The coarsening behavior of individual Pb islands on Si(111) surface has been studied by scanning tunneling microscopy. Traditionally island decay follows a smooth power-law dependence on the time until disappearance. In Pb/Si(111), some unstable islands are inactive for a long time but once their decay is triggered they suffer a “sudden death.” Four-layer islands are found to decay rapidly, increasing the area covered by seven-layer islands. All islands, decaying or otherwise, are accompanied by island size fluctuation which involve a large number of perimeter atoms moving collectively as a “quantized” unit. A stochastic model is developed to elucidate the mechanism behind this coarsening behavior of Pb islands. The distinct evolution of the islands with different heights is correctly predicted, and the size fluctuations of islands and the sudden death behavior observed in island coarsening are also recovered. The key ingredients are incorporation of accurate non-Gaussian statistics of the size fluctuations and also accounting for size changes in large quantized bursts. Disciplines Astrophysics and Astronomy | Physics Comments This article is from Physical Review B 82 (2010): 165414, doi:10.1103/PhysRevB.82.165414. Posted with permission. Authors G. P. Zhang, Myron Hupalo, M. Li, C. Z. Wang, James W. Evans, Michael C. Tringides, and K. M. Ho This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/190 Stochastic coarsening model for Pb islands on a Si(111) surface G. P. Zhang,1,2 M. Hupalo,1 M. Li,2,1 C. Z. Wang,1 J. W. Evans,1 M. C. Tringides,1 and K. M. Ho1 1Ames Laboratory-US DOE, Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA 2Department of Physics, Renmin University of China, Beijing 100872, People’s Republic of China Received 12 March 2010; revised manuscript received 9 August 2010; published 7 October 2010 The coarsening behavior of individual Pb islands on Si 111 surface has been studied by scanning tunneling microscopy. Traditionally island decay follows a smooth power-law dependence on the time until disappearance. In Pb/Si 111 , some unstable islands are inactive for a long time but once their decay is triggered they suffer a “sudden death.” Four-layer islands are found to decay rapidly, increasing the area covered by sevenlayer islands. All islands, decaying or otherwise, are accompanied by island size fluctuation which involve a large number of perimeter atoms moving collectively as a “quantized” unit. A stochastic model is developed to elucidate the mechanism behind this coarsening behavior of Pb islands. The distinct evolution of the islands with different heights is correctly predicted, and the size fluctuations of islands and the sudden death behavior observed in island coarsening are also recovered. The key ingredients are incorporation of accurate nonGaussian statistics of the size fluctuations and also accounting for size changes in large quantized bursts. DOI: 10.1103/PhysRevB.82.165414 PACS number s : 68.43.Jk, 68.35.Fx, 68.37.Nq, 68.65.Fg Growth and coarsening on surfaces have been the focus of intensive studies in the past few decades.1–3 In traditional epitaxial systems, the coarsening of two-dimensional or three-dimensional islands formed during growth is expected to be dominated by Oswald ripening OR , where diffusion of material across terraces is driven by differences between chemical potentials of islands with varying sizes. Smaller islands with higher chemical potentials shrink while larger islands with lower chemical potentials grow in size via the transport of adatoms from smaller to larger islands.1,2 Although it works well for many-surface deposition systems, this classical OR theory was challenged by recently discovered coarsening phenomena in Pb islands on Si 111 surface.4 A fast coarsening behavior of Pb islands was observed and attributed to quantum-size effects impacting the stability of islands with different heights and fast mass transport in the dense wetting layer.4–7 In addition, according to classic OR theory, the decay in area of unstable islands obeys simple power law in the time until disappearance. The exponent depends on whether the decay is diffusion-limited or interface-limited the latter case being associated with the presence of a substantial additional barrier inhibiting attachment of adatoms to islands . Another aspect of nonclassical behavior in Pb/Si 111 is revealed in the novel way in which unstable islands decay: the islands can remain unchanged for a very long time but when their decay is initiated it is catastrophic. We use the term “sudden death” to describe this very unusual and nonclassical behavior. It is the goal of the current paper to explain this intriguing phenomenon. Its broader implication is that this is another reason why the formation of stable height islands in Pb/Si is unusually fast. In this paper, we have performed a detailed analysis of coarsening dynamics of Pb islands on Si 111 surface using scanning tunneling microscopy STM , revealing the presence of strong fluctuation in the sizes areas of individual Pb islands surface during the coarsening process. This behavior occurs regardless of the height of the islands. Moreover, we also found that once the decay of an island is triggered, the island will disappear in a very short time. This sudden death behavior is observed for islands with both stable and unstable heights. This novel coarsening dynamics is intriguing and cannot be explained by either the classical coarsening theory or our previous mean-field theory of quantum-sizeeffect-mediated coarsening.5,6 In order to understand the mechanism of the area fluctuation and sudden death of Pb islands during the coarsening process, we develop a stochastic coarsening model for this interesting system. In this model, the fluctuation of island sizes are incorporated into a stochastic prescription of growth or decay of individual islands which are coupled through the wetting layer. Large quantized fluctuations are observed that involve hundreds of atoms that move collectively and the unusual mobility of the wetting layer facilitates their formation and fluctuating motion. The stochastic prescription leads to sudden decay of islands. As we will show later, the time evolution of islands with various heights from our theoretical model is in good agreement with experimental observations. In our previous STM experiments,6 the average coarsening behavior of Pb islands with different heights was investigated. It was found that the average area of four-layer islands decreases quickly, but the average area of seven-layer islands increases. As noted previously the initial distribution consists mainly of fourand seven-layer islands and a very small number of fiveand six-layer islands. Over the duration 100 min at 205 K of these experiments, most of the four-layer islands decay and the area covered by the sevenlayer islands correspondingly increases. This was accounted for by the strong dependence of the chemical potential on island height. Turning to stochastic aspects of the system, in fact we observed fluctuations the areas of islands of all heights. The small number of five-layer and six-layer islands remains unchanged despite these fluctuations so their average areas do not change much. In our current STM experiments, we focused on the coarsening of individual Pb islands on Si 111 surface. The experimental details are introduced in Refs. 4–6, the temperature during coarsening is T=205 K, and the coverage is =1.4 ML. Figure 1 shows the time evolution of areas of individual islands with different heights. It is clear that the coarsening behavior of islands with different heights is quite PHYSICAL REVIEW B 82, 165414 201