensional test case.The error with respect to the number of simulation particlesoccurs during the calculation of the internal electric field.The time step error, which is related to the splitting of transport andelectric field calculations, vanishes sufficiently fast.The error due to the approximation of the trajectories ofparticles depends on the ODE solver used in the algorithm.It is negligible compared to the other sources of time steperror, when a second order Runge-Kutta solver is used. The error related to the approximate scattering mechanismis the most significant source of error with respect to the time step.

Keywords

Boltzmann-Poisson equationselectronic devicesMonte Carlo simulations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 5: Special Issue on Probabilistic methods and their applications , September 2010 , pp. 1049 - 1068
Copyright
© EDP Sciences, SMAI, 2010

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