In the present work, we carried out Monte Carlo simulations in order to investigate the effects of surface steps on CuPt-type ordering in III-V semiconductor alloys grown on a slightly inclined (001) substrate, on the basis of an Ising-like crystal growth model. Two types of surface steps were considered: one is the surface step along the [11̄0] direction (the [11̄0] step), and the other is the surface step along the  direction (the  step). The former and the latter have a preference for unlike- and like-atom pairs along the step edge, respectively. Flows of the [11̄0] step leave CuPt-ordered domains of (1̄11) and (11̄1) variants with low degree of order. The domains elongate perpendicular to the growth direction of the crystal. After flows of the  step, on the other hand, only one variant is formed and large ordered domains grow from the interface with a substrate up to the top surface of the layer. The features of domain structure, such as the selection of variants and the morphology of the antiphase domains, are in good agreement with the previous experimental results obtained by transmission electron microscopy. It was found that (001) interplane interactions, which contribute to the ordering along the growth direction, play an important role for the difference of microstructures depending on the type of surface step. We also discuss the microstructure of the epilayer obtained by the motion of both surface steps on the surface layers.
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