Nucleation-Mediated Lateral Growth on Foreign Substrate

A model is developed to deal with lateral growth of a crystalline layer on a foreign substrate, which is mediated by successive nucleation at the concave corner defined by the meeting of a crystal facet and the substrate. It is demonstrated that due to an imbalance of surface/interface tensions at the concave corner, once the embryo of a nucleus is formed, the crystallographic orientation of the nucleus is spontaneously twisted. By successive nucleation at the concave corner, the crystalline layer develops laterally on the substrate, with its crystallographic orientation continuously rotated. In this way, a regular spatial pattern with well-defined long-range order is eventually achieved. Our model provides a criterion to predict when such an effect becomes observable in the nucleation-mediated lateral growth. The theoretical expectations are consistent with the experimental observations.