# 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

## Access Full Article

top## Abstract

top## How to cite

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 -

## References

top- A.M. Anile and O. Muscato, Improved hydrodynamical model for carrier transport in semiconductors. Phys. Rev. B51 (1995) 16728–16740.
- V. Borsari and C. Jacoboni, Monte Carlo calculations on electron transport in CdTe. Phys. Stat. Sol. (B) 54 (1972) 649–662.
- W. Fawcett, A.D. Boardman and S. Swain, Monte Carlo determination of electron transport properties in gallium arsenide. J. Phys. Chem. Solids31 (1970) 1963–1990.
- M.V. Fischetti and S.E. Laux, Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects. Phys. Rev. B38 (1988) 9721–9745.
- C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation. Springer, New York (1989).
- C. Jacoboni and L. Reggiani, The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials. Rev. Modern Phys.55 (1983) 645–705.
- C. Jungemann and B. Meinerzhagen, Hierarchical Device Simulation. The Monte-Carlo Perspective. Springer, Wien (2003). Zbl1107.82301
- 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. Zbl0768.65081
- J.M. Miranda, C. Lin, M. Shaalan, H.L. Hartnagel and J.L. Sebastian, 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.
- O. Muscato and W. Wagner, Time step truncation in direct simulation Monte Carlo for semiconductors. Compel24 (2005) 1351–1366. Zbl1079.82552
- 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. Zbl0769.65093
- H.D. Rees, Calculation of steady state distribution functions by exploiting stability. Phys. Lett. A26 (1968) 416–417.
- H.D. Rees, Calculation of distribution functions by exploiting the stability of the steady state. J. Phys. Chem. Solids30 (1969) 643–655.
- S. Rjasanow and W. Wagner, Stochastic Numerics for the Boltzmann Equation. Springer, Berlin (2005). Zbl1155.82021
- E. Sangiorgi, B. Ricco and F. Venturi, MOS2: an efficient Monte Carlo simulator for MOS devices. IEEE Trans. Computer-Aided Des.7 (1988) 259–271.
- V. Sverdlov, E. Ungersboeck, H. Kosina and S. Selberherr, Current transport models for nanoscale semiconductor devices. Mater. Sci. Eng. R58 (2008) 228–270.
- R.M. Yorston, Free-flight time generation in the Monte Carlo simulation of carrier transport in semiconductors. J. Comput. Phys.64 (1986) 177–194. Zbl0585.65001

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.