Polaron Effects in a Quantum Box

Abstract

The interaction Hamiltonian of an electron with LO phonons in a quantum box is derived. Within the framework of the effective-mass approximation, the electron self-energies due to the interaction of the electron with the confined LO-phonons that incorporate effects of phonon confinement in a quantum box have been calculated as a function of the size of the boxes by a perturbative method. The results show that for small boxes, the electron self-energy increases rapidly to a maximum and then decreases slowly to the limit of the wire value as the box trends to infinity in one direction while remaining fixed in the other two directions. The smaller the size of the box, the larger the absolute maximum of the self-energy. These results imply that the effects of phonon confinement are dominant in small boxes.