Temperature dependence of the inverse photoemission from copper surfaces

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Abstract
The temperature dependence of the intensity of inverse photoemission transitions into bulk and surface states has been studied on Cu(100), (110), and (111) surfaces. The temperature dependence is strongly influenced by multiple-scattering effects. For Cu(100) and (111) it can be fitted very well with a Debye-Waller law where the mean-square displacements of the surface atoms increase linearly with temperature. For Cu(110) we find an enhancement of the mean-square displacements above 400 K in agreement with surface-sensitive scattering experiments. Through the comparison of a given bulk transition on different surfaces, we find a strong influence of surface vibrations on the intensities of bulk transitions. A classification of the temperature dependence of the investigated bulk transitions is attempted in a two-band model, in a nearly-free-electron model, and in the one-step model of inverse photoemission incorporating bulk and surface phonons. The results are not quite satisfying, although they seem to show the right trend: the temperature dependence is stronger the higher the energy is. The temperature dependence of the surface-state transitions depends on their character. Transitions into image-potential surface states are temperature independent. Transitions into crystal-induced surface states respond to temperature changes. Transitions into states that are located in the same band gap and have nearly the same relative position in it show the same temperature dependence. The temperature dependence gets smaller the more bulklike the surface state gets.