Comparison of two experimental methods for the mechanical characterization of thin or thick films from the study of micromachined circular diaphragms

Abstract

The purpose of this study was to compare two experimental methods and evaluate the effectiveness of a set of analytical models in order to measure the initial stress and the Young's modulus value of thin and thick film materials. Two types of experiments were performed on micromachined circular diaphragms: bulge testing and vibrometry. The range of validity and accuracy of the analytical models with respect to the vibration of the diaphragms was discussed from the finite element simulations. It was shown that the a/t ratio should be considered carefully to determine the value of the Young's modulus by vibrometry with an acceptable error. A relative error of approximately ±10% on E was obtained for a/t ≤ 750. For 750 ≤ a/t ≤ 1000, the value of the dimensionless parameter k must also be considered. It has been shown that the residual stress value can be obtained with an accuracy of 10% or less, given that k > 12. As an illustration, experimental methods and models were applied to the characterization of a thick electroplated gold film and a sputter-deposited Inconel thin film. Circular structures were defined by vertical sidewalls etched on the back of a Si wafer using the deep reactive ion etching technique. In addition to analytical models, parametric finite element simulations and a design optimization technique were used to determine the material's mechanical properties. The static deflections of the diaphragms were measured as a function of the applied pressure. The resonant frequencies and mode shapes of the vibrating structures were observed under vacuum by white-light interferometric microscopy. For gold, it was found that E = (53 ± 20) GPa and σ(0) = (180 ± 10) MPa. For Inconel, it was found that E = (157 ± 14) GPa and σ(0) = (172 ± 5) MPa.