Sampling Time Effects for Persistence and Survival in Step Structural Fluctuations

TL;DR

This study investigates how sampling rate and measurement duration influence the observed persistence and survival probabilities of step fluctuations in various materials, revealing scaling behaviors independent of temperature.

Contribution

It demonstrates that persistence probability scales with sampling interval over measurement time, and survival probability depends on sampling interval and system size, aligning with theoretical predictions.

Findings

Persistence probability scales with t/Dt, independent of temperature.

Survival probability depends on Dt and total measurement time tm.

Scaling behaviors match theoretical models predicting size-dependent survival probabilities.

Abstract

The effects of sampling rate and total measurement time have been determined for single-point measurements of step fluctuations within the context of first-passage properties. Time dependent STM has been used to evaluate step fluctuations on Ag(111) films grown on mica as a function of temperature (300-410 K), on screw dislocations on the facets of Pb crystallites at 320K, and on Al-terminated Si(111) over the temperature range 770K - 970K. Although the fundamental time constant for step fluctuations on Ag and Al/Si varies by orders of magnitude over the temperature ranges of measurement, no dependence of the persistence amplitude on temperature is observed. Instead, the persistence probability is found to scale directly with t/Dt where Dt is the time interval used for sampling. Survival probabilities show a more complex scaling dependence which includes both the sampling interval and the total measurement time tm. Scaling with t/Dt occurs only when Dt/tm is a constant. We show that this observation is equivalent to theoretical predictions that the survival probability will scale as Dt/L^z, where L is the effective length of a step. This implies that the survival probability for large systems, when measured with fixed values of tm or Dt should also show little or no temperature dependence.