Spatial First-passage Statistics of Al/Si(111)-(root3 x root3) Step Fluctuations

TL;DR

This study measures spatial step edge fluctuations on Al/Si(111) surfaces using STM, confirming theoretical predictions of persistence exponents and survival probabilities, and demonstrating temperature independence of these spatial statistics.

Contribution

It provides the first experimental verification of theoretical spatial persistence exponents and survival probability scaling on a multi-component surface.

Findings

Persistence exponent measured as 0.498 ± 0.062, matching theory.

Survival probability scales with y/L and exhibits exponential decay.

Temperature independence of spatial fluctuation statistics confirmed.

Abstract

Spatial step edge fluctuations on a multi-component surface of Al/Si(111)-(root3 x root3) were measured via scanning tunneling microscopy over a temperature range of 720K-1070K, for step lengths of L = 65-160 nm. Even though the time scale of fluctuations of steps on this surface varies by orders of magnitude over the indicated temperature ranges, measured first-passage spatial persistence and survival probabilities are temperature independent. The power law functional form for spatial persistence probabilities is confirmed and the symmetric spatial persistence exponent is measured to be theta = 0.498 +/- 0.062 in agreement with the theoretical prediction theta = 1/2. The survival probability is found to scale directly with y/L, where y is the distance along the step edge. The form of the survival probabilities agree quantitatively with the theoretical prediction, which yields exponential decay in the limit of small y/L. The decay constant is found experimentally to be ys/L= 0.076 +/- 0.033 for y/L <= 0.2.