Elastic deformation of silicon (001) wafers due to thin film stresses

Single crystal silicon is an elastically anisotropic material. The in-plane elastic modulus of Si (001) wafers varies 30% with the orientation with respect to the crystal axes. The line tension exerted on a Si (001) wafer by a uniform isotropic film under compressive stress leads to a nonuniform deformation, reflecting the elastic anisotropy of the silicon single crystal. For low line tensions, this deformation has a fourfold symmetry, with larger deformation in the less stiff directions. For larger line tensions, a saddle point deformation superimposed on a cylindrical symmetric deformation is observed.