Island growth and step instabilities on flat and vicinal surfaces

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Doctoral thesis (article-based)
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62, [30]
Dissertations / Laboratory of Physics, Helsinki University of Technology, 120
Surface physics aims at understanding the basic atomistic processes and mechanisms responsible for the variety of observed structures during surface growth. In addition, surface growth has important consequences in modern technological applications. Molecular beam epitaxy (MBE) is an established method to grow surface structures, admitting also modeling surface growth through simple microscopic processes such as diffusion and deposition of atoms. The rather limited parameter range in MBE where smooth layer-by-layer growth is realized can be extended, e.g., with ion assisted deposition techniques. Thus new microscopic processes are added to traditional MBE growth. Customarily island growth and step-flow are treated as separate growth modes. Consequently, there does not exist a growth model which includes all relevant aspects of surface growth in a realistic way. The aim of this thesis is to bridge the gap between these traditional approaches. Including other microscopic processes in addition to deposition and surface diffusion introduces new scaling relations and length scales. In addition, not only the scaling of the growth structures but also their stability is of importance. Moreover, unstable growth often possesses a dynamically selected length scale. It is of interest to understand the behavior of these new time and length scales and their scaling properties when constructing more realistic growth models. To this end, we consider various aspects of surface growth. First, we simulate island growth with aggregation, fragmentation, and deposition on flat surfaces. The generalized rate equations are introduced, and the scaling forms for the island size distributions and the mean island size are proposed and compared with simulation results. Next, stability of circular islands is studied by generalizing the rectangular case to radial geometry. A stability criterion for the island radius is derived in the long wavelength limit. Then, stability of step edges on vicinal surfaces is considered. The simulation results demonstrate the dynamical wavelength selection with a quantitative prediction for the selected wavelength as well as the mechanism behind the instability. The average shape of the unstable step patterns is found to have an invariant form, insensitive to the parameters of the model. Finally, the simulations extended to include both island growth and step edge instability reveal that these growth modes are coupled with a new length scale, and are inpendent only in the submonolayer regime.
surface growth, growth instabilities, pattern formation, Monte Carlo simulations
Other note
  • Koponen, I., Rusanen, M. and Heinonen, J., 1998. Island size distributions in submonolayer growth with mobile islands and breakup. Physical Review E 58, pages 4037-4040.
  • Rusanen, M., Koponen, I. T. and Ala-Nissila, T., 2002. Meandering instability of curved step edges on growth of a crystalline cone. Surface Science 507-510, pages 305-310. [article2.pdf] © 2002 Elsevier Science. By permission.
  • Rusanen, M., Koponen, I. T., Heinonen, J. and Ala-Nissila, T., 2001. Instability and wavelength selection during step flow growth of metal surfaces vicinal to fcc(001). Physical Review Letters 86, pages 5317-5320.
  • Rusanen, M., Koponen, I. T., Ala-Nissila, T., Ghosh, C. and Rahman, T. S., 2002. Morphology of ledge patterns during step flow growth of metal surfaces vicinal to fcc(001). Physical Review B 65, pages 041404 : 1-4.
  • Rusanen, M., Koponen, I. T. and Kallunki, J., 2002. Mixing length scales: step meandering and island nucleation on vicinal surfaces. Submitted to Surface Science (7 pages).
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