Analysis of stress and strain distribution in thin films and substrates

Calculations are presented for the distribution of stress and strain in thin films and substrates from inhomogeneous plane stresses developed in the film during deposition. The results can be applied to the ’’bending‐plate method’’ of determining the unknown stresses in a film, in which the deformation of the substrate surface is measured. Thereby the local values of the stress tensor within the film plane (averaged through the film thickness) and the center of the stress distribution normal to the film plane can be obtained in principle. A more convenient evaluation based on linear approximations is applicable when the film thickness is small. Restrictions are discussed which result from neglecting the conditions of compatibility for the components of the strain tensor.