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A time-dependent, one-dimensional continuum model that includes both adatom diffusion and a nonlinear term for diatomic island formation is derived for describing growth on stepped surfaces. The equations are solved numerically to obtain the time evolution of the step velocity and adatom and island concentrations. Due to inclusion of the nonlinear term, the model reproduces and explains both the transient behavior of reflection high-energy electron-diffraction measurements of molecular-beam-epitaxial growth on stepped surfaces and their dependence on the growth conditions.
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Myers-Beaghton et al. (1990) studied this question.
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