Differences between plate theory and lumped element model in electrostatic analysis of one-sided and two-sided CMUTs with circular microplates

Abstract

An analytical study of capacitive micromachined ultrasonic transducers (CMUTs) with circular microplates has been carried out. The study comprises one-sided (single electrode back-plate) and two-sided (double electrode back-plate) systems, and derives universal correction factors for pull-in voltage and critical displacement to be used in lumped element model (LEM) analysis. We employ von Karman plate theory and the single-mode Galerkin decomposition method to solve the equations. Consequently, voltage–deflection relations have been derived. By comparing results from plate theory with LEM, it is concluded: (1) for the one-sided CMUT by neglecting geometrical nonlinearity, we find $$\frac{{{V_{\text {Pull in - P}}}}}{{{V_{\text {Pull in - LEM}}}}} = 1.327$$ and the ratio of critical displacement derived from plate theory over critical displacement from LEM is always 1.882. (2) For the one-sided CMUT including geometrical nonlinearity $$\frac{{{V_{\text {Pull in} - P}}}}{{{V_{\text {Pull in - LEM}}}}} = 1.45$$ and critical displacement from plate theory over critical displacement from LEM is 1.792, for a specific set of parameters. (3) For the two-sided CMUT, there is no differences in using linear nor nonlinear analysis and $$\frac{{{V_{\text {Pull in - P}}}}}{{{V_{\text {Pull in - LEM}}}}} = 1.276$$ . For all studied cases, finite element (FE) analysis has been performed to validate the analytical outcomes.