Spatial Firstpassage Statistics of Al/Si(111)(root 3X root 3) Step Fluctuations
Abstract
Step edge fluctuations on a multicomponent surface of Al/Si(111)( ) were measured via scanning tunneling microscopy over a temperature range of 720K1070K, for step lengths of 65160 nm. Even though the time scale of fluctuations of steps on this surface varies by orders of magnitude over the indicated temperature ranges, measured firstpassage spatial persistence and survival probabilities are shown to be temperature independent over the temperature and spatial range. The power law functional form for spatial persistence probabilities is confirmed and the spatial persistence exponent is measured to be 0.71 ± 0.13 in contrast to theoretical predictions of a value ≤ ½. The survival probability is found to scale directly with x/L, where x is the step edge displacement and L is the step length anallyzed, with minor corrections for the discrete measurement interval. The form of the survival agrees quantitatively with theoretical predictions, which reduce to an exponential decay at short distances (x/L <~ 0.3). The decay constant is found experimentally to be (0.076 ± 0.033)L Also, the functional form of the stationary single site height distribution is found to agree with predictions.
 Authors:
 Publication Date:
 Research Org.:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 903239
 Report Number(s):
 PNNLSA51908
Journal ID: ISSN 1063651X; PLEEE8; KP1504020; TRN: US200719%%519
 DOE Contract Number:
 AC0576RL01830
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 75(2 PT 1):443448; Journal Volume: 75; Journal Issue: 2 PT 1
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; ALUMINIUM; SILICON; SURFACE PROPERTIES; MORPHOLOGY; FLUCTUATIONS
Citation Formats
Conrad, Brad R., Cullen, W. G., Dougherty, D. B., Lyubinetsky, Igor, and Williams, E. D.. Spatial Firstpassage Statistics of Al/Si(111)(root 3X root 3) Step Fluctuations. United States: N. p., 2007.
Web. doi:10.1103/PhysRevE.75.021603.
Conrad, Brad R., Cullen, W. G., Dougherty, D. B., Lyubinetsky, Igor, & Williams, E. D.. Spatial Firstpassage Statistics of Al/Si(111)(root 3X root 3) Step Fluctuations. United States. doi:10.1103/PhysRevE.75.021603.
Conrad, Brad R., Cullen, W. G., Dougherty, D. B., Lyubinetsky, Igor, and Williams, E. D.. Thu .
"Spatial Firstpassage Statistics of Al/Si(111)(root 3X root 3) Step Fluctuations". United States.
doi:10.1103/PhysRevE.75.021603.
@article{osti_903239,
title = {Spatial Firstpassage Statistics of Al/Si(111)(root 3X root 3) Step Fluctuations},
author = {Conrad, Brad R. and Cullen, W. G. and Dougherty, D. B. and Lyubinetsky, Igor and Williams, E. D.},
abstractNote = {Step edge fluctuations on a multicomponent surface of Al/Si(111)( ) were measured via scanning tunneling microscopy over a temperature range of 720K1070K, for step lengths of 65160 nm. Even though the time scale of fluctuations of steps on this surface varies by orders of magnitude over the indicated temperature ranges, measured firstpassage spatial persistence and survival probabilities are shown to be temperature independent over the temperature and spatial range. The power law functional form for spatial persistence probabilities is confirmed and the spatial persistence exponent is measured to be 0.71 ± 0.13 in contrast to theoretical predictions of a value ≤ ½. The survival probability is found to scale directly with x/L, where x is the step edge displacement and L is the step length anallyzed, with minor corrections for the discrete measurement interval. The form of the survival agrees quantitatively with theoretical predictions, which reduce to an exponential decay at short distances (x/L <~ 0.3). The decay constant is found experimentally to be (0.076 ± 0.033)L Also, the functional form of the stationary single site height distribution is found to agree with predictions.},
doi = {10.1103/PhysRevE.75.021603},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 75(2 PT 1):443448},
number = 2 PT 1,
volume = 75,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 2007},
month = {Thu Feb 01 00:00:00 EST 2007}
}

The analysis of the dynamics of equilibrium step fluctuations has been extended to a chemically heterogeneous surface. The multicomponent reconstructed Al/Si~111!~)3)! surface has been studied using variabletemperature scanning tunneling microscopy at elevated temperatures. The temporal correlation functions for both single steps and step arrays follow a t1/2 dependence over the entire temperature range ~770–1020 K!, consistent with a rate limiting mechanism of random attachment and detachment of atoms at step edges. The alternative mechanism, diffusion from steptostep, is shown to be inconsistent with more detailed analytic approximations to the correlation function for the measured stepstep separation. An activation energy ofmore »