DIRECT TRANSITIONS, INDIRECT TRANSITIONS, AND SURFACE PHOTOEMISSION IN THE PROTOTYPICAL SYSTEM AG(111)

The sp band of Ag(111) is nearly free-electron like near the Fermi lev el. Photoemission from this band in the surface-normal direction gives rise to a direct-transition peak which disperses with varying photon energies. Contrary to predictions of the standard three-step model, th e line shape is significantly asymmetric. The lower binding-energy sid e of this peak has a higher intensity, and is joined by a broad indire ct-transition plateau extending to a rounded cut-off at the sp band ed ge. This study is an analysis of the asymmetry of the direct-transitio n peak and the intensity and line shape of the indirect-transition reg ion. The optical transition-matrix element consists of two terms. One is the usual momentum-matrix element dominated by the direct band-to-b and transitions in the bulk, with a small contribution from the surfac e due to the finite mean-free path. The other is a del.A term, which d ominates the surface contribution and gives rise to indirect transitio ns involving all valence states without any restrictions on the crysta l momentum. Interference between the bulk and surface contributions re sults in an asymmetric line shape for the direct-transition peak. The contribution from del.A is shown to be well correlated with the differ ence in dielectric function between Ag and vacuum. The effects discuss ed in this paper are fairly general in nature, and should be taken int o account in high-resolution photoemission work. (C) 1997 Elsevier Sci ence B.V.