Carrier-concentration dependence of plasmon-polar phonon coupling at semiconductor surfaces

We investigate the carrier-concentration dependence of 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 induced charge-density distribution in each coupled surface mode consists of 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 coupling character reveals itself in the amplitude ratio and the phase relation among these induced-charge components in variation along the propagating direction. This coupling character is reflected in the way in which each induced-charge component contributes to the energy loss involved in the dynamical surface response. The spatial structure of each coupled surface mode can be visualized in the contour map showing the induced charge-density distribution and in the electric-field profile. We follow the evolution of the coupling character and the spatial structure of each coupled surface mode with change of carrier concentration passing through a strong-coupling regime.