Temperature-dependent angle-resolved x-ray photoemission study of the valence bands of single-crystal tungsten: Evidence for direct transitions and phonon effects

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Abstract
High-resolution angle-resolved x-ray photoemission (XPS) valence-band spectra from a clean W (001) single crystal have been observed to show strong spectral variations both with electron-emission direction and temperature. The spectral changes with direction are in very good agreement with the predictions of a simple direct-transition model assuming free-electron final-state dispersion and constant matrix elements. The effect of photon wave-vector involvement in the wave-vector conservation has also been explicitly observed. The strong temperature dependence noted indicates the importance of phonon-assisted nondirect transitions for Brillouin-zone averaging and demonstrates conclusively the crucial role played by the Debye-Waller factor in the interpretation of photoemission spectra in the XPS regime. Valence-band spectra at various temperatures can, furthermore, be used for isolating the direct and nondirect components in spectra.