Transient Mobility on Submonolayer Island Growth: An Exploration of Asymptotic Effects in Modeling

In studies of epitaxial growth, modeling of the smallest stable cluster (i+1 monomers, with i the critical nucleus size), is paramount in understanding growth dynamics. Our previous work has tackled submonolayer growth by modeling the effect of ballistic monomers, \textit{hot-precursors,} on diffusive dynamics \footnote{J. R. Morales-Cifuentes, T. L. Einstein, and A. Pimpinelli. Phys. Rev. Lett. 113, 246101 (2014)}. Different scaling regimes and energies were predicted, with initial confirmation by applying to para-hexaphenyl submonolayer studies \footnote{L. Tumbek & A. Winkler, Surf. Sci. 606, L55 (2012)}. Lingering questions about the applicability and behavior of the model are addressed. First, we show how an asymptotic approximation based on the growth exponent, $\alpha$ ($N \propto F^\alpha$) allows for robustness of modeling to experimental data; second, we answer questions about non-monotonicity by exploring the behavior of the growth exponent across realizable parameter spaces; third, we revisit our previous para-hexaphenyl work and examine relevant physical parameters, namely the speed of the hot-monomers. We conclude with an exploration of how the new asymptotic approximation can be used to strengthen the application of our model to other physical systems.