Non-classical scaling in the Pb/Si(111) coarsening at low temperature

Recent coarsening experiments monitoring the evolution of a mixture of stable and unstable islands in Pb/Si(111) towards a mono-disperse 7-layer height distribution have revealed novel features that extend the classical curvature driven growth. Two complementary techniques are used, X-ray scattering and STM. In particular the coverage $\theta $ , temperature T and flux F dependence are the opposite of what is expected from the classical analysis. The coarsening time $\tau $ increases with increasing temperature T, coverage $\theta $ and decreases with increasing flux rate F according to the scaling relation $\tau $F=constant. These paradoxical results can be understood from the island stability dependence on lateral size L in addition to the QSE-driven well--analyzed height dependence. The decay constant of an unstable island is an increasing function of its lateral size and for sizes larger than Lc$\sim $50nm the unstable islands do not decay but grow in the next stable height. Since the lateral size increases with T, $\theta $ and decreases with F this can account for the novel coarsening results.