Theory of bulk and surface photoeffects in a free-electron metal

In order to obtain new, general, conceptual insight into some aspects of the theory of photoemission, a consistent treatment was developed for photoemission from a free-electron (FE) metal with vanishingly small absorption at photon energies larger than the bulk-plasmon excitation energy. The electromagnetic response of the FE metal was described by the dielectric function ε(→q,ω) derived by Melnyk and Harrison. Calculated photoelectron energy-distribution curves (EDC) differ significantly both in magnitude and dependence on photon energy from the conventional FE results. The wave-vector selection rule for photoemission from a semi-infinite FE solid was derived. The separation of bulk and surface contributions to photoemission and its relation to "direct" and "nondirect" electronic transitions are reexamined and shown to be less reliable than commonly assumed. A new bulk contribution to the photoemitted current is identified and is associated with transitions which do not conserve the component of momentum normal to the surface. These "direct-like" transitions are shown to be closely related to ordinary direct (bulk) transitions; their occurrence is independent of an explicit electron-electron or electron-phonon interaction, and is not necessarily related to a finite extraction depth of the electrons. A bulk enhancement of the classical surface photoeffect associated with the gradient of the surface barrier is also identified. The vectorial effect is shown not to discriminate between surface and bulk photoeffects. For p-polarized photons the EDC is shown to depend strongly on the photon angle of incidence. The photoyield is shown to exhibit a sharp peak at the critical angle for total reflection. In contrast to earlier calculations, our calculation of the high photon-energy limit of the photoelectric yield from the FE metal agrees with the asymptotic yield from an atom.