Electrostatic Microactuators Research Articles

Repetitive control of an electrostatic microbridge actuator: theory and simulation

Electrostatic microactuators are used extensively in MEMS sensors, RF switches andmicrofluidic pumps. The high bandwidth operation required by these applicationscomplicates the implementation of feedback controllers. This paper designs, proves stabilityand simulates a feedforward repetitive controller for an electrostatic microbridge.High residual stress creates tension in the microbridge that dominates bendingstiffness so a pinned string model with uniform electrostatic force loading is used formodel-based control. The control objective is to force the microbridge displacement tofollow prescribed spatial and periodic time trajectories. Viscous damping ensuresboundedness of the distributed transverse displacement in response to boundedinputs. The average displacement is measured by capacitive sensing and processedoffline using a repetitive control algorithm that updates a high speed waveformgenerator’s parameters. Simulations show that the performance depends on theamount of damping. With less than 1% damping in a representative microbridgestructure, repetitive control reduces the midspan displacement overshoot by 83%.

Material selection for electrostatic microactuators using Ashby approach

Due to variety of materials available to any designer for a particular application, there is a need for a proper technique to select. This paper focuses on the optimum selection of materials for electrostatic microactuators using Ashby approach. In this work, performance indices and material indices have been developed for electrostatic actuators and thereafter material selection chart is plotted. The selection chart shows that for high actuation voltage and high actuation force, diamond is the best possible candidate followed by silicon carbide and silicon nitride. On the other hand, if high speed electrostatic actuator is desired, then aluminum is the best possible candidate followed by nickel and copper.

A Versatile Integration Technology of SOI-MEMS/CMOS Devices Using Microbridge Interconnection Structures

In this paper, a versatile integration technology for thick-film silicon-on-insulator microelectromechanical systems (SOI-MEMS) devices with CMOS electronics using novel microbridge interconnections is reported. The microbridge interconnection proposed in this paper solves the problem regarding the electrical isolation and interconnection between CMOS and SOI-MEMS devices. The integration of SOI-MEMS requires only three additional photolithography steps for the CMOS wafers fabricated by a standard process. On the basis of the developed technology, SOI-MEMS devices integrated with CMOS circuits were fabricated using 20-μm-thick SOI wafers. No significant damage was observed in the measured characteristics of the fabricated CMOS after the integration of MEMS devices. In addition, the electrical isolation of SOI-MEMS from the CMOS substrate was successfully realized and confirmed in the experiment, keeping electrical connectivity between CMOS circuit terminals. The measured isolation resistance between MEMS and the CMOS substrate was more than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> Ω, and a proof voltage above 60 Vdc was observed. These values guarantee a small leakage current and a sufficient voltage swing for driving electrostatic microactuators. On the other hand, the resistance of the interconnection over a microbridge structure was below 1 Ω, which is sufficiently low for integrating low-noise microsensors. This integration technology can be used in realizing monolithically integrated SOI-MEMS sensor and actuator devices with high-aspect-ratio structures using the most cost-effective and versatile CMOS fabrication technologies.

MEMS-Based Micro-Electro-Discharge Machining (M$^{3}$ EDM) by Electrostatic Actuation of Machining Electrodes on the Workpiece

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper reports a micro-electro-discharge machining technique that is enabled by electrostatic microactuators. The 18-<formula formulatype="inline"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula>-thick movable copper electrodes that serve as machining tools are microfabricated directly on the surfaces of the workpiece and operated in dielectric machining fluid. A dc voltage of 80–140 V applied between the electrode and the workpiece through a resistance–capacitance pulse generation circuit is leveraged to electrostatically pull in the electrodes toward the workpiece, inducing a breakdown and spark discharge. The discharge lowers the gap voltage and releases the electrode, which is pulled in again as the capacitor is recharged through the resistor. This pull-in and discharge cycle is self-sustained to perform the removal of the workpiece material. The electrode's displacement of <formula formulatype="inline"><tex Notation="TeX">$\sim\!\! 30\ \mu\hbox{m}$</tex></formula> is measured at the machining/actuation voltage of 100 V. Micromachining of stainless steel is implemented using the planar electrode with <formula formulatype="inline"><tex Notation="TeX">$1.6 \times 1.03\hbox{-mm}^{2}$</tex></formula> area, achieving the removal depth of 20 <formula formulatype="inline"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula>. The double-layer electrodes that have electroplated microstructures with high-contrast patterns on the backside of the electrodes are developed to demonstrate custom micromachining. A dynamic characteristic of the built-in capacitance of the devices, which is used to form the pulse generation circuit, as well as their mechanical response during the machining process, is theoretically analyzed with the experimental results.<formula formulatype="inline"><tex Notation="TeX">$\hfill$</tex></formula> [2008-0299] </para>

Emerging Challenges of Microactuators for Nanoscale Positioning, Assembly, and Manipulation

The development of manufacturing tools and processes capable of precisely positioning and manipulating nanoscale components and materials is still in its embryonic stage. Microactuators are emerging as important tools capable of precisely positioning and manipulating nanoscale components and materials. This paper provides a summary of the state-of-the-art in the design, fabrication, and application of microactuators for nanoscale manufacturing and assembly. Key characteristics and design models of electrothermal and electrostatic microactuators are described and compared. Specific design requirements for their functionality at the nanoscale are discussed. The results demonstrate the limitations of existing microactuator designs and key challenges associated with their design, modeling, and performance characterization for nanoscale positioning, assembly, and manipulation.

Nonlinear Analysis of MEMS Electrostatic Microactuators: Primary and Secondary Resonances of the First Mode*

We use a discretization technique that combines the differential quadrature method (DQM) and the finite difference method (FDM) for the space and time, respectively, to study the dynamic behavior of a microbeam-based electrostatic microactuator. The adopted mathematical model based on the Euler— Bernoulli beam theory accounts for the system nonlinearities due to mid-plane stretching and electrostatic force. The nonlinear algebraic system obtained by the DQM—FDM is used to investigate the limit-cycle solutions of the microactuator. The stability of these solutions is ascertained using Floquet theory and/or long-time integration. The method is applied for large excitation amplitudes and large quality factors for primary and secondary resonances of the first mode in case of hardening-type and softening-type behaviors. We show that the combined DQM—FDM technique improves convergence of the dynamic solutions. We identify primary, subharmonic, and superharmonic resonances of the microactuator. We observe the occurrence of dynamic pull-in due to subharmonic and superharmonic resonances as the excitation amplitude is increased. Simultaneous resonances of the first and higher modes are identified for large orbits in both primary and secondary resonances.

Dynamics and Global Stability of Beam-based Electrostatic Microactuators

We investigate the dynamics and global stability of a beam-based electrostatic microactuator, which is modeled as a first-order approximation of a reduced-order model (ROM) derived using the differential quadrature method (DQM). We show that the ROM dynamics is qualitatively similar to that of a higher-order approximation. We simulate the occurrence of dynamic pull-in for excitations near the first primary resonance using the finite difference method (FDM) and long-time integration. Limit-cycle solutions are obtained using the FDM, the generated frequency- and force-response curves exhibit cyclic-fold, saddle-node, and period-doubling bifurcations. We verify that symmetry breaking is not likely to occur because the orbit is already asymmetric. We identify the basin of attraction of bounded motions using various approximation levels. The simulations reveal that the erosion of the basin of attraction depends heavily on the amplitude and frequency of the AC voltage. We show that smoothness of the boundary of the basin of attraction can be lost and replaced by fractal tongues, which dramatically increase the sensitivity of the microbeam to initial conditions. According to these simulations, the locations of the two fixed points are likely to be disturbed.

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.

Approximating the effect of the Casimir force on the instability of electrostatic nano-cantilevers

In this paper, the homotopy perturbation method (HPM) is used to investigate the effect of the Casimir force on the pull-in instability of electrostatic actuators at nano-scale separations. The proposed HPM is employed to solve nonlinear constitutive equations of cantilever beam-type nanoactuators. An analytical solution is obtained in terms of convergent series with easily computable components. Basic design parameters such as critical cantilever tip deflection and pull-in voltage of the nano-cantilevers are computed. As special cases of this work, freestanding nanoactuators and electrostatic micro-actuators are investigated. The analytical HPM results agree well with numerical solutions and those from the literature.

Modeling and Gain Scheduling Design for an Electrostatic Micro-Actuator with Squeezed Film Damping Effects

In the present article the modeling approach and the control design aspects of an electrostatic microactuator (EmA) under the effect of squeezed film damping are presented. The model of the system accounts for an EmA composed by a set of two plates. The bottom plate is clamped to the ground, while the moving plate is driven by an electrically induced force which is opposed by the force exerted by a spring element. The nonlinear model of the EmA is linearized at various operating points, and the feedforward compensator provides the nominal voltage. Subsequently a gain scheduled H∞ controller is used to tune the controller-parameters depending on the EmAs operating conditions. The controller is designed at various operating points based on the distance between the two plates. The controllers parameters are tuned in an optimal manner and are computed via the use of the Linear Matrix Inequalities. Special attention has been paid in order to examine the properties of the EmA regarding the bifurcations points. Finally, numerous simulation cases are presented in order to prove the efficacy of the presented controller.

Development of polymer electrostatic comb-drive actuator using hot embossing and ultraprecision cutting technology

We report the fabrication and evaluation of a PMMA electrostatic comb-drive microactuator using hot embossing and ultra-precision cutting technology. First, a two-step silicon mold is fabricated by bulk micromachining technology. Next, comb-drive microactuator structures are formed on a PMMA plate by hot embossing. Both finger width and gap between fingers are 5 µm, and finger thickness is larger than 70 µm. Then, the PMMA layer that remained after hot embossing is removed by ultra-precision cutting to release the movable parts. Last, the device is coated with a gold layer for the electrode. The PMMA comb-drive microactuator has been tested successfully.

A rotary microactuator supported on encapsulated microball bearings using an electro-pneumatic thrust balance

The development of a rotary microactuator supported on encapsulated microball bearings and driven by electro-pneumatic actuation is reported. The encapsulated bearing provides full support to an encased rotor, while an electro-pneumatic thrust balance is used to minimize rotor normal load. By minimizing normal load, bearing friction is reduced leading to increased speed and performance. Experimental results show that the microactuator is capable of repeatable operation and continuous 360° motion at speeds of 5–2000 rpm. This is the first demonstration of a ball bearing supported electrostatic microactuator with a fully encased rotor, capable of direct mechanical attachment or reliable interaction with external media.

Submicrometer Comb-Drive Actuators Fabricated on Thin Single Crystalline Silicon Layer

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Electrostatic comb-drive microactuators were fabricated by electron beam lithography on a 260-nm-thick silicon layer of a silicon-on-insulator wafer. The actuators consisted of comb electrodes, springs, and a frame. Two kinds of microactuators with doubly clamped and double-folded springs were designed and fabricated. The comb electrode was as small as 2.5 <formula formulatype="inline"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> wide and 8 <formula formulatype="inline"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> long and was composed of 250-nm-wide, 260-nm-thick, and 2-<formula formulatype="inline"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula>-long fingers. The air gap between the fingers was 350 nm. The spring was 250 nm wide, 260 nm thick, and 17.5 <formula formulatype="inline"><tex Notation="TeX">$\mu\hbox{m}$</tex> </formula> long, and the spring constant was 0.11 N/m. The force and displacement generated by the microactuator were <formula formulatype="inline"><tex Notation="TeX">$2.3 \times 10^{-7} \ \hbox{N}$</tex></formula> and 1.0 <formula formulatype="inline"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula>, respectively. Applying an ac voltage, the oscillation amplitude became maximum at a frequency of 132 kHz. The mechanical and electrical characteristics of the fabricated actuators were investigated quantitatively. </para>

Pitch-variable blazed grating consisting of freestanding silicon beams

Theoretical analysis is presented for a pitch-variable blazed grating which consists of freestanding silicon beams. The pitch-variable blazed grating is implemented by combining silicon-on-insulator (SOI) technology with microelectronicmechanical system (MEMS) technology. The whole device is fabricated on a 10 microm silicon device layer to guarantee sufficient stiffness. The 4-level blazed surface profile is realized by combining a two-mask process with fast atom beam etching. Electrostatic combdrive microactuators with double folded springs are proposed to stretch the freestanding grating beams. In association with reactive ion etching and vapor HF release, the freestanding grating beams and the microactuators are obtained, and a Cr/Au film is deposited onto the blazed grating surfaces by a protective mask process to improve the diffracted power. Mechanical response and diffraction efficiency of fabricated devices are characterized and the experimental results indicate that the fabricated 4- level blazed gratings extend both the tuning range and the diffraction efficiency of the 1st diffraction order of present MEMS diffraction gratings.

Robust adaptive tracking control of uncertain electrostatic micro-actuators with H-infinity performance

A novel adaptive robust tracking control scheme is proposed for a class of single-degree-of-freedom (1DOF) electrostatic micro-actuator systems in the presence of parasitics, parameter uncertainties and external disturbances. This method integrates the adaptive dynamic surface control and H-infinity control techniques. Based on this method, both the design procedure and the derived tracking controller itself are simplified, and the controller guarantees that the output tracking error satisfies the H-infinity tracking performance. In addition, the tracking accuracy can be adjusted by an appropriate choice of the design parameters of the controller. Simulation results show that prescribed transient output tracking performance can be achieved, and the closed-loop system exhibits good robustness to system uncertainties.

Adaptive Control of Electrostatic Microactuators With Bidirectional Drive

In this paper, adaptive control is presented for a class of single-degree-of-freedom (1DOF) electrostatic microactuator systems which can be actively driven bidirectionally. The control objective is to track a reference trajectory within the air gap without knowledge of the plant parameters. Both full-state feedback and output feedback schemes are developed, the latter being motivated by practical difficulties in measuring velocity of the moving plate. For the full-state feedback scheme, the system is transformed to the parametric strict feedback form, for which adaptive backstepping is performed to achieve asymptotic output tracking. Analogously, the output feedback design involved transformation to the parametric output feedback form, followed by the use of adaptive observer backstepping to achieve asymptotic output tracking. To prevent contact between the movable and fixed electrodes, special barrier functions are employed in Lyapunov synthesis. All closed-loop signals are ensured to be bounded. Extensive simulation studies illustrate the performance of the proposed control.

Microfriction analysis of novel two-dimensional electrostatic comb device

Constructed by a two-dimensional micro-electrostatic comb actuator fabricated by bulk micromachined process, a novel test device on chip was designed to study the phenomena of the microfrictions in the side wall between movable micro-electromechanical system elements. The general analytic expressions of the applied voltages, displacement, the static friction coefficient and the geometry parameters were established. It was found that the displacement was linear to Uy2, so the friction coefficient could be obtained by fitting them. And larger nb and l2 could help to decrease Uy and to increase the displacement.

A Robustness Approach for Handling Modeling Errors in Parallel-Plate Electrostatic MEMS Control

This paper addresses the control of electrostatic parallel-plate microactuators in the presence of such modeling errors as unmodeled fringing field effect and deformations. In general, accurate descriptions of these phenomena often lead to very complicated mathematical models, while ignoring them may result in significant performance degradation. In this paper, it is shown by finite-element-method-based simulations that the capacitance due to fringing field effect and deformations can be compensated by introducing a variable serial capacitor. When a suitable robust controller is used, the full knowledge of the introduced serial capacitor is not required, but merely its boundaries of variation. Based on this model, a robust control scheme is derived using the theory of input-to-state stability combined with backstepping state feedback design. Since the full state measurement may not be available under practical operational conditions, an output feedback control scheme is developed. The stability and performance of the system using the proposed control schemes are demonstrated through both stability analysis and numerical simulation. The present approach allows the loosening of the stringent requirements on modeling accuracy without compromising the performance of control systems.

A Low-Voltage Large-Displacement Large-Force Inchworm Actuator

Inchworm microactuators are popular in micropositioning applications for their long ranges. However, until now, they could not be considered for applications such as in vivo biomedical applications because of their high input voltages. This paper reports on the modeling, design, fabrication, and testing of a new family of pull-in-based electrostatic inchworm microactuators which provides a solution to this problem. Actuators with only 7-V operating voltage are achieved with a plusmn18-mum total range and a plusmn30-muN output force. Larger operating voltage (16 V) actuators show even better results in force (plusmn110 muN) and range (plusmn35 mum). The actuator has an in-plane angular deflection conversion which provides a force-displacement tradeoff and allows us to set step sizes varying from few nanometers to few micrometers with a minor change in design. In this paper, we designed 1- and 4-mum step-size devices. The actuator step size may change during the operation because of the slipping of the shuttle and the beam bending; however, our model successfully explains the reasons. One of our actuator prototypes has survived more than 25 million cycles without performance deterioration. The device is fabricated using the silicon-on-insulator-based multiuser MEMS process.

Innovative Numerical Methods for Nonlinear MEMS:\\ the Non-Incremental FEM vs. the Discrete Geometric Approach

Electrostatic microactuator is a paradigm of MEMS. Cantilever and double clamped microbeams are often used in microswitches, microresonators and varactors. An efficient numerical prediction of their mechanical behaviour is af- fected by the nonlinearity of the electromechanical coupling. Sometimes an addi- tional nonlinearity is due to the large displacement or to the axial-flexural coupling exhibitedin bending. To overcome thecomputationallimitsoftheavailablenumer- ical methods two new formulations are here proposed and compared. Modifying the classical beam element in the Finite Element Method to allow the implemen- tation of a Non incremental sequential approach is firstly proposed. The so-called Discrete Geometric Approach (DGA), already successfully used in the numerical analysis of electromagnetic problems, is then applied. These two methods are here formulated, for the first time, in the case of strongly nonlinear electromechanical coupling. Numerical investigations are performed to find the pull-in of microbeam actuators experimentally tested. The non incremental approach is implemented by discretizing both the structure and the dielectric region by means of the FEM, then by meshing the electric domain by the Boundary Element Method (BEM). A preliminary experimental validationis finally presented in the case ofplanar micro- cantilever actuators.