On equilibrium vicinal surfaces with mass transport dominated by terrace-diffusion, there could be crossover from terrace-diffusion to diffusion step-to-step behavior for fluctuation wavelength, λ, large compared to the step separation, l. It was shown that the temporal correlation function for 180°-out-of-phase fluctuations could be written as a function of a single dimensionless variable proportional to time/l3 and present an excellent, simple approximation for this scaling function. This formulation could be used to distinguish mass transport dominated by diffusion step-to-step versus evaporation–condensation (attachment–detachment) limited kinetics (for which the capillary-wave characteristic time exhibited the same λ2 behavior as diffusion step-to-step).

Crossover between Terrace-Diffusion and Diffusion Step-to-Step on Vicinal Surfaces - Scaling Function and Analytic Approximations. T.L.Einstein: Surface Science, 2002, 521[3], L669-73