The conventional method of modeling CMUTs use the isotropic plate equation to calculate the deflection, leading to deviations from FEM simulations including anisotropic effects of around 10% in center deflection. In this paper, the deflection is found for square plates using the full anisotropic plate equation and the Galerkin method. Utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The deflection was measured on fabricated CMUTs using a white light interferometer. Fitting the anisotropic calculated deflection to the measurement a deviation of 0.5-1.5% is seen for the fitted values. Finally it was also measured how the device behaved under increasing bias voltage and it is observed that the model including anisotropic effects is within the uncertainty interval of the measurements.
Proceedings of the 2013 Ieee International Ultrasonics Symposium, 2013, p. 2187-2190
Fields, Waves and Electromagnetics; Anisotropic magnetoresistance; Equations; Finite element analyses; Mathematical model; Silicon; Voltage measurement; Substrates
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2013 IEEE International Ultrasonics Symposium, 2013