Electrostatic and Small-Signal Analysis of CMUTs With Circular and Square Anisotropic Plates

Traditionally, Capacitive Micromachined Ultrasonic Transducers (CMUTs) are modeled using the isotropic plate equation and this leads to deviations between analytical calcu- lations and Finite Element Modeling (FEM). In this paper, the deflection is calculated for both circular and square plates using the full anisotropic plate equation. It is shown that the anisotropic calculations match perfectly with FEM while an isotropic ap- proach causes up to 10% deviations in deflection. For circular plates an exact solution can be found and for square plates using the Galerkin method and 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 theory of multilayer plates is also applied to the CMUT. The deflection of a square plate was measured on fabricated CMUTs using a white light interferometer. Fitting the plate parameter for the anisotropic calculated deflection to the measurement, a deviation of 0.07 % is seen. Furthermore, electrostatic analysis is performed using energy considerations and the calculated deflections to include the anisotropy. The stable position, effective spring constant, pull-in distance and pull-in voltage are found for both circular and square anisotropic plates and the pressure dependence is also included by comparing to the corresponding analysis for a parallel plate. Finally, it was also measured how fabricated devices with both circular and square plates behaved under increasing bias voltage and it is observed that the models including anisotropic effects are within the uncertainty interval of the measurements.