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Group classification of an energy transport model for semiconductors with crystal heating

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Abstract

We consider an energy transport model for semiconductors describing the electro-thermal effects. The unipolar model involves four equations: the continuity and the energy balance equations for the electrons, the thermal diffusion equation for the lattice and the Poisson equation for the electric potential. The model can be derived by moment method from the Boltzmann transport equation for electrons in semiconductors. For this model, we perform a symmetry group classification by the infinitesimal Lie method and exact solutions are found.

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Acknowledgments

We warmly thank Professor Vittorio Romano for enlightening discussions. R. T. thanks the support from University of Catania through PRA.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125, Catania, Italy

    Mariangela Ruscica & Rita Tracinà

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  1. Mariangela Ruscica
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  2. Rita Tracinà
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Correspondence to Rita Tracinà.

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Communicated by Jose Alberto Cuminato.

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Ruscica, M., Tracinà, R. Group classification of an energy transport model for semiconductors with crystal heating. Comp. Appl. Math. 34, 1167–1174 (2015). https://doi.org/10.1007/s40314-014-0175-2

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  • DOI: https://doi.org/10.1007/s40314-014-0175-2

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