@Article{CiCP-6-4, 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/2009-CiCP-7701}, url = {https://global-sci.com/article/81165/spurious-solutions-in-the-multiband-effective-mass-theory-applied-to-low-dimensional-nanostructures} }