Optical-phonon modes and electron-phonon interaction in arbitrary semiconductor planar microcavities

Within the framework of the standard dielectric continuum model, we solve the optical-phonon modes in an arbitrary semiconductor multilayer heterostructure using the transfer-matrix method and derive the dispersion relation for the interface modes. The explicit form of the polarization field and the electron-phonon interaction Fr\"ohlich-like Hamiltonian is obtained for the first time. The analytical formulas are universal, which can be applied to investigations of both the optical-phonon modes and the electron-phonon interaction operator in semiconductor planar microcavities (MC's), superlattices (SL's), and quantum wells (QW's). Our theory allows to obtain all important earlier results and predicts a phenomena. We find that, for a QW planar MC, the electron interaction with the QW modes is most important for larger wave vector k among all of the interface phonon modes. It can be approximately replaced by the electron-phonon interaction Hamiltonian in a single QW with the same width as the QW in the MC if k>~2×10⁵ cm^-1. The relative importance of the AlAs- and GaAs-type optical phonons for the GaAs/AlAs SLs is also discussed.