The paper studies the convergence behavior of Monte 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 and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field calculations, vanishes sufficiently fast. The error due to the approximation of the trajectories of particles depends on the ODE solver used in the algorithm. It is negligible compared to the other sources of time step error, when a second order Runge-Kutta solver is used. The error related to the approximate scattering mechanism is the most significant source of error with respect to the time step.
@article{M2AN_2010__44_5_1049_0,
author = {Muscato, Orazio and Wagner, Wolfgang and Di Stefano, Vincenza},
title = {Numerical study of the systematic error in Monte Carlo schemes for semiconductors},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {44},
year = {2010},
pages = {1049-1068},
doi = {10.1051/m2an/2010051},
mrnumber = {2731402},
zbl = {1198.82068},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2010__44_5_1049_0}
}
Muscato, Orazio; Wagner, Wolfgang; Di Stefano, Vincenza. Numerical study of the systematic error in Monte Carlo schemes for semiconductors. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) pp. 1049-1068. doi : 10.1051/m2an/2010051. http://gdmltest.u-ga.fr/item/M2AN_2010__44_5_1049_0/
[1] and , Improved hydrodynamical model for carrier transport in semiconductors. Phys. Rev. B 51 (1995) 16728-16740.
[2] and , Monte Carlo calculations on electron transport in CdTe. Phys. Stat. Sol. (B) 54 (1972) 649-662.
[3] , and , Monte Carlo determination of electron transport properties in gallium arsenide. J. Phys. Chem. Solids 31 (1970) 1963-1990.
[4] and , Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects. Phys. Rev. B 38 (1988) 9721-9745.
[5] and , The Monte Carlo Method for Semiconductor Device Simulation. Springer, New York (1989).
[6] and , The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials. Rev. Modern Phys. 55 (1983) 645-705.
[7] and , Hierarchical Device Simulation. The Monte-Carlo Perspective. Springer, Wien (2003). | Zbl 1107.82301
[8] , , 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. | Zbl 0768.65081
[9] , , , and , 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.
[10] and , Time step truncation in direct simulation Monte Carlo for semiconductors. Compel 24 (2005) 1351-1366. | Zbl 1079.82552
[11] , 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. | Zbl 0769.65093
[12] , Calculation of steady state distribution functions by exploiting stability. Phys. Lett. A 26 (1968) 416-417.
[13] , Calculation of distribution functions by exploiting the stability of the steady state. J. Phys. Chem. Solids 30 (1969) 643-655.
[14] and , Stochastic Numerics for the Boltzmann Equation. Springer, Berlin (2005). | Zbl 1155.82021
[15] , and , MOS2: an efficient Monte Carlo simulator for MOS devices. IEEE Trans. Computer-Aided Des. 7 (1988) 259-271.
[16] , , and , Current transport models for nanoscale semiconductor devices. Mater. Sci. Eng. R 58 (2008) 228-270.
[17] , Free-flight time generation in the Monte Carlo simulation of carrier transport in semiconductors. J. Comput. Phys. 64 (1986) 177-194. | Zbl 0585.65001