A model for curvature in film-substrate system

Growth of lattice mismatched films creates bending in the whole structure. There has been great interest in the study of these curvatures in epitaxially-grown materials. An analytical solution for the radius of curvature produced by stresses developed in growing lattice mismatched materials has been obtained. The analyses were based on beam bending theory and strain partitioning theory introduced by our group earlier. The expressions for radius of curvature were obtained for a two-layer heterostructure. The variation of the radius of curvature with the relative thicknesses, relative lattice constants, and relative elastic constants of the layers was determined. The model was verified by applying it to a symmetric tri-laminate structure. The above model can also be extended to determine the curvature for multi-layered heterostructures.