Design and Development of Capacitive Micromachined Ultrasonic Transducers
This thesis presents the design and analysis for development of a Capacitive Micromachined Ultrasonic Transducer (CMUT), a novel sensor and actuator, aimed at replacing the conventional piezoelectric transducers for air-coupled ultrasonic imaging applications. These CMUTs are fabricated using the silicon micromachining technology wherein all fabrication is done on the surface of a silicon wafer by means of thin-film depositions, patterning with photolithography and etching. The main emphasis of this study is on developing analytical models that serve as effective design tools for the development of these devices. A desirable goal of such study is to create reasonable mathematical models, obtain analytical solutions, wherever possible, for various measures of transducer performance and provide design aids. A logical start is the lumped parameter modeling wherein the explicit dependence of the physical parameters on the spatial extent of the device is ignored. The system lumped parameters, such as the equivalent stiffness, the equivalent mass, and the equivalent damping are extracted from reasonable analytical or numerical models and subsequently used in the static and dynamic analysis of the device. Useful predictions are made with regard to the key transducer parameters, such as, the pull-in voltage, the static deflection, the dynamic response and the acoustic field produced. The modeling work presented embodies two main objectives: (i) it serves to provide direction in the design phase, and, (ii) it serves to aid in the extraction of critical parameters which affect the device behavior. Comparison of the results with the more rigorous FEM simulations as well as with those present in the existing literature assure that the developed models are accurate enough to serve as useful design tools. The distributed parameter modeling is presented next. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electro-elastic coupling aspect in the design of these devices. An approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear, is presented. The model is based on the Kirchhoﬀ-Love assumptions that the plate is thin and the deflections and slopes are small. The classical thin-plate theory is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. This theory is used to determine the static deflection of the CMUT membrane due to a DC bias voltage. The thin-plate electro-elastic equation is solved using the Galerkin weighted residual technique under the assumption that the deflections are small in comparison to the thickness of the plate. The results obtained are compared to those obtained from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations. A simple analytical formula, which gives fairly accurate results (to within 3% of the value predicted by ANSYS simulations) for determination of the pull-in voltage, is also presented. As stated, this formula accounts for the elastic deflection of the membrane due to the coupled interaction with the electrostatic field. The effect of vacuum sealing the backside cavity of a CMUT is investigated in some detail. The presence or absence of air inside the cavity has a marked effect upon the system parameters, such as the natural frequency and the pull-in voltage. The possibility of using sealed CMUT cavities with air inside at ambient pressure is explored. In order to estimate the transducer loss due to the presence of air in the sealed cavity, the squeeze film forces resulting from the compression of the trapped air film are evaluated. Towards this end, the linearized Reynolds equation is solved in conjunction with the appropriate boundary conditions, taking the flexure of the membrane into account. From this analysis, it is concluded that, for a sealed CMUT cavity, the presence of air does not cause any squeeze film damping even when the flexure of the membrane is taken into account (the case of a rigid plate is already known). Although the emphasis of the study undertaken here is not on the physical realization of a working CMUT, a single cell as well as a linear array based on the design presented here, were fabricated (in a foundry elsewhere) in order to verify some of the most fundamental device parameters from experimental measurements. The fabricated devices have been characterized for their resonant frequency, quality factor, and structural integrity. These tests were conducted using the laser Doppler vibrometer and the Focused Ion Beam milling. Having investigated thoroughly the behavior of a single cell, we proceed to demonstrate how these cells can be arranged optimally in the form of an array to provide a comprehensive ultrasonic imaging system. A thorough analysis of the requirements for the array architecture is undertaken to determine the optimal configuration. The design constraints that need to be taken into account for CMUT arrays, especially for NDE applications, are presented. The main issue of designing an array consisting of a large number of CMUT cells required for producing a pressure wave of sufficient strength which is detectable upon reflection from the desired location even after suffering severe attenuation resulting from propagation in various media is addressed. A scalable annular array architecture of CMUT cells is recommended based on the analysis carried out.
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