A design of high-sensitivity micromachined capacitive ultrasonic mass resonators

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 10.08 MHz at bias voltage of 30 V; the resonance frequency decreases as bias is increased and is down to 9.86 MHz at 300 V. The reference mass sensitivity is -1312 cm²/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.