David Elata

An efficient DIPIE algorithm for CAD of electrostatically actuated MEMS devices

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 rate of this scheme gradually deteriorates as the pull-in state is approached. Moreover, the convergence is inconsistent and requires many mesh and accuracy refinements to assure reliable predictions. As a result, the design procedure of electrostatically actuated MEMS devices can be time-consuming. In this paper a novel Displacement Iteration Pull-In Extraction (DIPIE) scheme is presented. The DIPIE scheme is shown to converge consistently and far more rapidly than the Voltage Iterations (VI) scheme (>100 times faster!). The DIPIE scheme requires separate mechanical and electrostatic field solvers. Therefore, it can be easily implemented in existing MOEMS CAD packages. Moreover, using the DIPIE scheme, the pull-in parameters extraction can be performed in a fully automated mode, and no user input for search bounds is required.

On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources

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. This lower bound is based on the stable and unstable static response of the system, and can be rapidly extracted because it does not require time integration of momentum equations. As example problems, the dynamic pull-in of two prevalent electrostatic actuators is analyzed.

On the Dynamic Response of Electrostatic MEMS Switches

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 experimentally using test structures with parallel-plates actuators. It is shown that the analysis is also applicable for switches with more general geometry.

Contact force-displacement laws and the mechanical behavior of random packs of identical spheres

Abstract The contact force-displacement law of two identical elastic spheres can independently display: nonlinear response, path dependence and dissipation due to slip. Omitting relative roll and torsion between the two spheres, a general contact force-displacement law is derived analytically by integrating the differential form of the Hertz-Mindlin solution along the contact displacement path. The Hertz-Mindlin contact law and a different contact law formulated by K. Walton are special cases of this general contact law. Implementation of the contact law in numerical codes may be cumbersome because it requires a full description of the contact load history. Some simplified contact force-displacement laws proposed in the literature that overcome this difficulty are shown to be thermodynamically inconsistent (i.e., unphysical) since they permit energy generation at no cost. The mean-field approximation and statistical averaging for calculating macroscopic stress-strain relations are discussed with respect to various contact force-displacement laws.

Analysis of a novel method for measuring residual stress in micro-systems

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 monotonic function of the residual stress. Furthermore, the electromechanical bifurcation occurs for both compressive and tensile residual stresses. Ensuring that the postbuckling response is non-stable facilitates the identification of the bifurcation response. To this end, geometrical conditions are derived which ensure that the postbuckling state of the system is non-stable. It is shown that a single test structure can be used to measure residual stress in a continuous wide range.

The electromechanical response of multilayered piezoelectric structures

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 novel model of the electromechanical response of such structures is presented. This model accounts for the three-dimensional (3-D) kinematics of the structure deformation. Solution of example problems using the new model shows excellent agreement with full 3-D finite element simulations. These solutions are also compared to the results of previous two-dimensional (2-D) model approximations presented in literature, and the inaccuracies associated with these previous models are discussed.

Analytical approach and numerical /spl alpha/-lines method for pull-in hyper-surface extraction of electrostatic actuators with multiple uncoupled voltage sources

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 capabilities. It is therefore important to develop methods for analyzing this class of actuators. Pull-in is an inherent instability phenomenon that emanates from the nonlinear nature of the electromechanical coupling in electrostatic actuators. The character of pull-in in actuators with multiple uncoupled voltage sources is studied, and new insights regarding pull-in are presented. An analytical method for extracting the pull-in hyper-surface by directly solving the voltage-free K-N pull-in equations derived here, is proposed. Solving simple but interesting example problems illustrate these new insights. In addition, a novel /spl alpha/-lines numerical method for extracting the pull-in hyper-surface of general electrostatic actuators is presented and illustrated. This /spl alpha/-lines method is motivated by new features of pull-in, that are exhibited only in electrostatic actuators with multiple uncoupled voltage sources. This numerical method permits the analysis of electrostatic actuators that could not have been analyzed by using current methods.

Model and Observations of Dielectric Charge in Thermally Oxidized Silicon Resonators

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 model for the electromechanical effects of charge trapped in the dielectrics within the transduction gap of a resonator. Observations of resonance frequency against varying resonator bias voltage are fitted to this model in order to obtain estimates for the magnitude of the trapped oxide charge. Statistics collected from wet- and dry-oxidized devices show that lower fixed oxide charge can be expected upon dry oxidation. In addition, observations of time-varying resonator frequency indicate the presence of mobile oxide charge in a series of voltage biasing and temperature experiments.

How slender can comb-drive fingers be?

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 slender. To this end, the critical electromechanical state of individual comb fingers is analytically solved. This solution is in good agreement with finite elements simulations. The analytic solution can be used to design comb-drives in which side pull-in of individual fingers is avoided.

Experimental Validation of Electromechanical Buckling

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 mechanical load and a symmetric, transverse, electrostatic field. Experimental measurements of the electromechanical buckling voltage are in good agreement with the theoretical prediction