Elastic modulus of thin homogeneous films can be determined by indenting the specimen to various depths and extrapolating the measured (apparent) E-values to zero penetration. The paper shows the application of five approximation functions for this purpose: linear, exponential, reciprocal exponential, Gao's, and the Doerner and Nix functions. Comparison of the results for 26 film/substrate combinations has shown that the indentation response of film/substrate composites can, in general, be described by the Gao analytical function. In determining the thin film modulus from experimental data, satisfactory results can also be obtained with the exponential function, while linear function may be used only for thick films where the relative depths of penetration are small. The article explains the pertinent procedures and gives practical recommendations for the testing.

The recently reported hysteretic behavior of silicon under indentation (Clarke et al.1 and Pharret al.2-5) is investigated using an ultra-micro-indentation system with an 8.5 μm spherical-tipped indenter. The onset of “plastic” behavior during loading and hysteresis during unloading was readily observed at loads in excess of 70 mN. Cracking about the residual impression was observed only at loads of 350 mN and higher. An analysis of the data is presented that estimates the following: (1) the initial onset of deformation occurs at a mean pressure of 11.8 ± 0.6 GPa, (2) the mean pressure at higher loads is 11.3 ± 1.3 GPa, and (3) the hysteretic transition on unloading occurs at mean pressures between 7.5 and 9.1 GPa. These values are in good agreement with the accepted literature values for the known silicon transformation pressures. A simulation of the force-displacement data based on the analysis and model is presented and is found to fit the observations very well.

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