Research On Exciton Binding Energy In A Finite Rectangular Quantum Wire In A Magnetic Field

In this paper, we present a perturbation theory to investigate the ground states of the electron and hole in the presence of a magnetic field, which is the groundwork of the exciton binding energies obtained by using the one-dimensional effective potential model in a InAs/InP self-assembled rectangular quantum wire. We also study the exciton diamagnetic shifts for the magnetic field applied along the wire, taking into account the strain in the sample and the different masses inside and outside of the QWR for the different particles. The heavy hole state is the ground state for the InAs/InP QWR, therefore, we neglect the coupling between the heavy hole and light hole and consider the heavy hole only. A good agreement is obtained between our results and experimental points, which is better than early work.By calculating the ground states of the electron and heavy hole and the exciton diamagnetic shift in the InAs/InP rectangular quantum wire, we obtain the conclusions as follows:(1)The energy of the electron or the hole increases gradually as the magnetic field increasing and the width of the wire becoming small with the length of the wire being unvarying.(2)When the length of the wire is unvarying, the exciton binding energy will become small as the width of the wire decreasing and be affected by the magnetic field easier. That's because the width of the wire we studied is smaller than the critical width.We can get better result by using this method further. We can also use the perturbation theory to investigate the X ? state, X + state, X 2 state etc in the rectangular wire and study the states in the triangular-shaped or other shapes quantum wires.