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In this paper we discuss how finite data sets influence experimental measurements of the autocovariance function. Autocovariance estimators are biased, meaning that the expectation value for any measured autocovariance function is not identical to the actual autocovariance function. In this work we show that the measured autocovariance function for a finite length time series must become negative for some lag times. We derive analytic corrections to these finite time errors for different types of correlated random sequences. Our results explain the apparent anticorrelated noise observed in experimental observations.
We present the results of kinetics experiments on quantum-size-effects (QSE) Pb islands formed on Si(111). We have looked at the evolution of seven-layer Pb islands from five-layer Pb islands due to the transport of Pb atoms from the interisland region, overcoming a barrier at the island edges, and moving to the island tops. By analyzing low-energy electron-diffraction and scanning-tunneling microscopy data, we have estimated the barrier for layer formation in this system to be ∼0.32eV. This energy is much larger than that expected from QSE electronic contributions alone.
We present equilibrium measurements of the dynamics of steps on Si(001) using temporal electron-diffraction spectroscopy. Activation energies and the rate limiting kinetics are identified for 950K<~T<~1130K. Unlike previous studies at higher temperatures, we can exclude evaporation and condensation of atoms or dimers from the step edges as the rate limiting process in this temperature regime. The possible reason for this difference is discussed in terms of a crossover from different rate-limiting kinetics.
We present the first demonstration of Temporal LEED Spectroscopy’s ability to measure surface dynamics as shown by a study of step dynamics on vicinal Si(001). While we measure activation energies consistent with other work, the observed microscopic mechanism driving the fluctuations is inconsistent with previous claims. We exclude evaporation/condensation of atoms from the steps as the rate limiting kinetics in the temperature range of this experiment. Possible reasons for these differences are discussed.