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Plane-Wave Approaches to the Electronic Structure of Semiconductor Nanostructures

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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

This chapter is dedicated to different plane-wave based approaches to calculate the electronic structure of semiconductor nanostructures. We introduce semi-analytical and numerical methods to achieve a plane-wave based description of such systems. This includes use of plane-wave methods to calculate not just the electronic structure but also the built-in strain and the polarisation potential, with the strain and the polarisation potential each having a significant influence on the electronic properties of a semiconductor nanostructure. The advantages and disadvantages of different plane-wave based formulations in comparison to a real-space, finite element model will be discussed and we will present representative examples of semiconductor nanostructures together with their elastic and electronic properties, computed from semi-analytical and numerical approaches. We conclude that plane-wave-based methods provide an efficient and flexible approach when using k⋅p models to determine the electronic structure of semiconductor nanostructures.

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Acknowledgements

We thank Christopher A. Broderick for a careful reading and very useful suggestions regarding earlier versions of this chapter. We also thank the many other colleagues with whom we have had the pleasure to work on using plane-wave based methods, including J.A. Barker, S.B. Healy, S. Tomić and D.P. Williams. We acknowledge financial support for the work on (111)-oriented QDs from Science Foundation Ireland (10/IN.1/I299).

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Authors and Affiliations

  1. Tyndall National Institute, Cork, Ireland

    Eoin P. O’Reilly, Oliver Marquardt & Stefan Schulz

  2. Hitachi Cambridge Laboratory, Cambridge, UK

    Aleksey D. Andreev

Authors
  1. Eoin P. O’Reilly
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  2. Oliver Marquardt
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  3. Stefan Schulz
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  4. Aleksey D. Andreev
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Correspondence to Eoin P. O’Reilly .

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Editors and Affiliations

  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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O’Reilly, E.P., Marquardt, O., Schulz, S., Andreev, A.D. (2014). Plane-Wave Approaches to the Electronic Structure of Semiconductor Nanostructures. 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_5

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