Dielectric response at surfaces for semiconductors and insulators

The electrical polarizability of a semi-infinite system is analysed from a classical and a quantum-mechanical point of view for covalent semiconductors and insulators. For surface plasmons of low wavevector, general expressions are calculated for the separate dispersive effects of bulk anisotropy, smooth surface profile and bulk dielectric dispersion. For the last case a classical multipolar polarizability model of the bulk dispersion is used, which up to quadratic dispersion permits explicit inversion of the surface dielectric response function.