Abstract
A theoretical study of the electronic properties of silicon quantum dots (QDs) in applied electric and magnetic fields is presented in this work. To obtain the electronic states inside the quantum dots, a new finite-element method based technique is proposed within the effective mass approximation, in order to solve the time independent Schrodinger equation. The method allows for arbitrary shaped QDs in any material. Applied magnetic fields have been included in the most general way, such that 2-spinor wavefunctions may be obtained, which may be of more use in further work when considering many body effects within the framework of density functional theory. Applied electric fields using metal gates surrounding the QD have also been included in a new way, allowing for more realistic gate geometries. The new methods derived by the author allowed two studies to be performed. Firstly, a study of charge polarisation (localisation) inside Si double quantum dots (DQDs) in an applied magnetic field is presented, with varying DQD geometry. It is shown that the magnitude of the charge polarisation in the DQD is strongly related to the asymmetry of the DQD, and to the coupling strength between the two dots making the DQD, as well as its overall size. The applied magnetic field however, can be used to control the charge polarisation, as is demonstrated. Secondly, a study of a realistic gated Si DQD structure examined in experiments by Ferrus et al. It is demonstrated that the electric fields generated by gate potentials of the order used in the experiments have a strong ability to induce charge polarisation within the dot. The prospects for further development of the model are highlighted, to obtain more realistic simulations of electronic Si-based quantum structures.