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- W2015797462 abstract "We illustrate the use of the Chapman-Kolmogorov and Master equations as a frame-work for solving models of epitaxial growth. Within this probabilistic approach, we specify rules governing the incorporation and migration of individual atoms, which then determine the transition rates between surface configurations. The Chapman-Kolmogorov and Master equations are then solved for either the full probability distribution of surface configurations, or for a reduced distribution function. Several idealized models for epitaxial growth are formulated and solved based upon rules for adatom incorporation into the growth front. Atoms are immobile once attached to the surface. The models studied are: (i) the random deposition model, wherein incident atoms attach to the point of initial contact with the surface; (ii) the perfect layer growth model, in which incident atoms are incorporated into the highest unfilled layer; (iii) the local perfect layer growth model, where incident atoms are incorporated into the highest unfilled layer within subsections of an adjustable size; and (iv) the local island model, which takes into account the tendency of an adsorbing atom to select sites with nearest-neighbor atoms. Inclusion of this modification results in the growth of square or rectangular islands whose size increases with the size of a subsection. These models are exactly solvable using the Chapman-Kolmogorov equation, yet some exhibit complex behavior, including decaying oscillations in the diffracted intensity and non-trivial spatial correlations within the surface. The mechanism for the damping of the oscillations is shown to be phase incoherence between growth occurring in different subsections, which is also manifested by an increasing surface roughness as measured by the root-mean-square distribution of occupied layers. Examining the relationship between the evolutions of the step density and kinematic reflection high-energy electron-diffraction (RHEED) intensities in these models underscores the role of surface correlations in determining the profile of measured RHEED intensities." @default.
- W2015797462 created "2016-06-24" @default.
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- W2015797462 date "1990-06-01" @default.
- W2015797462 modified "2023-09-24" @default.
- W2015797462 title "Nonequilibrium lattice models of epitaxial growth" @default.
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- W2015797462 doi "https://doi.org/10.1016/0039-6028(90)90596-z" @default.
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