Temperature dependence of bulk and surface energy bands in copper using angle-resolved photoemission

Abstract

We have directly measured thermally induced changes in surface and bulk energy-band dispersions of copper by examining angle-resolved photoemission from Cu(111) and Cu(100) surfaces for temperatures from 25 to 500\ifmmode^\circ\else\textdegree\fi{}C. Polarized synchrotron radiation was used as the photon source. Observed shifts in the bulk band structure are in reasonable agreement with energy shifts calculated for the corresponding temperaturedependent lattice changes. The measured temperature coefficient for the upper $d$ band along $\ensuremath{\Lambda}$ is 1.5(\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV/K, while the lower edge of the $d$ bands shifts by 2.0(\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV/K. The $d$-band width decreases with temperature at a rate of 0.5(\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV/K as it shifts to higher energy. The Cu(111) surface state shifts toward ${E}_{F}$ with a measured temperature coefficient of 2.7(\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV/K.