Extraction of elastic modulus of porous ultra-thin low-k films by two-dimensional finite-element simulations of nanoindentation

Abstract

Continuous scaling of integrated circuits has led to the introduction of highly porous low dielectric constant (low-k) materials, whose inferior mechanical properties raise concerns regarding the reliability of integrated circuits. Nanoindentation is proven to be a straightforward method to study mechanical properties of films. However, in the case of low-k, the measurement and analysis are complex due to the porous nature of the films and reduced film thicknesses which give rise to substrate effects. A methodology that combines nanoindentation experiments with finite-element simulations is proposed and validated in this study to extract the substrate-free elastic modulus of porous ultra-thin low-k films. Furthermore, it is shown that imperfections of the nanoindentation probe significantly affect the finite-element results. An effective analytical method that captures the actual nanoindenter behavior upon indentation is proposed by taking both tip radius and conical imperfections into account. Using this method combined with finite element modeling, the elastic modulus of sub-100 nm thick low-k films is successfully extracted. Standard indentation tests clearly overestimated the actual modulus for such thin films, which emphasizes the importance of the proposed methodology.