Modeling Island-Growth Capture Zone Distributions (CZD) with the Generalized Wigner Distribution (GWD): New Developments in Theory and Experiment*

Earlier we showed [PRL 99, 226102 (2007)] that the CZD in growth could be well described by $P(s)=a s^\beta \exp(-bs^2)$, where $s$ is the CZ area divided by its average value. Painstaking simulations by Amar's [PRE 79, 011602 (2009)] and Evans's [PRL 104, 149601 (2010)] groups showed inadequacies in our mean field Fokker-Planck argument relating $\beta$ to the critical nucleus size. We refine our derivation to retrieve their $\beta \approx i + 2$ [PRL 104, 149602 (2010)]. We discuss applications of this formula and methodology to experiments on Ge/Si(001) and on various organics on SiO$_2$, as well as to kinetic Monte Carlo studies homoepitaxial growth on Cu(100) with codeposited impurities of different sorts. In contrast to theory, there can be significant changes to $\beta$ with coverage. Some experiments also show temperature dependence.