Circular membrane approximation model with the effect of the finiteness of the electrode’s diameter of MEMS capacitive micromachined ultrasonic transducers

In this paper, an analytical model for evaluation of membrane displacement, multiple resonances, mechanical impedances and bandwidth profile of capacitive micromachined ultrasonic transducers (CMUTs) developed by MEMS technology for medical imaging is presented. Improvement in the results is brought in by taking into account the finiteness of the electrodes diameter. 3-D models for practical membrane shapes are carried out by FEM PZFLEX simulation. The model shows that CMUT is a multiple resonance device. The analytical values of the fundamental resonance agree excellently with the published experimental results. The 50 µm radius devices are theoretically found to be most efficient at 2.35 MHz. The 3-dB fractional bandwidth is also evaluated from the improved analytical model. Moreover, physical solution insists that at a certain bias voltage, the residual force in the membrane will no longer resist the electrostatic force of attraction, resulting in membrane collapse which is clearly demonstrated in this work.