Dynamics of energy relaxation of adatoms in the exoergic recombination of gas atoms at solid surfaces: A master equation approach

The evolution of the energy distribution function of the adatoms is described by means of the Chapman–Kolmogorov equation with the inclusion of an extra term which takes account of diatom formation. At steady state the integrodifferential equation is solved in closed form for a two band system, where “hot adatoms” are assumed to populate the high energy band. It is shown that, depending on the ratio of the density of states of the bands and on the transition probabilities for both energy dissipation and recombination, a kinetic transition takes place which is accompanied by enhanced reaction rates. The model is discussed also in connection to previous approaches based on the diffusion equation in energy space and on rate equations for a discrete set of adatom states.