In this work, we report a method for simultaneous determination of E and σ by designing the test structures in the form of fixed-fixed beams and using their frequency response in buckled state. We exploit the invariance of even mode frequencies on residual stress to uncouple the effects of E and σ on the frequency, thus making it possible to determine E, along with another possible unknown- the underetch length. We subsequently use this information to find the residual stress from the odd mode frequencies. This evaluation requires a single sweep of frequency response from the buckled beam. The only condition here is that the beams have to be designed such that they result in buckled structures after release. This condition is essential, as only the buckled state guarantees the invariance of even modes on residual stress. Compared to other methods for determination of these properties, the advantage here is that we use a single method of measurement – LDV based frequency response measurement and a single type of test structures. Since the proposed method does not involve electrostatic actuation, in general it is applicable for dielectric thin films.
In order to ensure repeatability, we have used measured results from more than 100 test structures. For the procedure to work, we need at least one of each even and odd mode frequencies to estimate the unknown parameters. Since in our experiment we are able to measure first four frequencies, we have two modes each from odd and even category. Thus there are total four modal combinations of measured data available to proceed with estimation of material properties, i.e. 2nd – 1st, 2nd – 3rd, 4th – 1st, 4th – 3rd. However not all of these combinations are always equally feasible. We have developed a good understanding of the circumstances, which favours use of one combination against the others.