Modified Stoney's equation with anisotropic substrates undergoing large deformations

Thin film deposition is a key fabrication step in several opto-mechanical and electronics applications. For instance, thin film coatings can act as reflective interfaces, protective coatings or they can be used to modify the thermal behavior of the film-substrate system. For effective design, it is important to understand the deformation of the system in response to residual stresses during thin film deposition. The widely used Stoney's equation to measure this deformation assumes isotropic elasticity of the substrate together with infinitesimal strains and rotations. In this work we relax both constraints, where we study the deformation of commonly used substrates made of single crystal Si(001) and Si(111) wafers that undergo large rotations. We derive relations between normalized substrate curvature and thin film mismatch strain and validate our analysis with numerical results. The methodology presented can be used for more accurate understanding of a broad range of film-substrate systems in semiconductors.