David Elata

• D.Sc.
• Professor at Technion – Israel Institute of Technology

When a piezoelectric material is subjected to a quasi-static electric (or mechanical) load, part of the input energy is converted to the mechanical (or electric) domain. The piezoelectric coupling factor k² is defined as the ratio between the converted energy and the supplied energy. This factor is often considered as a measure of the transduction...

Vibrational wineglass modes in disk and rings that are made from (100) silicon are considered. It is shown that all odd-ordered wineglass modes are necessarily frequency-matched, each with its orthogonal conjugate. In contrast, all even-ordered wineglass modes are likely not to be frequency-matched with their orthogonal conjugate. Some specific cas...

We present a novel piezoelectric bulk-unimorph beam actuator that can be directly driven in twisting. The bulk-unimorph beam is driven by interdigitated electrodes (IDEs), deposited over its top and bottom surfaces. These IDEs are oriented at 45° relative to the beam axis, and they are used for both poling and actuation. When subjected to a driving...

In recent years, increasing attention is given to parametric resonators, in which an unbounded response may be induced by periodically modulating one of the system parameters. Parametric resonators with a single degree of freedom have many windows of unbounded response in which the response frequency is different from the modulation frequency. This...

We present a new method for achieving a parallel out-of-plane (piston) motion, by using torsion actuation of a bulk, unimorph, piezoelectric actuator. Three piezoelectric spiral arms support a central stage, the arms are both poled and driven by interdigitated electrodes (IDEs) deposited directly on the top side of the structure. We show that when...

We present a bulk unimorph piezoelectric beam, which is directly actuated in a torsional mode. The direct torsion actuation is achieved by Interdigitated Electrodes (IDE), oriented at 45° relative to the beams axis. The IDE are deposited directly on a bulk piezoelectric plate, which serves as both the substrate and as the device layer. Elimination...

We present a thermoelastic micromotor for driving a rigid plate in an out-of-plane motion. The plate is suspended on spiral thermoelastic bimorph arms, made of a nitride layer coated by gold. Heating of the thermoelastic arms is achieved by driving electric current, either through polysilicon resistors that are embedded in the nitride layer, or thr...

We present a new intuitive and rational model of parametric resonance. In parametric resonators one of the system parameters, usually stiffness, is modulated in time. Due to this time modulation the system may develop a periodic response. It is well known that when this modulation is sufficiently strong and at an appropriate frequency, the periodic...

We present a two axis actuator which can be controlled both in-plane, and out-of-plane. Previously we demonstrated a conversion mechanism in which in-plane motion was translated to out-of-plane motion. That mechanism harnesses comb-drive actuation and converts the in-plane motion of the comb-drive shuttle to a parallel out-of-plane motion of a rigi...

We present a microelectromechanical systems realization of a classic parametric resonator. This parametric resonator is ideal in the sense that the electrostatic stiffness, which may be time modulated, is not affected by motion. We also present a simple, efficient, and intuitive model of parametric excitation. This model predicts the minimal modula...

We present a mechanism that converts in-plane to out-of-plane motions, which is fully compatible with mass-fabrication processes. By using selective stiffening, we induce coupling between in-plane and out-of-plane responses of the mechanism. The conversion ratio is constant (i.e., linear response), and it can be easily tailored by the number of sti...

The standard folded-beam suspension is often used in electrostatic comb-drive resonators with the intention of achieving a system with a linear response. However, we show that the harmonic response of the standard folded-beam suspension is not linear at the fundamental resonance frequency of the system. Specifically, we show that at the fundamental...

We present an electrostatic transducer in which voltage remains constant while charge is stored or extracted from the device. We achieve this by designing a nonlinear mechanical spring, which exactly counteracts the nonlinearity associated with electrostatic attraction forces. In essence, the new device responds like a rechargeable battery, only th...

The electromagnetic interaction forces between two noncoaxial circular coils have been previously analyzed. In the present study we revisit that solution and rederive these forces in a new functional form which provides new insight. Specifically, we revisit the notion of a neutral plane, at a critical vertical separation, in which alignment forces...

We present for the first time ever, a method for reversing the response of thermoelastic bimorph actuators, without changing the order of their layers. Our device is constructed from a flat stage that is suspended on three thermoelastic bimorph spiral arms. We demonstrate that the thermoelastic response of the spiral bimorphs can be affected by usi...

We present a new simple constitutive model for dielectric charging. The model is motivated by the functional form of the Frenkel-Poole conduction, but it enables to track the time evolution of charge distribution within the dielectric. The prediction of charge distribution is used to deduce the voltage buildup in the dielectric. Based on this model...

We show that nonlinear elastic springs can be used to counteract the nonlinearity of electrostatic forces in gap-closing electrostatic actuators. We demonstrate this in two types of devices. In the first, we use a nonlinear spring to extend the stable range of the parallel-plates actuator, and to ensure that the response in this extended range is l...

We demonstrate frequency tuning of the first instability window of a MEMS Meissner parametric resonator. Our parametric resonator includes a transducer which provides a negative electrostatic stiffness that is not affected by motion. We therefore refer to this transducer as a linear anti-spring. We achieve parametric excitation by time-modulation o...

We present a mechanism that converts in-plane to out-of-plane motion, which is fully compatible with standard mass-fabrication methods. The mechanism harnesses the well-established in-plane actuation achieved by comb-drives, and converts it to out-of-plane motion. The motion conversion ratio is constant (i.e. linear conversion), and it can be easil...

We present a complete methodology for designing a new folded-beam suspension which responds as a linear spring at the fundamental resonance. This is in sharp contrast to the response of standard folded-beam suspensions. The static response of the standard folded-beam suspension is linear over a wide range of motions. But, surprisingly, the dynamic...

We present a self-excited MEMS Franklin oscillator, which responds in steady state vibrations when subjected to a sufficient dc voltage. The system is constructed from an electrostatically-floating rotor, which sequentially transfers charge between a source and drain electrodes. We present a comprehensive analysis of the electromechanical response...

We present a novel motion conversion mechanism which is fully compatible with standard mass-fabrication micromachining. The new mechanism is designed to linearly convert in-plane motion induced by electrostatic comb-drive actuators, to out-of- plane motion. The conversion mechanism is constructed from pairs of beams with two different heights. Moti...

Folded-beam suspensions are designed to respond as linear springs. In this work we show that even if their design and construction is perfect, their response is linear only for static applications. We show that the dynamic response of perfect folded- beam suspensions is inherently nonlinear. Surprisingly, the nonlinearity becomes dominant when the...

We present an ideal MEMS parametric resonator. The resonator is ideal in the sense that it is driven by modulation of a linear stiffness. The resonator is based on an electrostatic anti-spring which only effects stiffness, and in contrast to previous transducers, does not induce any other linear or nonlinear force. The significance of this work is...

We present for the first time ever, a perfect electrostatic anti-spring. This electrostatic actuator is a symmetric double-sided comb-drive with uniform-width fingers and a linear tapering of the lengths of the rotor fingers. When both stators are grounded and a constant dc bias is applied to the rotor, this actuator induces a diverging electrostat...

We present analytic expressions for three common measures of the dynamic response in gap-closing electrostatic resonators. We show that peak gain, peak sharpness and logarithmic decrement are distinctively different and are not equal to the quality-factor of the unloaded system. We experimentally validate our theoretical predictions by characterizi...

We present a gap-closing electrostatic actuator with a linear extended range. We achieve this by designing a nonlinear spring which exactly counteracts the nonlinear effects of electrostatic attraction forces in gap-closing actuators. We demonstrate this on parallel-plates actuators with a nominal gap of g=21μm. The initial response up to a deflect...

Gap-closing electrostatic actuators are inherently nonlinear and their dynamic range is often limited by the pull-in instability. To overcome this, we propose a nonlinear spring that counteracts the nonlinear effects of electrostatic attraction. The nonlinear spring is designed to extend the stable range of the actuator and to enforce a linear elec...

The electromechanical response of a symmetric electret parallel-plates actuator is analyzed. The actuator is constructed from a dielectric plate that is suspended by a linear spring between two electrodes of a planar capacitor. The dielectric plate is loaded with fixed charge, and is displaced due to the interaction between this charge and the elec...

This paper considers the electromechanical response of electrostatic actuators that are driven by both voltage and charge. The model system is an electrostatic actuator in which the suspended electrode is subjected to a driving voltage and the fixed electrode, which is electrostatically floating, is loaded by charge. The response of the system is a...

The electrostatic field in a dielectric layer, which is in contact with a conducting electrode, is considered. It is shown that the geometrical nature of contact causes a considerable local amplification of the electrostatic field. This provides insight, and explains why dielectric charging occurs even when the nominal electrostatic fields seems to...

Three measures of the dynamic response of micro-resonators are considered: gain, sharpness of peak, and quality-factor which is measured by logarithmic decrement. Analytic expressions for the three measures are derived and it is shown that they are not necessarily equivalent. The conditions for the equivalence of these three measures are discussed....

This paper reports the parallel internal electrostatic transduction of a laterally driven Lamé-mode polysilicon resonator. The transducer is fabricated using a manufacturable double nanogap process, where the 50 nm silicon nitride dielectric layers are formed on sidewalls of an optically defined trench by a conformal deposition, which is followed b...

An up-to-date guide to the theory and applications of RF MEMS. With detailed information about RF MEMS technology as well as its reliability and applications, this is a comprehensive resource for professionals, researchers, and students alike. • Reviews RF MEMS technologies • Illustrates new techniques that solve long-standing problems associated w...

This paper investigates the effects of dielectric charge on resonant frequency in thermally oxidized silicon resonators hermetically encapsulated using ??epi-seal.?? SiO₂ coatings are effective for passive temperature compensation of resonators but make the devices more susceptible to charging-related issues. We present a theoretical mod...

This paper reports the use of internal electrostatic transduction to excite and detect the fifth bulk lateral mode of a 54 mum outer-diameter, 12 mum-wide, and 2.5 mum-thick poly-silicon ring resonator at 1.95 GHz, with a quality factor Q~8000 in room air. The resonator is fabricated on a quartz substrate to reduce electrical feedthrough. The trans...

We demonstrate a new method for direct wire-bonding of silicon devices, which does not require any metal bond-pads. A wire bond-ball is pressed into a hole etched in the silicon device layer, and is wedged in the hole by plastic deformation. Experimental measurements show that strength and conductivity of direct-bonds are comparable to those of sta...

This paper reports the parallel internal electrostatic transduction of a laterally driven Lame-mode polysilicon resonator. This resonator is fabricated using a manufacturable double nanogap process that provides ultrathin high-aspect ratio lateral gaps. The transduction electrodes are optimally placed and oriented to maximize electromechanical tran...

This paper presents a new efficient technique for simulating the dynamic response of electrostatic micro switches. It is demonstrated that the dynamic response of a switch can be well predicted based on only a few static states of the system. Using energy methods the deformation of the system is approximated by a single adaptive mode, such that tim...

In this work it is theoretically shown that thermoelastic incompatibility between Silicon structures and their native-oxide layers induces thermoelastic damping. This damping dominates in structures that are packaged in vacuum and vibrate in pure axial motion. Analytic solutions of the thermoelastic response of axially loaded laminated bars are use...

In the above titled paper (ibid., vol. 13, no. 2, pp. 332-341, Apr 04), equations (12) and (13) contain typographical errors. The corrections are presented here.

In this paper, we introduced for the first time the energy-reversible complementary nanoelectromechanical (ER CNEM) logic gates and demonstrated their superiority over the conventional relays in terms of voltage, energy, and reliability. The ER CNEM logic a promising candidate for low standby and low operating power applications.

In current devices, dielectrophoresis (DEP) is implemented by connecting microelectrodes to external voltage signals. This study presents an alternative approach for implementing DEP in which some electrodes are left electrostatically floating. It is demonstrated experimentally and theoretically that these electrodes produce effective DEP forces. F...

The undamped dynamic response of electrostatic MEMS switches that are driven by a step-function voltage is investigated. A systematic analysis using energy methods is presented. An analytic expression for switching time is derived and this expression may be used as a design rule for electrostatic switches. The analytic predictions are validated exp...

In this work, new analytic expressions for the frequency of large vibrations and for the switching time, of electrostatic actuators, are presented. These expressions predict that the frequency and switching time are linearly related to specific measures of the applied voltage, on a logarithmic scale. Test devices were designed, fabricated, and char...

The operation and performance of complementary nanoelectromechanical (CNEM) logic gates are investigated. NEMS structures featuring dimensions 2 to 3 orders of magnitude smaller than the present MEMS relays are considered. Various metals are benchmarked to silicon as the cantilever beam material. We show that the CNEM inverters featuring laterally...

The mechanical properties of compliant materials such as biological tissues and biocompatible soft polymers are essential in medical research and engineering applications. These properties are often determined using techniques that require costly instrumentation (e.g. pull test machines). Alternative and more accessible methods can significantly ai...

This work investigates the interstitial fluid flow through the osteocytic-lacunar-canalicular system of cortical bone. The study assumes that it is a dynamic environment that undergoes continuous morphological changes. The model employed is a typical canaliculus (an annular region filled with a gel-like matrix that has a characteristic external dia...

Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

This paper presents a novel high-stability electrically-driven algorithm for the simulation of the electro-mechanical actuation of electrostatic MEMS devices. The stability of this algorithm improves on that of voltage- and charge-drive algorithms. Key in our algorithm are the use of a local charge density as driver for an adapted relaxation algori...

Electrostatic actuation of micro-devices was introduced four decades ago in the pioneering work of Nathanson et al. [1], and many applications have been found since [2, 3]. Electrostatic actuation is prevalent in MEMS due to its compatibility with microfabrication technology, and its low power consumption. Many studies of electrostatic actuators ha...

We present a novel tilting micro-mirror that has a triangular waveform resonance response, and a resonance frequency that can be continuously and reversibly adjusted. The triangular waveform and the adjustability of the resonance frequency are crucially important for raster-scanning applications. Although the mirror is driven by electrostatic force...

This paper presents analytic modeling, simulations, and experimental validation of RF MEMS switch actuation using tailored voltage waveforms. This actuation scheme can eliminate impact bouncing during switch activation and can significantly reduce harmonic oscillations during switch release.

The design of more reliable and sophisticated Micro Electro Mechanical Systems (MEMS) relies on the knowledge, understanding, and ability to control their mechanical response. In recent years, enormous progress has been made in developing new measurement techniques for studying the mechanical response of μm and sub-μm scale specimens (e.g. Kraft an...

We show that a symmetric electrostatic field can precipitately instigate buckling in a sub- critically loaded slender structure, and even instigate buckling when the slender structure is subjected to a tensile load. This work includes both theoretical analysis and experimental validation of electromechanical buckling. To this end, special microdevi...

A first-ever experimental validation of the electromechanical buckling response is presented. Electromechanical buckling is the coupling of two bifurcation responses: mechanical buckling and electromechanical bifurcation. In this paper, electromechanical buckling is demonstrated on a clamped-guided beam that is simultaneously subjected to an axial...

In practice, dielectrophoresis (DEP) devices are based on micropatterned electrodes. When subjected to applied voltages, the electrodes generate nonuniform electric fields that are necessary for the DEP manipulation of particles. In this study, electrically floating electrodes are used in DEP devices. It is demonstrated that effective DEP forces ca...

A new test device for measuring strength of brittle microbeams was recently proposed. This test device requires no measurement of applied forces or of deformation. In this work, the theoretical analysis that explains how the strength of microbeams may be deduced from the length of the remaining ligament of broken beams is presented.

The constitutive equations of multi-layered piezoelectric structures are derived in a new form. In this form, the electromechanical coupling is presented as an additional stiffness matrix. This matrix is a true property of the piezoelectric structure and is independent of specific mechanical boundary conditions that may apply to the structure. A no...

In this work, a new test structure and method for measuring residual stress is presented. The test structure is a single clamped-clamped beam with electrodes symmetrically positioned along both sides of the beam. The electromechanical buckling response is used to measure the residual stress. It is shown that a single test structure of the proposed...

In this work systematic approaches for extracting parameters of the static and dynamic response of electrostatic switches are presented. A novel strategy enables accurate and efficient extraction of the static pull-in state of voltage and charge driven actuators. Another strategy enables to extract parameters of the dynamic pull-in while only consi...

The electromechanical buckling of a prestressed microbeam bonded to a dielectric elastic foundation is analyzed. It is shown that electrostatic forces can precipitately instigate buckling even when the prestress in the microbeam is lower than the critical value that would cause mechanical buckling. We show that electrostatic potential can be used t...

A novel method and test structure for measuring the strength of brittle microbeams is presented. The method does not require any measurement of forces or displacements. The test structure includes a microbeam that is wrapped over a curved side-wall by application of an unmeasured force. With the progression of wrapping, increasing tensile stresses...

This study considers the dynamic response of electrostatic actuators with multiple degrees of freedom that are driven by multiple voltage sources. The critical values of the applied voltages beyond which the dynamic response becomes unstable are investigated. A methodology for extracting a lower bound for this dynamic pull-in voltage is proposed. T...

In this work we demonstrate that thermoelastic actuation can be used to drive tilting micromirrors to large angles at high frequencies. We present a Single Crystalline Silicon (SCS) micromirror with 1 mm diameter that achieves a scanning deflection angle of ± 8.5 ° at 9.5 kHz, which is driven by a 1.5 Volt source. The key feature that enables the h...

The behavior of short and very short fatigue cracks, emanating from so called “smooth” specimens with stress concentrations has been an intriguing research topic for a long time. It is well known that micro-cracks are embedded in the surface of any smooth specimen and are created during the manufacturing process. A few of these micro-cracks will ev...

A systematic approach for analyzing the static and dynamic electromechanical response of electrostatic actuators is presented. The analysis is based on energy methods. An analysis approach for extracting dynamic response parameters of electrostatic actuators, while only considering static states of the system, is presented. This is an efficient met...

The postbuckling deflection of an infinite beam that is bonded to a linear elastic foundation and is subjected to an internal compressive stress is analyzed. The nonlinear equilibrium equation that governs the problem considers extensional deformation of the beam. An analytic solution of the nonlinear equilibrium equation is presented and is found...

In this work we analyze the undamped response of charge-driven and voltage-driven electrostatic switches. We show that charge actuation can drastically reduce the impact velocity between the movable and fixed electrodes and reduce unwanted vibrations during switch release. In voltage-driven switches, a considerable reduction of the impact velocity...

In this study, the affect of a project-based learning introductory course on the Capacity for Engineering Systems Thinking (CEST) of freshman students is considered. The qualitative paradigm was found to be appropriate for this study because the focus was on learning processes and the development of concepts. Four aspects of engineering systems thi...

This work considers microresonators that are driven by a temperature-gradient actuator. The driving forces in the temperature-gradient actuation scheme are internal mechanical moments induced by temperature gradients. In this work, a model for analyzing the dynamic thermomechanical response of temperature-gradient actuators is presented. In this mo...

In this work, the electromechanical stability of individual comb-drive fingers is considered. Previous studies have shown that optimal design of elastic suspensions can prevent the side pull-in instability of comb-drive rotors. In this work it is shown that side pull-in can nevertheless occur in individual comb fingers, if they are exceedingly slen...

A novel method for measuring residual stress is proposed and analyzed in this study. The method is based on the electromechanical bifurcation response of a clamped–clamped beam. The stressed beam is subjected to a symmetric electrostatic field. The presented analysis shows that the critical voltage which induces the bifurcation response is a monoto...

In this study, the affect of a project-based learning (PBL) introductory course on the Capacity for Engineering Systems Thinking (CEST) of freshman students, is considered. Four aspects of engineering systems thinking were evident in the students' responses: conceptualization, requirements, alternatives, and optimum. The findings of this study indi...

It is demonstrated that the strength of brittle micro-beams can be measured without measuring any forces or displacements. A novel test device is presented in which the strength of brittle beams is directly deduced from their size after failure.

In this work the electromechanical buckling of a clamped-clamped beam is analyzed. This instability is induced by simultaneous application of internal (residual) stress and a symmetric electrostatic field. In this work it is shown that the critical applied voltage that induces electromechanical buckling is a monotonic function of the internal stres...

The constitutive equations of multilayered piezoelectric structures are derived in a new form. In this form, the electromechanical coupling is presented as an additional stiffness matrix. This matrix is a true property of the piezoelectric structure and is independent of specific mechanical boundary conditions that may apply to the structure. A nov...

A new model for simulating the mechanical response of a wire rope with an independent wire rope core is presented. The rope is subjected to both an axial load and an axial torque. In contrast with previous models that consider the effective response of wound strands, the present model fully considers the double-helix configuration of individual wir...

A major high-order thinking skill that enables engineers to successfully perform the integration and the design processes is Engineering System Thinking. To successfully integrate subsystems into a whole system, the systems engineer needs a high Capacity for Engineering System Thinking (CEST). This paper presents principles for quantitatively measu...

The ElectroMechanical Buckling (EMB )o f ap re- stressed layer bonded to an elastic foundation is analyzed. A new analytic solution of the mechanical post-buckling is presented. In addition, it is shown that electrostatic forces can precipitately instigate buckling even when the pre- stress is lower than the critical value that allows mechanical bu...

This work presents a systematic analysis of electrostatic actuators driven by multiple uncoupled voltage sources. The use of multiple uncoupled voltage sources has the potential of enriching the electromechanical response of electrostatically actuated deformable elements. This in turn may enable novel MEMS devices with improved and even new capabil...

This paper presents perceptions and attitudes of freshmen students that have participated in an introductory Project-Based Learning (PBL) course in engineering. The course, `A creative introduction to mechanical engineering', was developed and is taught in the Faculty of Mechanical Engineering at the Technion. In this course, teams of students carr...

In prevalent torsion actuators the angular travel range and pull-in instability are set and cannot be changed once the device is fabricated. The current work presents a novel adjustable micromirror device. By using multiple electrodes, the novel design allows continuous and reversible adjustment of the electromechanical response and pull-in instabi...

The pull-in state of electrostatic actuators that are driven by a single varying voltage is the equilibrium state for which the applied voltage is maximal. In contrast, electrostatic actuators driven by multiple voltage sources have an infinite number of critical states that constitute the pull-in hyper-surface. This work reports on a novel methodo...

This paper presents a qualitative study of students' capacity for systems engineering thinking as it develops during a Problem-Based Learning (PBL) introductory course. This course is given to Mechanical Engineering freshmen and aims to provide a broad view of the field and of the process of engineering design. Data was collected in semi-structured...

In this letter, a novel adjustable micromirror device using multiple electrodes is presented. The novel design allows post fabrication continuous and reversible adjustment of the electromechanical response and pull-in instability. This property is demonstrated on a fabricated device and is used for analog adjustment of the stable angular travel ran...

The purpose of this work is to demonstrate the significance, and to quantify and model the effect, of secondary degrees-of-freedom (DOF) on the response and instability of electrostatically actuated MEMS devices. Also, a novel reduced-order modeling approach is presented, and is used to interpret and analyze the measured electromechanical response...

Pull-in instability is a crucial effect in electrostatically-actuated microelectromechanical devices. This phenomenon was recently shown to occur under both voltage and charge control. So far, for all known cases, it has been shown that, under charge excitation, electrostatic actuators have a larger range of stability than under voltage excitation....

Pull-in parameters are important properties of electrostatic actuators. Efficient and accurate analysis tools that can capture these parameters for different design geometries, are therefore essential. Current simulation tools approach the pull-in state by iteratively adjusting the voltage applied across the actuator electrodes. The convergence rat...

Pull-In parameters are important properties of electrostatic actuators. Efficient and accurate analysis tool that can capture these parameters for different design geometries, are therefore essential. Current simulation tools approach the Pull-In state by iteratively adjusting the voltage applied across the actuator electrodes. The convergence rate...

A poroelastic material with arbitrary pore space geometry is considered. The porous material is made of a single phase solid constituent. The pressure of the non-porous solid constituent is considered to be a unique function of relative volume, and the average solid pressure is assumed to be a unique function of solid relative volume. The assumptio...

In this work the stability of electrostatic actuators with multiple uncoupled voltage sources applied to separate isolated excitation electrodes is analyzed. These electrodes are used to drive a continuous deformable element. A novel computational strategy and an efficient numerical scheme for simulating such problems are presented. The theory of t...

This paper describes a new introductory course developed at the Technion for freshmen Mechanical Engineering students. Through unconventional teaching methods, this course provides a clear overview of the different fields within Mechanical Engineering, and also provides a clear description of the engineer's work. By challenging the students to desi...

The surface displacements and contact stress induced by rigid inclusions between two dissimilar elastic half-spaces are considered. Previous studies limited to flat rigid inclusions have revealed that the contact stress on opposite sides of the inclusions are identical and that the surface displacements of the two half-spaces are proportional. The...