Layer-dependent Debye temperature and thermal expansion of Ru(0001) by means of high-energy resolution core-level photoelectron spectroscopy

The layer-dependent Debye temperature of Ru(0001) is determined by means of high-energy resolution core-level photoelectron spectroscopy measurements. The possibility to disentangle three different components in the $\text{Ru}3d_{5/2}$ spectrum of Ru(0001), originating from bulk, first-, and second-layer atoms, allowed us to follow the temperature evolution of their photoemission line shapes and binding energies. Temperature effects were detected, namely, a lattice thermal expansion and a layer-dependent phonon broadening, which was interpreted within the framework of the Hedin-Rosengren formalism based on the Debye theory. The resulting Debye temperature of the top-layer atoms is $295\pm 10\text{K}$, lower than that of the bulk $\left(T=668\pm 5\text{K}\right)$ and second-layer $\left(T=445\pm 10\text{K}\right)$ atoms. While these results are in agreement with the expected phonon softening at the surface, we show that a purely harmonic description of the motion of the surface atoms is not valid, since anharmonic effects contribute significantly to the position and line shape of the different core-level components.

Figure 1

(Color online) Selected high-resolution $\text{Ru}3d_{5/2}$ spectra measured at different photon energies and photoemission angles $\left(T=80\text{K}\right)$. The spectra are acquired at (a) normal emission and (b) in forward-scattering geometry. The deconvolution into bulk, surface, and second-layer components is shown superimposed.

Figure 2

(Color online) Correlation matrix for the fitting coefficients of the $\text{Ru}3d_{5/2}$ spectrum acquired at normal emission and $h\nu =403\text{eV}$. $r_{ij}$ describes the degree of correlation between the parameters $i$ and $j$.

Figure 3

(Color online) Two-dimensional contour plots referred to the fit of $\text{Ru}3d_{5/2}$ core-level spectrum measured at $h\nu =403\text{eV}$ at normal emission. The plots show the normalized chi square $\left({\chi }^2/{\chi }_{\text{MIN}}^2\right)$ as a function of (a) asymmetry and Gaussian width of the bulk component and (b) Lorentzian and Gaussian width of the surface component.

Figure 4

(Color online) (a) Selected high-resolution $\text{Ru}3d_{5/2}$ core-level spectra acquired at normal emission at different constant temperatures $\left(h\nu =403\text{eV}\right)$. (b) Total squared Gaussian width versus temperature for $\text{Ru}3d_{5/2}$ bulk, surface, and second-layer components, as obtained from a least-squares fit to the spectral sequence reported in (a). A linear fit to the data is shown superimposed, as a guide to the eyes.

Figure 5

(Color online) (a) Thermal evolution of the $\text{Ru}3d_{5/2}$ core levels during cooling of the sample (series acquired in fixed mode, at normal emission, and $h\nu =403\text{eV}$). The acquisition time is 1 s per spectrum. (b) $\text{Ru}3d_{5/2}$ spectra corresponding to $T=1050\text{K}$ and $T=90\text{K}$.

Figure 6

(Color online) Squared Gaussian FWHM vs temperature for bulk, surface, and second-layer components, as obtained from a least-squares fit to the time-resolved $\text{Ru}3d_{5/2}$ spectral sequence acquired in snapshot mode, at normal emission and $h\nu =403\text{eV}$. The fits to the experimental data using the HR model are shown superimposed.

Figure 7

(Color online) Thermally induced CLS of (a) surface and (b) second-layer components in the range 80–1050 K, as obtain from a least-square fit to the time-resolved data acquired in snapshot mode, reported in Fig. 5.