ANALYSIS OF INDENTATION DEPTH DEPENDENCE OF ELASTIC PROPERTIES OF INTER-LAYER DIELECTRIC FILMS ON SILICON

摘要

Analysis of indentation depth dependence of elastic modulus of soft films on silicon substrate measured by nanoindentation was studied. The experimental results were compared with two existing models that describe the effects of the substrate on elastic modulus of layered solid. Saha-Nix model that is the recent modification of King model agreed well with the experimental results to a certain limit of the indentation depth. It was found that the depth limit which Saha-Nix model is valid depended almost linearly on the relative elastic modulus of the film to the substrate E_(f)/E_(s). We further introduced an additional scaling parameter that is a linear function of E_(f)/E_(s) in Saha-Nix model. The improved model was applied to porous silica low-k films. The model predicted a constant intrinsic elastic modulus of the film up to a depth of 30 percent of the film thickness.