Analytic modeling of loss and cross-coupling in capacitive micromachined ultrasonic transducers

The structural loss mechanism of capacitive micromachined ultrasonic transducer (cMUT) is investigated using finite element analysis and the normal mode theory. A single micromachined transducer membrane on an infinite silicon substrate is simulated by incorporating absorbing boundary conditions in the finite element method. This enables direct evaluation of the mechanical impedance of the membrane. Furthermore, the field distribution along the thickness of the silicon substrate due to outward radiating wave modes is obtained. The normal mode theory is applied to extract the contributions of different wave modes to the complicated field distributions. It is found that, the lowest order Lamb wave modes are responsible for the loss. Evaluation of absolute and relative power losses due to individual modes indicate that the lowest order anti-symmetric (A0) mode is the dominant radial mode in agreement with experimental measurements. The results of the analysis are used to derive a detailed equivalent circuit model of a cMUT with structural loss.