Abstract
Using dislocation slip, a simple model of plastic flow is used to derive an expression relating strain relaxation to film thickness and grain size in thin films constrained by a substrate. In this model the strain energy, dislocation line and dislocation interaction energies and the surface energy are minimized with respect to the residual elastic strain. The model predicts a critical film thickness below which plastic flow is not expected and above which the residual elastic strain shows an inverse thickness dependence.
It is shown that the model predicts the values of residual elastic strain as a function of film thickness measured by Murakami on lead films. It is in qualitative accord with the grain-size dependence.
