Effects of surface stress on the elastic moduli of thin films and superlattices

A thermodynamic model which predicts a significant sample-size effect on the elastic properties of very thin films and small-period superlattices is presented. Compressive surface stresses cause the in-plane interatomic distances in a thin metal film to decrease as the thickness decreases. For copper films with a thickness of 0.75 nm, a 1% in-plane biaxial compressive strain is obtained which gives rise to a 50% increase in the biaxial modulus. This model also predicts a similar modulus enhancement (supermodulus effect) in multilayered thin films due to strains caused by incoherent interfacial stress.