Transitions conserving parallel momentum in photoemission from the (111) face of copper

Photoelectric yields and directional photoemission spectra for clean (100) and (111) faces of copper measured with provision for varying the angle of incidence and the light polarization, and with photon energies up to 6.60 eV, are presented. Contrasting the structureless Fowler-like behavior of the (100) face, the (111) face shows two transitions conserving momentum parallel to the surface as peaks in the energy spectra and structure in the yield. A sharp peak excited by obliquely incident $p$-polarized light and responsible for a strong vector effect, is ascribed to a surface band in the band gap at the $L$ point. This peak, located 0.40±0.02 eV below the Fermi level in forward emission, disappears when the surface is significantly changed by oxygen exposure. At lower energies a wider peak identified with direct bulk transitions near the $L$ point accounts for structure present in the yield even at normal incidence. From selection rules for momentum and energy, and parabolic approximations for the participating energy bands, theoretical predictions are derived for the peak positions at various frequencies and emission angles, and for the total yields. Parameters determined for the bulk transitions are in good over-all agreement with band-structure data, while an effective mass of ${m_s}^{*}=(0.42\mathrm{}\pm 0.05)m$, close to a corresponding mass in the bulk, is found for the surface band. The yields have thresholds exceeding the photoelectric work function, and their saturation beyond certain critical frequencies given by the band parameters, is reasonably well described by a matrix element pertinent to an image-potential surface barrier. For the surface band beyond its critical frequency the directional yield as well is in agreement with the theory. The emission is then confined to a forward cone becoming narrower with increasing photon energy.