Mathematical models and numerical analysis of the conduction and valence band engineering in cylindrical quantum dots

Prabhakar, S., Takhtamirov, E., Melnik, R.

Applied Mathematics and Informatics (European Conference for the Applied Mathematics and Informatics, Greece, Dec, 2010), Eds. N. Mastorakis et al, pp. 201-206, 2010, ISSN: 1792-7390, ISBN: 978-960-474-260-8

Abstract:

We develop a mathematical model for the analysis of conduction and valence band eigenenergy in quantum dots.  We apply this model to study the band structure of low dimensional semiconductor nanostructures (LDSNs) such as wurtzite AlN/GaN quantum dots in cylindrical coordinates in the presence of applied magnetic field along z-direction. We use a finite element method to solve the resulting model and to obtain eigenvalues and wave functions of cylindrical quantum dots. We provide details of the methodology of solution and appropriate boundary conditions. A special attention is given to the case of applied magnetic field along z-direction where we found localized eigenstates and wave functions in the conduction and valence bands for which our results open new possibilities for the design of such optoelectronics devices where the combination of electron-hole pairs can be used as tuning parameters.

Keywords: quantum dots, mathematical models, spintronics, wurtzite structures, localized states, finite element method, magnetic field effects.