Spatial first-passage statistics of Al/Si(111)-(square root 3 x square root 3) step fluctuations

Spatial step edge fluctuations on a multicomponent surface of Al/Si(111)-(square root 3 x square root 3) were measured via scanning tunneling microscopy over a temperature range of 720-1070 K, 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 range, 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 agrees quantitatively with the theoretical prediction, which yields exponential decay in the limit of small y/L. The decay constant is found experimentally to be y(s)/L=0.076+/-0.033 for y/L