Collapse Voltage Research Articles

Capacitive micromachined ultrasonic transducer design for high power transmission

Capacitive micromachined ultrasonic transducers (cMUTs) were developed to meet the demands of the ultrasonic industry. To achieve maximum efficiency, the conventional operation of the cMUT requires a bias voltage close to the collapse voltage. Total acoustic output pressure is limited by the efficiency of the cMUT and the maximum-allowed pulse voltage on the membrane. In this paper, we propose the collapse-snapback operation of the cMUT: the membrane is collapsed onto the substrate in the collapsing cycle, and released in the snapback cycle. The collapse-snapback operation overcomes the above-mentioned limitations of the conventional operation. The collapse-snapback operation utilizes a larger range of membrane deflection profiles (both collapsed and released profiles) and generates higher acoustic output pressures. The static finite element calculations were performed to design cMUTs with specific collapse and snapback voltages by changing the electrode parameters (radius (re), position (de), and thickness (te)). These designs were refined for optimum average displacement per cycle. An electrode radius greater than 60% of the membrane radius significantly improved the displacement per volt. Moderately thick membranes (te approximately 0.2 microm) were preferred, as thicker membranes reduced the displacement per volt. Under proper bias conditions, the collapse-snapback operation, designed for high-power transmission, allowed the application of pulse voltages larger than the difference of collapse and snapback voltages. Dynamic finite element calculations of an infinite cMUT array on the substrate loaded with acoustic fluid medium were performed to determine the dynamic response of the cMUT. Commercially available FEM packages ANSYS and LS-DYNA were used for static and dynamic calculations, respectively. The cMUTs were fabricated for optimal performance in the collapse-snapback operation. The transmit experiments were performed on a 2-D cMUT array using a calibrated hydrophone. Taking into account the attenuation and diffraction losses, the pressure on the cMUT surface was extracted. The cMUT generated 0.47 MPa (6 kPa/V) and 1.04 MPa (11 kPa/V) in the conventional and collapse-snapback operations, respectively. Therefore, collapse-snapback operation of the cMUTs was superior for high-power transmission.

Low temperature fabrication of immersion capacitive micromachined ultrasonic transducers on silicon and dielectric substrates

A maximum processing temperature of 250/spl deg/C is used to fabricate capacitive micromachined ultrasonic transducers (CMUTs) on silicon and quartz substrates for immersion applications. Fabrication on silicon provides a means for electronics integration via post-complementary metal oxide semiconductor (CMOS) processing without sacrificing device performance. Fabrication on quartz reduces parasitic capacitance and allows the use of optical displacement detection methods for CMUTs. The simple, low-temperature process uses metals both as the sacrificial layer for improved dimensional control, and as the bottom electrode for good electrical conductivity and optical reflectivity. This, combined with local sealing of the vacuum cavity by plasma-enhanced chemical-vapor deposition of silicon nitride, provides excellent control of lateral and vertical dimensions of the CMUTs for optimal device performance. In this paper, the fabrication process is described in detail, including process recipes and material characterization results. The CMUTs fabricated for intravascular ultrasound (IVUS) imaging in the 10-20 MHz range and interdigital CMUTs for microfluidic applications in the 5-20 MHz range are presented as device examples. Intra-array and wafer-to-wafer process uniformity is evaluated via electrical impedance measurements on 64-element ring annular IVUS imaging arrays fabricated on silicon and quartz wafers. The resonance frequency in air and collapse voltage variations are measured to be within 1% and 5%, respectively, for both cases. Acoustic pressure and pulse echo measurements also have been performed on 128 /spl mu/m/spl times/32 /spl mu/m IVUS array elements in water, which reveal a performance suitable for forward-looking IVUS imaging at about 16 MHz.

A comparison of micro-switch analytic, finite element, and experimental results

Electrostatically actuated, metal contact, micro-switches depend on having adequate contact force to achieve desired, low contact resistance. In this study, higher contact forces resulted from overdriving cantilever beam style switches, after pull-in or initial contact, until the beam collapsed onto the drive or actuation electrode. The difference between initial contact and beam collapse was defined as the useful contact force range. Micro-switch pull-in voltage, collapse voltage, and contact force predictions, modeled analytically and with the CoventorWare finite element software package, were compared to experimental results. Contact resistance was modeled analytically using Maxwellian spreading resistance theory. Contact resistance and contact force were further investigated by varying the width of the drive electrode. A minimum contact resistance of 0.26 Ω was measured on micro-switches with 150 μm-wide drive electrodes. The useful contact force range for these devices was between 22.7 and 58.3 V. Contributions of this work include: a contact force equation useful for initial micro-switch designs, a detailed pull-in voltage, collapse voltage, and contact force investigation using CoventorWare, a direct comparison of measured results with analytic and finite element predictions, and a means of choosing a micro-switch operating point for optimized contact resistance performance.

The effects of membrane metallization in capacitive microfabricated ultrasonic transducers.

The mechanical effects of the metal layer on the membranes of capacitive micromachined ultrasonic transducers (CMUTs) are analyzed in this paper by means of finite element simulations. The influence of electrode size and thickness on the electrostatic behavior of the single CMUT cell, including diaphragm displacement, cell capacitance, and collapse voltage, is explored. The effect on device sensitivity is investigated through the transformation factor of the cell, that is computed by FEM and compared with the parallel plate model prediction. It is found that for a non-negligible electrode thickness, as in the majority of fabricated devices, both the static and dynamic performance of the cell can be affected in a significant way. Thus, the effects of membrane metallization must be taken into account in CMUT design and optimization.

Analytical solution of a plate bending problem using symbolic algebra

AbstractThe estimation of critical voltage in a capacitive micro‐switch leads to a thin plate bending problem. This paper deals with the correct mathematical formulation taking into account deflection‐dependent electrostatic force. The relative simple geometry allows the reduction of the structure to a beam problem. With the use of Ritz‐method and the variational symbolic program Mathematica analytical closed form solutions have been obtained. Polynomial and trigonometric trial functions have been used to determine the deflection of the plate. It has been proved, that the critical collapse voltage is much overestimated, if constant electrostatic forces are assumed.

Optimization of the fabrication of sealed capacitive transducers using surface micromachining

Processing issues for the fabrication of capacitive micromachined ultrasonic transducer (cMUT) arrays have been studied using surface micromachining. This work focuses on the critical steps of process fabrication such as membrane formation, sacrificial layer properties and vacuum sealing performance of cavity. We describe a four-mask process for the realization of sealed cMUT. We demonstrate that the use of a sacrificial layer with a columnar structure gives a fast etching rate (29 nm s−1) in a buffered hydrofluoric acid solution. The mechanical stress of LPCVD silicon nitride (SiNx), used as membrane, was evaluated. We compared the vacuum sealing performance of different materials in order to find the best material in terms of lateral deposition inside the cavity. Functional transducers have been obtained. We proposed an electrical test in order to evaluate the vacuum sealing of the cavity based on the collapse voltage determination. Laser interference measurements were used to characterize the dynamic displacement of the membrane.

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.

Mechanical characterization of micromachined capacitive switches: design consideration and experimental verification

The mechanical modeling and experimental study of radio frequency (RF) micromachined capacitive switches is presented in this paper. The micromachined capacitive switch, fabricated using bulk and surface micromachining techniques, consists of a thin metal membrane suspended over a center conductor, and fixed at both ends to the ground conductors of a coplanar waveguide (CPW) line. A static mechanical model considering complicated geometry and the residual stress effect of the bridge is established to demonstrate the pull-in instability phenomenon of the micromachined capacitive switch, and to predict the effective stiffness constant and critical collapse voltage of the bridge for several typical bridge geometries. An optoelectronic laser interferometric system, based on a modified Michelson interferometer incorporated with optoelectronic devices is developed to evaluate the membrane deformation characteristics of the micromachined capacitive switch with different applied dc bias voltages. It is illustrated that the analytical solution is well agreed with the numerical simulation and experiment.

Fabricating capacitive micromachined ultrasonic transducers with wafer-bonding technology

Introduces a new method for fabricating capacitive micromachined ultrasonic transducers (CMUTs) that uses a wafer bonding technique. The transducer membrane and cavity are defined on an SOI (silicon-on-insulator) wafer and on a prime wafer, respectively. Then, using silicon direct bonding in a vacuum environment, the two wafers are bonded together to form a transducer. This new technique, capable of fabricating large CMUTs, offers advantages over the traditionally micromachined CMUTs. First, forming a vacuum-sealed cavity is relatively easy since the wafer bonding is performed in a vacuum chamber. Second, this process enables better control over the gap height, making it possible to fabricate very small gaps (less than 0.1 /spl mu/m). Third, since the membrane is made of single crystal silicon, it is possible to predict and control the mechanical properties of the membrane to within 5%. Finally, the number of process steps involved in making a CMUT has been reduced from 22 to 15, shortening the device turn-around time. All of these advantages provide repeatable fabrication of CMUTs featuring predictable center frequency, bandwidth, and collapse voltage.

Mechanical design and optimization of capacitive micromachined switch

Design and optimization of a shunt capacitive micromachined switch is presented. The micromachined switch consists of a thin metal membrane called the “bridge” suspended over a center conductor, and fixed at both ends to the ground conductors of a coplanar waveguide (CPW) line. A static electromechanical model considering the residual stress effects is developed to predict the effective stiffness constant and the critical collapse voltage of the bridge for several typical bridge geometries. The deformation of the bridge and its contact behavior with the dielectric layer are analyzed using the finite element method (FEM) in order to explore a good contact field with different bridge geometries. Furthermore, a nonlinear dynamic model that captures the effects of electrostatic forces, elastic deformation, residual stress, inertia, and squeeze film damping is developed, and is used for predicting the switching speed (including the switching-down and the switching-up time) and the Q-factor. The effects of variation of important parameters on the mechanical performance have been studied in detail, and the results are expected to be useful in the design of optimum shunt capacitive micromachined switch. The results may also be useful in the design of actuators with membranes or bridges.

Finite-element method for determination of electromechanical coupling coefficient for piezoelectric and capacitive micromachined ultrasonic transducers

Research has been reported on ultrasonic transduction using capacitive micromachined ultrasonic transducers (cMUTs). These are thin membranes of diameters of order 100 μm suspended over a silicon substrate with a gap of order 1 μm. The devices become transducers when a bias voltage is applied, causing electrostatic forces to draw the membranes closer to the substrate. Operation is by applying an electrical signal to excite a vibration in the membrane, or an ultrasonic wave to excite an ac voltage. The cMUT literature includes equivalent circuits and studies on losses and spurious waves, and discussion of output, sensitivity, and bandwidth. Transducer engineers would like to see analogies to the properties of piezoelectric transducers, in order to compare the cMUTs to traditional designs. An extension of the definition of the piezoelectric coupling coefficient to an effective coupling coefficient for cMUT transducers is presented. A finite-element method has been developed using the pzflex software package to determine its value, and used for evaluating cMUT designs. Accepted values are obtained for a piezoelectric material, and it is shown that an ideal cMUT has a coupling coefficient approaching 1 at the membrane collapse voltage, while practical devices are often limited to lower values.

Mechanical characterization of thick polysilicon films: Young's modulus and fracture strength evaluated with microstructures

Young's modulus and the fracture strength of thick polysilicon films were evaluated with surface micromachined test structures. The polysilicon films were deposited in an epitaxial reactor and were about 10.5 µm thick. Four different processing schemes of doping and annealing were used and thus four different sets of test structures were micromachined. A micromanipulator system developed at Uppsala University was used to make tensile tests. The micromanipulator is adapted to a scanning electron microscopy environment and all tests were done in situ so that the testing procedure could be monitored at high magnification. From the tensile tests Young's modulus as well as the mean fracture strength and Weibull modulus of each of the films were evaluated. Young's modulus was also evaluated from the collapse voltage of test structures consisting of an electrostatically movable plate suspended by springs. Film texture measurements by x-ray diffraction and cross sectional transmission electron microscopy revealed that the silicon grains had preferential orientations. A mean value of Young's modulus of the film was calculated based on the Young's modulus values of the preferred orientations. It was found that Young's modulus of polysilicon evaluated by the three methods presented agree with each other as well as with other reliable data.

Fuzzy reasoning for knowledge-based assessment of dynamic voltage security

An easy-to-use knowledge-based fuzzy approach is proposed to evaluate the dynamic voltage security including both voltage collapse and unacceptable voltage profiles following disturbances. The dynamic voltage-stability behaviour of the power system, however complex and nonlinear in nature, is simply mapped into a fuzzy severity index by means of approximate fuzzy reasoning and a series of fuzzy calculus. In addition to providing a mere two-region demarcation, the fuzzy severity index can also generally give a relative severity indication to discriminate between various post-disturbance system states. A systematic methodology for initial fuzzy-parameter setting and fuzzy-variable selection is also presented and discussed.

Improvement of the performance of microphones with a silicon nitride diaphragm and backplate

The performance of a single-wafer fabricated silicon condenser microphone has been improved by increasing the stress and the acoustic hole density of the backplate and by decreasing the diaphragm thickness. The best microphones show a sensitivity of 5.0 mV Pa −1, which corresponds to an open-circuit sensitivity of 10 mV Pa −1 for a microphone capacitance of 6.6 pF. The measured frequency response is flat within ±2 dB from 100 Hz to 14 kHz, which is better than the requirements for a hearing-aid microphone. The operating voltage of these microphones is only 5.0 V, which is about 60% of the collapse voltage. The measured noise level of the microphones is 30 dBA SPL, which is approximately as low as required for a hearing-aid microphone ( <29.5 dBA SPL).

Domain collapse in amorphous magnetostrictive wires

In magnetostrictive amorphous wires of composition (Fe/sub 77.5/Si/sub 7.5/B/sub 15/) the process of domain collapse is an important ingredient of reentrant reversal. During collapse, a narrow and high voltage pulse is generated due to the formation of an unstable domain. Experimental results showing the influence of an external magnetic field and an applied longitudinal tensile stress on the voltage pulse shape agree well with those calculated on the basis of an ellipsoidal domain model for the collapsing domain. An experiment similar to the Sixtus-Tonks experiment on a long wire was used to model a short wire in a way that is more reproducible and controllable than the self-nucleation of a free wire. The shape of this pulse has been found to change with increase of applied magnetic field or tension. >

Characterization of InGaAs/AlGaAs pseudomorphic modulation-doped field-effect transistors

High-performance pseudomorphic In <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-y</inf> As/Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.15</inf> - Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.85</inf> As ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.05 \le y \le 0.2</tex> ) MODFET's grown by MBE have been characterized at dc (300 and 77 K) and RF frequencies. Transconductances as high as 310 and 380 mS/mm and drain currents as high as 290 and 310 mA/mm were obtained at 300 and 77 K, respectively, for 1-µm gate lengths and 3-µm source-drain spacing devices. Lack of persistent trapping effects, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I-V</tex> collapse, and threshold voltage shifts observed with these devices are attributed to the use of low mole fraction Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> As while still maintaining 2DEG concentrations of about 1.3 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . Detailed microwave S-parameter measurements indicate a current gain cut-off frequency Of 24.5 GHz When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y = 0.20</tex> , which is as much as 100 percent better than similar GaAs/AlGaAs MODFET structures, and a maximum frequency of oscillation of 40 GHz. These superior results are in part due to the higher electron velocity of InGaAs as compared with GaAs. Velocity field measurement performed up to 3 kV/cm using the magnetoresistance method indicates an electron saturation velocity of greater than 1.7 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> cm/s at 77 K for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y = 0.15</tex> , which is 20 percent higher than GaAs/AlGaAs MODFET's of similar structure.