Electron–LO-phonon interaction in semiconductor double heterostructures

The electron--LO-phonon interaction Hamiltonian is deduced in a systematic way from a model of dispersive polar-optical vibrations for a semiconductor double heterostructure. LO phonons are introduced along the lines of the Born-Huang approach valid in the long-wavelength limit, while phonon confinement effects are included in a model which can be imagined as a jellium slab disposed between two rigid walls. The obtained Hamiltonian includes screening along the lines of the static three-dimensional (3D) Thomas-Fermi approximation and contains the 3D Frohlich Hamiltonian as a limiting case. The case of a single heterostructure is also contained as another limit. We compare our results with earlier works on the subject. Estimations of the polaronic energy shift and mass are reported.