Transient Mobility Revisited: Impact on Signatures of Island Growth on Surfaces

T.L. Einstein1, J.R. Morales-Cifuentes1 and A. Pimpinelli2

1.Dept. of Physics and CMTC, University of Maryland, College Park, MD 20742 USA

2.Rice Quantum Institute and MSNE Dept., Rice University, Houston, TX 77005 USA

Transient mobility has a long history in the study of accommodation of incident particles. However, its effect of growth exponents has not heretofore been treated. In the study of the case of parahexaphenyl (6P) on sputter-modified mica [1], there were inconsistencies between two standard methods of analyzing island growth: the growth exponent alpha (island density log N ~ alpha log F, for flux F) and the capture-zone distribution (CZD) of the islands. The CZ’s are the proximity cells (Voronoi tessellations) of the islands, the areas of which are usually well described by the generalized Wigner distribution (GWD)[2,3]. Specifically, the characteristic exponent of the GWD is simply related to the critical nucleus size i [2,3], which in this case was much smaller than the value deduced from N(F) scaling. In treating transient mobility, we used a rate-equation approach [4]. Two key parameters are the competing times of ballistic monomers decaying into thermalized monomers vs. being captured by an island. There are several other times and energies in the model, with simplifications need on binding and phonon energies to achieve a tractable problem. We obtain an implicit analytic solution and a convenient asymptotic approximation for limiting values of key dimensionless ratios. Our model exhibits non-monotonic crossover of exponents and several intermediate scaling regimes, marked by distinctive values of alpha and an effective activation energy. One of these, rather than ALA, gives the best fit of the experimental data and a value of i consistent with the CZD analysis. Our approach yields not only the scaling exponent but also the effective bonding energy in an Arrhenius plot. The resulting energies accord well with other assessments of these energies. Applications to other systems and indications of when these effects are likely are discussed.

*Work at UMD supported by NSF CHE 13-05892

  1. L. Tumbek and A. Winkler, Surface Sci. 606, L55 (2012).
  2. T.L. Einstein, Alberto Pimpinelli, and Diego Luis González, J. Cryst. Growth 401, 67 (2014).
  3. T.L. Einstein, A. Pimpinelli, D.L. González, J. Cryst. Growth 401, 627 (2014); TLE, AP, DLG, J.R. Morales-Cifuentes, J. Physics: Conf. Ser. J. Phys.: Conf. Series 640, 012024 (2015).
  4. Josue Morales-Cifuentes, T.L. Einstein, and Alberto Pimpinelli, Phys. Rev. Lett. 113, 246101 (2014); longer version, preprint.