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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 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.
While surface kinetics measurements for single atom diffusion have proliferated, little work exists attempting to measure surface dynamics under equilibrium conditions. We will present our recent work on developing Temporal LEED Spectroscopy (TLS) as a dynamic probe of surfaces capable of kinetics measurements at both high temperatures and surface coverages. By tuning the diffraction to specific structural entities such as steps, islands, etc., and monitoring the diffracted signal as a function of time, dynamics information about these structures can be obtained. As an example we will present TLS results for the dynamics of step fluctuations on Si(001) [1]. We have measured activation energies and identified step-edge diffusion as the rate limiting process for 950K < T < 1130K. Although this result is in apparent disagreement with earlier work, a careful analysis, considering crossover temperatures between different microscopic processes, can reconcile the differences. 1. M. Kammler, et al., Phys. Rev. B (in press).
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.
As demonstrated with SPA-LEED and STM uniform height islands of preferred thickness form during the growth of Pb on Si(111). The islands form at temperatures T<250K and for fluxes F 1/60ML/sec which requires fast kinetics and balance between several atomic processes: diffusion towards the islands , diffusion to higher layers and preference for the atoms to remain on top of the preferred height islands. We have carried out SPA-LEED experiments to measure the barriers of the processes: we prepare an initial predominantly 5-step island height distribution and we deposit an additional 0.5ML Pb at different growth temperatures Tg to determine the transition to the next preferred height of 7-step islands (i.e. 2-step islands on top of the 5-step islands) with Spot Profile Analysis(SPA-LEED). We observe that 7-step island formation is possible above a minimum temperature Tg*=175K which indicates that the transfer of atoms from the surrounding region to the top of the islands is the main controlling process.