Capacitive Micromachined Ultrasonic Transducer Membrane Research Articles

An Improved Static Membrane Deflection Analysis for Collapse Mode CMUT Fabricated by Sacrificial Release Method

To improve the accuracy of the static membrane deflection calculation for the collapse mode capacitive micromachined ultrasonic transducer (CMUT) fabricated by sacrificial release (SR) method. The beam theory was used and the substrate supporting force can be modeled by a coefficient to the load on the membrane. The surrounding supporting post bending can be modeled by applying the elastic support boundary conditions (ESBCs) for the peripheral part of the membrane. CMUT devices have been fabricated using the SR process to validate this analytical analysis. Young’s modulus of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {Si}_{{3}} \text {N}_{{4}}$ </tex-math></inline-formula> was derived as 200 GPa by a method using center deflections of several different radii single-layer conventional devices under 1 atm. The analytical deflection results and contact radius results for the collapse mode CMUT membranes were testified by experimental results under 1 atm and were found matching the experimental results. This showed that the analysis can provide improved results for SR fabricated CMUT devices by including the substrate supporting effect and the post bending effect.

Design and Implementation of Low-Voltage Tunable Capacitive Micro-Machined Transducers (CMUT) for Portable Applications.

Capacitive micromachined ultrasonic transducers (CMUT) are MEMS-based transducers with advantages over conventional ultrasonic transducers, such as their small size, the ease of integration with semiconductor electronics, and batch fabrication. In this study, the effect of different membrane topologies on the displacement, resonant frequency, and output pressure of the CMUT membrane is investigated in the transmission mode in an air environment. A novel structural-support feature, the rocker stem, is introduced, where the membrane is weakly held to the substrate in order to minimize mechanical constraints. Four different CMUT topologies are designed and assessed to analyze the impacts of topological variations. A new CMUT array configuration is also designed to provide an approach for maximizing CMUT density. This study aims to contribute to efficient CMUT design and the determination of optimum structural parameters for portable applications in air.

Use of Supporting Post Width to Increase the CMUT’s Resonant Frequency

A new method is proposed to increase the resonant frequency of a Capacitive Micromachined Ultrasonic Transducer (CMUT) device while keeping the radii unchanged for devices fabricated by sacrificial release (SR) method. The resonant frequency of a CMUT cell is determined by the properties of the membrane such as the Young&#x2019;s modulus, membrane dimensions and effective membrane mass. Effective Young&#x2019;s modulus is used to calculate the resonant frequency of CMUT fabricated by SR method. The supporting post structure will affect the boundary conditions at the edge of the CMUT membrane and in turn affect the deflection together with the effective Young&#x2019;s modulus of the membrane. The perturbation method is used to derive the solution for the governing von K&#x00E1;rm&#x00E1;n equations. The results show that the thicker is the supporting post width, the higher is the resonant frequency. This method can also be used to simplify the mask design and CMUT fabrication process.

Inkjet-printed CMUT humidity sensors with high sensitivity and low hysteresis

Capacitive micromachined ultrasonic transducer (CMUT) is a proven MEMS based gravimetric sensor featuring high mass sensitivity. It can be highly sensitive for relative humidity (RH) measurement when drop-casted with moisture-sensitive graphene oxide (GO) film. However, high hysteresis appears to be a critical problem for the sensor partially due to the non-uniformity of the sensing film. Here, we present miniaturized CMUTs that are functionalized by the inkjet-printed GO film and exhibit high sensitivity and meanwhile low hysteresis. Hexagon CMUTs with a side length of 500 μm were designed and fabricated by the nitride-to-oxide wafer bonding process. GO inks were prepared using a mixture of DI water and ethanol as the solvent. A square pattern formed by a 2D array of ink droplets was inkjet printed on the CMUT membranes. GO films with different thicknesses were deposited on three CMUTs. The humidity sensing performance of the sensors was evaluated by measuring the resonance frequency shifts induced by the added mass of adsorbed water molecules. The sensors delivered high RH sensitivity of up to 3.35 kHz/%RH, short response/recovery time down to 8 s/2 s, and hysteresis as low as 2.6 %RH. This work demonstrates that the inkjet printing technique is an excellent tool to functionalize CMUT with the advantages of minimized material consumption, batch-production capability, and exceptional control over the film thickness and quality. The CMUT printed with GO film has also shown to be a promising candidate as a miniaturized humidity sensing platform.

An Analytical Model for Bandwidth Enhancement of Air-Coupled Unsealed Helmholtz Structural CMUTs

Capacitive micromachined ultrasonic transducers (CMUTs) were reported to own high potential in air-coupled ultrasonic applications such as noncontact nondestructive examination and gas flow measurement. The unsealed CMUTs which utilized the squeeze film effect were reported to overcome the narrow output pressure bandwidth of the conventional sealed CMUTs in air operation. This kind of unsealed CMUTs can also be regarded as Helmholtz resonators. In this work, we present the air-coupled unsealed Helmholtz structural CMUTs which utilize both the squeeze film effect and the Helmholtz resonant effect to enhance the output pressure bandwidth. Based on the mechanism of vibration coupling between membrane and air pistons in membrane holes, we propose an analytical model to aid the design process of this kind of CMUTs. We also use finite element method (FEM) to investigate this kind of CMUTs for our analytical model validation. The FEM results show that the significant bandwidth enhancement can be achieved when the Helmholtz resonant frequency is designed close to the fundamental resonant frequency of the CMUT membrane. Compared with the conventional sealed CMUT cell, the 4-hole unsealed Helmholtz structural CMUT cell improves both the 3-dB fractional bandwidth and SPL-bandwidth product around 35 times. Furthermore, it is found that, with more holes under the same hole area ratio or with a smaller ratio of the cavity height to the viscous boundary layer thickness, the Helmholtz resonant effect becomes weaker and thus the output pressure bandwidth decreases.

Capacitive Micromachined Ultrasonic Transducer (CMUT): Analytical Evaluation of Membranes Performance Under Fabrication Related Stress

Kapasitif Mikro İşlenmiş Ultrasonik Çevirgeç (kMUÇ)’in alıcı ve verici performansı gap (kavite) yüksekliği, zar kalınlığı ve zar çapı gibi birçok parametreye bağlıdır. YHigh power transmission from CMUT (capacitive micromachined ultrasonic transducer) surface depends on output pressure and membrane displacement. Moreover, fabrication process related stress on membrane should also be considered because it affects CMUT performance in terms of collapse voltage, resonance frequency and gap distance. Therefore, stress on membrane becomes important criteria for CMUT modelling and fabrication. Surface micromachining and wafer bonding technologies are widely used for CMUT fabrications. These fabrication processes include several depositions and etching steps that those induce stress on CMUT membrane. Fabrication process related stress are classified as compressive or tensile. In this study, three common CMUT membranes, Si3Ni4, Poly-Si and SiC, were selected for analytic calculations and displacement and output pressure of these CMUT membranes were evaluated under built in stress. It was shown that stress on membrane has significant effect on membrane deflection and pressure from device surface for three membranes. As a result, stress on vibrating membrane should be minimized and optimized for reliable and high performance device fabrication when considering wide range of CMUT applications.

A new compact analytical model of nanoelectromechanical systems-based capacitive micromachined ultrasonic transducers for pulse echo imaging

A compact analytical model of a capacitive micromachined ultrasonic transducer (CMUT) exhibiting a damped oscillatory output for pulse echo imaging is proposed. The analysis is improved herein by taking into account the acoustic damping coefficient, proportional to the velocity of vibration of the CMUT membrane equation of motion. Solutions for both radial and temporal variables of the modeled equation are obtained. The result is found to be a comprehensively damped oscillation that would enable an enhanced time interval for a pulse echo imaging sensor system. Finite element method modeling of the CMUT was also performed using PZFlex, a finite element analysis-based simulation tool. The results obtained from the analytical model are in good agreement with those from PZFlex.

Finite Element Simulation and Analysis of Capacitive Micromachined Ultrasonic Transducer

Capacitive micromachined ultrasonic transducers(CMUTs), which are suitable for operation in both air and water, have been simulated and fabricated with sacrificial release method. We have proposed four models for CMUT, that are block-shape membrane model, the BOX model, the BOX model with etch holes and the BOX model with etching channels that were more closely match the actual structure. And, the effects of those models on the resonant frequency are analyzed. It can be concluded that the value of percent difference between block-shape membrane model and the BOX model is about 8.7% when the ratio of L/W is above 4. In addition the thinner the CMUT membrane thickness, the smaller the percent difference. We analyzed the size of the etching channel. A dynamic range in less of (0.125% or 0.25%) is observed when the height ratio of cavity and (channel or hole) increased. When the width ratio of cavity and (channel or hole) is analyzed, the results obtained are also very small. Based on the analysis of the size of the etched hole, the influence of the etching channel on the structure frequency can be obtained as a result of the small percent difference.

Improved Analytical Modeling of Membrane Large Deflection With Lateral Force for the Underwater CMUT Based on Von Kármán Equations

This paper is to develop analytical models for the underwater capacitive micromachined ultrasonic transducer (CMUT) to understand its large deflection effect from the water pressure. To accurately model the displacement profile of the CMUT under the water pressure, Von Karman equations and the perturbation method are employed to calculate the membrane deformation from a uniform pressure. The equations for an annular-ring plate model are first applied to calculate the displacement profile of the uniform CMUT membrane. The lateral force due to the membrane elongation is considered in the proposed model, which is used to calculate the displacement profiles for both conventional and collapse mode CMUTs under different external pressures. When compared with finite-element method results, the proposed model can predict the displacement profiles of the conventional-mode CMUT under water pressure ranging from 0.8 to 4 MPa with an error of <1%. It can also estimate CMUT membrane that operates in collapse mode with an error in the deflection profile for <4.7% from 5 to 14 MPa. In addition, it is worth to mention that the proposed model can cover the small deflection scenarios but with relatively larger error under collapse mode.

An improved analytical and finite element method model of nanoelectromechanical system based micromachined ultrasonic transducers

This paper accurately models the silicon nitride membrane displacement profile of nanoelectromechanical system (NEMS) capacitive micromachined ultrasonic transducer (CMUT). The general analytical model is proposed for the linear and non-linear region of operation with the choice of the appropriate spring constant value. Calculated results are validated with 2-D finite element method (FEM) solver PZFLEX. Full 3-D simulations are carried out to show that for a constant area the circular geometry gives maximum displacement followed by hexagonal and square membranes, respectively. Variation of the membrane displacement with its thicknesses, radii, the electrode separation and voltages are plotted. These demonstrate how a CMUT membrane's displacement can be optimized with a change in structural geometries and biases which is a necessary condition for obtaining the required sensitivity. The model evaluates the collapse voltage very close to experimental and FEM results. The dependency of the resonances on the thickness of the membrane is evaluated. Though this phenomenon is not noticed in the available literature, the FEM results support it. The FEM strain profile also reveals that at the operating biases the structure is working well under its strain limit as predicted by the analytical model.

An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method.

Capacitive micromachined ultrasonic transducer (CMUT) multilayer membrane plays an important role in the performance metrics including the transmitting efficiency and the receiving sensitivity. However, there are few studies of the multilayer membranes. Some analytical models simplify the multilayer membrane as monolayer, which results in inaccuracies. This paper presents a new analytical model for CMUTs with multilayer membranes, which can rapidly and accurately predict static deflection and response frequency of the multilayer membrane under external pressures. The derivation is based on the Ritz method and Hamilton’s principle. The mathematical relationships between the external pressure, static deflection, and response frequency are obtained. Relevant residual stress compensation method is derived. The model has been verified for three-layer and double-layer CMUT membranes by comparing its results with finite element method (FEM) simulations, experimental data, and other monolayer models that treat CMUTs as monolayer plates/membranes. For three-layer CMUT membranes, the relative errors are ranging from 0.71%–3.51% for the static deflection profiles, and 0.35%–4.96% for the response frequencies, respectively. For the double-layer CMUT membrane, the relative error with residual stress compensation is 4.14% for the central deflection, and −1.17% for the response frequencies, respectively. This proposed analytical model can serve as a reliable reference and an accurate tool for CMUT design and optimization.

Lumped Electromechanical Modeling of Capacitive Micromachined Ultrasonic Transducers

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.

Capacitive micromachined ultrasonic transducer (CMUT) array with single‐layer graphene membrane

A capacitive micromachined ultrasonic transducer (CMUT) with a graphene membrane is reported. The CMUT membranes were commonly made from very thin silicon nitride or metal material. To date, no graphene CMUT has been successfully used. In this reported work, a photomask were used for the cavity pattern to make a 1μm layer EPON SU-8 photoresist on the silicon substrate. Then a single-layer graphene were tranferred directly to be attached to the EPON SU-8 cavity layer to form the CMUT with a graphene membrane. The resonance frequency was measured to be 95 MHz in air.

Detailed investigation of capacitive micromachined ultrasonic transducer design space

In this study, we present general design guidelines for MEMS ultrasonic transducers, capacitive micromachined ultrasonic transducers (CMUTs), obtained from finite element models with a statistical design of experiment approach. The design space is illustrated using 2-D response surfaces as a function of various geometrical parameters and material selections. Important transducer figure of merits such as operation frequency, fractional bandwidth, collapse voltage and transformer ratio are investigated. Our study illustrates that while keeping geometrical parameters constant, changing the material selection to silicon carbide from silicon dioxide results in a 2.4 times increase in the transformer ratio, and more than 2.5 times increase in the operating frequency while keeping the bandwidth the same. Furthermore, our studies indicate that for a CMUT membrane with an aspect ratio of 4, using a spring constant value obtained analytically results in an error of 160% for the collapse voltage and transformer ratio values.

CMUTS with dual electrode structure for improved transmit and receive performance

In this paper, we introduce capacitive micro-machined ultrasonic transducers (CMUTs) with electrically isolated multiple electrodes embedded in the same silicon nitride CMUT membrane. Some of the advantages of this structure are demonstrated using a dual-electrode CMUT with separate transmit and receive electrodes as an example. By locating the transmit electrodes near the edges of a rectangular CMUT membrane, the stable displacement range, hence the maximum pressure amplitude during transmit mode is increased without collapsing the membrane when operated within static collapse voltage range. In the receive mode, the center receive electrode is brought closer to the substrate by biasing the side electrodes, and a higher electromechanical transformer ratio is obtained at low direct current (DC) bias. Therefore, dual-electrode CMUT has an effectively larger gap as compared to conventional CMUT during transmit, and it has an effectively smaller gap during receive. Demonstrative experiments are performed on dual-electrode CMUTs with rectangular membranes with different side and center electrode sizes for transmit and receive measurements. By using the two 4-microm wide side electrodes and an 8-microm wide center electrode on a 20-microm wide membrane, a 6.8 dB increase in maximum output pressure is obtained with side electrode excitation as compared to conventional center electrode. Similarly, the receive performance improvement was demonstrated while reducing the DC bias requirements. Simple finite-element and equivalent circuit-based models were developed to successfully model the behavior of dual-electrode CMUTs. Simulations show that, with simple modifications, more than 10 dB overall sensitivity improvement is feasible with dual-electrode CMUTs with rectangular membranes.

Capacitive micromachined ultrasonic transducers with diffraction-based integrated optical displacement detection.

Capacitive detection limits the performance of capacitive micromachined ultrasonic transducers (CMUTs) by providing poor sensitivity below megahertz frequencies and limiting acoustic power output by imposing constraints on the membrane-substrate gap height. In this paper, an integrated optical interferometric detection method for CMUTs, which provides high displacement sensitivity independent of operation frequency and device capacitance, is reported. The method also enables optoelectronics integration in a small volume and provides optoelectronic isolation between transmit and receive electronics. Implementation of the method involves fabricating CMUTs on transparent substrates and shaping the electrode under each individual CMUT membrane in the form of an optical diffraction grating. Each CMUT membrane thus forms a phase-sensitive optical diffraction grating structure that is used to measure membrane displacements down to 2 x 10(-4) A/square root(Hz) level in the dc to 2-MHz range. Test devices are fabricated on quartz substrates, and ultrasonic array imaging in air is performed using a single 4-mm square CMUT consisting of 19 x 19 array of membranes operating at 750 kHz.

Capacitive micromachined interdigital transducers

Capacitive Micromachined Ultrasonic Transducers (CMUTs) have become very popular for medical imaging and sonar applications during the last decade. They can compete with piezoelectric transducers in terms of efficiency and bandwidth. Recently, it has been noticed that these devices couple energy into silicon wafer in addition to the immersion medium. By placing the CMUTs on a substrate in an interdigitated configuration, Lamb wave or Rayleigh wave modes can be excited with very high efficiency without a need for any piezoelectric material. In this study, the acoustic power coupled into the silicon substrate as well as the acoustic impedance of the CMUT membrane are calculated by using finite element analysis. Normal mode theory is used to find the distribution of the acoustic power among different Lamb wave modes. For low frequency (1 MHz) devices, the lowest order antisymmetric (A0) mode Lamb wave is the dominant mode in the substrate. For high frequency devices (100 MHz), interdigital CMUTs excite Rayleigh wave with efficiencies comparable to piezoelectric surface acoustic wave (SAW) devices. Experimental results for Lamb wave devices in the vicinity of 1 MHz will also be presented. [Work supported by ONR.]