Deep-reactive ion-etched compliant starting zone electrostatic zipping actuators

This paper presents the modeling, design, fabrication and testing of monolithic electrostatic curved-electrode zipping actuators fabricated by deep reactive ion etching (DRIE). In contrast to traditional curved-electrode zipping actuators, the design of the actuators presented here utilizes a compliant starting cantilever to significantly reduce the initial pull-in voltage by closing the gap (kerf) generated by DRIE. Thus, the actuators achieve high actuation force at a relatively low voltage. For example, two actuators each with dimensions of 4.5 mm*100 /spl mu/m*300 /spl mu/m are used to drive a bistable MEMS relay. Together, the two actuators provide up to 10 mN of force over their 80 /spl mu/m stroke at 140 V. Measurements of the force-displacement relation of these actuators confirm theoretical expectations based both on numerical and analytical methods. Finite element analysis is employed to predict the behavior of the complete bistable relay system. [1231].     

Experimental verification of a design methodology for torsion actuators based on a rapid pull-in solver

In this work, an experimental and theoretical study of the effect of various geometrical parameters on the electromechanical response and pull-in parameters of torsion actuators is presented. A lumped two-degrees-of-freedom (L2DOF) pull-in model that takes into account the bending/torsion coupling, previously proposed for cantilever suspended actuators, is tailored for the torsion actuators under study. This model is shown to better capture the measured pull-in parameters than previously proposed lumped single-degree-of-freedom (L1DOF) models. The measurements were conducted on torsion actuators with various shapes, fabricated on silicon-on-insulator (SOI) wafers using deep reactive ion etching (DRIE) and flip-chip bonding. Furthermore, a novel rapid solver, for extracting the pull-in parameters of the L2DOF model of the torsion actuators, is proposed. The proposed solver is based on a Newton-Raphson scheme and the recently presented DIPIE algorithm and is shown to be /spl sim/10 times faster than the prevalent voltage iterations based solvers. The rapid and more accurate pull-in extraction of the proposed approach renders it as a tool for extensive analysis and design optimization of torsion actuators.     

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.     

A methodology and model for the pull-in parameters of electrostaticactuators

This paper presents a generalized model for the pull-in phenomenon in electrostatic actuators with a single input, either charge or voltage. The pull-in phenomenon of a general electrostatic actuator with a single input is represented by an algebraic equation referred to as the pull-in equation. This equation directly yields the pull-in parameters, namely, the pull-in voltage or pull-in charge and the pull-in displacement. The model presented here permits the analysis of a wide range of cases, including nonlinear mechanical effects as well as various nonlinear, nonideal, and parasitic electrical effects. In some of the cases, an analytic solution is derived, which provides physical insight into how the pull-in parameters depend upon the design and properties of the actuator. The pull-in equation can also yield rapid numerical solutions, allowing interactive and optimal design. The model is then utilized to analyze analytically the case of a Duffing spring, previously analyzed numerically by Hung and Senturia, and captures the variations of the pull-in parameters in the continuum between a perfectly linear spring and a cubic spring. Several other case studies are described and analyzed using the pull-in equation, including parallel-plate and tilted-plate (torsion) actuators taking into account the fringing field capacitance, feedback and parasitic capacitance, trapped charges, an external force, and large displacements     

Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.     

Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam

Analyzing the dynamic response of electrostatic devices is problematic due to the complexity of the interactions between the electrostatic coupling effect, the fringing field effect and the nonlinear electrostatic force. To resolve this problem, this study presents an efficient computational scheme in which the nonlinear governing equation of the electrostatic device is obtained in accordance with Hamilton’s principle and is then solved using a hybrid differential transformation/finite difference method. The feasibility of the proposed approach is demonstrated by modeling the dynamic responses of two micro fixed-fixed beams with lengths of 250 and 350 μm, respectively. The numerical results show that the pull-in voltage reduces as the beam length increases due to a loss in the structural rigidity. Furthermore, it is shown that the present results for the pull-in voltage deviate by no more than 0.75% from those derived in the literature using a variety of different schemes. Overall, the results presented in this study demonstrate that the proposed hybrid method represents a computationally efficient and precise means of obtaining detailed insights into the nonlinear dynamic behavior of micro fixed-fixed beams and similar micro-electro-mechanical systems (MEMS)-based devices.     

Row/Column Addressing Scheme for Large Electrostatic Actuator MEMS Switch Arrays and Optimization of the Operational Reliability by Statistical Analysis

This paper investigates the design and optimization of a row/column addressing scheme to individually pull in or pull out single electrostatic actuators in an N² array, utilizing the electromechanical hysteresis behavior of electrostatic actuators and efficiently reducing the number of necessary control lines from N² complexity to 27 V. This paper illustrates the principle of the row/column addressing scheme. Furthermore, it investigates the optimal addressing voltages to individually pull in or pull out single actuators with maximum operational reliability, determined by the statistical parameters of the pull-in and pull-out characteristics of the actuators. The investigated addressing scheme is implemented for the individual addressing of cross-connect switches in a microelectromechanical systems 20 X 20 switch array, which is utilized for the automated any-to-any interconnection of 20 input signal line pairs to 20 output signal line pairs. The investigated addressing scheme and the presented calculations were successfully tested on electrostatic actuators in a fabricated 20 X 20 array. The actuation voltages and their statistical variations were characterized for different subarray cluster sizes. Finally, the addressing voltages were calculated and verified by tests, resulting in an operational reliability of 99.9498% (502 parts per million (ppm) failure rate) for a 20 X 20 switch array and of 99.99982% (1.75 ppm failure rate) for a 3 X 3 subarray cluster. The array operates by AC-actuation voltage to minimize the disturbing effects by dielectric charging of the actuator isolation layers, as observed in this paper for DC-actuation voltages.     

A rotary comb-actuated microgripper with a large displacement range

This paper reports a novel design for electrostatic microgrippers. The new structure utilizes rotary comb actuators to solve the pull-in problem of microgrippers during large displacement manipulation and therefore avoids the widely used conversion systems which necessitate a high driving voltage. The gripper is fabricated using a SOI process with a 60 μm structural layer. Test results show the gripper obtained a displacement of 94 μm with an applied voltage of 100 V. An animal hair is gripped to demonstrate the applicability of the gripper for micro object manipulations.     

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.     

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.     

Closed-form empirical relations to predict the static pull-in parameters of electrostatically actuated microcantilevers having linear width variation

We develop novel closed-form empirical relations to estimate the static pull-in parameters of electrostatically actuated tapered width microcantilever beams. A computationally efficient single degree-of-freedom model is employed in the setting of Ritz energy technique to extract the static pull-in parameters of the distributed electromechanical model that takes into account the effects of fringing field capacitance. The accuracy of this single-dof model together with the variable-width equivalent of the Palmer’s fringing model is established through a comparison with 3D finite element simulations. A unique surface fitting model is proposed to characterize the variations of both the pull-in displacement and pull-in voltage, over a realistically wide range of system parameters. Optimum coefficients of the proposed surface fitting model are obtained using nonlinear regression analysis. Empirical estimates of pull-in parameters are validated against finite element simulations, and available experimental and numerical data. An excellent agreement indicates that the proposed relationships are sufficiently accurate to be safely used for the electromechanical design of tapered microcantilever beams.     

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     

Position control of parallel-plate microactuators for probe-based data storage

In this paper, we present the use of closed-loop voltage control to extend the travel range of a parallel-plate electrostatic microactuator beyond the pull-in limit. Controller design considers nonlinearities from both the parallel-plate actuator and the capacitive position sensor to ensure robust stability within the feedback loop. Desired transient response is achieved by a pre-filter added in front of the feedback loop to shape the input command. The microactuator is characterized by static and dynamic measurements, with a spring constant of 0.17 N/m, mechanical resonant frequency of 12.4 kHz, and effective damping ratio from 0.55 to 0.35 for gaps between 2.3 to 2.65 /spl mu/m. The minimum input-referred noise capacitance change is 0.5 aF//spl radic/Hz measured at a gap of 5.7 /spl mu/m, corresponding to a minimum input-referred noise displacement of 0.33 nm//spl radic/Hz. Measured closed-loop step response illustrates a maximum travel distance up to 60% of the initial gap, surpassing the static pull-in limit of one-third of the gap.     

Design, fabrication, and control of MEMS-based actuator arrays for air-flow distributed micromanipulation

This paper reports the design, fabrication and control of arrayed microelectromechanical systems (MEMS)-based actuators for distributed micromanipulation by generation and control of an air-flow force field. The authors present an original design of pneumatic microactuator, improving reliability and durability of a distributed planar micromanipulator described in the previous study. The fabrication process is based on silicon-on-insulator (SOI) wafer and HF (hydroflouric acid) vapor release, which also significantly increases the production yield of the 560 microactuator array device of 35/spl times/35 mm/sup 2/. Minimization of the electrostatic actuation pull-in voltage through suspension shaping fabrication was also studied, and successfully validated for electrical efficiency improvement. A distributed control method to achieve good conveyance performance and reduce motion control instability was investigated. An emulation approach was chosen to validate a decentralized control strategy on the distributed active surface in order to conduct a proof-of-concept of a future smart structure, integrating sensors, intelligence, and microactuators. Thus, a centralized/decentralized control flow, inspired by autonomous mobile robot principles, was applied. It was modeled and implemented using C-programming language. Experimental and characterization results validate the control method for feedback micromanipulation with good velocity and load capacity performance.     

MEMS薄膜弹性模量及残余应力提取的数值算法

材料弹性模量、残余应力的在线提取,已成为MEMS领域中日益迫切的需要。文中首先简要介绍现有的一些主要的材料参数提取方法,然后提出了一种无需静电作用下两端固支梁吸合电压的显式解析表达式,而是利用决定静电作用固支梁弯曲挠度的微分方程直接计算吸合电压,再提取材料参数的算法。避免了在推导吸合电压的显式表达式过程中可能引入的误差,有利于保证材料参数测量的精度。模拟结果表明这种算法速度快、精度高,对实际应用有较好的参考价值。     

A Model for Electrostatic Actuation in Conducting Liquids

This paper presents a generalized model that describes the behavior of micromachined electrostatic actuators in conducting liquids and provides a guideline for designing electrostatic actuators to operate in aqueous electrolytes such as biological media. The model predicts static actuator displacement as a function of device parameters and applied frequency and potential for the typical case of negligible double-layer impedance and dynamic response. Model results are compared to the experimentally measured displacement of electrostatic comb-drive and parallel-plate actuators and exhibit good qualitative agreement with experimental observations. The model is applied to show that the pull-in instability of a parallel-plate actuator is frequency dependent near the critical frequency for actuation and can be eliminated for any actuator design by tuning the applied frequency. In addition, the model is applied to establish a frequency-dependent theoretical upper bound on the voltage that can be applied across passivated electrodes without electrolysis.     

Static and electrically actuated shaped MEMS mirrors

A novel digitally-actuated shaped micromirror for on-off optical switch applications is described. Reflective static spherical mirrors were designed and fabricated using conventional surface micromachining and the MultiPoly process, a technique for depositing multilayers of LPCVD polysilicon in order to control the overall stress and stress gradient. The resulting mirrors were measured to have radii of curvature of approximately 9 mm in agreement with design predictions. Based upon these static mirrors, an actuatable micromirror (diameter=500 /spl mu/m, static radius curvature=6.4 mm) was designed for snap action. This mirror was simulated using an electromechanical coupled-field model and fabricated using the MultiPoly process. Its performance was measured dynamically using an interferometer. A curved-to-flat digital actuation of the mirror was successfully achieved with a pull-in voltage of 38 V.     

Solution of nonlinear pull-in behavior in electrostatic micro-actuators by using He’s homotopy perturbation method

The work presented here is about the nonlinear pull-in behavior of different electrostatic micro-actuators. He’s homotopy perturbation method (HPM) is applied to solve different types of micro-actuators like Fixed–Fixed beam and Cantilever beam actuators. Simulated results are presented for further analysis. Also the obtained results compare well with the literature.     

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.