Rate equation modeling of interface width

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Abstract
A recently developed rate equation model describing epitaxial growth is described. This method consists of a set of equations that govern the concentration of islands of varying sizes and heights above the substrate. There is one equation for the time rate of change of the number of islands of each possible size at the jth level above the substrate. Diffracted-intensity oscillations can be calculated, as can a qualitatively detailed intensity profile, when combined with some simple arguments from statistical mechanics. The dependence of the interface width (the number of incomplete layers) on temperature, deposition rate, and binding energies is considered. A qualitative criterion is given that determines when an interface is ‘‘rough’’ or ‘‘smooth,’’ and a quantitative restatement of this criterion then allows us to calculate two transition temperatures T1 and T2<TR (where TR is the equilibrium roughening temperature). This result implies that for T1<T<T2, the interface width is bounded, while for temperatures outside this interval, a transition to unbounded growth should be observed. Factors that influence a comparison with diffraction experiments are briefly discussed.

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