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Diffusive Limit of the Two-Band k⋅p Model for Semiconductors

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Abstract

We derive semiclassical diffusive equations for the densities of electrons in the two energy bands of a semiconductor, as described by a k⋅p Hamiltonian. The derivation starts from a quantum kinetic (Wigner) description and resorts to the Chapman-Enskog method as well as to the quantum version of the minimum entropy principle. Four different regimes are investigated, according to different scalings of the k⋅p band-coupling and band-gap parameters with respect to the scaled Planck constant.

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Authors and Affiliations

  1. Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Luigi Barletti

  2. Dipartimento di Matematica Applicata “G. Sansone”, Università di Firenze, Via Santa Marta 3, 50139, Firenze, Italy

    Giovanni Frosali

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  1. Luigi Barletti
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  2. Giovanni Frosali
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Correspondence to Luigi Barletti.

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Barletti, L., Frosali, G. Diffusive Limit of the Two-Band k⋅p Model for Semiconductors. J Stat Phys 139, 280–306 (2010). https://doi.org/10.1007/s10955-010-9940-9

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  • DOI: https://doi.org/10.1007/s10955-010-9940-9

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