Circular Capacitive Micromachined Ultrasonic Transducers Research Articles

Squeeze Film Effect in Surface Micromachined Nano Ultrasonic Sensor for Different Diaphragm Displacement Profiles

In the present paper, we have analytically explored the small variations of the local pressure in the trapped air film of both sides of the clamped circular capacitive micromachined ultrasonic transducer (CMUT), which consists of a thin movable membrane of silicon nitride (Si3N4). This time-independent pressure profile has been investigated thoroughly by solving the associated linear Reynold’s equation in the framework of three analytical models, viz. membrane model, plate model, and non-local plate model. The solution involves Bessel functions of the first kind. The Landau–Lifschitz fringing technique has been assimilated to engrave the edge effects in estimation of the capacitance of CMUT, which should be considered in the micrometer or lesser dimension. To divulge the dimension-based efficacy of the considered analytical models, various statistical methods have been employed. Our use of contour plots of absolute quadratic deviation revealed a very satisfactory solution in this direction. Though the analytical expression of the pressure profile is very cumbersome in various models, the analysis of these outputs exhibits that the pressure profile follows the displacement profile in all the cases indicating no viscous damping. A finite element model (FEM) has been used to validate the systematic analyses of displacement profiles for several radii and thicknesses of the CMUT’s diaphragm. The FEM result is further corroborated by published experimental results bearing excellent outcome.

Comparative Study of Gravimetric Humidity Sensor Platforms Based on CMUT and QCM.

Humidity sensors with comprehensive performance are of great interest for industrial and environmental applications. Most sensors, however, have to compromise on at least one characteristic such as sensitivity, response speed, and linearity. This paper reports a gravimetric humidity sensor based on a capacitive micromachined ultrasonic transducer (CMUT) with exceptional all-around performance, and presents a side-by-side comparative investigation of two types of gravimetric humidity sensors for a better understanding of their characteristics and sensing mechanisms. For these purposes, a circular CMUT and a quartz crystal microbalance (QCM) with a resonance frequency of 10 MHz were designed and fabricated. Poly(vinyl alcohol) (PVA) was employed as the humidity sensing layer for its hydrophilicity and ease of film formation. The electrical properties of the sensors, including the electrical input impedances and quality factors, were characterized by a vector network analyzer. The relative humidity (RH) sensing performance of the sensors was evaluated and compared from RH levels of 11% to 97%. Both sensors exhibited good repeatability and low hysteresis. The unique microscale resonant structure of the CMUT humidity sensor contributed to a high sensitivity of 2.01 kHz/%RH, short response and recovery times of 8 s and 3 s, respectively, and excellent linearity (R2 = 0.973), which were far superior to their QCM counterparts. The underlying mechanism was revealed and discussed.

Design and analysis of CMUT device using COMSOL for Radio frequency applications

This paper presents the design and analysis of Capacitive Micro-machined Ultrasonic Transducers (CMUTs) for a resonant frequency of 1.48 MHz. The CMUT has been designed using COMSOL and the results are found to be closely matching with the analytical calculations. The circular CMUT cell consists of polysilicon and silicon dioxide as the top membrane and polysilicon as the bottom membrane with an air gap. The eigen frequency analysis and pull-in analysis of the device has been performed. The solid mechanics module and electrostatic module of COMSOL Multiphysics have been used for performing the simulations. This device can be used for radio frequency applications as it has low displacement.

Boundary Conditions Analysis of Circular Capacitive Micromachined Ultrasonic Transducer (CMUT) Devices

Background: Capacitive Micromachined Ultrasonic Transducer (CMUT) is a new type of ultrasound transducer that has gained much research interest in ultrasound imaging because of its wider bandwidth, higher receiving sensitivity, and is more likely to be integrated with an integrated circuit (IC). The analytical solution is intuitive, fast, and convergent among simulation methods. The membrane deflection is important to the CMUT performance. The deformation of a circular CMUT under an external force can be described by von Kármán equations. Objective: To find suitable boundary conditions that are crucial for the governing equations to be properly solved to get the analytical solutions for membrane deformation. Methods: Features of two commonly used CMUT fabrication methods, Sacrificial Release method (SR) and Wafer Bonding (WB) method, are introduced. The force and moment equilibrium conditions of the supporting post are analyzed to get the boundary condition equations. Results: The analytical results match well with the Finite Element Method (FEM) results for the fixed boundary condition while there are still some differences for the elastic boundary condition. Conclusion: The boundary conditions for SR fabricated devices are elastic support while the boundary conditions for WB fabricated devices are fixed.

Optimized Design of CMUT with Hexagonal Membranes

A Capacitive Micro-machined Ultrasonic Transducer (CMUT) with hexagonal membrane is constructed to work as a transmitter and compared to a CMUT with circular membrane. In this paper, three desirable combination of circular and hexagon are analyzed to select the dimensions for hexagonal shaped CMUT. Capacitive Micro-machined Ultrasonic Transducer (CMUT) is a micro constructed transducer used both as transmitter for generating ultrasonic waves and as receiver to modulate the electrical capacitance of the capacitive transducer. It can be fabricated with many geometries especially circular, square, rectangular, and hexagon. Circular CMUTs offers optimum performance in terms of deflection with DC, deflection of biased membrane with AC bias, resonant frequency, capacitance and deflection along frequency but for array formation the wafer area is wasted. A CMUT with hexagonal membrane gives an ultrasonic signal of constant amplitude with less deflection of membrane within the cavity and the outside environment. Stationary analysis is carried out with electro-mechanics for discussing the capacitance change of CMUT. The collapse or pull in voltage of hexagon CMUT is found to be high and increases the bandwidth of CMUT. The absolute percent difference of resonant frequency is observed to be 2.3 % with dimensions selected from the COH configuration of the CMUT.

A Nonlinear Lumped Equivalent Circuit Model for a Single Uncollapsed Square CMUT Cell.

An accurate nonlinear lumped equivalent circuit model is used for modeling of capacitive micromachined ultrasonic transducers (CMUTs). Finite-element analysis (FEA) is a powerful tool for the analysis of CMUT arrays with a small number of cells while with the harmonic balance (HB) analysis of the lumped equivalent circuit model, the entire behavior of a large-scale arbitrary CMUT array can be modeled in a very short time. Recently, an accurate nonlinear equivalent circuit model for uncollapsed single circular CMUT cells has been developed. However, the need for an accurate large-signal circuit model for CMUT cells with square membranes motivated us to produce a new nonlinear large-signal equivalent circuit model for uncollapsed CMUT cells. In this paper, using analytical calculations and FEA as the tuning tool, a precise large signal equivalent circuit model of square CMUT dynamics was developed and showed excellent agreement with finite-element modeling (FEM) results. Then, different CMUT single cells with square and circular membranes were fabricated using a standard sacrificial release process. Model predictions of resonance frequencies and displacements closely matched experimental vibrometer measurements. The framework presented here may prove valuable for future design and modeling of CMUT arrays with square membranes for ultrasound imaging and therapy applications.

Impact Analysis of Variation in Geometrical Features on Intrinsic Characteristics of Capacitive Micro-machined Ultrasonic Transducers

Capacitive Micro-machined Ultrasonic Transducers (CMUTs) are the ultrasonic devices which produce better features in contrast to piezoelectric transducers. The intrinsic parameter of CMUT varies with the variation in geometrical dimension of the device. The cavity height and the radius of the CMUT with circular membrane is varied in the lumped parallel plate model for its impact on the parameters. In this paper, analytical model of circular CMUTs is developed and analyzed by using the parallel-plate capacitor equations. The impact of geometrical changes has been discussed with the parametric analysis of deflection, capacitance, pull in voltage and pressure. The results discussed here will be more helpful in deciding the miniaturization limit of the CMUT prior to fabrication.

Unbiased Charged Circular CMUT Microphone: Lumped-Element Modeling and Performance

An energy-consistent lumped-element equivalent circuit model for charged circular capacitive micromachined ultrasonic transducer (CMUT) cell is derived and presented. It is analytically shown and experimentally verified that a series dc voltage source at the electrical terminals is sufficient to model the charging in CMUT. A model-based method for determining this potential from impedance measurements at low bias voltages is presented. The model is validated experimentally using an airborne CMUT, which resonates at 103 kHz. Impedance measurements, reception measurements at resonance and off-resonance, and the transient response of the CMUT are compared with the model predictions.

An Optimization and Comparative Study of Air-Coupled CMUT Cells With Circular and Annular Geometries.

Air-coupled capacitive micromachined ultrasonic transducers (CMUTs) with annular cell geometry have recently been reported to have a promising transmit sensitivity. This paper reports three optimization schemes, which further improve the transmit sensitivity and also help achieve a reasonable comparison between the novel annular and conventional circular cells. Lumped element models of both cell types with laminate plate structures are presented. Based on these models, a design optimization flowchart was constructed to facilitate analytical optimization on the three schemes. Circular and annular CMUTs with a common 97-kHz natural resonance frequency were fabricated and characterized to verify the efficacy of the optimization principle. Using the optimization flowchart, annular and circular cells with frequencies ranging from 100 to 300 kHz were analytically optimized and then compared. The comparison results demonstrate that, given the same dc bias and ac excitation voltage, the output power density at the plate surface of the optimized annular cell is double that of the optimized circular cell. Additionally, when generating the same surface power density, an optimized annular cell requires either half the dc bias or half the ac excitation voltage of an optimized circular cell. This paper provides a practical optimization framework for CMUT cell design and demonstrates the superiority of annular cells for air-coupled applications.

Investigation of Silicon Nitride as an Excellent Membrane Material for MEMS Ultrasonic Transducers

Silicon micromachining techniques developed over the last few decades’ aid in precise control over nanometer scale structures. Using these techniques to fabricate transducer elements with small electrode spacing efficient and broadband ultrasonic air transducers can be made. In this paper frequency response profile of a circular capacitive micromachined ultrasonic transducer (CMUT) element with silicon nitride as the membrane material is analytically modelled and compared with FEM simulation results. It is observed that the resonance frequency is highly dependent on the membrane material and structural properties. Silicon nitride serves as an excellent material for generation and detection of ultrasonic waves in air. The results are compared with published experimental values and appreciable agreement is obtained.

Pull-In Analysis of the Flat Circular CMUT Cell Featuring Sealed Cavity

Capacitive micromachined ultrasonic transducers (CMUTs) are one of the appealing MEMS devices. Most studies treat CMUTs as rigid plates vibrating in open air, ignoring the mechanical boundary conditions for simplification and resulting in cumulative errors in coupled fields. This paper presents a new analytical model for the pull-in characteristics of the flat circular CMUT cell featuring sealed cavity. Utilizing the plate theory coupled with Boyle’s law, the paper establishes a strong relation between the pressures inside the sealed cavity and the pull-in characteristics for the first time. Not only did we point out that the existence of the pressure inside the sealed cavity cannot be omitted, but we also quantified the direct effect of the pressure ratios on the pull-in phenomenon. The pull-in voltages increase while the pull-in ratios decrease with the pressure ratios of the pressure inside the sealed cavity to the ambient pressure. The proposed calculation process delivers a good approximation of the pull-in voltages and displacements, which are consistent with COMSOL simulation results. Particularly, the percentage error of our calculation process is 6.986% for the worst case. Therefore, our proposed analytical model accurately and efficiently predicts the pull-in characteristics and this paper offers new perspectives and reference value in designing and modeling the CMUTs.

Study on Predicting the Deformed Membranes Based on Silicon Nitride Materials with New Deflection Functions for Calculating the Capacitance of Circular Diaphragm CMUTs

A new idea is presented which develops a general model predicting the deflection profile of clamped circular diaphragm of Capacitive Micromachined Ultrasonic Transducers (CMUTs) in order to calculate its capacitance. The CMUTs we consider is made of silicon nitride material which is widely used because of its low intrinsic stress. And the general model proposed in this paper is highly accurate in predicting the deformed membranes and exhibits excellent agreement with 3D-FEA results in capacitance deviation less than 1%. These new established deflection functions can be used to implement a much higher accurate design methodology for CMUTs and other MEMS-based capacitive type sensors built with circular diaphragm.

Diamond-based capacitive micromachined ultrasonic transducers in immersion

Diamond is a superior membrane material for capacitive micromachined ultrasonic transducers (CMUTs). By using ultrananocrystalline diamond (UNCD) membrane and plasma-activated wafer bonding technology, a single diamond-based circular CMUT is demonstrated and operated in immersion for the first time. The diamond-based CMUT, biased at 100 V, is excited with a 10-cycle burst of 36 V(p-p) sine signal at 3.5 MHz. Pressure generated on a 2-D plane coincident with the normal of the CMUT is measured using a broadband hydrophone. Peak-to-peak hydrophone voltage measurements along the scan area clearly indicate the main lobe and the side lobes, as theoretically predicted by our directivity function calculations. The peak-to-peak hydrophone voltage on the axial direction of the CMUT is found to be in agreement with our theoretical calculations in the Fraunhofer region (-45 mm <y <-15 mm). The spectrum of the diamond-based CMUT is measured for a dc bias of 100 V, and ac excitation with 30-cycle bursts of 9, 36, and 54 V(p-p) sine signal. A peak response at 5.6 MHz is measured for all ac amplitudes. Overall, diamond is shown to be an applicable membrane for CMUT devices and applications.

An improved lumped element nonlinear circuit model for a circular CMUT cell

This paper describes a correction and an extension in the previously published large signal equivalent circuit model for a circular capacitive micromachined ultrasonic transducer (CMUT) cell. The force model is rederived so that the energy and power is preserved in the equivalent circuit model. The model is able to predict the entire behavior of CMUT until the membrane touches the substrate. Many intrinsic properties of the CMUT cell, such as the collapse condition, collapse voltage, the voltage-displacement interrelation and the force equilibrium before and after collapse voltage in the presence of external static force, are obtained as a direct consequence of the model. The small signal equivalent circuit for any bias condition is obtained from the large signal model. The model can be implemented in circuit simulation tools and model predictions are in excellent agreement with finite element method simulations.

Radiation impedance of collapsed capacitive micromachined ultrasonic transducers

The radiation impedance of a capacitive micromachined ultrasonic transducer (CMUT) array is a critical parameter to achieve high performance. In this paper, we present a calculation of the radiation impedance of collapsed, clamped, circular CMUTs both analytically and using finite element method (FEM) simulations. First, we model the radiation impedance of a single collapsed CMUT cell analytically by expressing its velocity profile as a linear combination of special functions for which the generated pressures are known. For an array of collapsed CMUT cells, the mutual impedance between the cells is also taken into account. The radiation impedances for arrays of 7, 19, 37, and 61 circular collapsed CMUT cells for different contact radii are calculated both analytically and by FEM simulations. The radiation resistance of an array reaches a plateau and maintains this level for a wide frequency range. The variation of radiation reactance with respect to frequency indicates an inductance-like behavior in the same frequency range. We find that the peak radiation resistance value is reached at higher kd values in the collapsed case as compared with the uncollapsed case, where k is the wavenumber and d is the center-to-center distance between two neighboring CMUT cells.

CMUT array modeling through free acoustic CMUT modes and analysis of the fluid CMUT interface through Fourier transform methods

A method for analyzing capacitive micromachined ultrasonic transducer (CMUT) arrays and arrays of elements composed of several CMUTs is proposed. It is based on a combination of a free acoustic mode description of an isolated CMUT, and the coupling of these modes to the fluid in which waves should be excited or detected through an impedance matrix that will depend on frequency. The parameters of the model describing the isolated CMUT is independent of frequency and excitation of neighbor CMUTs, whereas the acoustic impedance matrix describing the coupling to the fluid will depend on both the excitation of neighbor CMUTs and frequency. Hence, this splitting of the calculations has a potential for saving computer time. The analysis gives transfer functions from excitations that vary harmonically with time and space along the array surface to CMUT parameters as current, mode excitations, or output acoustic pressure. Based on this, the response of essentially arbitrary excitations of the CMUTs may be obtained. The method is used to analyze an infinitely large array of circular CMUTs on a rectangular grid. The CMUTs are assumed to be operating in collapsed mode. Sharp resonances are shown to occur that could be significantly damped by adding series resistors to the CMUTs or increasing the water viscosity.