Calculation of the Deformation of a Circular Fixed Silicon Membrane with Prestress by Finite Element Analysis

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Abstract With the aim to improve the accuracy of MEMS microphones, our research topic is the simulation of the thermo-mechanical behaviour of MEMS microphones. The MEMS microphones consist of a sensor chip, which is a capacitive transducer, where a thin and flexible silicon membrane and two perforated backplates form a capacitor. The change in capacitance depends on the distance between the silicon membrane and the backplates. Therefore, we determined the deformation of a circular fixed silicon membrane with prestress by Finite Element Analysis (FEA). The calculation was performed with the simulation software Code-Aster. For comparison, the deformation was also analytically calculated according to Timoshenko. The good agreement between FEA and analytical calculation revealed that Code-Aster is suitable for these kinds of simulations.