Persistence in Step Fluctuations 

D.B. Dougherty, I. Lyubinetsky and E.D. Williams
Materials Research Science and Engineering Center
University of Maryland, College Park 

All materials systems have an underlying stochastic nature due to thermal motion.  For macroscopic systems, the system average over the thermal motion is the important quantity in predicting materials properties.  However, for nanoscale structures, individual rather than system average behavior will be increasingly important in materials performance.  In this case a typical type of question might be, “What is the first time that a nanoscale structure fluctuates into its active configuration?”  The newly developing field of first passage (or persistence) theory offers an approach to dealing with such problems.  We have performed the first experimental test of the predictions of persistence theory in a solid-state system, by measuring the persistence probability for fluctuating steps on a solid surface.  The results both confirm the applicability of persistence theory, and demonstrate its additional power to distinguish different underlying kinetic mechanisms.  This success is the first step in extending persistence predictions to more complex structures and structure-property correlations.

Figure:  Left panel – Time image of two steps on an aluminized Si surface measured at 970K.  Spatial scans across a 100 nm displacement were repeated temporally (bottom to top) over a 38 s time interval revealing the fluctuations of the step edges. 
Right panel – The temporal correlation function G(t) displays a power law time dependence tz, with z, the dynamic exponent, measured to be 0.47 ± 0.04, and the persistence probability p(t) has a power law dependence t-q, where q is non-trivially related to the dynamic exponent, and is measured to be 0.77±0.03.