Transport Phenomena and Kinetic Theory
DOI: 10.1007/978-0-8176-4554-0_7
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Deterministic kinetic solvers for charged particle transport in semiconductor devices

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Cited by 10 publications
(14 citation statements)
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“…Furthermore, a deterministic simulation has several advantages over direct Monte-Carlo simulations due to the results being noise-free, the accurate resolution of transients, and the possibility of obtaining all macroscopic quantities of interest directly from suitable moments of the pdf, ρ(t, v, g). A similar strategy was adopted for obtaining highly accurate resolution of the charged particle transport in semiconductors (see [14,15,10] and references therein). One of the possible drawbacks of the deterministic simulation of the Fokker-Planck equation (3) is its computational cost.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Furthermore, a deterministic simulation has several advantages over direct Monte-Carlo simulations due to the results being noise-free, the accurate resolution of transients, and the possibility of obtaining all macroscopic quantities of interest directly from suitable moments of the pdf, ρ(t, v, g). A similar strategy was adopted for obtaining highly accurate resolution of the charged particle transport in semiconductors (see [14,15,10] and references therein). One of the possible drawbacks of the deterministic simulation of the Fokker-Planck equation (3) is its computational cost.…”
Section: Introductionmentioning
confidence: 99%
“…The accurate approximation of the v and g derivatives allows us to use explicit time integrators with a fairly moderate CFL condition. The derivation of this scheme follows similar ideas as in work done in Boltzmann-Poisson kinetic systems for semiconductors [14,15,10]. Also, splitting schemes were developed for plasmas and semiconductor modelling [17,16], which may be applied to the present situation for further computational savings.…”
Section: Introductionmentioning
confidence: 99%
“…Very recently, deterministic solvers to the BoltzmannPoisson system (1) for two-dimensional devices were proposed [1][2][3]7]. These methods provide accurate results which, in general, agree well with those obtained from Monte Carlo (DSMC) simulations, often at a fractional computational time.…”
Section: Methodsmentioning
confidence: 62%
“…Time-dependent solutions of the Boltzmann-Poisson system contain all the information on the evolution of the carrier distribution. In (1), f represents the electron probability density function (pdf ) in phase space k at the physical location x and time t. E is the electric field and ε is the energy-band function. Physical constants and q are the Planck constant divided by 2π and the positive electric charge, respectively.…”
Section: Introductionmentioning
confidence: 99%
“…Due to the mathematical difficulties that arise by this interaction, operators as well as the large number of unknowns, the numerical approximation of such kinetic transport models is highly demanding from a computational standpoint. Traditional computational schemes for this type of linear transport developed several decades ago were based in Discrete Simulations Monte Carlo (DSMC) [3,39] or more recently deterministic approaches initiated by [26,37] and more recently extended WENO finite difference based schemes [6,7,8,9,5].…”
Section: Introductionmentioning
confidence: 99%