Relation between macroscopic and microscopic activation energies in non-equilibrium surface processing

Realistic Monte Carlo simulations show that the apparent macroscopic activation energy is only partially explained by the expected expression for the average over the microscopic activation energies for surface processing. An additional term accounting for the existence of fluctuations in the fractions of particles has to be taken into account. In all cases considered, the additional term can be accurately estimated by a posteriori analysis of the temperature dependence of the surface densities. In addition, we demonstrate that the relative contribution of the different competing microscopic processes to the macroscopic activation energy can be accurately obtained during the simulations, allowing for the unambiguous identification of the particular surface species which effectively control the process. As an example of the nonequilibrium open interfaces to which the results apply, the case of wet chemical etching of crystalline silicon is considered. The results can be directly applied to surface growth.