The Effective Mass of Impurity–bound Polaron in a Two- and Three-Dimensional Quantum Dot

Abstract

Within the framework of the Landau–Pekar variational method we have derived an analytical expression for the ground-state binding energies and the effective mass of an electron bound to a Coulomb impurity in a polar semiconductor quantum dot (QD) with parabolic confinement in both two and three dimensions. We have also calculated the number of phonons in the cloud of this bound polaron. It is found that the effective mass increase with increasing the Coulomb binding parameter and increase with the decrease in size of the QD. The results also indicate that this effect becomes much more pronounced with decreasing dimensionality.