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.

[1]  Generalized material model for lead magnesium niobate (PMN) and an associated electromechanical equivalent circuit , 1998 .

[2]  Quasistatic coupling coefficients for electrostrictive ceramics , 2001 .

[3]  O. Oralkan,et al.  Capacitive micromachined ultrasonic transducer arrays for medical imaging: experimental results , 2001, 2001 IEEE Ultrasonics Symposium. Proceedings. An International Symposium (Cat. No.01CH37263).

[4]  R. Carotenuto,et al.  Vibration maps of capacitive micromachined ultrasonic transducers by laser interferometry , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[5]  W. P. Mason,et al.  Piezoelectric Crystals and Their Applications to Ultrasonics , 1951 .

[6]  Butrus T. Khuri-Yakub,et al.  The microfabrication of capacitive ultrasonic transducers , 1998 .

[7]  O. Oralkan,et al.  Initial pulse-echo imaging results with one-dimensional capacitive micromachined ultrasonic transducer arrays , 2000, 2000 IEEE Ultrasonics Symposium. Proceedings. An International Symposium (Cat. No.00CH37121).

[8]  Josef Binder,et al.  A new class of capacitive micromachined ultrasonic transducers , 2000, 2000 IEEE Ultrasonics Symposium. Proceedings. An International Symposium (Cat. No.00CH37121).

[9]  C. Hom,et al.  Calculation of quasi-static electromechanical coupling coefficients for electrostrictive ceramic materials , 1994, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[10]  Giosue Caliano,et al.  An accurate model for capacitive micromachined ultrasonic transducers , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[11]  B. Khuri-Yakub,et al.  Surface micromachined capacitive ultrasonic transducers , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[12]  Butrus T. Khuri-Yakub,et al.  Fabrication and characterization of surface micromachined capacitive ultrasonic immersion transducers , 1999 .

[13]  Lawrence E. Kinsler,et al.  Fundamentals of acoustics , 1950 .

[14]  Don Berlincourt,et al.  3 – Piezoelectric and Piezomagnetic Materials and Their Function in Transducers , 1964 .

[15]  I. Ladabaum,et al.  Theory and analysis of electrode size optimization for capacitive microfabricated ultrasonic transducers , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[16]  W. P. Mason.  An Electromechanical Representation of a Piezoelectric Crystal Used as a Transducer , 1935 .

[17]  B. Khuri-Yakub,et al.  A surface micromachined electrostatic ultrasonic air transducer , 1996, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.