Electronic band structure of III-V quantum dots using tight-binding and the k.p approximation

Quantum dot nanostructures incorporate unique mechanical and electronic properties that dictate their use in numerous applications such as photovoltaics, LED's, and quantum computing. The \textbf{k}{$\cdot$}\textbf{p} approximation and O(N) moments based tight-binding model for electronic band structure calculations are implemented for several cases relating to quantum dot nanostructures where various mechanical models are investigated. First, a comparison is made between the two for an equivalent sized ellipsoidal InAs/GaAs quantum dot by reconstructing an effective continuum local density of states using FEM solutions to the Schr{\"o}dinger equation. The local density of states predicted by the tight-binding model is shown to compare qualitatively to the continuum reconstructed LDOS. The local charge density between models is also investigated with some consistency where possible sources of discrepencies are noted. The \textbf{k}{$\cdot$}\textbf{p} method is investigated further in relation to nanostructured GaSb/GaAs systems. Effects on the observed type-I/type-II band alignment of such systems are explored by using cross-sectional STM images of GaSb nanostructures for composition input into a continuum model. Based on a rule-of-mixtures assumption about material properties as a function of composition, the strain field due to lattice mismatch is calculated and used with deformation potential theory and the \textbf{k}{$\cdot$}\textbf{p} approximation to determine the resulting conduction/valence band offsets and energy states. This predicts a large type-I to type-II transition, with conduction band offsets greater than those observed experimentally via scanning tunneling spectroscopy (~0.1ev). Strain relaxing misfit dislocations are then considered as the source of this quantitative disagreement; both strain and charging effects of dislocations are investigated computationally, and found to have a large effect on the band alignment. The resulting spontaneous emission spectra are then computed for comparison to experimental photoluminescence data