Charge control of parallel-plate, electrostatic actuators and the tip-in instability

Controlling the charge, rather than the voltage, on a parallel-plate, electrostatic actuator theoretically permits stable operation for all deflections. Practically, we show that, using charge control, the maximum stable deflection is limited by 1) charge pull-in, in which the actuator snaps due to the presence of parasitic capacitance and 2) tip-in, in which the rotation mode becomes unstable. This work presents a circuit that controls the amount of charge on a parallel-plate, electrostatic actuator. This circuit reduces the sensitivity to parasitic capacitance, so that tip-in is the limiting instability. A small-signal model of the actuator is developed and used to determine the circuit bandwidth and gain requirements for stable deflections. Four different parallel-plate actuators have been designed and tested to verify the charge control technique as well as to verify charge pull-in, tip-in, and the bandwidth requirements. One design travels 83% of the gap before tip-in. Another design can only travel 20% of the gap before tip-in, regardless of whether voltage control or charge control is used.     

Application of piezoelectric layers in electrostatic MEM actuators: controlling of pull-in voltage

In this paper, a novel method has been developed to control the pull-in voltage of the fixed-fixed and cantilever MEM actuators and measure the residual stress in the fixed-fixed model using of the piezoelectric layers that have been located on the upper and lower surfaces of actuator. In the developed model, the tensile or compressive residual stresses, fringing-field and axial stress effects in the fixed-fixed end type micro-electro-mechanical systems actuator have been considered. The non-linear governing differential equations of the MEM actuators have been derived by considering the piezoelectric layers and mentioned effects. The results show that due to different applied voltage to the piezoelectric layers, the pull-in voltage can be controlled and in the fixed-fixed type the unknown value of the residual stress can be obtained.     

A water-tight packaging of MEMS electrostatic actuators for biomedical applications

This paper presents a flip-chip based packaging technique for encapsulating MEMS electrostatic actuators for biomedical applications. High-performance electrostatic inchworm actuators are used to demonstrate the packaging technique. A wall structure is put around the actuator surrounding it completely but leaving a small clearance where the actuator shuttle can extend off the edge of the chip. A cap chip is fabricated separately, and flip-chipped onto the actuator. Au–Au thermal bonding technique is used to fix the cap. Finally, rendering the surfaces of the clearance hydrophobic prevents the water ingress when the actuator operates in water.     

Influence of van der Waals and Casimir forces on electrostatic torsional actuators

The influence of van der Waals (vdW) and Casimir forces on the stability of the electrostatic torsional nanoelectromechanical systems (NEMS) actuators is analyzed in the paper. With the consideration of vdW and Casimir effects, the dependence of the critical tilting angle and pull-in voltage on the sizes of structure is investigated. The influence of vdW torque is compared with that of Casimir torque. The modified coefficients of vdW and Casimir torques on the pull-in voltage are, respectively, calculated. When the gap is sufficiently small, pull-in can still take place with arbitrary small angle perturbation because of the action of vdW and Casimir torques even if there is not electrostatic torque. And the critical pull-in gaps for two cases are, respectively, derived.     

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.     

Influence of van der Waals force on the pull-in parameters of cantilever type nanoscale electrostatic actuators

In this paper, the influence of the van der Waals force on two main parameters describing an instability point of cantilever type nanomechanical switches, which are the pull-in voltage and deflection are investigated by using a distributed parameter model. The fringing field effect is also taken into account. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. The integral equation is solved analytically by assuming an appropriate shape function for the beam deflection. The detachment length and the minimum initial gap of the cantilever type switches are given, which are the basic design parameters for NEMS switches. The pull-in parameters of micromechanical electrostatic actuators are also investigated as a special case of our study by neglecting the van der Waals force.     

Dynamic response of a torsional micromirror to electrostatic force and mechanical shock

In this paper dynamic characteristics of a capacitive torsional micromirror under electrostatic forces and mechanical shocks have been investigated. A 2DOF model considering the torsion and bending stiffness of the micromirror structure has been presented. A set of nonlinear equations have been derived and solved by Runge–Kutta method. The Static pull-in voltage has been calculated by frequency analyzing method, and the dynamic pull-in voltage of the micromirror imposed to a step DC voltage has been derived for different damping ratios. It has been shown that by increasing the damping ratio the dynamic pull-in voltage converges to static one. The effects of linear and torsional shock forces on the mechanical behavior of the electrostatically deflected and undeflected micromirror have been studied. The results have shown that the combined effect of a shock load and an electrostatic actuation makes the instability threshold much lower than the threshold predicted, considering the effect of shock force or electrostatic actuation alone. It has been shown that the torsional shock force has negligible influence on dynamic response of the micromirror in comparison with the linear one. The results have been calculated for linear shocks with different durations, amplitudes, and input times.     

A methodology and model for the pull-in parameters of magnetostatic actuators

Magnetostatic actuators exhibit bistability similarly to the pull-in phenomena of electrostatic actuators. In this paper a methodology and model for the extraction of the magnetic Pull-In parameters of magnetostatic actuators are derived. The flux-controlled magnetostatic actuator is analyzed based on the energy representation and the magnetomotive force-controlled magnetostatic actuator is analyzed in the thermodynamic potential energy (or co-energy) representation. An algebraic equation, referred to as the magnetic Pull-In equation, for each of the two cases (flux-controlled and magnetomotive force-controlled actuators) is derived. By solving these Pull-In equations either analytically or numerically, the magnetic Pull-In parameters are obtained. Several case studies, covering displacement and torsion magnetic actuators, are presented and analyzed, illustrating the usefulness of the proposed methodology, its relative simplicity as well as the adaptability and practical usage in wide spectrum of magnetic actuators. [1425].     

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.     

Design of large deflection electrostatic actuators

Electrostatic, comb-drive actuators have been designed for applications requiring displacements of up to 150 /spl mu/m in less than 1 ms. A nonlinear model of the actuator relates the resonant frequency and the maximum stable deflection to the actuator dimensions. A suite of experiments that were carried out on deep reactive ion etched (DRIE), single-crystal silicon, comb-drive actuators confirm the validity of the model. Four actuator design improvements were implemented. First, a folded-flexure suspension consisting of two folded beams rather than four and a U-shaped shuttle allowed the actuator area to be cut in half without degrading its performance. Second, the comb teeth were designed with linearly increasing lengths to reduce side instability by a factor of two. Third, the folded-flexure suspensions were fabricated in an initially bent configuration, improving the suspension stiffness ratio and reducing side instability by an additional factor of 30. Finally, additional actuation range was achieved using a launch and capture actuation scheme in which the actuator was allowed to swing backward after full forward deflection; the shuttle was captured and held using the backs of the comb banks as high-force, parallel-plate actuators.     

Auto-calibration of capacitive MEMS accelerometers based on pull-in voltage

This paper describes an electro-mechanical auto-calibration technique for use in capacitive MEMS accelerometers. Auto-calibration is achieved using the combined information derived from an initial measurement of the resonance frequency and the measurement of the pull-in voltages during device operation, with an estimation of process-induced variations in device dimensions from layout and deviations in material properties from the known nominal value. An experiment-based analytical model is used to compute the required electrostatic forces required to simulate external accelerations allowing the electro-mechanical calibration of the accelerometer. Measurements on fabricated devices confirm the validity of the proposed technique and electro-mechanical calibration is experimentally demonstrated.     

Microscale materials testing using MEMS actuators

Small size scale and high resolutions in force and displacement measurements make MEMS actuators appropriate for micromechanical testing. In this paper, for the first time, we present methodologies for uniaxial tensile and cantilever bending testing of both micrometer- and submicrometer-scale freestanding specimens using MEMS actuators. We also introduce dry fabrication processes for the specimens. The methodologies allow freestanding single or multilayered thin-film specimens to be fabricated separately from the MEMS actuators. For the uniaxial tension test, tensile forces are applied by lateral comb drive actuators capable of generating a total load of 383 μN at 40 V with resolutions on the order of 3 nN. A similar actuator is used in the bending test, with load resolution of 58 nN and spring constant of 0.78 N/m. The tensile testing methodology is demonstrated with the testing of a 110-nm-thick freestanding aluminum specimen. The cantilever bending experiment is performed on a 100-nm-thick aluminum specimen. The experimental setups can be mounted in a SEM (and also in a TEM after modifications for tensile testing) for in situ observation of materials behavior under different environmental conditions. Remarkable strengthening is observed in all the specimens tested compared to their bulk counterparts in both tensile and bending experiments. Experimental results highlight the potential of MEMS actuators as a new tool for materials research     

Speed-energy optimization of electrostatic actuators based onpull-in

The speed and total energy required to accomplish pull-in switching of a generic electrostatic actuator is examined. It is found that the value of the source resistance of the voltage drive used for switching has a profound effect on both switching speed and energy requirements. The source resistance governs the charging time for the actuating capacitor. As long as this time is slower than the time required to accelerate the moving mass to maximum speed in the presence of damping, the total energy required for switching can be dramatically reduced without a significant increase in switching time. Indeed, there exists a clear optimum source-resistance value that minimizes the product of switching time and switching energy. These findings are demonstrated theoretically and then applied to specific examples from the literature. In addition, the limiting case of very large source resistance, essentially a current drive, is evaluated and compared to the voltage-driven case. It is found that for equivalent switching times, the current drive requires less total energy for a switching event     

Robust control of the electrostatic torsional micromirrors

In order to simplify the sensors subsystems of the electrostatic torsional micromirrors (ETMs), the output feedback control for the ETM systems is investigated in this paper. The dynamics of the systems is established by combining the dynamics of both the mechanical and electronic subsystems, and it is proved that the dynamics of the overall system with uncertainties in electrical parameters can be exactly transformed into the third order linear system. Then an output feedback finite-time stabilizing (FTS) controller is presented by composing of a full state FTS observer and a state feedback FTS controller for the third order linear systems, such that the ETM systems can be stabilized in its full travel range by merely measuring the tilt angle. Some numerical simulations demonstrate the stability of the proposed output feedback FTS controller.     

Microfabricated torsional actuators using self-aligned plastic deformation of silicon

In this paper, we describe angular vertical-comb-drive torsional microactuators made in a new process that induces residual plastic deformation of single-crystal-silicon torsion bars. Critical dimensions of the vertically interdigitated moving-and fixed-comb actuators are self-aligned in the fabrication process and processed devices operate stably over a range of actuation voltages. We demonstrate MEMS scanning mirrors that resonate at 2.95kHz and achieve optical scan angles up to 19.2 degrees with driving voltages of 40V/sub dc/ plus 13V/sub pp/. After continuous testing of five billion cycles at the maximum scanning angle, we do not observe any signs of degradation in the plastically deformed silicon torsion bars.     

Extending the travel range of analog-tuned electrostatic actuators

The pull-in instability limits the travel distance of elastically suspended parallel-plate electrostatic microactuators to about 1/3 of the undeflected gap distance. In this paper, we examine the “leveraged bending” and “strain-stiffening” methods for extending the travel range of electrostatic actuators. The leveraged bending effect can be used to achieve full gap travel at the cost of increased actuation voltage. The strain-stiffening effect can be used to minimize actuation voltage for a given travel range. An analytical approximation shows that the strain-stiffening effect can be used to achieve a stable travel distance up to about 3/5 of the gap. A tunable reflective diffraction grating known as the polychromator has been designed using these actuation techniques, and selected designs have been fabricated and tested for actuation behavior. Gratings with 1024 flat, closely packed grating-element actuators have been fabricated with over 1-cm-long mirrors, achieving stable vertical travel distances of more than 1.75 μm out of a 2-μm gap     

Design considerations of rectangular electrostatic torsionactuators based on new analytical pull-in expressions

An important design issue of electrostatic torsion actuator is the relative locations of the actuating electrodes, where the bias voltage is applied. These geometrical design parameters affect both the pull-in angle as well as the pull-in voltage. In this paper, a new approximated analytical solution for the pull-in equation of an electrostatic torsion actuator with rectangular plates is derived. The analytical expression is shown to be within 0.1% of the one degree of freedom (1DOF) lumped-element model numerical simulations. Moreover, the analytical expressions are compared with the full coupled-domain finite-elements/boundary-elements (FEM/BEM) simulations provided by MEMCAD4.8 Co-solve tool, showing excellent agreement. The approach presented here provides better physical insight, more rapid simulations and an improved design optimization tool for the actuator     

Flexible, dry-released process for aluminum electrostatic actuators

We present an all-aluminum MEMS process (Al-MEMS) for the fabrication of large-gap electrostatic actuators with process steps that are compatible with the future use of underlying, pre-fabricated CMOS control circuitry. The process is purely additive above the substrate as opposed to processes that depend on etching pits into the silicon, and thereby permits a high degree of design freedom. Multilayer aluminum metallization is used with organic sacrificial layers to build up the actuator structures. Oxygen-based dry etching is used to remove the sacrificial layers. While this approach has been previously used by other investigators to fabricate optical modulators and displays, the specific process presented herein has been optimized for driving mechanical actuators with relatively large travels. The process is also intended to provide flexibility for design and future enhancements. For example, the gap height between the actuator and the underlying electrode(s) can be set using an adjustable polyimide sacrificial layer and aluminum “post” deposition step. Several Al-MEMS electrostatic structures designed for use as mechanical actuators are presented as well as some measured actuation characteristics