Monte Carlo study of lattice-mismatched epitaxy

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Abstract
The Monte Carlo method is used to study epitaxial overlayer systems on a substrate with substantial lattice mismatch. The equilibrium atomic configurations are obtained for a wide range of the ratio of intra-layer and inter-layer interactions with various degrees of mismatch. Different modes in the relaxed lattice configuration for different regimes of interaction ratio are revealed. In addition to periodic boundary conditions, a circular-box boundary condition is investigated, which elucidates island structures and size-dependent alignment of axes in the overlayer in agreement with experimental results on the van der Waals epitaxy.