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

The self-diffusion of hydrogen on the (100) copper surface is investigated using a quantum kinetic equation approach. The dynamics of the adatom is de scribed with a multiple-band model and the surface phonons represent the th ermal bath responsible for the diffusion mechanism. Using the Wigner distri bution formalism, the diffusive motion of the adatom is characterized in te rms of the correlation functions of the adatom-phonon interaction. The diff usion 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 interact ion and a slab calculation to characterize the surface phonons. These calcu lations show that two-phonon processes represent the relevant contribution involved in the adatom-phonon coupling. The temperature dependence of the d iffusion constant is thus presented and the relative contribution of the in coherent versus the coherent part is analyzed. Both contributions exhibit a change of behavior around 100 K from an exponential to a power law tempera ture dependence as the temperature decreases. This change is due to the con finement of the motion of the adatom in the ground energy band at low tempe rature. The incoherent part is shown to be the dominant contribution at hig h temperature and is characterized by an activation energy and a prefactor equal to Delta E=0.49 +/- 0.01 eV and D(0)approximate to 2.44x10(-3) cm(2)/ s, respectively. At low temperature, the power law dependence of the two co ntributions is different since the coherent part increases slowly as the te mperature decreases whereas the incoherent part decreases. The crossover te mperature is estimated to be equal to T*=125 K. Below T*, the coherent part becomes the main contribution and the diffusion constant exhibits an almos t temperature independent behavior. (C) 2000 American Institute of Physics. [S0021-9606(00)70227-3].