Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications

We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) $P(s)=a{s}^{\beta }\exp (-b{s}^2)$, where $s$ is the CZ area divided by its average value. This approach offers arguably the best method to find the critical nucleus size $i$, since $\beta \approx i+2$. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime $0.5<s<2$, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied.