Measurement and calculation of polarization and potential-energy effects on core-electron binding energies in solids: X-ray photoemission of rare gases implanted in noble metals

The binding energies of core electrons on Ne, Ar, Kr, and Xe implanted in Cu, Ag, and Au have been measured by x-ray photoemission and are found to be 2-4 eV smaller in magnitude than the corresponding binding energies obtained from gas-phase measurements. All implanted data have been referenced to the vacuum level of the appropriate metal and are therefore absolute energies suitable for gas-phase comparison. For a given noble-metal host, the magnitude of the binding-energy shift decreases monotonically from Ne to Xe, while for a given rare-gas core electron the shift is largest in Ag and smallest in Cu. Investigation of both these trends allows for the study of the two contributions responsible for these shifts. First, the self-consistent potential experienced by the core level is changed upon implantation (the initial state). Second, the polarization of metal-host electrons upon photoionization (the final state) provides relaxation energy not present in the free atom. Both these effects have been calculated using a model which represents the metal-host valence $s$ electrons as free, the host outer $d$ electrons as a dielectric, and the neutral and photoionized rare gas by a pseudopotential. The model is treated using a density-functional method that allows for both self-consistency and nonlinear screening by the host electrons. All the parameters in the model are empirically determined independently of the present experiment. The results show that the potential shift and polarization energy are of comparable magnitude and opposite sign, so that significant cancellation occurs. The calculated trends in total binding-energy shift for the series of gases in each metal are in excellent agreement with the experimental results, and the trends for each gas from metal to metal are reasonably well reproduced. An essentially uniform discrepancy of 1.4 eV between the absolute calculated and measured values is ascribed to limitations of the model and detailed knowledge of the implantation-site geometry.