Our research activity focuses on modeling of micro actuators and design of innovative devices with tailored properties. In our modeling work we investigate the static and dynamic response of electrostatic, piezoelectric, thermoelastic, and electromagnetic micro actuators. We strive to provide insight, efficient modeling tools and design rules for the benefit of the MEMS community. In our design work we try to be creative and find innovative solutions for specific challenges. Typical fruits of our work are posted on this page. We are eagerly seeking collaboration and if you have interesting problems or challenges we would love to hear about them.
An electret gap-closing transducer with a linear response
We have analyzed the electromechanical response of a symmetric electret parallel-plates actuator. 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 electrostatic field. The electrostatic field that displaces the charged dielectric has three components: a field induced by the voltage difference across the capacitor plates, a field induced by the anti-symmetric part of charge, and a field induced by the combined effect of the symmetric part of charge and the displacement of the plate itself. The analysis shows that the displacement of the electret actuator is a linear function of the driving voltage, and that a full range of stable motion can be achieved. Furthermore, it is shown that all important characteristics of the fixed charge can be deduced from simple measurements.
To learn more please refer to our paper: The Electromechanical Response of a Symmetric Electret Parallel-Plates. D. Elata, Sensors and Actuators A, 173, 197-201, 2012.
Measuring the strength of brittle microbeams
We have developed a device and method for measuring the strength of brittle microbeams which requires no measurements of forces or displacements. Euler Bernoulli beam theory trivially predicts that the maximal tension stress in an initially straight beam is linearly proportional to the curvature of the beam when it is bent. So in our device we design a curved wall over which we wrap a test beam by application of an unmeasured force. The curvature of the curved wall increases linearly with circumferential distance along the wall. Therefore, the maximal curvature in the wrapped beam occurs at the last point of contact between the beam and the curved wall.
In an ideal world, once the beam has broken we may determine the maximal curvature which developed at the fractured edge by measuring the length of the remaining segment. In reality, the beam does not break where stress is maximal but rather where the local stress reaches the lever of the local strength. Since strength is a stochastic property, some statistical analysis must be performed. We have shown that the mean and variance of the location of failure are uniquely related to the Weibull parameters that characterize the strength statistics of the beam.
Our complete analysis may be found in our paper: A novel method for measuring the strength of microbeams. D. Elata and A. Hirshberg,IEEE JMEMS, 15(2), 396-405, 2006.
ElectroMechanical Buckling (EMB)
Consider a thin, compressively stressed conductive layer, which is bonded to a dielectric elastic foundation that is fixed to a stiff conductive substrate. With no electrostatic loading, it is well known that if the compressive stress is larger than a critical value, the flat top layer will spontaneously buckle.
We have analyzed the electromechanical equilibrium of this system and have shown that if the compressive stress is lower than this critical value, buckling of the top layer can be reversibly switched on and off by application of a voltage across the conducting layers. This device couples mechanical buckling with electrostatic bifurcation and we termed this coupled response ElectroMechanical Buckling (EMB).
To learn more please refer to our paper: Analysis of electromechanical buckling of a pre-stressed micro beam that is bonded to an elastic foundation. D. Elata and S. Abu-Salih, J. of Mech. Mat. Struc., 1(5), 911-923, 2006. URL
Measuring residual stress in conductive layers
Residual stress may cause permanent deformations and adversely affect the response of released micro structures. The common method to identify residual stress is by observing the response of passive test structures. Compressive stress will induce buckling in released clamped-clamped beams that are longer then a threshold value. Measurement of compressive stress in a wide range requires many clamped-clamped beams with different lengths, where the number of lengths determines the measurement resolution. Tensile stress can be measured by Guckel rings, and here too the geometry and number of different rings determines the range and resolution of measurements. Thus measurement by passive structures may cost a lot in terms of wafer area.
We have proposed and validated a single structure that can measure residual stress in conductive layers, in a continuous wide range (measures both compressive and tensile stress). In our device a clamped-clamped beam is subjected to both residual stress and a symmetric external electrostatic field. This device couples mechanical buckling with electrostatic bifurcation and we termed this coupled response ElectroMechanical Buckling (EMB). The voltage at which the structure buckles is monotonically proportional to the residual stress which may be compressive or tensile.
To learn more please refer to our papers: Analysis of a novel method for measuring residual stress in micro-systems. D. Elata and S. Abu-Salih, J. Micromech. Microeng., 15(5), 921-927, 2005. . Experimental validation of ElectroMechanical Buckling. S. Abu-Salih and D. Elata, IEEE JMEMS, 15(6), 1656-1662, 2006.
Tilting micromirrors with a linear response
Tilting micromirrors are often actuated by vertically staggered electrostatic comb-drives. Electrostatic comb-drives have been first introduced to enable large in-plane motions. They are preferable to gap-closing actuators because in comb-drives the electrostatic force is unaffected by motion and this motion is not confined by the gap. The in-plane motion of a double-sided comb-drive is linearly proportional to the rotor voltage for an appropriate setting of the stators voltage. Attempts were made to adapt this concept to tilting micromirrors. We have shown that double-sided tilting micromirrors do not have a linear response because the unwarranted transverse forces are induced which affect the tilting motion.
Our solution is to use dual-gap fingers in the stator combs. This decreases the unwarranted transverse forces and results in a tilting response that is linearly proportional to the rotor voltage.
To learn more, please refer to our conference paper: Vertical comb-drive angular actuators with a linear electrostatic response. M. Naftali, J.B. Kim, D. Elata and L. Lin, Eurosensors XVIII, Rome, Italy, September 2004.
Tilting micromirror with a triangular dynamic waveform
Raster scanning is used in imaging and display systems. In the TI-DLP® technology most of the light is redirected to an absorbing target, thus this projection method is power inefficient. In contrast, in raster scanning all generated light is reflected onto the target screen and is therefore power efficient. An ideal scanning mirror should have a triangular dynamic waveform with adjustable frequency. These requirements enable synchronization of the mirror with the video input and make it possible to avoid distortion and non-uniform intensity of the projected image. However, to reduce driving voltages most tilting micromirrors achieve the required angle range by driving it in resonance, which inevitably results in a sinusoidal dynamic waveform.
Though it is often argued that any problem can be solved by electronic hardware and by software, we present a mechanical solution that produces a triangular waveform with a frequency that is simply adjusted by changing the amplitude of the driving voltage.
To learn more, please refer to our conference paper: A novel tilting micromirror with a triangular waveform resonance response and an adjustable resonance frequency for raster scanning applications. D. Elata, V. Leus, A. Hirshberg, O. Salomon and M. Naftali, Transducers 2007, Lyon, France, June 2007.
High frequency thermoelastic actuation
Thermoelastic actuators utilize thermal expansion of elastic materials to achieve large displacements or forces. Deformable structural elements are heated by electric current and are cooled by conduction. The characteristic time scale of heat transfer is L2/α* where L is a relevant length. α* is the thermal diffusivity which is the ratio between heat conduction and heat capacity. If we have built a thermoelastic actuator and we increase its dimensions by a factor β, then its response is slowed by β2. This (and other factors such as low efficiency) is why thermoelastic actuators are not used in macro-scale. It turns out that most thermoelastic actuators (the prevalent types are: bi-morphs; hot-cold arms; and chevron) are to slow for many micro applications as well.
We have demonstrated a temperature gradient thermal actuator, and have driven a tilting micromirror to amplitudes of ±8° at a frequency of 9.5kHz using 1.5 Volts. The relevant length for gradient is the beams width which is 100 times shorter than the beam length and hence the short thermal response time.
To learn more please refer to our paper: A temperature-gradient driven micromirror with large angles and high frequencies. D. Elata and R. Mahameed, IEEE MEMS 2006, 850-853. Istanbul, Turkey, January 2006.
Dynamic pull-in
When gap-closing electrostatic actuators are subjected to a step-function voltage, they respond with a periodic vibration (for V<Vcr) or a switching response (for V>Vcr). The critical voltage Vrc that is between the periodic and switching response is the dynamic pull-in voltage.
We have proposed a modeling approach to extract the dynamic pull-in voltage without performing time integration of the momentum equations. Our model is based on energy considerations and yields a lower bound for the dynamic pull-in voltage for distributed actuators.
For the classic parallel-plates actuator the dynamic pull-in voltage and displacement are Vpi=1/2, xpi=1/2 (the related values for the static response are Vpi2=8/27 , xpi=1/3).
To learn more, please refer to our paper: On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources. D. Elata and H. Bamberger, IEEE JMEMS, 15(1), 131-140, 2006.
Switching time of electrostatic actuators
We derived new analytic expressions for the frequency of large vibrations and for the switching time, of electrostatic actuators that are driven by a step-function of voltage. These expressions predict that the frequency and switching time are linearly related to specific measures of the applied voltage, on a logarithmic scale. The key to this relation is expressing the voltage in terms of the Dynamic Pull-In Voltage (see previous research posting).
Test devices were designed, fabricated, and characterized, and measurements are shown to be in very good agreement with predictions. These linear relations are important and relevant as design rules for electrostatic switches.
To learn more, please refer to our paper: On the dynamic response of electrostatic MEMS switches. V. Leus and D. Elata, IEEE JMEMS, 17(1), 236 – 243, 2008.
Direct wire bonding on silicon
We have 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 of direct-bonds is comparable to those of standard wire-bonds on metal pads. The relevance of direct wire-bonding is that by eliminating metal bond-pads, constraints on high temperature processing steps and limitations on sacrificial release steps, are alleviated.
To learn more, please refer to our conference paper: Direct Wire-bonding of Silicon Devices without Metal Pads. A. Hirshberg and D. Elata, IEEE-MEMS 2009, Sorrento, Italy, January 2009.
The response of multi-layered piezoelectric structures
The driving force in multi-layered piezoelectric actuators is internal moment. If not constrained, the actuators deforms in to a spherical shell (double-curvature). Since the approximation of narrow beams is in compatible with most multi-layered piezoelectric actuators, all models that assume cylindrical bending are fundamentally flawed. Furthermore, the assumption that the response of multi-layered piezoelectric actuators is bounded between the simplified models of plane-strain and plane-stress is not applicable to microstructures. This is because in microstructures the thickness of piezo layers may be comparable to the thickness of structural substrate layers.
We have developed a comprehensive rational model of the electromechanical response of multi-layered piezoelectric actuators. Our model is in excellent agreement with full-fledged 3D finite-elements analysis, and elucidates the limitations of previous models.
To learn more, please refer to our paper: The electromechanical response of multi-layered piezoelectric structures. E. Elka, D. Elata and H. Abramovich, IEEE JMEMS, 13(2), 332- 341, 2004. Addendum