Measuring substrate-independent modulus of thin films

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 to be able to extract the film modulus (Ef) from the measured substrate-affected modulus, assuming that the film thickness (t) and substrate modulus (Es) 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 proposed. This new model is shown by finite-element analysis to be able to accurately predict composite response over the domain 0.1 <Ef/Es< 10. Finally, the new model is used to analyze experimental data for compliant films on stiff substrates and stiff films on compliant substrates.