N. Ben Abdallah, P. Degond, P.A. Markowich, C. Schmeiser, High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors, preprint (http://mip.upstlse. fr). Home/Search Document Details and Download
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Low And High Field Scaling Limits For The Vlasov- And.. - Arnold, Carrillo.. (1999) (Correct)
....let us remark that very recently Fokker Planck type equations have been derived from the Boltzmann equation for semiconductors using the BS and a spherical harmonic expansion (SHE model) In the SHE model one obtains an equation for the distribution function in energy position space. We refer to [4, 5, 27] for this kind of models. 17 6 Numerical simulation The aim of this section is to show that the three presented scaling regimes indeed appear in a realistic simulation of a simple problem. We shall present simulations for a silicon n n n diode, and we shall see that di erent regimes ....
N. Ben Abdallah, P. Degond, P. Markowich, C. Schmeiser, High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors, preprint TMR.
Low And High Field Scaling Limits For The Vlasov- And.. - Arnold, Carrillo.. (1999) (Correct)
....let us remark that very recently Fokker Planck type equations have been derived from the Boltzmann equation for semiconductors using the BS and a spherical harmonic expansion (SHE model) In the SHE model one obtains an equation for the distribution function in energy position space. We refer to [4, 5, 27] for this kind of models. 6 Numerical simulation The aim of this section is to show that the three presented scaling regimes indeed appear in a realistic simulation of a simple problem. We shall present simulations for a silicon n Gamma n Gamma n diode, and we shall see that different ....
N. Ben Abdallah, P. Degond, P. Markowich, C. Schmeiser, High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors, preprint TMR.
The High Field Asymptotics for Degenerate Semiconductors - Abdallah, Chaker Self-citation (Abdallah) (Correct)
....situations where both collision and electric effects are dominant. In this case the asymptotic procedure is called a High field limit. This limit has been studied in [1, 15] starting from the linear Boltzmann equation. Recently, a High Field model has been derived starting from the SHE model [6]. In this paper, we are concerned with the high field limit of the Boltzmann equation for degenerate semiconductors, where Pauli exclusion terms are taken into account in the collision operator. The mathematical tools are closely related to those used in Poupaud s work [15] for the linear case. As ....
N. Ben Abdallah, P. Degond, P.A. Markowich, C. Schmeiser, High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors, preprint (http://mip.upstlse. fr).
Macroscopic Models for Ionization in the Presence of.. - Degond, Nouri, Schmeiser Self-citation (Degond Schmeiser) (Correct)
....between the Maxwellian distribution for low fields and the Druyvenstein distribution for low temperatures. The resulting equation for the macroscopic density contains field dependent transport parameters and ionization rates. A related treatment for the transport in semiconductors can be found in [2]. 2 Properties of the collision operator Before carrying out the limit 0 in (1.5) we collect some properties of the collision operator Q coll (f) v) oe coll Z IR 3 Z (v Gamma v ) Delta Omega 0 jv Gamma v j(f 0 M 0 Gamma fM )d Omega dv ; where here and in the ....
N. Ben Abdallah, P. Degond, P.A. Markowich, C. Schmeiser, High field approximations of the spherical harmonics expansion model for semiconductors, manuscript, TU Wien, 1998.
Macroscopic Models for Almost Elastic Nonlinear Electron-Phonon.. - Schmeiser (1998) Self-citation (Schmeiser) (Correct)
....SHE (spherical harmonics expansion) models. In general, SHE models contain scattering terms with a tendency to move the distribution towards equilibrium. Thus, the long time behaviour is described by macroscopic equations for the parameters in the equilibrium distribution. Of recent interest [2] are macroscopic limits for high field situations where the ground state is influenced by an electric field balancing the scattering mechanisms. The present work is concerned with the transport of electrons in a semiconductor crystal subject to acceleration by a prescribed electric field and to ....
....derived in section 4. The scattering operator is a first order degeneration of the second order Fokker Planck operator. Finally, section 6 is concerned with a macroscopic limit for high fields of the SHE model derived in section 4. This is a nonlinear (and nonisotropic) extension of a result from [2]. A first order continuity equation for the macroscopic density is derived, containing a conductivity matrix with a nonlinear dependence on the density and on the electric field. The asymptotic behaviour for large fields and the nonlinear structure are studied showing that compression shocks are ....
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N. Ben Abdallah, P. Degond, P.A. Markowich, C. Schmeiser, High field approximations of the spherical harmonics expansion model for semiconductors, manuscript, TU Wien, 1998.
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