Determination of young's modulus and yield stress of porous low-k materials by nanoindentation

Abstract In the present study, the concept of the ‘effectively shaped indenter’ was used to analyse nanoindentation data of rather soft films on hard substrates. This approach was introduced for monolithic materials by Pharr and co-workers some years ago [G.M. Pharr, A. Bolshakov: J. Mater. Res. 17 (2002) 2660, A. Bolshakov, W.C. Oliver, G.M. Pharr, MRS Symp. Proc 356 (1995) 675]. Substrate to layer moduli ratios range from nearly 60 to 160. With such soft and brittle materials (Young's modulus nearly 3 GPa or smaller, yield strength around 100 MPa), no completely elastic measurements can be performed even at low loads. Hence, an established method for the determination of yield stresses by means of nanoindentation, namely that of loading-partial-unloading [N. Schwarzer: ASME J. Tribology 122 (2000) 672, T. Chudoba, N. Schwarzer, F. Richter: Thin Solid Films 355–356 (1999) 284, T. Chudoba, N. Schwarzer, F. Richter: Surf. Coat. Technol. 127 (2000) 9] was not applicable. However, the ‘effectively shaped indenter concept’ allows one to separate the elastic stresses due to the penetration from the residual stresses caused by the inelastic deformation, assuming that their influence on the elastic stress field is small. Thus, by using this approach critical yield stresses of soft porous materials have been obtained. Additionally, the Young's modulus of these materials has also been determined by means of laser-generated surface acoustic wave (LSAW) measurements and the Oliver and Pharr method. In the latter case, a special extrapolation method for the indentation modulus had to be applied to correct for the substrate influence. The results by the different methods are compared and their deviations are discussed. As there is no complete solution available for the correction of the substrate influence on Young's modulus of the film when plastic deformation occurs during indentation, the authors are searching for an approach to approximate the elastic properties of a soft film on a hard substrate. It seems that the determination of the Young's modulus of very soft films cannot be separated from the determination of the yield stress. As an example for a low-k material actually of interest, porous silica xerogel films on silicon with porosities of 38 up to 51 vol.% were investigated.