Volume 6, Issue 4
Spurious Solutions in the Multiband Effective Mass Theory Applied to Low Dimensional Nanostructures

B. Lassen ,  R. V. N. Melnik and M. Willatzen

Commun. Comput. Phys., 6 (2009), pp. 699-729.

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  • Abstract

In this paper we analyze a long standing problem of the appearance of spurious, non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures. The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem. We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi- cients to small k components would lead to the appearance of non-physical solutions. We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution. This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures. Finally, based on the above requirement of small k, we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.

  • History

Published online: 2009-06

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