POLARON EFFECTS IN A QUANTUM BOX

The interaction Hamiltonian of an electron with LO phonons in a quantu m box is derived. Within the framework of the effective-mass approxima tion, the electron self-energies due to the interaction of the electro n with the confined LO-phonons that incorporate effects of phonon conf inement in a quantum box have been calculated as a function of the siz e of the boxes by a perturbative method. The results show that for sma ll 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 d irections. The smaller the size of the box, the larger the absolute ma ximum of the self-energy. These results imply that the effects of phon on confinement are dominant in small boxes.