Determination of Young's modulus of thin films using the concept of the effective indenter

Abstract

Since the introduction of a new analytical technique for elastic–plastic indentation experiments, i.e. the model of the ‘effective indenter’ combined with the Extended Hertzian Approach [J. Phys. D: Appl. Phys. 37 (2004) p. 2761], a number of publications have reported successful determination of the yield strength of bulk materials and thin films with this new approach for a large group of materials, including SiO2 and a-C:H. However, this approach also allows the determination of the Young's modulus of thin films. In this contribution, we have investigated the extent to which the model of the ‘effective indenter’ can be used to determine the Young's modulus of films. Thermally grown SiO2 and a-C:H films deposited by PECVD were used. For each sample, elastic–plastic load–depth curves (Berkovich) for a series of varying maximum loads were analyzed to gather data regarding the ratio of contact depth to film thickness. For each unloading curve, the shape of the effective indenter and the Young's modulus value of the film were determined. Modulus values were in reasonable agreement with those obtained by elastic spherical indentations if the contact depth to film thickness ratio was sufficiently low. The approach used in the paper fails if the latter ratio exceeds a certain limit, which is specific for the given combination of substrate and film material. Physical mechanisms are discussed as reasons for this behavior.