Si(001) Homoepitaxial Growth
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Abstract Epitaxial growth is generally treated as a far-from-equilibrium process, dominated by kinetic restraints rather than thermodynamic driving forces. In this paper we show that homoepitaxial growth, at temperatures exceeding ,-•500°C, is a process that can be approached very well from a thermodynamic equilibrium viewpoint, augmented with classical homogeneous nucleation theory. Introduction Here, we will approach epitaxial growth from a thermodynamic equilibrium view point. First, to understand true equilibrium surface dynamics we will discuss capillary fluctuations of stepedges at high temperature. Such fluctuations are limited by the kinetics of adatom exchange between stepedges and atomic terraces. The Langevin theory described by Bartelt et al./I/ accounts for experimental observations made with in situ Low Energy Electron Microscopy in detail. From these observations we extract step free energies and step mobilities as a function of temperature /2/. Next we turn to Ostwald ripening of a population of 2-dimensional (monolayer
high) islands of Si on a large Si(001) terrace, at -670 'C./3/ From a detailed analysis of Low Energy Electron Microscopy (LEEM) video data we find that mean-field theory (assuming that the adlntom chemical potential is uniform across the island population) is invalid. In fact, experimental maps of the chemical potential show variations up to a factor 3, with the highest chemical potential near the center of the terrace. A simple nearest neighbor interaction in which the chemical potential 'seen' by an island is given by the proper geometric average of the chemical potential of it neighbors allows us to accurately simulate the time development of not only the average properties of the population, but even the development of individual islands. Again, this is done in the framework of stepterrace exchange kinetics.
Finally, we turn to nucleation. The Ostwald ripening experiment shows how the surface responds to a gradient in chemical potential. But in the ripening problem the chemical potential is determined internallii and nucleation is absent. In epitaxial growth, however, the chemical potential is externally regulated. If the supersaturation is sufficiently high, nucleation of 2D islands will occur. We have made quantitative measurements of nucleation of islands on Si(001), at 650 'C. /4/ We show explicitly that the surface is very close to thermodynamic equilib107 Mat. Res. Soc. Symp. Proc. Vol. 404 0 1996 Materials Research Society
rium (the supersaturation, i.e. the ratio of adatoms derived from the external flux, to the equilibrium concentration of 'thermal' adatoms, is about 2 percent). Under these conditions classical homogeneous nucleation theory /5/ can be used to predict nucleation rates, again using quantitative knowledge of step-terrace exchange kinetics and stepedge energetics to obtain values for the nucleation barrier, the critical nucleus size, and the nucleation rate. Direct, quantitative comparison with our experimental results show a critical nucleus size of ab
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