Bound Polaron In Quantum-Dot Quantum Well Structures

In this paper, the bound polaron in Quantum-dot Quantum well structures is investigated based on the continuous medium model and effective mass approximation, the effective Hamiltonian of the phonon and the polarization potential of the impurity are obtained by the first canonical transformation, the ground state of the electron is worked out by using the variational method after the second canonical transformation, the influence of electron-phonon interaction to the ground state of a bound polaron is also analysed. The result shows that the contribution of the interaction energy is negative to the total energy.The ground state energy and the binding energy of a bound polaron in Quantum-dot Quantum well structure are calculated, and the free polaron is also studied. It is found that the ground state energy of the bound polaron increases gradually firstly and then rapidly with decreasing of the well width, this is because the kinetic energy of the electron becomes too big in a narrow well, especially in the total energy of the electron may change from negative to positive at a certain well width and finally diverges to infinity as the well approach zero. However, the binding energy of the bound polaron decreases remarkably as the well decreases in a wider well in the beginning, and approaches a steady value in a narrower well subsequently. The change tendency of the ground state energy and the binding energy of the free polaron are similar to that of the bound polaron, respectively, but the energy of the free polaron is higher than that of the bound polaron, which is resulted in because of the negative coulomb energy of impurity and electron.