OPTICAL-PHONON MODES AND ELECTRON-OPTICAL-PHONON INTERACTION IN A COUPLED-QUANTUM-WELL

By applying the dielectric continuum model, optical-phonon modes of th e lattice vibration and a complete: interaction Frohlich-like Hamilton ian between an electron and the optical phonons including the interfac e phonons, the confined LO phonons and the half-space LO phonons are d erived for a general coupled quantum well (GCQW) structure of polar cr ystals. The dispersion curves of the interface modes and the electron- interface-phonon coupling function as functions of coordinate z and wa venumber ic are given and discussed for a GCQW. We find that there are eight (not ten) frequency solutions for the interface optical-phonon modes in GCQW and that, in the long-wavelength limit, the longitudinal and transverse modes; in the two side materials 1 and 5 are forbidden and two new frequency solutions wi are obtained instead. Moreover, we also find that the electron-interface-phonon coupling functions am co mplicated functions of k and that the phonons with long wavelengths ar e important and the higher-frequency modes are more important than the lower-frequency modes for the electron-phonon interaction.