Multigroup Equations for the Description of the Particle Transport in Semiconductors

Abstract

Multigroup equations for the description of the particle transport in semiconductors / Martin Galler. ISBN 981-256-355-5 (alk. paper) Title. 11. Series. p. cm.-(Series on advances in mathematics for applied sciences ; v. 70) 1. Transport theory-Mathematics. 2. Semiconductors-Mathematics. I. QC793.3.V G35 2005 530.13'8-dc22 200504943 I British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs

“…The semi-lagrangian scheme allows for larger time-stepping than the finite-difference method since there is no CFL condition while the finite-differences method is more accurate in time than the semi-lagrangian method. Other methods can be used for the transport/collision part as the multi-group methods proposed in [23,24].…”

“…(1)-(4). The advantages of fully deterministic schemes compared to Monte-Carlo solvers available can be summarized analogously to the case of semiclassical Boltzmann-Poisson solvers [12][13][14][23][24][25] as:…”

Recovering doping profiles in semiconductor devices with the Boltzmann–Poisson model

“…To compute the Fréchet derivatives of the objective functional with respect to the unknown for this minimization problem, we can adopt the same strategy of adjoint equations. It turns out that the adjoint problems are almost identical to the adjoint problems in (24) and (25). To save spaces, we do not present those equations here.…”

“…We remark finally that the models we consider here are called unipolar models because we only consider the transport of electrons while neglected the transport of holes. Also, in real device simulation, both the Boltzmann-Poisson equation system and its boundary conditions can be more complicated than what we have presented here; see for example the abovementioned references and [18,25,33,54].…”

DSMC versus WENO-BTE: A double gate MOSFET example

“…In Eq. (2), 0 is the dielectric Deterministic solvers to the Boltzmann-Poisson system (1)-(2) for two-dimensional devices have been proposed in [1][2][3][4]. These methods provide accurate results which, in general, agree well with those obtained from Monte Carlo simulations.…”