Temperature dependence of direct transitions in angle-resolved photoemission and its application to InSb

Abstract

Based on angle-resolved photoemission measurements between 30 and 500 K, we derive the temperature coefficients of the linewidth and the energy separation of selected direct bulk and surface transitions in InSb. The temperature coefficients are compared with theoretical predictions based on the renormalizaton of band energies via the electron-phonon interaction. Differences in energy shifts between features are generally nonobservable within our experimental accuracy except for two cases for which the temperature coefficients are 0.23 and 0.13 meV/K. The temperature coefficients for the linewidths of bulk transitions lie in the 0.04--0.13 meV/K range; for the final state (conduction band) we obtain an average temperature coefficient of 0.44\ifmmode\pm\else\textpm\fi{}0.10 meV/K. The initial-state widths of the Sb-derived dangling-bond and backbond surface states have large temperature coefficients of 0.30\ifmmode\pm\else\textpm\fi{}0.04 and 0.14\ifmmode\pm\else\textpm\fi{}0.04 meV/K, respectively. These values suggest vibrational amplitudes of the surface atoms that are two to three times larger than those of the bulk. The In 4d core levels exhibit no measurable change in width between 30 and 500 K.