Finite-element method for determination of electromechanical coupling coefficient for piezoelectric and capacitive micromachined ultrasonic transducers

Research has been reported on ultrasonic transduction using capacitive micromachined ultrasonic transducers (cMUTs). These are thin membranes of diameters of order 100 μm suspended over a silicon substrate with a gap of order 1 μm. The devices become transducers when a bias voltage is applied, causing electrostatic forces to draw the membranes closer to the substrate. Operation is by applying an electrical signal to excite a vibration in the membrane, or an ultrasonic wave to excite an ac voltage. The cMUT literature includes equivalent circuits and studies on losses and spurious waves, and discussion of output, sensitivity, and bandwidth. Transducer engineers would like to see analogies to the properties of piezoelectric transducers, in order to compare the cMUTs to traditional designs. An extension of the definition of the piezoelectric coupling coefficient to an effective coupling coefficient for cMUT transducers is presented. A finite-element method has been developed using the pzflex software package to determine its value, and used for evaluating cMUT designs. Accepted values are obtained for a piezoelectric material, and it is shown that an ideal cMUT has a coupling coefficient approaching 1 at the membrane collapse voltage, while practical devices are often limited to lower values.