Crossover between terrace-diffusion and diffusion step-to-step on vicinal surfaces: scaling function and analytic approximations

On equilibrium vicinal surfaces with mass transport dominated by terrace-diffusion (TD), there can be crossover from TD to diffusion step-to-step (DSS) behavior for fluctuation wavelength lambda large compared to the step separation l. We show that the temporal correlation function for 180degrees-out-of-phase fluctuations can be written as a function of a single dimensionless variable proportional to time/l(3) and present an excellent, simple approximation for this scaling function. This formulation can be used to distinguish mass transport dominated by DSS versus evaporation-condensation (attachment-detachment) limited kinetics (for which the capillary-wave characteristic time tau has the same lambda(2) behavior as DSS). (C) 2002 Elsevier Science B.V. All rights reserved.