Electromechanical coupling factor of capacitive micromachined ultrasonic transducers

Recently, a linear, analytical distributed model for capacitive micromachined ultrasonic transducers (CMUTs) was presented, and an electromechanical equivalent circuit based on the theory reported was used to describe the behavior of the transducer [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 159-168 (2002)]. The distributed model is applied here to calculate the dynamic coupling factor k(w) of a lossless CMUT, based on a definition that involves the energies stored in a dynamic vibration cycle, and the results are compared with those obtained with a lumped model. A strong discrepancy is found between the two models as the bias voltage increases. The lumped model predicts an increasing dynamic k factor up to unity, whereas the distributed model predicts a more realistic saturation of this parameter to values substantially lower. It is demonstrated that the maximum value of k(w), corresponding to an operating point close to the diaphragm collapse, is 0.4 for a CMUT single cell with a circular membrane diaphragm and no parasitic capacitance (0.36 for a cell with a circular plate diaphragm). This means that the dynamic coupling factor of a CMUT is comparable to that of a piezoceramic plate oscillating in the thickness mode. Parasitic capacitance decreases the value of k(w), because it does not contribute to the energy conversion. The effective coupling factor k(eff) is also investigated, showing that this parameter coincides with k(w) within the lumped model approximation, but a quite different result is obtained if a computation is made with the more accurate distributed model. As a consequence, k(eff), which can be measured from the transducer electrical impedance, does not give a reliable value of the actual dynamic coupling factor.