Effect Of Electron-Phonon Interaction On A Hydrogenic Impurity In A Spherical Quantum Dot Under A Magnetic Field

Within the effective-mass approximation, a variational approach is used to study the ground-state binding energy and polaronic effect of a hydrogenic impurity in nitride spherical quantum dots.Firstly, a variational method is used to calculate the binding energies of impurity states in spherical GaN quantum dot structures under an external magnetic field for infinite barriers. Using a modified LLP variational method, the binding energies are calculated as functions of the quantum dot size and the impurity position by considering the effects of the interaction of an electron with both the confined longitudinal optical(LO) phonons and the surface optical(SO)phonons. Numerical results showed that the binding energy of a spherical quantum dot increases monotonously with the decrease of the quantum dot size as well as the increase of applied magnetic field. The electron-phonon interaction increases the binding energy. The contribution of electron-LO phonon decreases as the impurity is moved from the center of the quantum dot to the edge of it, and the contribution of electron-SO phonon increases and then decreases. It is also found that a magnetic filed strengthens electron-LO phonon interaction and weakens electron-SO phonon interaction.Then, a variational method is adopted to investigate impurity states of nitride quantum dots with finite potential barriers by taking the couplings of impurity-LO phonon and impurity-SO phonon into account. The binding energies are calculated as functions of the quantum dot size and the impurity position. Numerical results showed that the binding energies increase with the potential energy. The polaronic effect obviously decreases the binding energy. The contribution of LO phonons increases and then decreases as the dot radius is decreased, but the contribution of SO phonons increases. It also indicated that the contribution of LO phonons decreases as the impurity is moved from the center of quantum dot to the edge of it, whereas the contribution of SO phonons increases.