Correlation Time for Step Structural Fluctuations

TL;DR

This study uses time-dependent STM to analyze step fluctuations on Ag(111) films, revealing that the correlation time is weakly temperature dependent and governed by the longest wavelength of fluctuations sampled during measurement.

Contribution

It demonstrates that the apparent correlation length is strongly temperature dependent and can be explained by the longest wavelength sampled within the measurement time interval.

Findings

Correlation function scales as t^{1/n} with 1/n ≈ 0.24

Correlation time is weakly temperature dependent with activation energy ~0.21 eV

Measurement time to correlation time ratio is about 10

Abstract

Time dependent STM has been used to evaluate step fluctuations as a function of temperature (300-450 K) on Ag(111) films grown on mica. The temporal correlation function scales as a power law in time, t^1/n with measured values of 1/n varying over a range of 0.19 pm 0.04 to 0.29 pm 0.04 with no dependence on temperature. The average value of 1/n = 0.24 pm 0.01 is consistent with step-edge diffusion limited fluctuations (n = z = 4, conserved noise). The magnitude of the time correlation function and the width of the fluctuations both scale with temperature with the same apparent activation energy of Eeff = 0.21 pm 0.02 eV, indicating that the correlation time is at most weakly temperature dependent. Direct analysis of the autocorrelation function confirms that the correlation time is at most weakly temperature dependent, and thus the apparent correlation length is strongly temperature dependent. This behavior can be reproduced by assuming that the apparent correlation length is governed by the longest wavelength of step fluctuations that can be sampled in the measurement time interval. Evaluation of the correlation time for previous measurements for Al/Si(111) (z =2) yields the same conclusion about measurement time interval. In both cases the ratio of the measurement time to the effective correlation time is on the order of 10.