Lumped Electromechanical Modeling of Capacitive Micromachined Ultrasonic Transducers

Abstract

Conventional plane piston lead zirconium titanate (PZT) based transducers perform poorly for audio speakers and as capacitance receivers due to the lack of proper matching layer materials. Conventional designs have relatively large gaps, 50-100 μm, and use the air in the gap as the restoring force of the vibrating electrode. With the help of silicon micromachining, Capacitive Micromachined Ultrasonic Transducers (CMUTs) are defined. The gaps are made to be as small as 500Å, and the restoring force of the vibrating electrode is the stiffness of the electrode itself. In this paper, a single CMUT element is represented by the lumped electromechanical model. It is realized with comparison of the experimental and simulated outcomes that a single spring constant value is not sufficient to faithfully describe the entire region of operation of CMUT. The search results in two optimized values of spring constants, one fits well to describe the low bias voltage region and the other the collapse voltage regime, where the membrane touches the substrate and is unable to produce vibrations. The membrane displacement behavior under static bias is analyzed. It is found that the displacement at the centre of the membrane is a function of not only the bias but depends highly on the membrane structural geometries and physical characteristics. CMUT membrane’s displacement can be optimized with a change in the above which is a necessary condition for obtaining the required sensitivity. Numerical calculations are done with the help of MATLAB and Finite Element Method (FEM) simulations are aimed with help of PZFlex.