複層量子結構中雜質能階及外加磁場效應之研究

Abstract

The energy states of a hydrogenic impurity located at the center of a quasi-zero dimensional coated quantum dot (CQD) are investigated. We also study the electronic energy levels in a quasi-one dimensional coated quantum wire (CQW) with an applied magnetic field along the wireaxis. In both of the CQD and CQW systems, we solve the Schroedingerequations analytically, and obtain the electronic eigenstates as functionsof the radius of the CQD and CQW and the material parameters. Our resultsshow that the ground state energies for both systems are deeply influencedby the shell thickness and approach the correct limit of the bulk case, asthe radius of the inner layer becomes very large. It is also found that theground state energy of the CQD is higher than that of the CQW because the former system has one more dimensional confinement. However, the ground state energies for both two systems approach the same value, as the shellpotentials are negative enough. In the study of the effect of external magneticfield, our results show that in a moderate magnetic field strength availablein the laboratory, the magnetic length is usually large. Thus the potentialbarrier is always the winner of the competition with a magnetic field in the coated quantum wire without impurity. Image potential effect in the Schroedinger equation is ignored and the effective mass approximation is employed. The eigenfunctions can be expressedin terms of the Whittaker functions. For numerical calculations, we onlycalculate the ground state energy, although the excited state energies can beobtained straightforwardly. We must emphasis here the numerical method employedin this thesis is novel and has general significance.