Analytical calculation of collapse voltage of CMUT membrane [capacitive micromachined ultrasonic transducers]

Because the collapse voltage determines the operating point of the capacitive micromachined ultrasonic transducer (CMUT), it is crucial to calculate and control this parameter. In this paper, we propose a fast numerical algorithm for the calculation of collapse voltage. The algorithm uses the parallel plate method to approximate the force distribution over the membrane, and then applies an analytical solution for the plate equation, loaded by the approximated force distribution. Using this method, we are able to calculate the collapse voltage in a couple of seconds, within 0.1% accuracy. We report on the collapse voltage calculation results using our method for four different design structures. While the computation time of our method is about three orders of magnitude less than the finite element method, the percentage error of collapse voltage calculation is, nevertheless, less than four percent in all the design structures. The proposed algorithm is also suitable for the inclusion of any external force distribution on the membrane, such as atmospheric pressure.