Simple mathematical modes are presented that exhibit features observed in reflection high-energy electron diffraction (RHEED) studies of crystal growth by molecular beam epitaxy. These models are based on a birth-death analysis of growth on low-index surfaces. These are mean field models which after an initial transient give RHEED intensity oscillations with varying degrees of damping. For moderate values of interlayer transfer the oscillations are nearly sinusoidal with maxima that do not necessarily correspond to the deposition of integral numbers of layers. As the transfer is increased, the oscillations become more cusp-like, as would be expected for perfect layer-by-layer growth. The results agree qualitatively with the intensity oscillations that are observed on low-index surfaces.
Bibliographical noteFunding Information:
This work was partially supported by the National Science Foundation under grant DMR-8615207 and the National Research Council of Canada. We are very grateful to M. Henzler for a preprint of his work on which much of this effort was based. A Rockett, M. Horn, S.T. Purcell, T-L. Rinstein, T.L. Templeton and A. Tazmenbaum made valuable comments.