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The Multi-Band k⋅p Hamiltonian for Heterostructures: Parameters and Applications

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Book cover Multi-Band Effective Mass Approximations

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 94))

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Abstract

In this contribution all the various definitions of the k⋅p parameters available in the literature are summarized, and equations that relate them to each other are provided. We believe that such a summary for both zinc blende and wurtzite crystals on a few pages is very useful, not only for beginners but also for experienced researchers that quickly want to look up conversion formulas. Results of k⋅p calculations for bulk semiconductors are shown for diamond, and for unstrained and strained InAs. Several examples of k⋅p calculations for heterostructures are presented. They cover spurious solutions, a spherical quantum dot and heterostructures showing the untypical type-II and type-III band alignments. Finally, self-consistent k⋅p calculations of a two-dimensional hole gas in diamond for different substrate orientations are analyzed. Wherever possible, the k⋅p results are compared to tight-binding calculations. All these calculations have been performed using the nextnano software (nextnano: The nextnano software can be obtained from http://www.nextnano.com; Birner et al., IEEE Trans. Electron Dev. 54:2137–2142, 2007). Therefore, this contribution provides some specific details that are relevant for a numerical implementation of the k⋅p method.

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Authors and Affiliations

  1. Walter Schottky Institute and Physics Department, Technische Universität München, Am Coulombwall 4, 85748, Garching, Germany

    Stefan Birner

  2. Institute for Nanoelectronics, Technische Universität München, Arcisstr. 21, 80333, München, Germany

    Stefan Birner

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  1. Stefan Birner
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  1. & Numerische Mathematik, Bergische Universität Wuppertal Lehrstuhl für Angewandte Mathematik, Wuppertal, Germany

    Matthias Ehrhardt

  2. Forschungsgruppe “Partielle Differentialgleichungen", Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, Germany

    Thomas Koprucki

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Birner, S. (2014). The Multi-Band k⋅p Hamiltonian for Heterostructures: Parameters and Applications. In: Ehrhardt, M., Koprucki, T. (eds) Multi-Band Effective Mass Approximations. Lecture Notes in Computational Science and Engineering, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-01427-2_6

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