An equivalent circuit model for curved piezoelectric micromachined ultrasonic transducers with spherical-shape diaphragms (original) (raw)
Related papers
IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2016
Equivalent circuit models of large arrays of curved (spherical-shape) and flat Piezoelectric Micromachined Ultrasonic Transducers (pMUTs) have been developed for complex pMUT arrays design and analysis. The exact solutions for circuit parameters in the electromechanical domain, such as: mechanical admittance, input electrical impedance, and electromechanical transformer ratio were analytically derived. By utilizing the array solution methods previously established for the thickness-mode piezoelectric devices and Capacitive Micromachined Ultrasonic Transducers (cMUT), single pMUT circuit model can be extended to models for array structures. The array model includes both the self- and mutual-acoustic radiation impedances of individual transducers in the acoustic medium. Volumetric displacement, induced piezoelectric current, and pressure field can be derived with respect to the input voltage matrix, material and geometrical properties of each individual transducer and the array struct...
Lumped Electromechanical Modeling of Capacitive Micromachined Ultrasonic Transducers
Materials Today: Proceedings, 2016
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.
Procedia Engineering
In this work, we present a complete multiphysics modelling (via the Finite Element Method, FEM) of an air coupled piezoelectric micromachined ultrasonic transducer (PMUT) with preliminary experimental validations. The PMUT is a suspended layered membrane, in which one of the layers is made of piezoelectric material. By means of an applied voltage over the piezoelectric layer thickness, the device emits acoustic waves in air. The model takes into account the multiple interactions between electrical, mechanical and acoustic fields, and in particular gives a realistic estimation of the device quality factor by means of a proper modelling of thermo-viscous losses in the fluid domain. The complexity of the model is increased by the presence of initial large deformations in the membrane and fabrication induced residual stresses. Preliminary experimental matchings are presented for static pre-deflection of the membrane due to residual stresses and for the eigenfrequency corresponding to acoustic wave emission.
2003
Equivalent circuit model has been widely used to predict the bandwidth of capacitive micromachined ultrasonic transducers (CMUTs). According to this model, the lower cutoff of the bandwidth is determined by the time constant of the parallel RC where R is dictated by the radiation and C is determined by the electrical capacitance of the transducer. The higher cutoff, on the other hand, is determined by the membrane's anti-resonance. In the mechanical part of the model, the radiation impedance is simply added to the membrane impedance assuming that the membrane impedance does not change when it operates in the immersion medium. Therefore, the mass loading effect of the medium is neglected. Our finite element method calculations showed that the mass loading on the membrane impedance drastically lowers the membrane anti-resonance frequency degrading the bandwidth. In this paper, we present results of equivalent circuit modeling combined with finite element analysis. We constructed a 3D finite element model for one element of a 1D array. The element has 7 hexagonal membranes in the width dimension and it is assumed that the membranes are replicated in the length dimension infinitely by using symmetry boundary conditions. By combining membrane impedance with equivalent circuit model, we found that the center frequency of operation is 11 MHz and the bandwidth is 12.5 MHz close to the collapse voltage. We also investigated the effect of the DC bias on the center frequency. Decreasing the bias voltage increased the center frequency without affecting the bandwidth assuming the source impedance is zero.
Sensors
With the development of technology, systems gravitate towards increasing in their complexity, miniaturization, and level of automation. Amongst these systems, ultrasonic devices have adhered to this trend of advancement. Ultrasonic systems require transducers to generate and sense ultrasonic signals. These transducers heavily impact the system’s performance. Advancements in microelectromechanical systems have led to the development of micromachined ultrasonic transducers (MUTs), which are utilized in miniaturized ultrasound systems. Piezoelectric micromachined ultrasonic transducers (PMUTs) exhibit higher capacitance and lower electrical impedance, which enhances the transducer’s sensitivity by minimizing the effect of parasitic capacitance and facilitating their integration with low-voltage electronics. PMUTs utilize high-yield batch microfabrication with the use of thin piezoelectric films. The deposition of thin piezoelectric material compatible with complementary metal-oxide sem...
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2000
Representing a new approach to ultrasound generation and detection, study on piezoelectric micromachined ultrasonic transducers (pMUTs) has been a growing research area in recent years. Intensive research work has been directed on the deposition of lead zirconate titanate (PZT) films on silicon substrates for their excellent piezoelectric coefficients and electromechanical coupling coefficients. However, the high processing temperature required for PZT crystallization results in a low device yield and also makes it difficult to integrate with control circuits. In this paper, a fabrication technology of pMUTs based on piezoelectric P(VDF-TrFE) 70/30 copolymer films has been adopted, with the maximum processing temperature not exceeding 140°C allowing for post-IC compatibility. The entire processing procedures are simple and low cost, as compared with those of capacitive micromachined ultrasonic transducers (cMUTs) and ceramic-based pMUTs. The applications of the fabricated pMUTs as airborne ultrasonic transducers and transducer arrays have been demonstrated. Reasonably good device performances and high device yield have been achieved.
Electromechanical coupling factor of capacitive micromachined ultrasonic transducers
The Journal of the Acoustical Society of America, 2003
Recently, a linear, analytical distributed model for capacitive micromachined ultrasonic transducers ͑CMUTs͒ was presented, and an electromechanical equivalent circuit based on the theory reported was used to describe the behavior of the transducer ͓IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 159-168 ͑2002͔͒. The distributed model is applied here to calculate the dynamic coupling factor k w of a lossless CMUT, based on a definition that involves the energies stored in a dynamic vibration cycle, and the results are compared with those obtained with a lumped model. A strong discrepancy is found between the two models as the bias voltage increases. The lumped model predicts an increasing dynamic k factor up to unity, whereas the distributed model predicts a more realistic saturation of this parameter to values substantially lower. It is demonstrated that the maximum value of k w , corresponding to an operating point close to the diaphragm collapse, is 0.4 for a CMUT single cell with a circular membrane diaphragm and no parasitic capacitance ͑0.36 for a cell with a circular plate diaphragm͒. This means that the dynamic coupling factor of a CMUT is comparable to that of a piezoceramic plate oscillating in the thickness mode. Parasitic capacitance decreases the value of k w , because it does not contribute to the energy conversion. The effective coupling factor k eff is also investigated, showing that this parameter coincides with k w within the lumped model approximation, but a quite different result is obtained if a computation is made with the more accurate distributed model. As a consequence, k eff , which can be measured from the transducer electrical impedance, does not give a reliable value of the actual dynamic coupling factor.
2003
Equivalent circuit model has been widely used to predict the bandwidth of capacitive micromachined ultrasonic transducers (CMUTs). According to this model, the lower cutoff of the bandwidth is determined by the time constant of the parallel RC where R is dictated by the radiation and C is determined by the electrical capacitance of the transducer. The higher cutoff, on the other hand, is determined by the membrane's anti-resonance. In the mechanical part of the model, the radiation impedance is simply added to the membrane impedance assuming that the membrane impedance does not change when it operates in the immersion medium. Therefore, the mass loading effect of the medium is neglected. Our finite element method calculations showed that the mass loading on the membrane impedance drastically lowers the membrane anti-resonance frequency degrading the bandwidth. In this paper, we present results of equivalent circuit modeling combined with finite element analysis. We constructed a 3D finite element model for one element of a 1D array. The element has 7 hexagonal membranes in the width dimension and it is assumed that the membranes are replicated in the length dimension infinitely by using symmetry boundary conditions. By combining membrane impedance with equivalent circuit model, we found that the center frequency of operation is 11 MHz and the bandwidth is 12.5 MHz close to the collapse voltage. We also investigated the effect of the DC bias on the center frequency. Decreasing the bias voltage increased the center frequency without affecting the bandwidth assuming the source impedance is zero.
Dynamic analysis of capacitive micromachined ultrasonic transducers
IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2005
Electrostatic transducers are usually operated under a DC bias below their collapse voltage. The same scheme has been adopted for capacitive micromachined ultrasonic transducers (cMUTs). DC bias deflects the cMUT membranes toward the substrate, so that their centers are free to move during both receive and transmit operations. In this paper, we present time-domain, finite element calculations for cMUTs using LS-DYNA, a commercially available finite element package. In addition to this DC bias mode, other new cMUT operations (collapse and collapse-snapback) have recently been demonstrated. Because cMUT membranes make contact with the substrate in these new operations, modeling of these cMUTs should include contact analysis. Our model was a cMUT transducer consisting of many hexagonal membranes; because it was symmetrical, we modeled only one-sixth of a hexagonal cell loaded with a fluid medium. The finite element results for both conventional and collapse modes were compared to measurements made by an optical interferometer; a good match was observed. Thus, the model is useful for designing cMUTs that operate in regimes where membranes make contact with the substrate.
Micromachined Ultrasonic Transducers and Acoustic Sensors Based on Piezoelectric Thin Films
Journal of Electroceramics, 2000
A review is given on the current state of the art in piezoelectric micromachined ultrasonic transducers (pMUT). It is attempted to quantify the limits of pMUT's with respect to the electromechanical coupling, and to relate current achievements. Main needs for future research are identified in design, micromachining and further improvements of PZT films. Applications are shortly reviewed.