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Author: Muscato, Orazio ×

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    Numerical study of the systematic error in Monte Carlo schemes for semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Muscato, Orazio; Di Stefano, Vincenza; Wagner, Wolfgang
    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.
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    A variance-reduced electrothermal Monte Carlo method for semiconductor device simulation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Muscato, Orazio; Di Stefano, Vincenza; Wagner, Wolfgang
    This paper is concerned with electron transport and heat generation in semiconductor devices. An improved version of the electrothermal Monte Carlo method is presented. This modification has better approximation properties due to reduced statistical fluctuations. The corresponding transport equations are provided and results of numerical experiments are presented.
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    Properties of the steady state distribution of electrons in semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Muscato, Orazio; Wagner, Wolfgang; Di Stefano, Vincenza
    This paper studies a Boltzmann transport equation with several electron-phonon scattering mechanisms, which describes the charge transport in semiconductors. The electric field is coupled to the electron distribution function via Poisson's equation. Both the parabolic and the quasi-parabolic band approximations are considered. The steady state behaviour of the electron distribution function is investigated by a Monte Carlo algorithm. More precisely, several nonlinear functionals of the solution are calculated that quantify the deviation of the steady state from a Maxwellian distribution with respect to the wave-vector. On the one hand, the numerical results illustrate known theoretical statements about the steady state and indicate possible directions for future studies. On the other hand, the nonlinear functionals provide tools that can be used in the framework of Monte Carlo algorithms for detecting regions in which the steady state distribution has a relatively simple structure, thus providing a basis for domain decomposition methods
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    A stochastic algorithm without time discretization error for the Wigner equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Muscato, Orazio; Wagner, Wolfgang
    Stochastic particle methods for the numerical treatment of the Wigner equation are considered. The approximation properties of these methods depend on several numerical parameters. Such parameters are the number of particles, a time step (if transport and other processes are treated separately) and the grid size (used for the discretization of the position and the wavevector). A stochastic algorithm without time discretization error is introduced. Its derivation is based on the theory of piecewise deterministic Markov processes. Numerical experiments are performed in a one-dimensional test case. Approximation properties with respect to the grid size and the number of particles are studied. Convergence of a time-splitting scheme to the no-splitting algorithm is demonstrated. The no-splitting algorithm is shown to be more efficient in terms of computational effort.
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    A class of stochastic algorithms for the Wigner equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Muscato, Orazio; Wagner, Wolfgang
    A class of stochastic algorithms for the numerical treatment of the Wigner equation is introduced. The algorithms are derived using the theory of pure jump processes with a general state space. The class contains several new algorithms as well as some of the algorithms previously considered in the literature. The approximation error and the efficiency of the algorithms are analyzed. Numerical experiments are performed in a benchmark test case, where certain advantages of the new class of algorithms are demonstrated.