Measuring Substrate-Independent Young’s Modulus of Thin Films

Abstract

Substrate influence is a common problem when using instrumented indentation (also known as nano-indentation) to evaluate the elastic modulus of thin films. Many have proposed models in order to be able to extract the film modulus (E _f ) from the measured substrate-affected modulus, assuming that the film thickness (t) and substrate modulus (E _s ) are known. Existing analytic models work well if the film is more compliant than the substrate. However, no analytic model accurately predicts response when the modulus of the film is more than double the modulus of the substrate. In this work, a new analytic model is reviewed. Using finite-element analysis, this new model is shown to be able to accurately determine film modulus (E _f ) over the domain 0.1 < E _f /E _s < 10. Finally, the new model is employed to determine the Young’s modulus of low-k and silicon carbide films on silicon.