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 of 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, h_c, for domain formation is developed. For cases in which the c-axis is rotated 90° about the axis in the plane of the 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 a multiple domains is derived. For such multiple domains, a minimum wall separation distance exists which depends non-linearly on the film thickness.