Bound Polaron In A Parabolic Quantum Well

In this paper, we study the bound polaron in the GaAs/AlxGa1-xAs parabolic quantum well (PQ W). The study has taken the effects of bulk longitudinal optical (LO) phonons and the interfacelongitudinal optical (10) phonons into account. We utilize the method that has been used by Melnicov and his workmates in the work of bound polaron in a quantum dot (QD). We deal with the electron-optical phonon interaction and electron-donor ion interaction by two canonical transformations. The polarization potential can be gained by the first canonical transformation. By using the second canonical transformation, we can work out the ground state energy and the energy shift and the binding energy of the bound polaron in the infinite PQW. It is found that, for a narrow PQW, the effects of LO phonons and 10 phonons must be considered at the same time. The contribution of LO phonon to the polarization potential is more important in the center of the well. But the contribution of 10 phonon to the polarization potential is more important at the edge of the well. The ground state energy and the energy shift and the binding energy decrease rapidly with increasing the well width (L) at the beginning, then decrease very slowly with increasing L and finally closes to the 3D-value in GaAs. The changing trend of the binding energy of the bound polaron with L is qualitatively the same as that of the energy shift of the bound polaron with L. The main difference is that the binding energy is lower than the energy shift at fixed value of the well width.