Mathematical properties of a kinetic transport model for carriers and phonons in semiconductors |
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Authors: | M Galler F Schürrer |
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Institution: | (1) Institute of Theoretical and Computational Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria |
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Abstract: | We present studies on the mathematical properties of a multigroup formulation of the Bloch–Boltzmann–Peierls equations. The
considered model equations are based on a general carrier dispersion law and contain the full quantum statistics of both the
carriers and the phonons. Moreover, the transport model allows the investigation of particle distributions with arbitrary
anisotropy with respect to the main direction. We prove the boundedness of the solution according to the Pauli principle and
study the conservational properties of the multigroup equations. In addition, the existence of a Lyapounov functional to the
proposed model equations is proved and expressions for the equilibrium solution are given. Numerical results are presented
for the stationary state distributions of a coupled system of electrons and longitudinal optical phonons in GaAs. |
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Keywords: | 82 08 82C70 82D37 |
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