Surface-stress effects on elastic properties. I. Thin metal films

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Abstract
We present a detailed model describing the effects of surface stress on the equilibrium spacing and biaxial modulus of thin metal films. The model predicts that very thin films will equilibrate to a spacing in the plane substantially smaller than the bulk spacing for the material, and that this biaxial strain will vanish as the reciprocal of the film thickness. The model predicts enhancements in the biaxial modulus of thin metal films which also scale with the reciprocal of the film thickness. The magnitude of both the strain and the resulting change in biaxial modulus are proportional to the magnitude of the surface stress. We verified the predictions of the surface-stress model by performing molecular-dynamics computer simulations of thin metal films using an analytic form of the embedded-atom-method potential. The model was found to predict accurately the equilibrium properties of thin metal films.