Final-state effects on photoemission line shapes at finite temperature

We have measured angle-resolved photoemission spectra from A1(001) over a large range of temperatures and photon energies. These data were analyzed using a model that allows one to calculate the photoemission intensity for transitions with the simultaneous excitation/absorption of 0, 1, 2, etc., phonons. By making a simple simulation of the line shape, we show that the so-called direct transition (or quasiparticle) peaks always contain a significant contribution from photoemission events with a simultaneous excitation and/or absorption of 1 and 2 phonons, i.e., from transitions that are actually indirect. At low photon energies and/or low temperatures these contributions are small; but as the photon energy or the temperature is raised they increase relative to the elastic or zero-phonon contribution and eventually become the dominant contribution to the so-called direct transition peak. The effect of these phonon-assisted transitions is a significant change of the photoemission line shape. Our model gives a good description of the temperature dependence in the experimental data but only if the phonon-assisted contributions to the photoemission peak are taken into account.