Surface self-diffusion of hydrogen on Cu(100): A quantum kinetic equation approach

Abstract

The self-diffusion of hydrogen on the (100) copper surface is investigated using a quantum kinetic equation approach. The dynamics of the adatom is described with a multiple-band model and the surface phonons represent the thermal bath responsible for the diffusion mechanism. Using the Wigner distribution formalism, the diffusive motion of the adatom is characterized in terms of the correlation functions of the adatom–phonon interaction. The diffusion coefficient exhibits two terms related to phonon mediated tunneling (incoherent part) and to dephasing limited coherent motion (coherent part). The competition between these two contributions induced a transition from a thermally activated regime to an almost temperature independent regime at a crossover temperature T*. A numerical analysis is performed using a well-established semiempirical potential to describe the adatom–surface interaction and a slab calculation to characterize the surface phonons. These calculations show that two-phonon processes represent the relevant contribution involved in the adatom–phonon coupling. The temperature dependence of the diffusion constant is thus presented and the relative contribution of the incoherent versus the coherent part is analyzed. Both contributions exhibit a change of behavior around 100 K from an exponential to a power law temperature dependence as the temperature decreases. This change is due to the confinement of the motion of the adatom in the ground energy band at low temperature. The incoherent part is shown to be the dominant contribution at high temperature and is characterized by an activation energy and a prefactor equal to ΔE=0.49±0.01 eV and D0≈2.44×10−3 cm2/s, respectively. At low temperature, the power law dependence of the two contributions is different since the coherent part increases slowly as the temperature decreases whereas the incoherent part decreases. The crossover temperature is estimated to be equal to T*=125 K. Below T*, the coherent part becomes the main contribution and the diffusion constant exhibits an almost temperature independent behavior.