Determination of elastic modulus of thin layers using nanoindentation

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Abstract
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.