The Boltzmann equation in presence of boundary and initial conditions, which describes the general case of carrier transport in microelectronic devices is analysed in terms of Monte Carlo theory. The classical Ensemble Monte Carlo algorithm which has been devised by merely phenomenological considerations of the initial and boundary carrier contributions is now derived in a formal way. The approach allows to suggest a set of event-biasing algorithms for statistical enhancement as an alternative of the population control technique, which is virtually the only algorithm currently used in particle simulators. The scheme of the self-consistent coupling of Boltzmann and Poisson equation is considered for the case of weighted particles. It is shown that particles survive the successive iteration steps.
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Mixed initial-boundary value problem in particle modeling of microelectronic devices
1 Institute for Microelectronics, TU Vienna, Gusshausstrasse 27–29 E360, 1040 Vienna, Austria. Email: mixi@iue.tuwien.ac.at
2 Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287-5706, USA. Email: vasileska@asu.edu
3 Institute for Parallel Processing, Bulgarian Academy of Sciences, 1113 Sofia, and ACET Centre, University of Reading, Whiteknights P.O. Box 217, Reading RG6 6AH, Bulgaria/UK. Email: i.t.dimov@reading.ac.uk
4 Faculty of Electrical Engineering and Information Technologies, SS “Cyril and Methodius” University, Skopje, Karpos II b.b., P.O. Box 574, 1001 Skopje, Macedonia, Macedonia. Email: g.arsov@ieee.org
Citation Information: Monte Carlo Methods and Applications mcma. Volume 13, Issue 4, Pages 299–331, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: 10.1515/mcma.2007.017, December 2007
- Received:
- 2007-06-08
- Revised:
- 2007-10-28
- Published Online:
- 2007-12-04
Keywords: Boltzmann equation; carrier transport in semiconductors; event biasing; integral equations
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