Photoemission spectroscopy—Correspondence between quantum theory and experimental phenomenology

We describe the relation between the observed behavior of photoemission energy distributions vs frequency, angle, etc., and the quantum theory of photoemission as recently set forth formally by Caroli et al. We derive a Fermi's Golden-Rule formula for the angle- and energy-resolved photocurrent from an independent electron solid, and show in detail the approximations which render this formula equivalent to that of the familiar three-step model of bulk photoemission. In terms of the Golden-Rule formula, we account for the direct-transition band-structure regime generally observed at low photon energies ($h\nu \lesssim 20-30$ eV) and the "photoemission density of states", or x-ray-photoemission-spectroscopy regime, observed at higher energies. We also propose an explanation of Feuerbacher et al.'s observation of "direct photoemission into the vacuum" from single-crystal tungsten surfaces. Finally, we discuss the criteria which determine the relative magnitudes of photocurrents from a surface adsorbate layer and an underlying substrate.