Size effect on the static behavior of electrostatically actuated microbeams

We present a new analytical model for electrostatically actuated microbeams to explore the size effect by using the modified couple stress theory and the minimum total potential energy principle. A material length scale parameter is introduced to represent the size-dependent characteristics of microbeams. This model also accounts for the nonlinearities associated with the mid-plane stretching force and the electrostatical force. Numerical analysis for microbeams with clamped-clamped and cantilevered conditions has been performed. It is found that the intensity of size effect is closely associated with the thickness of the microbeam,and smaller beam thickness displays stronger size effect and hence yields smaller deffection and larger pull-in voltage. When the beam thickness is comparable to the material length scale parameter,the size effect is significant and the present theoretical model including the material length scale parameter is adequate for predicting the static behavior of microbeam-based MEMS.

Analytical modeling of static behavior of electrostatically actuatednano/micromirrors considering van der Waals forces

In this paper, the effect of van der Waals （vdW） force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum po- tential energy principle is utilized to find the equation gov- erning the static behavior of nano/micromirror under electro- static and vdW forces. Then, the stability of static equilib- rium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of dif- ferent design parameters on the mirror＇s pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the mirror. At the end, the nonlinear equilibrium equation is solved numer- ically and analytically using homotopy perturbation method （HPM）. It is observed that a sixth order perturbation approx- imation can precisely model the mirror＇s behavior. The re- suits of this paper can be used for stable operation design and safe fabrication of torsional nano/micro actuators.

A 16×16 Micro Mirror Array for Optical Switches

This paper reports on the design, fabrication,and performance of a high-reflectivity large-rotation mirror array for MEMS （micro-electro-mechanical system） 16 × 16 optical switches. The mirror in the array can enlarge its rotation an- gles up to 90° and keep a steady state to steer the optical signal. According to the large-rotation behavior, an electro- mechanical model of the mirror is presented. By monolithic integration of fiber grooves and mirrors fabricated by a sur- face and bulk hybrid micromachining process, the coarse passive alignment of fiber-mirror-fiber can be achieved. The re- flectivity of the mirror is measured to be 93.1% ~96.3%. The switches demonstrate that the smallest fiber-mirror-fiber insertion loss is 2. ldB using OptiFocusTM collimating lensed fibers. Moreover,only about ＋- 0.01dB oscillating amplitude of insertion loss is provoked after the device is tested for 15min for 5-90Hz in the vertical vibration amplitude of 3mm.

Electrostatic Actuating Bendable Flat Electrode for Micro Electrochemical Machining

In micro-electrochemical machining(μECM), material dissolution takes place at very close vicinity of tool electrode due to localization of electric field. Controlling the gap between tool electrode and workpiece is the key to μECM. Therefore, a new method is proposed to solve a variety of problems in small gap control. In the present context, experiments were carried out with an indigenously developed setup to fabricate cylindrical arrays. During the machining process, the flat electrode bends due to electrostatic force in pulse on-time, which self-adaptively narrows the gap between the electrode and the workpiece. The workpiece material will be removed once the gap meets the processing condition. Therefore, this method has advantages of reducing dependence on high precision machine tools and of avoiding complex servo control. The flat electrode quickly restores to its original condition when it is in pulse off-time, making the gap much larger than that in traditional electrochemical machining(ECM). The large gap benefits debris removing, which improves the machining accuracy. The influence of different experimental parameters on accuracy and efficiency during the machining process has been investigated. It is observed that with the increase in applied voltage or concentration of electrolyte, the material removal rate and the process gap both increase. The detailed analysis of the experimental results is described in this paper.

Suppression of chaos in a MEMS resonator by delayed position feedback

A delayed position feedback control is applied on DC of a typical MEMS resonator actuated by electrostatic forces voltage source for suppressing chaos A theoretical necessary condition for chaotic oscillation of the controlled system is presented. Numerical results and the analytical prediction reveal the evolution of dynamical behavior of the system with AC voltage amplitude and the control effect of delayed feedback on reducing chaos of the system. It shows that the delayed feedback control is effective on suppressing chaos of the micro mechanical resonator.

Macro Model Study for Nonlinear Spring of Tense Torsion Bar in Gap-Closing Type Electrostatic Micromirror

Nonlinear spring characteristics of the tense torsion bar in the gap-closing type electrostatic micromirror are examined. The macro model is introduced for the experimental study. The tension applied in the torsion bar is well controlled using the electromagnetic attraction. This controllability is suited for clearing the nonlinear nature. The tension is confirmed to have the effect to widen the controllable angle range of the mirror suppressing the pull-in. The pull-in angle is observed to increases to about 74% of the mechanical limit angle at the tension of 0,96 N. This is significantly larger than 44% of the case with the linear spring. The larger resonant frequency is maintained. The hardening of the spring can keep the balance with the electrostatic force over the limit of the linear spring. The observed features are explained reasonably with the combination of twisting and bending displacements of the torsion bar.

A Silicon Integrated Micro Positioning xy-Stage for Nano-Manipulation

An integrated micro positioning xy-stage with a 2mm × 2mm-area shuttle is fabricated for application in nano- meter-scale operation and nanometric positioning precision. It is mainly composed of a silicon-based xy-stage,electrostatics comb actuator,and a displacement sensor based on a vertical sidewall surface piezoresistor. They are all in a monolithic chip and developed using double-sided bulk-micromachining technology. The high-aspect-ratio comb-driven xy-stage is achieved by deep reactive ion etching （DRIE） in both sides of the wafer. The detecting piezoresistor is located at the vertical sidewall surface of the detecting beam to improve the sensitivity and displacement resolution of the piezoresistive sensors using the DRIE technology combined with the ion implantation technology. The experimental results verify the integrated micro positioning xy-stage design including the micro xy-stage, electrostatics comb actuator,and the vertical sidewall surface piezoresistor technique. The sensitivity of the fabricated piezoresistive sensors is better than 1.17mV/μm without amplification and the linearity is better than 0. 814%. Under 30V driving voltage, a ± 10vm single-axis displacement is measured without crosstalk and the resonant frequency is measured at 983Hz in air.

Dynamics of Droplets of Biological Fluids on Smooth Superhydrophobic Surfaces under Electrostatic Actuation

This study describes the dynamic behaviour of droplets of biological liquids on hydrophobic surfaces under electrostatic actuation, to devise sample handling in lab-on-chip diagnostic tools. Bovine Serum Albumin （BSA） is taken as a representative biomolecule, since it is often used in adsorption studies. Green Fluorescence Protein （GFP） is also considered, given its natural fluorescence. Several effects such as sample concentration and pH are discussed. The results show negligible effects of proteins concentration in electrowetting, although increased concentrations endorse passive adsorption mechanisms, which alter the local wettability of the substrates precluding droplet motion. Bioinspired surfaces promote the largest spreading diameter, which is beneficial for droplet motion. However, surface roughness promotes energy dissipation limiting the receding droplet motion. Hence, the most effective approach is altering the surface chemistry. The coating is applied to a surface with a mean roughness smaller than 20 nm and does not alter significantly the topography, thus leading to the so-called smooth superhydrophobic surface. This coating also reduces passive proteins adsorption, as confirmed by Confocal Microscopy （CM）, which is beneficial for droplet motion. Evaluating absorption spectra of protein solutions evidences an increase in protein concentration ascribed to droplet evaporation as confirmed by theoretical analysis and time resolved infrared visualization.

Design and Fabrication of Micromechanical Optical Switches Based on the Low Applied Voltage

A micromechanical optical switch driven by electrostatic was fabricated with (100) silicon and tilted 2.5° (111) silicon. The pull-in voltage is 13.2V, the insertion loss is less than 1.4dB, the crosstalk is less than -50 dB.

Application of Modified Couple Stress Theory and Homotopy Perturbation Method in Investigation of Electromechanical Behaviors of Carbon Nanotubes

The paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method.Due to the less accuracy of the classical elasticity theorems,the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes.Both of the static and dynamic behaviors under static DC and step DC voltages are discussed.The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.