The layer-by-layer growth of an increasing number of materials have now been studied by monitoring intensity oscillations in reflection high-energy diffraction (RHEED). These cyclic intensity oscillations have a characteristic damping during growth and, often, a characteristic recovery once growth is interrupted. To understand the essential features of these oscillations we have developed two simple, mathematical models that qualitatively agree with the data. The first is a birth-death model that would be appropriate to growth on a near ideal low-index plane. This is a mean field model with one hopping parameter in a set of coupled nonlinear differential equations. From the solution we calculate intensity oscillations in the kinematic approximation. An analytic form of the recovery is obtained. The second model is appropriate to a vicinal surface in which growth is considered as a deposition onto a moving staircase of steps. Here, each step acts as a perfect sink for the adatoms. The calculated oscillation maxima and minima individually converge to an intermediate value. At this point the convective motion has equilibrated with the diffusive motion.
Bibliographical noteFunding Information:
This work was supported by the Division of Materials Research of the National Science Foundation.
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