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We investigate the evolution of elementary excitations at a doped polar semiconductor surface in a depletion-layer formation process. The elementary excitations analyzed are two coupled plasmon-phonon modes and a surface optical-phonon mode involving screening charges. Surface excitations of free carriers are calculated by taking account of the Coulomb interaction between carriers, the dynamical exchange-correlation effect, and the coupling with surface polar phonons, on the basis of thermal-equilibrium states calculated self-consistently by the local-density approximation. We focus our attention on the coupling character and the spatial structure of each surface-excitation mode, as well as the energy dispersion and the energy-loss intensity involved in the excitation. The induced charge-density distribution in the excitation mode is composed of a carrier component due to carrier density fluctuation, a phonon component arising from longitudinal polar-phonon polarization, and two on-surface components originating from the termination of the polar phonon and background polarization at the surface. The coupling character is elucidated by the phase relation and the amplitude ratio among these induced charge components. The spatial structure is visualized by the contour map of the induced charge-density distribution. We follow the variation in the coupling character and the spatial structure in the depletion-layer formation process. Our analysis gives a clear explanation of the variation in each of the three loss peaks in the electron energy-loss spectrum

Evolution of elementary excitations at a doped polar semiconductor surface in a depletion-layer formation process