Coupled Multiphysics Models for the Analysis of the Conduction and Valence Band Eigenenergies in Cylindrical Quantum Dots
S. Prabhakar, E. Takhtamirov and R. Melnik
bM2NeT Laboratory, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, N2L 3C5, Canada
Full Text PDF
We develop a mathematical model for the analysis of conduction and valence band eigenenergy in quantum dots. We apply the model to study the band structure calculations of low dimensional semiconductor nanostructures such as wurtzite AlN/GaN quantum dots in cylindrical coordinates in 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, we found localized eigenstates and wave functions in the conduction and valence bands for which our results open new possibilities for the design of the optoelectronics devices where the combination of electron-hole pairs can be used as tuning parameters.
DOI: 10.12693/APhysPolA.121.85
PACS numbers: 71.15.-m, 73.21.La, 62.23.Eg