Shudun Liu

The mobility of Pt atoms and small Pt clusters on Pt(111) and its implications for the early stages of epitaxial growth

Abstract We use the effective medium approximation to calculate the activation energy for the site-to-site motion of Pt atoms and Pt clusters with two to seven atoms, on the Pt(111) surface. We find that clusters are highly mobile and will move as a whole rather than by breaking into fragments that reunite in a different place. The results are used to examine the properties of the islands formed in the earliest stages of Pt deposition on the surface. We show that island formation at temperatures below 500 K occurs through the formation of stable clusters. There is no critical nucleus and the density of the supersaturated gas of single atoms on the surface is very close to zero; the islands do not originate through density fluctuations. We also rationalize the existence of three distinct regimes in the temperature dependence of island sizes at low coverage. They are due to absence of atom “evaporation” from islands onto the surface, at low temperature; to evaporation from open shell islands but not from the closed shell ones, at intermediate temperature; and to evaporation from all islands, at higher temperature.

Inter-layer diffusion and motion of adatoms in the vicinity of steps

Abstract Kinetic Monte Carlo simulations are extensively used to simulate the aggregation of atoms deposited on a surface during epitaxial growth. In almost all cases the rate constants for the displacements of the adsorbed atoms are guessed with the help of simple rules. Here we use effective medium theory to calculate the activation energies controlling the rates, for Pt atoms deposited on Pt(111). While the calculations are not highly accurate it is hoped that they represent qualitatively the relative magnitudes of the rates and are an improvement over simple rules (e.g. bond counting) used so far. We calculate the activation energy for a particle that starts on top of an island and descends from it onto the surface on which the island is located. The rate and the mechanism of this process depend on the step type and island size. At one type of the step the particle descends most rapidly from the island by rolling over the edge; at the other it inserts itself into the island by pushing an edge atom away. If the islands are very small the descent rate is very high, since the insertion process takes place with ease. The diffusion of an atom on the terrace towards the island is accelerated as the atom approaches the island, as inferred by Wang and Ehrlich. The diffusion of an atom along the two kinds of island edges differs little from one edge to another. This small difference is, however, essential for explaining why island shape is very sensitive to growth temperature.

An effective medium theory study of Au islands on the Au(100) surface: reconstruction, adatom diffusion, and island formation

Abstract We have used the effective medium theory to examine two kinetics phenomena related to the aggregation of the Au atoms deposited on a hex-reconstructed Au(100) surface. The island density can be analyzed by using scaling arguments derived from kinetic equations based on an assumed growth mechanism. The correct mechanism is still uncertain. The calculations reported here suggest that the diffusion of an isolated adsorbed atom is two-dimensional, the dimer is mobile, and the critical nucleus size is one. The scanning tunneling microscope experiments of Gunther, Kopatzki, Bartelt, Evans, and Behm have shown that the islands formed by the Au atoms are elongated rectangles and their widths are likely to be “quantized”. Since the second surface layer has square symmetry and the top layer is hexagonal, the rectangular shape of the islands is not obvious. We suggest that this form appears because the atoms in the surface layer below the island are unreconstructed (i.e., revert to a square symmetry during island formation), while the atoms in the island have a hexagonal structure. Kinetics favors a six-atom-wide island: the diffusion of an atom along the long side of such an island is much faster than when the island width differs from six; the atoms sticking to the long side of a six-atom-wide island are rapidly transported to its short side, adding to the length and not to the width of the island. This transport is inefficient when the width differs from six.

The effect of island coalescence on island density during epitaxial growth

The effect of island coalescence on island density during epitaxial growth is studied by kinetic Monte Carlo simulations. We find that the ratio N/Nc between the island density N at time t and the number Nc of islands per unit area that have coalesced up to the time t is a function of the coverage, but is independent of the specific material or the growth conditions. We analyze the results of our simulations by using several mean-field kinetic models of increasing complexity. They show that the simulation results are reproduced accurately only by a kinetic model which includes the spatial correlation between the location of the islands. The existence of a denuded zone around each island is particularly important, as it pushes the onset of coalescence towards higher coverages and increases the coalescence rate when the process starts.

A kinetic model for island shape variations under epitaxial growth conditions

Abstract We propose a simple mean-field kinetic model describing the time evolution of the shape of a two-dimensional island formed during epitaxial deposition. The evolution calculated from our equation agrees with that observed experimentally. The model gives the correct equilibrium shape, consistent with the Wulff condition.