Elastic properties of thin films of cubic system

Abstract A study has been made of the linear elastic response of a thin film, whose plane is along the (h k l) plane, under uniaxial and biaxial stresses. The expressions for Young's modulus and Poisson's ratio of the (h k l) thin film along an arbitrary direction on the film plane have been derived. The tensile properties on the (1 1 1) plane are planar isotropic. The formulas for the biaxial elastic moduli of the (h k l) thin film under equibiaxial stress and equibiaxial strain states have been derived. The biaxial elastic modulus for the equibiaxial stress state is generally planar anisotropic, whereas the biaxial elastic modulus for the equibiaxial strain state is planar isotropic and is closely linked with the strain energy. For the (1 0 0) and (1 1 1) thin films, the equibiaxial elastic moduli under the equibiaxial stress and strain states are the same. The biaxial elastic modulus under the equibiaxial strain state represents an appropriate mean biaxial elastic modulus of an equibiaxially stressed thin film.