Energy Release Due to Domain Formation in the Strained Epitaxy of Multivariant Films

Twin related domain formation is examined as a strain relaxation mechanism for a heteroepitaxial tetragonal film on a cubic substrate. Elastic relaxations are calculated for a single twin band in which the c-axis of the tetragonal domains is either related by a 90* rotation about an axis in the plane of the film or by a 90* rotation about the surface normal. In all cases, the strain energy change is evaluated for both the film and the substrate. A domain pattern map is developed that predicts single domain and multiple domain fields depending on the relative misfit strains and domain wall energy. The concept of a critical thickness, hc, for domain formation is developed. For cases in which the c-axis is rotated 90* about an axis in the plane of the film, the critical thickness depends only on the relative coherency strain between the substrate and film and the ratio of the domain wall energy to the stored elastic energy. For the case of a pattern consisting of energetically equivalent domains with the c-axis in plane, the equilibrium distance of multiple domains is derived. For such multiple domains, a minimum wall separation distance exists which depends non-linearly on the film thickness.