Hostname: page-component-7b7567c8c-jswmv Total loading time: 0 Render date: 2026-11-15T20:24:18.224Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anile, A.M. and Muscato, O., Improved hydrodynamical model for carrier transport in semiconductors. Phys. Rev. B 51 (1995) 16728–16740. CrossRef
V. Borsari and C. Jacoboni, Monte Carlo calculations on electron transport in CdTe. Phys. Stat. Sol. (B) 54 (1972) 649–662.
Fawcett, W., Boardman, A.D. and Swain, S., Monte Carlo determination of electron transport properties in gallium arsenide. J. Phys. Chem. Solids 31 (1970) 1963–1990. CrossRef
Fischetti, M.V. and Laux, S.E., Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects. Phys. Rev. B 38 (1988) 9721–9745. CrossRef
C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation. Springer, New York (1989).
Jacoboni, C. and Reggiani, L., The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials. Rev. Modern Phys. 55 (1983) 645–705. CrossRef
C. Jungemann and B. Meinerzhagen, Hierarchical Device Simulation. The Monte-Carlo Perspective. Springer, Wien (2003).
S.E. Laux, M.V. Fischetti, Numerical aspects and implementation of the DAMOCLES Monte Carlo device simulation program, in Monte Carlo Device Simulation: Full Band and Beyond, K. Hess Ed., Kluwer, Boston (1991) 1–26.
Miranda, J.M., Lin, C., Shaalan, M., Hartnagel, H.L. and Sebastian, J.L., Influence of the minimization of self-scattering events on the Monte Carlo simulation of carrier transport in III-V semiconductors. Semicond. Sci. Technol. 14 (1999) 804–808. CrossRef
Muscato, O. and Wagner, W., Time step truncation in direct simulation Monte Carlo for semiconductors. Compel 24 (2005) 1351–1366. CrossRef
U. Ravaioli, Vectorization of Monte Carlo algorithms for semiconductor simulation, in Monte Carlo Device Simulation: Full Band and Beyond, K. Hess Ed., Kluwer, Boston (1991) 267–284.
Rees, H.D., Calculation of steady state distribution functions by exploiting stability. Phys. Lett. A 26 (1968) 416–417. CrossRef
Rees, H.D., Calculation of distribution functions by exploiting the stability of the steady state. J. Phys. Chem. Solids 30 (1969) 643–655. CrossRef
S. Rjasanow and W. Wagner, Stochastic Numerics for the Boltzmann Equation. Springer, Berlin (2005).
Sangiorgi, E., Ricco, B. and Venturi, F., MOS2: an efficient Monte Carlo simulator for MOS devices. IEEE Trans. Computer-Aided Des. 7 (1988) 259–271. CrossRef
Sverdlov, V., Ungersboeck, E., Kosina, H. and Selberherr, S., Current transport models for nanoscale semiconductor devices. Mater. Sci. Eng. R 58 (2008) 228–270. CrossRef
Yorston, R.M., Free-flight time generation in the Monte Carlo simulation of carrier transport in semiconductors. J. Comput. Phys. 64 (1986) 177–194. CrossRef