Distinguishing step relaxation mechanisms via pair correlation functions

Theoretical predictions of coupled step motion are tested by direct STM measurement of the fluctuations of near-neighbor pairs of steps on $\mathrm{Si}(111)\ensuremath{-}\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\mathrm{R}30\ifmmode^\circ\else\textdegree\fi{}$ Al at $970\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The average magnitude of the pair-correlation function is within one standard deviation of zero, consistent with uncorrelated near-neighbor step fluctuations. The time dependence of the pair-correlation function shows no statistically significant agreement with the predicted ${t}^{1∕2}$ growth of pair correlations via rate-limiting atomic diffusion between adjacent steps. The physical considerations governing uncorrelated step fluctuations occurring via random attachment/detachment events at the step edge are discussed.

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