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The layer-dependent Debye temperature of Ru (0001) is determined by means of high-energy resolution -level photoelectron spectroscopy measurements. The possibility to disentangle three different components the Ru 3d5/2 spectrum of Ru (0001), originating from bulk, first-, and second-layer atoms, allowed us to the temperature evolution of their photoemission line shapes and binding energies. Temperature effects detected, namely, a lattice thermal expansion and a layer-dependent phonon broadening, which was within the framework of the Hedin-Rosengren formalism based on the Debye theory. The resulting temperature of the top-layer atoms is 295 K, lower than that of the bulk T=668 K and -layer T=445 K atoms. While these results are in agreement with the expected phonon softening the surface, we show that a purely harmonic description of the motion of the surface atoms is not valid, since effects contribute significantly to the position and line shape of the different core-level.
Ferrari et al. (Wed,) studied this question.