Occupied and unoccupied band structure of Ag(100) determined by photoemission from Ag quantum wells and bulk samples

Abstract

Angle-resolved photoemission spectra taken from atomically uniform films of Ag on Fe(100) show layer-resolved quantum-well peaks. The measured peak positions as a function of film thickness permit a unique determination of the initial band dispersion via the Bohr-Sommerfeld quantization rule. This information, combined with normal-emission data taken from a single crystal Ag(100), leads to a unique determination of the final band dispersion. In this study, we employ a two-band model with four adjustable parameters for a simultaneous fit to these experimental results. The initial and final band dispersions deduced from the fit are accurate to better than 0.03 eV at any wave vector k within the range of measurement. The analytic formula for the band dispersions and the parameters for the best fit are given for future reference. The Fermi wave vector along [100], normalized to the Brillouin-zone size, is determined to be ${\mathbf{k}}_{F}/{\mathbf{k}}_{\ensuremath{\Gamma}X}=0.828\ifmmode\pm\else\textpm\fi{}0.001,$ which is more accurate than the de Haas--van Alphen result. The corresponding Fermi velocity is ${\ensuremath{\nu}}_{F}=1.06$ in units of the free-electron value. The combined reflection phase for the electron wave at the two boundaries is also deduced and compared with a semiempirical formula. This comparison allows us to deduce the edges of the hybridization gap in the Fe substrate.