@Article{CiCP-6-699,
author = {B. Lassen, R. V. N. Melnik and M. Willatzen},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7701.html}
}