Instability of Epitaxially Strained Thin Films Based on Nonlocal Elasticity

We perform a linear analysis of the elastic fields and stability of epitaxially strained thin films based on nonlocal elasticity. We derive expressions of perturbed stresses to the first order of perturbation amplitude, which show that the stresses are directly proportional to the lattice mismatch and the perturbation amplitude, and decrease with an increase in the perturbation wavelength. The critical perturbation wavelength distinguishes whether the flat film for the perturbation is stable, which is inversely proportional to the square of the mismatch and decreases with the thickness of the film.