Electrostatic Cantilever Research Articles

Self-excited MEMS Oscillator using an Electrostatic Cantilever

In this paper, we propose a new use of an electrostatic MEMS cantilever structure as a voltage-controlled oscillator (VCO). A cantilever made of plated gold is accompanied with a drive electrode to turn on the contact switch upon voltage application. The electrical interconnection is arranged to discharge the cantilever when it is brought into contact with the switch, thereby promptly losing the electrostatic force and opening the contact switch again. As a result, the electrostatic cantilever spontaneously repeats the electrostatic pull-in and release at a frequency determined by the DC level of the applied voltage. A metallic cantilever of 500 μm long, 8 μm wide, and 12 μm thick is experimentally confirmed to work as an VCO in the frequency range between 8.4 kHz and 10.7 kHz controlled by the DC voltage between 160V and 180V.

Stepwise Actuation of an Electrostatic Bimorph Cantilever Actuator Using a Patterned Bottom Electrode

The electrostatic actuation method has not been used widely in bimorph cantilevers despite its advantage of large displacement and low power consumption, mostly owing to the fact that it is limited to just two stable positions: 1) initial curled; and 2) final flat positions. In this paper, we first demonstrate a bimorph cantilever actuator having multiple steady-state positions in between those two boundary positions, accomplished by simply dividing the bottom electrode. We found that the number of steady-state positions and the steady-state tip heights can be controlled by the design of the bottom electrode. In our test experiment, the steady-state bimorph cantilever tip heights were 48 $\mu \text{m}$ at 0 V, 28 $\mu \text{m}$ at 21 V, 7 $\mu \text{m}$ at 25 V, and 0 $\mu \text{m}$ (flat) at 29 V, respectively. In order to relieve low reliability of the electrostatic bimorph cantilever, we devised non-contact actuation method and demonstrated that the lifetime of the electrostatic bimorph actuator greatly increased. This paper will pave the way to utilize bimorph cantilever actuators with greater versatility. [2016-0081]

Frequency and displacement analysis of electrostatic cantilever-based MEMS sensor

In this work we present behavior level modeling to predict the frequency and displacement of electrostatic cantilever based microelectromechanical system sensor for mass detection. Linear time invariant (LTI) technique is used to study the linear and nonlinear behavior of the device. The shift in resonance frequency in damped and undamped medium is formulated by using the conception of dynamic mass and law of identity. First a complete analytical model is developed by coupling electrostatic force with the bending moment of cantilever to produce vertical actuation at a resonance frequency. Then displacement of the cantilever is correlated with piezoresistive mechanism for mass sensing. We assumed mass of blood cells as the external load on cantilever tip which results in shift in resonance frequency. Simulink tool is used to develop the LTI model that is based on electromechanical coupling of linear and nonlinear equations. The same device is then designed using COMSOL tool and FEM analysis is performed. For validation, the analytical results are compared with the FEM simulations.

Design and fabrication of MEMS based electrostatic cantilever as ultrasonic signal generator

This paper presents the design and fabrication of a 500μm×200μm×0.070μm micro-cantilever as ultrasonic frequency generator. Actuation energy (up to 4.1V dc) after fixed intervals was necessary to produce stable oscillations. The device relies on the principle of electrostatic effect and the output in the form of low ultrasonic frequency signal is generated from the piezoelectric surface (ZnO) due to switching action. The dimensions of the proposed device are first optimized by modeling and the same design is then fabricated and characterized as high frequency signal generator. From the results, a huge difference between the simulated (22.67kHz) and experimental (30.76kHz) output signals has been found out. This may be caused due to a propagation delay and slow switching action in fabricated device. This work may be useful as an electrostatic micro-switch where low actuation dc voltage is needed to generate ultrasound signals.

Pull-in Voltage Study of Various Structured Cantilever and Fixed-Fixed Beam Models using COMSOL Multiphysics

The present work involves the study of pull-in voltage of MEMS electrostatic Cantilever beam, Fixed-Fixed beam and modified beam structures with perforations of square, rectangular and circular shapes. The analysis is done using COMSOL 4.3 software. The dimensions of the Cantilever beam, Fixed-Fixed beam and three various structured beams modeled in this paper are length = 300 μm, width = 50 μm, thickness = 3 μm and gap between top electrode and ground plane is 2.5 μm. The pull-in voltage obtained for Cantilever beam is 17.6 V and for Fixed-Fixed beam is 118.8 V. For the modified models with square, rectangular and circular perforations are 12.18 V, 15.45 V and 13.75 V respectively. The results of the work demonstrate an ability to achieve lower pull-in voltage levels for three various structured beams modeled in this paper when compared to cantilever and Fixed-fixed beams. The dependence of the pull-in voltage on geometrical parameters, thrusts on stringent design considerations even at the initial stages.

Design and fabrication of electrostatic micro-cantilever array as audible frequency generator

Abstract In assistive technologies involving voice communication, an audio signal with specific shape is needed. In this regard, the design and fabrication of an electrostatic cantilever array is proposed. An array of four metallic micro-cantilevers with dimensions 650 μm × 200 μm × 0.3 μm is fabricated on the silicon substrate. The working principle is based on the electrostatic effect generated due to a conductive path applied between the electrodes. The results are taken from zinc oxide (ZnO) piezoelectric thin film that allows making contact with the vibrating cantilevers on a specified applied input impulse signals. The results demonstrated the switching action of the cantilevers that depends on the polarity of the input pulses. The results obtained are compared with the FEM based (COMSOL Multiphysics) model that is designed and analyzed prior to the experiment. Further, the experimental results showed a good agreement with the predicted values calculated by the simulated model for the input impulse signal applied synchronously to all the micro-cantilevers. However, for asynchronous actuation mode, the result of the as-fabricated device showed a variation than the simulated results. The vibrations are generated periodically from all the cantilevers and the output shows the resultant signals that are very much in the audible frequency range.

Analysis of Impact of Bottom Electrode Position on Dynamic Pull-In Parameters of Microcantilevers

The stable range of MEMS electrostatically actuated beam during the pull-in process is crucial to the device performance. Different devices have specific requirements for stable pull-in region based on their applications. In this paper, Rayleigh-Ritz energy method is used to establish dynamic pull-in model of electrostatic cantilever actuated by a step voltage. Modified trial function is derived according to different position of bottom electrode. The model takes into account the effects of fringe capacitance and variable cross-sectional beam. Published numerical methods and experimental data are used to verify the model . The impact of bottom electrode position on pull-in parameters is analyzed in present model. With fitting empirical equations, pull-in parameters can be easily satisfied through the distribution of bottom electrode, which provide an effective reference for the design of MEMS electrostatically actuated beam under given pull-in parameters .

Analysis of MEMS Electrostatic Actuator using SIMULINK Software Tool

The study includes Micro-Electro-Mechanical System (MEMS) electrostatic actuator using SIMULINK software tool considering equivalent mathematical model. This paper deals with the equation of motion, electrostatic force for the analysis of pull in voltage and displacement of an electrostatic cantilever with respect to the changes in applied force (voltage). Considering these equation, we have developed SIMULINK model to analyze pull in voltage, and displacement for the various applied input voltage. Keywords: MEMS, electrostatic cantilever, SIMULINK Cite this Article: Huddar S, Sheeparamatti BG, Hallikeri G, et al. Analysis of MEMS electrostatic actuator using SIMULINK software tool. Journal of Instrumentation Technology & Innovations. 2015; 5(1): 32–35p.

2D MEMS electrostatic cantilever waveguide scanner for potential image display application

This paper presents the current status of our micro-fabricated SU-8 2D electrostatic cantilever waveguide scanner. The current design utilizes a monolithically integrated electrostatic push-pull actuator. A 4.0 μm SU-8 rib waveguide design allows a relatively large core cross section (4μm in height and 20 μm in width) to couple with existing optical fiber and a broad band single mode operation (λ= 0.7μm to 1.3μm) with minimal transmission loss (85% to 87% output transmission efficiency with Gaussian beam profile input). A 2D scanning motion has been successfully demonstrated with two fundamental resonances found at 202 and 536 Hz in vertical and horizontal directions. A 130 μm and 19 μm, corresponding displacement and 0.062 and 0.009 rad field of view were observed at a +150V input. Beam divergence from the waveguide was corrected by a focusing GRIN lens and a 5mm beam diameter is observed at the focal plane. The transmission efficiency is low (~10%) and cantilever is slightly under tensile residual stress due to inherent imperfection in the process and tooling in fabrication. However, 2D light scanning pattern was successfully demonstrated using 1-D push-pull actuation.

Electrostatic cantilever resonators under a double-sided pull–pull drive scheme

Electrostatically-driven, cantilever-shaped resonators under a pair of parallel-plate electrodes with the ‘pull–pull drive’ scheme have been demonstrated and characterized. Theoretical analyses have been established based on the force balance among the electrostatic excitation, the mechanical elastic restoring force and air damping reactions. It is found that the ‘pull–pull drive’ setup can exhibit nonlinear characteristic in the output response, and consequently achieve about 3.8 times the maximum resonance amplitude as compared with the conventional single electrode setup. Furthermore, by adjusting the position of the cantilever between the parallel-plate electrodes, the magnitude of pull-in voltage as well as the maximum resonance amplitude can be changed. As such, the ‘pull–pull drive’ scheme provides an easy and alternative way to increase the response of the electrostatically-actuated resonators for various potential applications in resonator-based sensors and actuators.

Analytical Approach to Compute the Internal Stress Field of NEMS Considering Casimir Forces

This paper study the effect of Casimir intermolecular force on stress distribution of electrostatic cantilever nano-electromechanical systems (NEMS) using homotopy perturbation method (HPM). An analytical closed-form solution has been obtained in terms of convergent series with easily computable components. The shear force, bending moment and stress distribution along the cantilevers at the onset of instability, which are important parameters for designing electromechanical systems are computed and compared with numerical solution. Furthermore, the results computed by HPM method agree with numerical solutions and those from the literature.

Closed-form Approximations of the Pull-in Parameters and Stress Field of Electrostatic Cantilever Nano-actuators Considering van der Waals Attraction

Herein, homotopy perturbation method (HPM) is used to investigate the effect of van der Waals force on the pull-in parameters and stress distribution and the instability of electrostatic actuators at nano-scale separations. The shear force, bending moment and stress distribution along the cantilevers at the onset of instability, which are important parameters for designing and manufacturing nano-actuators, are computed. An analytical closed-form solution is obtained and compared with numerical solution and those from literature. It has been shown that van der Waals attraction can highly influences the pull-in parameters and internal stress field of the nano-actuator.

Dry release fabrication and testing of SiC electrostatic cantilever actuators

This paper presents a simple, dry etching-based surface micromachining technique for the fabrication of single-layer polycrystalline 3C–SiC electrostatic actuators. The technique has utilized a single inductively coupled plasma recipe to etch and release metal patterned SiC structural layers. To demonstrate the simplicity of the process, SiC cantilever actuators with different beam lengths have been successfully fabricated using this method. By applying a combination of ac and dc voltages, the fabricated devices have been electrostatically actuated. The fundamental resonance frequencies of fabricated cantilevers with different lengths have been observed to range from 66.65 KHz to 1.729 MHz. The amplitudes of the fundamental resonance peaks with respect to the excitation voltages have also been systematically studied.

Principle of ferroelectric domain imaging using atomic force microscope

The contrast mechanisms of domain imaging experiments assisted by atomic force microscope (AFM) have been investigated by model experiments on nonpiezoelectric (silicon oxide) and piezoelectric [Pb(Zr,Ti)O3] thin films. The first step was to identify the electrostatic charge effects between the tip, the cantilever, and the sample surface. The second step was to explore the tip–sample piezoelectric force interaction. The static deflection of the cantilever was measured as a function of dc bias voltage (Vdc) applied to the bottom electrode (n-type Si wafers) for noncontact and contact modes. In addition, a small ac voltage (Vac sin ωt) was applied to the tip to measure the amplitude (Aω) and phase (Φω) of the first harmonic (ω) signal as a function of Vdc. By changing from the noncontact to the contact mode, a repulsive contribution to the static deflection was found in addition to the attractive one and a 180° phase shift in Φω was observed. These results imply that in the contact mode the cantilever buckling is induced by the capacitive force between the cantilever and the sample surface. This interaction adds to the tip–sample piezoelectric interaction thereby overlapping the obtained tip vibration signal. Therefore, the antiparallel ferroelectric domain images obtained at zero dc bias voltage will show a variation in Aω but a negligible one in Φω. The capacitive force contribution to the tip vibration signal was further verified in piezoelectric hysteresis loop measurement assisted by the AFM. The observed vertical offset of the loops was explained by the contact potential difference between the cantilever and the bottom electrode. The shape of the curve could be explained by the capacitive force interaction combined with the tip–sample piezoelectric interaction. The experimental results obtained in this study support the interpretation of the cantilever–sample capacitive force contribution to the tip vibration signal in ferroelectric domain imaging experiments using AFM as a probing tool. The use of a large area top electrode between the tip and the sample resulted in the elimination of the electrostatic cantilever–sample interaction with negligible degradation of the domain contrast. This method proved to be successful because the cantilever–sample interaction was hardly detected and only the tip–sample interaction was observed.