A Multigroup-WENO Solver for the Non-Stationary Boltzmann-Poisson System for Semiconductor Devices

Galler, Martin; Majorana, Armando; Schürrer, Ferdinand

doi:10.1007/978-3-540-32862-9_47

Cited by 4 publications

(7 citation statements)

References 9 publications

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“…None the less, the simulated case can be seen as an almost one-valley transport. Hence, the shapes of macroscopic quantifies versus position agree qualitatively with those obtained for simulating a silicon n + -n-n + diode [13].…”

Section: Gaas N + -N I -N + Diodesupporting

confidence: 72%

“…The mean electron energy tends to saturate to a constant low slope for high electric fields, since most of the energy input is transfered to the lattice by − L and L − L transitions. All of these features are typical for the common III-V compound semiconductors such as GaAs [9] and well distinct from those of the elementary semiconductors like silicon [13]. Finally, we point out the excellent agreement between the results of the deterministic solver and the stochastic Monte Carlo scheme.…”

Section: Bulk Gaasmentioning

confidence: 79%

“…Because of these promising results, we intend to extend our method to the spatially twodimensional case for simulating the practically relevant GaAs-MESFETs. This extension can be performed straight forward as it is described in [13] for a silicon MESFET. The electron distribution functions f ν are assumed to depend on the two spatial variables x and y, the momentum variables transformed to the energyE and the angle variables µ and ϕ as well as on time t. This allows us to rewrite the BTEs in a conservative form similar to (8).…”

Section: Conclusion and Future Tasksmentioning

confidence: 99%

“…Consequently, we combine our multigroup transport equations with a weighted essentially non-oscillatory (WENO) code [12] for approximating the spatial derivatives in the diffusion term of the BTEs. Therefore, we follow the main ideas proposed in [13], where a multigroup-WENO solver for silicon devices is presented. In this paper, we extend this approach by regarding the multi-valley regime typical for polar semiconductors and by taking into account the anisotropy of some of the main scattering mechanisms of GaAs.…”

Section: Introductionmentioning

confidence: 99%

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A Deterministic Solver for the 1D Non-Stationary Boltzmann-Poisson System for GaAs Devices: Bulk GaAs and GaAs n+-n i -n+ Diode

Galler

Schürrer

2005

J Comput Electron

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We present a deterministic method for describing the electron transport in spatially one-dimensional gallium arsenide devices. This numerical procedure is based on the combination of kinetic Boltzmann-type equations for a two-valley model of the GaAs conduction band and the Poisson equation in order to consider the electrostatic potential self-consistently. All of the important intra-and intervalley scattering mechanisms for GaAs are taken into account. The dependence of the electron distribution functions on the electron wave vector is treated by means of the multigroup approach, whereas their spatial dependences are handled by a weighted essentially non-oscillatory (WENO) scheme. Numerical results are given for the main transport quantities as functions of time, position and electric field in bulk material and in a n + -n i -n + diode. In addition, the proposed numerical method is validated by comparing the results with those of Monte Carlo calculations and the influence of the discretization used in the numerical procedure is discussed.

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Section: Gaas N + -N I -N + Diodesupporting

confidence: 72%

Section: Bulk Gaasmentioning

confidence: 79%

Section: Conclusion and Future Tasksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Deterministic Solver for the 1D Non-Stationary Boltzmann-Poisson System for GaAs Devices: Bulk GaAs and GaAs n+-n i -n+ Diode

Galler

Schürrer

2005

J Comput Electron

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“…This approach, however, is not conservative at the interfaces between the different domains. Encouraged by the very good results obtained with the high-order WENO finite-difference scheme [13,18] on uniform grids, we develop a strategy to apply this method to non-uniform discretizations in a conservative way.…”

Section: Non-uniform Discretization In Real Spacementioning

confidence: 99%

Numerical schemes for solving the non-stationary Boltzmann-Poisson system for two-dimensional semiconductor devices

2005

Self Cite

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Abstract. In this paper we present a new way of discretizing the Boltzmann-Poisson system describing the electron transport in semiconductor devices. The new method is based on a cell average technique for the momentum space combined with a non-uniform discretization in real space. Results of the simulation of a 2D silicon MOSFET are shown and compared with Monte Carlo data. We found that the proposed scheme reduces both the number of grid points and the CPU time, without loss of accuracy.Résumé. Dans cet article, on présente une nouvelle façon de discrétiser le système de BoltzmannPoisson décrivant le transport desélectrons dans les semi-conducteurs. Cette nouvelle méthode est fondée sur des techniques de moyennes par cellule pour l'espace des moments combinées avec une discrétisation non uniforme sur l'espace réel. Des résultats de simulation d'un MOSFET 2D Silicone sont présentés et comparés avec des données Monte-Carlo. On trouve que le schéma proposé réduità la fois le nombre de points de grille et le temps CPU, sans perte de précision.

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A direct multigroup-WENO solver for the 2D non-stationary Boltzmann–Poisson system for GaAs devices: GaAs-MESFET

Galler

Schürrer

2006

Journal of Computational Physics

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A Multigroup-WENO Solver for the Non-Stationary Boltzmann-Poisson System for Semiconductor Devices

Cited by 4 publications

References 9 publications

A Deterministic Solver for the 1D Non-Stationary Boltzmann-Poisson System for GaAs Devices: Bulk GaAs and GaAs n+-n i -n+ Diode

A Deterministic Solver for the 1D Non-Stationary Boltzmann-Poisson System for GaAs Devices: Bulk GaAs and GaAs n+-n i -n+ Diode

Numerical schemes for solving the non-stationary Boltzmann-Poisson system for two-dimensional semiconductor devices

A direct multigroup-WENO solver for the 2D non-stationary Boltzmann–Poisson system for GaAs devices: GaAs-MESFET

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