Kinetics of evaporation of beaded thin films

Abstract

Theoretical description of the time-dependence of the effective thickness of a beaded thin film, h eff, and the average radius of beads, R̄, is given supposing evaporation. Besides the evaporation and surface diffusion the role of the boundary reaction of exchange of atoms between beads and absorbed surface gas layer is also taken into account. The basic mechanism of the kinetics is not the direct evaporation of atoms from the surface of beads but the desorption of adatoms from the surface of the substrate during their “time of life” τ. Thus the basic parameters of the theory are the surface diffusion length of adatoms λ s = (D sτ) 1 2 , surface diffusion coefficient of adatoms, D s, and kinetic coefficient β s, which determines the velocity of exchange of adatoms between the beads and the surface layer. Analytical expressions for the time dependence of h eff and R̄ are given for different regimes of diminution (i.e. for surface diffusion and surface reaction controls) of individual particles and of an ensemble of overlapping diffusional fields as well. Using the example of a Cu-beaded film on Mo(110) and Mo(100) surfaces it is illustrated, that by measuring the kinetics of the effective thickness in the case of reaction control, we can determine the value β' sλ s 2/ D' s, where β' s = β s c s0 and D' s = D s c s0 are the surface mass transport coefficients and c s0 is the equilibrium surface concentration. Furthermore, from the saturation vapor pressure we can get the ratio D' s/λ s 2, and thus β' s can be calculated.