| AVS 54th International Symposium | |
| Surface Science | Tuesday Sessions |
| Session SS2-TuM |
| Session: | Surface Structure and Growth on Metals |
| Presenter: | T.L. Einstein, University of Maryland |
| Authors: | T.L. Einstein, University of Maryland A. Pimpinelli, Univ. of Maryland & U. Blaise Pascal--Clermont 2, France |
| Correspondent: | Click to Email |
As one approaches the nanoscale, fluctuations play an ever more important role in the physics of systems. Universal aspects of fluctuations are thus an especially timely topic. The Wigner distribution from random matrix theory has successfully described a vast array of physical phenomena, from energy spacings between nuclear levels to conductance fluctuations in wires, as well correlations of stock prices, spaces between parked cars, and times between successive unscheduled buses. It is easy to use, having the simple, one-parameter form a sβ exp (-bs2) [with a and b being constants assuring normalization and unit mean, and s the fluctuating variable divided by its mean]. Here we apply this approach to the long-standing problem of island-size distributions during growth. We consider the distribution of the areas of Voronoi polygons (proximity cells) around nucleation centers, i.e. the capture zones (CZ). Generalizations of the Wigner distribution (to allow more than the 3 values of β based on symmetry) account well for data generated in kinematic Monte Carlo studies by several groups, much as it did for terrace-width distributions (TWD) on vicinal surfaces. For CZ distributions we find β = i + 1, where i is the size of the critical nucleus. (In spatial dimension d = 1, β = 2(i + 1).) We demonstrate excellent fits of numerical data for both d = 1 and d = 2. To clarify the underlying physics, we present a phenomenological derivation by constructing a Langevin equation similar to that used in accounting for the equilibration of TWDs; we discuss the competing forces that lead to the WD. Our expression also describes well experimental data for pentacene adsorption and for CZ distribution of growing quantum dots. We compare this analysis with others using less-well-motivated Gamma distributions or more complicated expressions.
Work at UMD supported by the MRSEC, NSF Grant DMR 05-20471. Visits to UMD by AP supported by a CNRS Travel Grant, and TLE partially supported by DOE CMSN grant DEFG0205ER46227.