Calculation of the Surface Photoelectric Effect

Abstract

A modified form of the Mitchell—Makinson time-dependent perturbative calculation of the surface photoelectric effect has been carried out based on a significantly improved treatment of surface-polarization charge-density variations. The approach taken allows calculation of the excitation current back into the metal as well as into vacuum, and is generally applicable to the surface wave (plasmon) or to the direct optical mode of $p$-polarized-light excitation of the surface effect. Numerical results are presented for aluminum, but the general conclusions of the paper should be applicable to all nearly-free-electron metals. The behavior of the surface charge is shown to have a fundamental effect upon the frequency dependence of the surface effect, causing a marked enhancement in the effect at low energies followed by an almost total suppression of the surface effect at energies near the volume plasma energy. Surface photoexcitation at these lower energies is shown to dominate the photoemission from surface-wave decay as well as from direct optical excitation at high angles of light incidence. The surface-wave (plasmon) mode of excitation is shown to be particularly strong, with surface excitation dominating the decay of the high-$k$ plasmons typically excited on real surfaces. Comparisons of the results of this calculation are made with existing experimental data, and the prediction that surface waves (plasmons) should form a uniquely strong mode of surface-effect excitation is shown to be quantitatively consistent with recent experimental studies of photoemission in surface-plasmon decay. The historical failure to observe direct optical excitation of the surface photoelectric effect in the alkalis is explained, and a suggestion for detecting direct-optical excitation of the effect in other nearly-free-electron metals is made based on the results of this calculation.