Hydrogenic Impurity States And Excitons In Parabolic Quantum Wells

The characteristics of hydrogenic impurity states and excitons in parabolic quantum wells (PQWs) and relative problems have been investigated theoretically. There are five parts in this thesis.Firstly, the special properties for PQW structures and their potential application to develope new optoelectronic devices are introduced. The development of the theoretical studies for the electrons, hydrogenic impurity states, excitons, biexcitons and the electron-phonon interaction in PQWs is reviewed. The motivation of the present work is clarified.Secondly, the energy and effective mass of an electron interacting with longitudinal optical (LO) phonons in a PQW system are investigated by using LLP-like transformations and a variational approach. The results show that both of the self-trapping energy and effective mass of a polaron in a finite PQW have expected maximums but decrease monotonously for an infinite PQW as the well-width increases. It is verified that the approximation of bulk LO phonon mode is an adequate formulation for the electron-phonon coupling in PQWs, even the phonon structure in this kind of systems is complicated. The conclusion will be helpful for the further works in this field.Thirdly, the binding energy and transition energy of 1s→2p_for a hydrogenic impurity state in a PQW under a magnetic field perpendicular to the well plane are calculated variationally by using a trial wave function with three-parameters. It is found that the binding energy and transition energy of the hydrogenic impurity state have their maximums with variation of the well-width, but the binding energy increases monotonously with the magnetic field whereas a minimum appears for the transition energy. The results show that our method is practicable and helpful inunderstanding the characteristics of hydrogenic impurity state in PQWs.The fourth part is the center of the thesis. In this part, by linking the LLP transformations, variational methods as well as a fractional-dimensional approach, in which the real semiconductor heterostructure system is substituted by an effective isotropic environment with a fractional dimension, we expend successfully the fractional-dimensional approach into the exciton-phonon system in PQWs. The polaron effects on excitons and Stark shifts of the exciton binding energies are discussed by using the developed method. The results for GaAsZAlo.3Gao.7As PQWs show that the tendency of exciton binding energy varying with well-width of PQWs is similar to that for square quantum wells (SQWs), namely, the binding energy first increases rapidly, reaches a maximum value, then decrease slowly with increase of the well-width, finally trends to the effective Rydberg energy of the well material. The binding energies of excitons in PQWs are less than that in SQWs for the narrow well case, but bigger for the wide well case. It is also found that the exciton binding energy is reduced by the exciton-phonon interaction. The phonon contribution to the binding energy has a maximum at a very narrow well-width and the polaron effects on the exciton binding energy can not be neglected. Both of the binding energy and phonon contribution decrease with increasing the electric-field strength and the decrease is much more significant for wide well-width.Finally, we improve the geometrical model for a two-dimensional biexciton proposed by Singh et al to study the binding energies of biexcitons both in SQWs and PQWs with a fractional-dimensional approach. The results show that the biexciton binding energy has a maximum at certain well-width, and the Haynes factor varies from 0.324 to 0.228 when the effective mass ratio of electron to hole increases from 0 to 1. Our results agree fairly well with the previous experimental results, which fiirthur demonstrate the validity and applicability of the fractional-dimensional approach.