Dielectric response of a semi-infinite layered electron gas and Raman scattering from its bulk and surface plasmons

An exact solution of the random-phase-approximation equations is worked out for the density-density correlation function of a semi-infinite system of two-dimensional electron-gas layers, with different dielectrics outside and inside the layered system. From this solution, analytic formulas are derived for the dispersion relations of the bulk and surface plasmons and for the intensity of the light scattered inelastically from such a system. The intensity is written as a sum of the bulk and the surface terms. The theory is applied to semiconductor multilayers. The line shape of the bulk-plasmon peak, obtained after cancellation of van Hove singularities in the bulk piece by the surface piece, is compared with experiment. Conditions for observation of the Giuliani-Quinn surface plasmon are outlined.