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

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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 sβ(-b s²), 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 β≈ 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.