Nanoparticulate origin of intrinsic residual stress in thin films

The formation of grains in thin films generates intrinsic residual stress. In this work, we present a model of intrinsic residual stress calculation based on the size-dependent phase transitions of the nanograins. Evaporated thin films are produced by condensation from the vapor on the substrate. It is assumed that the starting nanograins grow from the liquid phase. It is well established that the melting temperature of nanoparticles is a function of their size. By assuming that the intrinsic stress originates from the volume change of the nanograins, and taking into account relaxation processes, the generated intrinsic residual stress in the films is evaluated. The results of the model are compared quantitatively with experimental data obtained from Ta, Mo, Pd and Al films deposited on Si. This model also gives a theoretical interpretation of Thornton and Hoffman's modelling of the stress-temperature diagram of thin films.