Diffusion and growth of steps and islands on surfaces

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Doctoral thesis (monograph)
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Dissertations / Laboratory of Physics, Helsinki University of Technology, 110
Surface science aims at the control of surface structures even on atomistic scales. Growth of metal and semiconductor crystal surfaces requires accurate growth techniques, among which Molecular Beam Epitaxy (MBE) has a special status since it can be very efficiently used to produce growth in well defined layer-by-layer growth mode. Growth during MBE is a non-equilibrium process, which is influenced by kinetic properties and thermodynamics of the system. This Thesis focuses on several aspects of surface dynamics which are signicant in surface growth problems. To this end, both simple model systems and models based on microscopic calculations are studied. First a simple model for the growth of an isolated step with infinitely strong step edge barrier is introduced and studied. The destabilizing effect of the one-sided biased diffusion field coupled with strongly anisotropic adatom dynamics makes the step edge morphologically unstable, with finger-like structures developing separated by deep cracks. Second, it is demonstrated for island growth with island break-up that the rate equations give accurate description of the growth and predict correctly the island size distributions. A generalized scaling description is presented, which describes the initial, irreversible stage of growth, and the final stage where aggregation is affected by break-up. Island diffusion is one of the central processes in surface growth. This problem on fcc(100) metal surfaces is studied and it is found that vacancy diffusion inside an island is an important microscopic mechanism. The simulation model predicts that the diffusion of vacancy island is essentially similar to adatom island diffusion since the rate-limiting mechanisms are symmetric for both cases. In addition, persistent oscillations in the diffusion coefficient, that are due to entropic reasons are found at low temperatures. An essential part of this Thesis concerns the development of better methodology to study stochastic surface dynamics. In the study of step roughening, a Green's function method is introduced, which is important to speed up the numerical calculations of diffusion of a single particle on a terrace. In the simulations of island diffusion, the Bortz-Kalos-Lebowitz (BKL) algorithm is employed instead of the standard Metropolis Monte Carlo. It is shown how physical quantities such as short time velocity correlations can be calculated efficiently by using BKL type of approach. An accurate way to calculate the diffusion coefficient is also discussed.
island diffusion, island growth, step growth, Monte Carlo
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