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

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

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

Published online: 2009-06

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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 coefficients 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.

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@Article{CiCP-6-699, author = {}, title = {Spurious Solutions in the Multiband Effective Mass Theory Applied to Low Dimensional Nanostructures}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {4}, pages = {699--729}, 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 coefficients 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7701.html} }
TY - JOUR T1 - Spurious Solutions in the Multiband Effective Mass Theory Applied to Low Dimensional Nanostructures JO - Communications in Computational Physics VL - 4 SP - 699 EP - 729 PY - 2009 DA - 2009/06 SN - 6 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/cicp/7701.html KW - AB -

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 coefficients 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.

B. Lassen, R. V. N. Melnik & M. Willatzen. (2020). Spurious Solutions in the Multiband Effective Mass Theory Applied to Low Dimensional Nanostructures. Communications in Computational Physics. 6 (4). 699-729. doi:
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