Quantum dot molecules and their electromagnetic response

There exists a broad range of semiconductor nanostructures that can be fabricated with a variety of geometries and properties. The breadth of applications of these systems is remarkable having proven useful in biological sensing, single photon sources and quantum computing, to name a few. The consistently improving ability to meticulously tailor these structure presents a considerable amount of work for theorists modelling these systems. In this thesis we put forward an efficient modelling framework capable of exploring the properties of a semiconductor nanostructures. We demonstrate that the finite element method in conjunction with the Schrödinger-Poisson equations is a sufficiently flexible method to examine many of these structures. This modelling framework can account for quantum dot structures in the presence of electromagnetic fields. Furthermore, it can accurately model the quasi-particle excitations that emerge in these systems, excitons, that consist of an electron-hole pair bound by the Coulomb interaction. With this modelling framework we explore a variety of semiconductor nanostructures. Our initial investigation considers single quantum dots, some in the presence of electromagnetic fields. However, we extend our analysis to include quantum dot molecules. These include pairs of vertically stacked quantum dots grown via the Stranski-Krastanov method where an electric field is utilised to separate the electron and the hole. Other systems examined are colloidal quantum dots bound by organic linker molecules and three quantum dot arrays arranged in a triangular formation that have their emission properties altered by a perpendicular magnetic field. The specific systems we examine provide insights into their physical properties but also demonstrates how our modelling framework could be applied to many other structures.