Numerical study of the systematic error in Monte Carlo schemes for semiconductors

Orazio Muscato; Wolfgang Wagner; Vincenza Di Stefano

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 5, page 1049-1068
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Muscato, Orazio, Wagner, Wolfgang, and Di Stefano, Vincenza. "Numerical study of the systematic error in Monte Carlo schemes for semiconductors." ESAIM: Mathematical Modelling and Numerical Analysis 44.5 (2010): 1049-1068. <http://eudml.org/doc/250785>.

@article{Muscato2010,
abstract = { 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. },
author = {Muscato, Orazio, Wagner, Wolfgang, Di Stefano, Vincenza},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Boltzmann-Poisson equations; electronic devices; Monte Carlo simulations; Monte Carlo simulations},
language = {eng},
month = {8},
number = {5},
pages = {1049-1068},
publisher = {EDP Sciences},
title = {Numerical study of the systematic error in Monte Carlo schemes for semiconductors},
url = {http://eudml.org/doc/250785},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Muscato, Orazio
AU - Wagner, Wolfgang
AU - Di Stefano, Vincenza
TI - Numerical study of the systematic error in Monte Carlo schemes for semiconductors
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/8//
PB - EDP Sciences
VL - 44
IS - 5
SP - 1049
EP - 1068
AB - 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.
LA - eng
KW - Boltzmann-Poisson equations; electronic devices; Monte Carlo simulations; Monte Carlo simulations
UR - http://eudml.org/doc/250785
ER -

References

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