Spurious Solutions in the Multiband Effective Mass Theory Applied to Low Dimensional Nanostructures (Communications in Computational Physics, 2009)
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 tolow dimensional nanostructures. The theory results in a system of coupled eigenvaluePDEs that is usually supplemented by interface boundary conditions that can be derivedfrom a variational formulation of the problem. We analyze such a system for theenvelope 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 simpleand effective solution. This solution is demonstrated on an example of a two-bandmodel for both bulk materials and low-dimensional nanostructures. Finally, based onthe above requirement of small k, we derive a model for nanostructures with cylindricalsymmetry and apply the developed model to the analysis of quantum dots usingan eight-band model.