How Hot Precursor Modify Island Nucleation: A Rate-Equation Model

We describe the analysis, based on rate equations, of the hot precursor model mentioned in the previous talk.\footnote{J.R. Morales-Cifuentes, T.L. Einstein, \& A. Pimpinelli, PRL, in press} Two key parameters are the competing times of ballistic monomers decaying into thermalized monomers vs.\ being captured by an island, which naturally define a ``thermalization" scale for the system. We interpret the energies and dimmensionless parameters used in the model, and provide both an implicit analytic solution and a convenient asymptotic approximation. Further analysis reveals novel scaling regimes and nonmonotonic crossovers between them. To test our model, we applied it to experiments on parahexaphenyl (6P) on sputtered mica.\footnote{L. Tumbek \& A. Winkler, Surf. Sci. 606, L55 (2012)} With the resulting parameters, the curves derived from our analytic treatment account very well for the data at the 4 different temperatures. The fit shows that the high-flux regime corresponds not to ALA (attachment-limited aggregation) or HMA (hot monomer aggregation) but rather to an intermediate scaling regime related to DLA (diffusion-limited aggregation). We hope this work stimulates further experimental investigations.