Abstract
In this paper, we present a new scaling limit of the semiconductor Boltzmann equation which yields the so-called Energy-Transport model. This model consists of a set of continuity equations for the density and energy together with constitutive relations for the particle and energy fluxes. These fluxes are expressed in terms of gradients of the entropic variables, through a diffusivity matrix related to the Boltzmann collision operators. The present work is devoted to a scaling limit in which the only operator involved in the definition of the diffusivity is the elastic collision operator. Previous derivations required a two-step procedure, resorting to an intermediate model, the so-called Spherical Harmonics Expansion (or SHE) model. We shall present and review the relationship between all these models.
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Degond, P., Levermore, C.D., Schmeiser, C. (2004). A Note on the Energy-Transport Limit of the Semiconductor Boltzmann Equation. In: Abdallah, N.B., et al. Transport in Transition Regimes. The IMA Volumes in Mathematics and its Applications, vol 135. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0017-5_8
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DOI: https://doi.org/10.1007/978-1-4613-0017-5_8
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