The persistence behavior for fluctuating steps on the Si(111)-$(\sqrt{3}\times \sqrt{3})R30°$-Al surface was determined by analyzing time-dependent STM images for temperatures between 770 and 970 K. Using the standard persistence definition, the measured persistence probability displays power-law decay with an exponent of $\theta =0.77\pm 0.03$. This is consistent with the value of $\theta =3/4$ predicted for attachment-detachment limited step kinetics. If the persistence analysis is carried out in terms of return to a fixed-reference position, the measured probability decays exponentially. Numerical studies of the Langevin equation used to model step motion corroborate the experimental observations.

• Received 26 December 2001

DOI:https://doi.org/10.1103/PhysRevLett.89.136102