We report a novel method to measure Poisson's ratio v of compressively prestressed thin films. The method exploits a v-dependent mechanical instability transition of buckled long rectangular membranes under differential pressure. This allows to determine v with high accuracy, using a physical model of the plate instability. The method was used to extract v=0.253+-0.017 from 0.704+-0.003 mu m thick PECVD silicon nitride films.
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