# 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

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topMuscato, 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 -

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