A theoretical model and mathematical description for silicon micromachined electrostatic or capacitive ultrasonic imaging transducers have been developed. According to the model the basic performance parameters of such a transducer, such as natural frequencies, eigenfunctions, resonance and anti-resonance frequencies, and the mechanical impedance of the diaphragm can be predicted from the geometry of the transducer and property parameters of materials used. The paper reveals that this type of transducers has two basic operation modes, corresponding to the resonance of a mass-spring oscillator comprised of the diaphragm and the air cushion, and the first-order bending mode of the diaphragm itself respectively, and presents an optimal method for extending the bandwidth by making the two modes coupled, and thereby provides a theoretical basis for the optimal design.

The TDK model originally developed for capacitive micromachined ultrasonic transducers (CMUT) is applied to the modeling and design of capacitive ultrasonic mass resonators (CUMR). The diaphragm of CUMRs is treated as a laminated plate in tension and supported by elastic foundation, and then its fundamental frequency can be expressed in terms of the stiffness of the diaphragm, tension in it, the electrostatic negative stiffness caused by bias voltage, the frequency parameter of the vibration of diaphragm, and area density of diaphragm. Furthermore, the mass sensitivity of CUMRs, which is intrinsically nonlinear, is derived and its first order approximation and the reference sensitivity are also defined. The design of CUMRs then can be computationally performed for different geometric dimensions of the device and the physical parameters of material used. Finally, a design of CUMRs is given based on the TDK model. Its fundamental frequency is 10.08MHz at bias voltage of 30V; the resonance frequency decreases as bias is increased and is down to 9.86MHz at 300V. The reference mass sensitivity is -1312cm2/g,so 1 Hz resonance frequency shift corresponds to an added mass of 76 pg/cm2. Comparing with piezoelectric ultrasonic mass resonators (PUMR), CUMRs can be an attractive choice for chemical and biological detections.