Formation of self-assembled heteroepitaxial islands in elastically anisotropic films

The formation of self-assembled heteroepitaxial islands in elastically anisotropic cubic films is investigated by a three-dimensional dynamic method. In the formulation, the {100} film surfaces evolve through surface diffusion driven by the gradient of the surface chemical potential. Our simulations reveal that when the elastic anisotropic strength A [A is defined as 2C₄₄/(C₁₁-C₁₂), where C₁₁, C₁₂, and C₄₄ are elastic constants] is larger than 1 the formed islands are preferentially aligned along 〈100〉 directions, while when A is smaller than 1 the formed islands are preferentially aligned along the 〈110〉 directions. It is found that the stronger the elastic anisotropy, the stronger the island self-assembly. In addition, the island alignment and averaged island spacing right after island formation are found to be related to the smallest fastest surface instability wavelength of the elastically anisotropic films.