Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

A data analysis procedure has been developed to estimate the contact area in an elastoplastic indentation of a thin film bonded to a substrate. The procedure can be used to derive the elastic modulus and hardness of the film from the indentation load, displacement, and contact stiffness data at indentation depths that are a significant fraction of the film thickness. The analysis is based on Yu’s elastic solution for the contact of a rigid conical punch on a layered half-space and uses an approach similar to the Oliver-Pharr method for bulk materials. The methodology is demonstrated for both compliant films on stiff substrates and the reverse combination and shows improved accuracy over previous methods. Since 1992, the analysis method proposed by Oliver and Pharr 1 has been established as the standard procedure for determining the hardness and elastic modulus from the indentation load-displacement curves for bulk materials. In the Oliver-Pharr method, the projected contact area between indenter tip and material is estimated using the equations for the elastic contact of an indenter of arbitrary shape on a uniform and isotropic half space. 2 The indentation modulus and hardness of the material can thus be calculated without the necessity of imaging the indentation after the experiment. The Oliver-Pharr method was initially developed for analyzing indentations in bulk materials, not for films on substrates, and no information about a possible substrate is included in the analysis. The Oliver-Pharr method is, however, frequently used by researchers to interpret indentations performed on thin films in an attempt to obtain approximate film properties regardless of the effect of substrate properties on the measurement. The accuracy of such a measurement depends on the film and substrate properties and on the indentation depth as a fraction of the total film thickness. In general, the error due to the substrate effect increases with increasing indentation depth and with increasing elastic mismatch between film and substrate. 3–7 To minimize the effect of the substrate on the measurement, the indentation depth is often limited to less than 10% of the film thickness. 5 This empirical rule is not always reliable, especially if the elastic mismatch between film and substrate is large. The 10% rule is also not useful for thin films when experimental issues make it difficult to obtain accurate results for shallow indentations. Evidently there exists a need for a method that can be used to analyze thin-film indentation data for indentation depths where the substrate effect cannot be ignored. A number of studies with several different approaches to modeling the substrate effect have been reported. 7–13 King used numerical techniques to model the elastic indentation of a layered half space with flat-ended punches of various cross sections. 8 The depth dependence of the effective indentation modulus of the composite system Meff was represented numerically as a function of the punch size a normalized by the film thickness t using the following phenomenological formula