Analytical calculation of collapse voltage of CMUT membrane

Because the collapse voltage determines the operating point of the capacitive micromachined ultrasonic transducer (CMUT), it is crucial to calculate and control this parameter. One approach uses parallel plate approximation, where a parallel plate motion models the average membrane displacement. This usually yields calculated collapse voltage 25 percent higher than the actual collapse voltage. More accurate calculation involves finite element method (FEM) analysis. However, depending on the required accuracy, the computation time may require many hours

Influence of the electrode size and location on the performance of a CMUT

The collapse voltage of micromachined capacitive ultrasonic transducers (CMUT) depends on the size, thickness, type, and position of the metal electrode within the membrane. This paper reports the result of a finite element study of this effect. The program (ANSYS 5.7) is used to model a circular membrane on top of a Si substrate covered by a Si3N4 insulation layer. We find that the collapse voltage increases in proportion to the metal thickness for constant membrane thickness. The collapse voltage of a membrane with a thin metal electrode decreases as the metal plate moves closer to the bottom of the membrane; whereas, for electrodes with larger metal thickness, the collapse voltage has a peak intermediate value. Decreasing the outer radius of the metal plate results in an asymptotic increase of the collapse voltage. For a finite metal thickness, an initial decrease in the collapse voltage is seen as the outer radius decreases. The collapse voltages of half-metallized and full-metallized structures are almost equal for typical metal plate thickness. The asymptotic increase of the collapse voltage is seen for ring shaped metal plates as the inner radius is varied from the center to the outer radius. In summary, we find that the influence of the metal electrode on the collapse voltage is a very important parameter in determining optimum performance of a CMUT

Finite element modeling of capacitive micromachined ultrasonic transducers

Transducers based on piezoelectric crystals dominate the biomedical ultrasonic imaging field. However, fabrication difficulties for piezoelectric transducers limit their usage for complex imaging modalities such as 2D imaging, high frequency imaging, and forward looking intravascular imaging. Capacitive micromachined ultrasonic transducers (CMUTs) have been proposed to overcome these limitations and they offer competitive advantages in terms of bandwidth and dynamic range. Further, the ease of fabrication enables manufacturing of complex array geometries. A CMUT transducer is composed of many electrostatically actuated membranes. Earlier analysis of these devices concentrated on an equivalent circuit approach, which assumed the motion of the membrane was approximated by a parallel plate capacitor. Finite element analysis is required for more accurate results. In this paper, we present the finite element model developed to evaluate the performance of the CMUTs. The model is composed of a membrane radiating into immersion medium. Electrostatic actuation is added on using electromechanical elements. Symmetry boundary conditions are imposed around the sidewalls of the finite element mesh, so that the model reflects the properties of a cell driven with the same phase as its neighboring membranes in an infinitely large array. Absorbing boundaries are implemented one wavelength away from the membrane to avoid reflections from the end of the finite element mesh. Using the model, we optimized the membrane radius, membrane thickness and gap height. Our optimized designed yielded a center frequency of 13 MHz with hundred percent bandwidth. A maximum output pressure of 20 kPascal per volt was obtained

A new regime for operating capacitive micromachined ultrasonic transducers

We report on a new operation regime for capacitive micromachined ultrasonic transducers (cMUTs). Traditionally, cMUTs are operated at a bias voltage lower than the collapse voltage of their membranes. In the new proposed operation regime, first the cMUT is biased past the collapse voltage. Second, the bias voltage applied to the collapsed membrane is reduced without releasing the membrane. Third, the cMUT is excited with an ac signal at the bias point, keeping the total applied voltage between the collapse and snapback voltages. In this operation regime, the center of the membrane is always in contact with the substrate. Our finite element methods (FEM) calculations reveal that a cMUT operating in this new regime, between collapse and snapback voltages, possesses a coupling efficiency (k(T)(2)) higher than a cMUT operating in the conventional regime below its collapse voltage. This paper compares the simulation results of the coupling efficiencies of cMUTs operating in conventional and new operation regimes

Dynamic analysis of CMUTs in different regimes of operation

This paper reports on dynamic analysis of an immersed single capacitive micromachined ultrasonic transducer (CMUT) cell transmitting. A water loaded 24 mum circular silicon membrane of a transducer was modeled. The calculated collapse and snapback voltages were 80 V and 50 V, respectively. The resonance frequency, output pressure and nonlinearity of the CMUT in three regimes of operation were determined. These regimes were: a) the conventional regime in which the membrane does not make contact with the substrate, b) the collapsed regime in which the center of the membrane is in constant contact with the substrate, and c) the collapse-snapback regime in which the membrane intermittently makes contact with the substrate and releases. The average membrane displacement was compared as the CMUT was operated in these regimes. A displacement of 70 A in the collapsed regime and 39 Angstrom in conventional regime operation were predicted when a 5 V pulse was applied to the CMUT cell biased at 70 V. The CMUT showed a 2(nd) harmonic at -16 dB and -26 dB in conventional and collapsed regimes of operation, respectively. Collapse-snapback operation provided increased output pressure at the expense of a 3(rd) harmonic at -10 dB. Our simulations predicted that the average output pressure at the membrane could be 90 kPa/V with collapse-snapback operation compared to 4 kPaN with conventional operation

Calculation and measurement of electromechanical coupling coefficient of capacitive micromachined ultrasonic transducers

The electromechanical coupling coefficient is an important figure of merit of ultrasonic transducers. The transducer bandwidth is determined by the electromechanical coupling efficiency. The coupling coefficient is, by definition, the ratio of delivered mechanical energy to the stored total energy in the transducer. In this paper, we present the calculation and measurement of coupling coefficient for capacitive micromachined ultrasonic transducers (CMUTs). The finite element method (FEM) is used for our calculations, and the FEM results are compared with the analytical results obtained with parallel plate approximation. The effect of series and parallel capacitances in the CMUT also is investigated. The FEM calculations of the CMUT indicate that the electromechanical coupling coefficient is independent of any series capacitance that may exist in the structure. The series capacitance, however, alters the collapse voltage of the membrane. The parallel parasitic capacitance that may exist in a CMUT or is external to the transducer reduces the coupling coefficient at a given bias voltage. At the collapse, regardless of the parasitics, the coupling coefficient reaches unity. Our experimental measurements confirm a coupling coefficient of 0.85 before collapse, and measurements are in agreement with theory

Residual stress and Young's modulus measurement of capacitive micromachined ultrasonic transducer membranes

Membranes supported by posts are used as vibrating elements of capacitive micromachined ultrasonic transducers (CMUTs). The residual stress built up during the fabrication process determines the transducer properties such as resonance frequency, collapse voltage, and gap distance. Hence, it is important to evaluate and control the stress in thin film CMUT membranes. The residual stress in the membrane causes significant vertical displacements at the center of the membrane. The stress bends the membrane posts, and the slope at the membrane edges result in amplified displacement at the center by the radius of the membrane. By measuring the center displacement, it is possible to determine the stress provided that Young's modulus of the thin film is known accurately. Usually, in thin film structures Young's modulus differs from that of bulk materials and it depends on thin film deposition technique. In this paper, we propose a novel technique for the measurement of stress and Young's modulus of CMUT membranes. The technique depends on the measurement of membrane deflection and resonance frequency. We modeled the stress and Young's modulus dependence of membrane deflection and resonance frequency using finite element analysis. We used the atomic force microscope (AFM) to measure the membrane deflection and the laser interferometer to determine the resonance frequency of the membrane. The technique is tested on a CMUT membrane. We found that our LPCVD deposition technique yields residual stress of around 100 MPa and Young's modulus of around 300 GPa

Dynamic FEM analysis of multiple cMUT cells in immersion

This paper reports on the accurate modeling of immersion capacitive micromachined ultrasonic transducers (cMUTs) using the time-domain, nonlinear finite element package, LS-DYNA, developed by Livermore Software Technology Corporation (LSTC). A capacitive micromachined ultrasonic transducer consists of many cMUT cells. In this paper, a square membrane was used as the unit cell to cover the transducer area by periodic replication on the surface. The silicon membrane, silicon oxide post and insulation layer were modeled, and the contact region was defined on the membrane and the substrate surfaces. The 3-D finite element model also included a 500 mu m-thick substrate and the acoustic fluid medium, to take into account two main sources of coupling in cMUTs: Scholte wave propagating at the solid-fluid interface and Lamb wave propagating in the substrate. A highly efficient perfectly matched layer (PAIL) absorbing boundary condition was designed for the acoustic medium to truncate the computational domain. The cMUT was biased in-collapse or out-of-collapse with an applied potential difference between the membrane and substrate electrodes: a rectangular pulse excitation was then used for the conventional, collapsed or collapse-snapback operations of the cMUT. Collapsed operation of the cMUT generated six times greater acoustic output pressure (641 kPa) than the conventional operation (107 kPa) at both the same bias voltage (83 V) and the pulse amplitude (+5 V). The vacuum backing and impedance-matched backing were compared to determine the influence of wave reflections from the bottom of the substrate in the collapsed operation. The dynamic FEN,I results were compared to the experimental results for conventional and collapse-snapback operations by applying step voltages on biased cMUT membranes. The acoustic output pressure measurements of the cMUT were performed with a hydrophone. The hydrophone calibration data was used to find the sensed pressure. Taking the attenuation and diffraction losses into account, the pressure on the cMUT surface was extracted. The cMUT generated 348 kPa and 1040 kPa in the conventional and collapse-snapback operations, respectively, and good agreement was observed with the dynamic FEM results

CMUT ring arays for forward-looking intravascular imaging

This paper describes an annular CMUT ring array designed and fabricated for the tip of a catheter used for forward-looking intravascular imaging. A 64-element, 2-mm average diameter array is fabricated as an experimental prototype. A single element in the array is connected to a single-channel custom front-end integrated circuit for pulse-echo operation. In conventional operation the transducer operated at around 10 MHz. In the collapsed regime, the operating frequency shifted to 25 MHz and the received echo amplitude tripled. The SNR is measured as 23 dB in a 50-MHz measurement band width for an echo signal from a plane reflector at 1.5 mm. We also performed a nonlinear dynamic transient finite element analysis for the described transducer, and found these results are in good agreement with the experimental measurements, both for conventional and collapsed operation