Analysis of spring softening effect on the collapse voltage of capacitive MEMS ultrasonic transducers

This paper explained the dependency of collapse voltage on semiconductor device structural features (membrane diameter, membrane thickness and the vertical distance between the electrodes) and physical characteristics (mechanical residual stress of the silicon nitride membrane) considering the electro-mechanical model of MEMS based Capacitive micromachined ultrasonic transducer (CMUT). To have sensitivity comparable to that of piezoelectric ultrasonic transducers (UTs), CMUTs need to be biased close to the collapse voltage. Maximum efficiency is achieved in the conventional mode of operation by biasing the device close to the collapse voltage. The total acoustic output pressure is determined by the efficiency of the device. Hence a careful investigation of the same is decidedly required. Finite element method (FEM) model by PZFlex and analytical model of single element CMUT with 0.75 µm thick silicon nitride membranes suspended on 0.5 µm thick cavity were developed showing resonance frequency at 5 MHz. Through these analyses, it is observed that membrane and vacuum gap thickness are both directly proportional to collapse voltage, while radius of the membrane and also its area are inversely proportional to collapse voltage. Initially the spring softening effect of the membrane has been neglected. Later the effect has been included in the proposed model and analyzed. It has been shown that the spring softening effect cannot be neglected for accurate CMUT modeling. A capacitive micromachined ultrasound transducer can be realized with the model described in this paper.