Study On Properties Of Exciton In Parabolic Quantum Dot

The study of low-dimensional systems has received much attention in recent years, especially due to the discovery of such effects as the quantum Hall effect in two-dimensional systems. The physics in low-dimensional systems presents new challenges both theoretically and experimentally. With the development of modern technology, it is now possible to produce 0D systems that confine electrons in all three spatial dimensions. Because quantum dot maybe can be used in different areas, it has become one of the most important issues in modern physics.In the first chapter of my dissertation, the conceptions of exciton and quantum dot, the research back ground, method and recent research achievements in exciton and quantum dot have been summarized. There after, parabolic quantum dots are selected as our research objects.In the second chapter, some foundational properties of exciton for parabolic quantum dot, such as ground-state energy and ground-state binding energy, are studied. Firstly, the first approximation eigenfunctions and eigenenergies of the ground-state are obtained by using the effective-mass approximation, with centre-of-mass and relative coordinate. Then the ground-state energy and ground-state binding energy of exciton are obtained by using the perturation method. Finally, numerical results are presented for typical GaAs parabolic quantum dots. The results show that the ground-state energy and ground-state binding energy of exciton for parabolic quantum dots become large with the characteristic frequency increases. We also find that with the dot radius increases, the ground-state energy and ground-state binding energy of exciton regularly reduce. But when the dot radius reaches long enough, the ground-state energy do not decrease more. The value that the ground-state energy and ground-state binding energy reached is the very value that is obtained in the model of quantum well. In order to research the properties of exciton better, we also compute the energy when the interaction between electron and hole is regardless. Meanwhile, the difference between first excited energy of the exciton and ground-state energy of the exciton are calculated.In the third chapter, we studied the influence of the dot radius and magnetic field to the ground-state energy and ground-state binding energy. Due to the existence of magnetic field, we obtained such a term that include centre-of-mass and relative coordinate when we simple the Hamiltonian with centre-of-mass and relative coordinate. Fortunately, when we compute the energy using perturation method we find that this term becomes zero. Like in the second chapter, numerical results are presented for typical GaAs parabolic quantum dots. The results show that, the ground-state energies and ground-state binding energies for different dot radiuses become larger with the increase of magnetic field. But the energy of different dot radiuses increased differently. In our numerical calculation, we also find that the different between the first excited-state energy and the ground-state energy of exciton firstly reduces with the increase of magnetic field, but when reached a lowest dot, it become increase with magnetic field. This phenomenon results in the competition among all energies of exciton. Like what did in the second chapter, the energy is computed when the interaction between electron and hole is regardless. Finally, the difference between first excited energy of the exciton and ground-state energy of the exciton as a function of magnetic field are calculated.In the last chapter, the main contents and conclusions of my dissertation have been summarized, and sequential research work is specified.