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VLSI Design
Volume 13 (2001), Issue 1-4, Pages 349-354

Approximation of the BTE by a Relaxation-time Operator: Simulations for a 50 nm-channel Si Diode

1Dipartimento di Matematica, Universitá di Catania, Italy
2Department of Mathematics, University of Texas at Austin, USA
3Department of Mathematics, University of Texas at Austin, USA
4Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
5Departamento de Matematica Aplicada, Universidad de Granada, Granada 18071, Spain

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.


In this work we present comparisons between DSMC simulations of the full BTE and deterministic simulations of a relaxation-time approximation for a nowadays size Si diode. We assume a field dependent relaxation time fitted to give the same drift speed (mean velocity) as DSMC simulations for bulk Si. We compute the density, mean velocity, force field, potential drop, energy and I-V curves of both models and plot the pdf of the deterministic relaxation-time model. We also compare the results to augmented drift-diffusion models proposed in the literature to approximate the relaxation time system in the quasi-ballistic regime. The quasi-ballistic and ballistic regimes are distinguished by using local dimensionless parameters.