Analyzing capture zone distributions (CZD) in growth: Theory and applications

• Comprehensive summary of status of use of capture-zone distributions (CZDs) to extract critical nucleus size.
• Survey and critique of extensive computer simulations to investigate this problem, with discussion and proposed resolution of different results in these simulations and open questions that remain.
• Comparison with other methods to extract critical nucleus size from experimental data.
• Discussion of fitting to experimentally accessible central regime near peak versus fitting tails in CZDs from simulations.
• Survey and capsule summaries of wide-ranging applications of CZD analysis to actual experimental systems.

We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) P(s)=asβexp(−bs2), where s is the CZ area divided by its average value. This approach offers arguably the most robust (least sensitive to mass transport) method to find the critical nucleus size i  , since β≈i+2β≈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