Atom Probe Tomography for Modelling Eigenstates in a Quantum Dot Ensemble

Abstract

Epitaxially grown quantum dots (QDs) make up a significant portion of nanoscale semiconductor research, yet precise solutions for their eigenstates in complex geometries are often unknown. Eigenstates are extremely relevant as they impact the emission wavelength, performance, and stability of many optoelectronic devices. In this thesis, atomic force microscopy, transmission electron microscopy, and atom probe tomography (APT) are used to assess and compare QD size and core concentration. APT by means of isosurface reconstruction provides the most accurate ensemble averaged quantum dot size and core concentration. High-angle annular dark-field imaging quantifies core concentration very well, but fails in comparison to precisely quantify QD size. Ensemble averaging is discarded in favour of using the raw APT data to devise a model that can solve the Schrödinger equation in 3-dimensional space and can be expanded upon to include non-trivial quantum dot geometries of any kind. The electron and hole eigenstates for an entire quantum dot ensemble are solved using this model. Hybridized eigenstates between neighbouring quantum dots are realized and found to experience both bonding and anti-bonding of the charge carriers. The existence of a degenerate state is also discovered. The simulated eigenenergies are compared to the photoluminescence emission spectrum and found to accurately represent the exciton recombination energy. This makes it possible to obtain very realistic 3-D eigenstate representations for a variety of complex structures. The modelling technique outlined in this thesis is not constrained to just QDs, but can also be applied to an array of many other nanoscale structures.