Carrier Plasmon-Polar Phonon Coupling at Semiconductor Surfaces

We investigate the carrier plasmon-polar phonon coupling at semiconductor surfaces by taking account of the dielectric response of a semi-infinite carrier-electron gas and the polar-phonon polarization. The dynamical response of carriers is treated with the random-phase approximation, and the phonon polarization is described by the Lorentzian oscillator model. The coupling character of each coupled surface mode can be clarified by decomposing the induced charge-density distribution into a carrier component due to carrier density fluctuation, a phonon component originating from longitudinal polar-phonon polarization, and two on-surface components arising from termination of the phonon and the background polarization at the surface. The spatial structure of each surface mode can be visualized in the contour map showing the induced charge-density distribution and in the electric-field profile. We examine the coupling character and the spatial structure of each coupled surface mode, the evolution of the character and the structure of each mode with change of carrier concentration, and the origin of three coupled surface modes