Design Of MEMS Devices Research Articles

The Homotopy Perturbation Method for Electrically Actuated Microbeams in Mems Systems Subjected to Van Der Waals Force and Multiwalled Carbon Nanotubes

Abstract This paper presents a summary of a study that uses the Aboodh transformation and homotopy perturbation approach to analyze the behavior of electrically actuated microbeams in microelectromechanical systems that incorporate multiwalled carbon nanotubes and are subjected to the van der Waals force. All of the equations were transformed into linear form using the HPM approach. Electrically operated microbeams, a popular structure in MEMS, are the subject of this work. Because of their interaction with a nearby surface, these microbeams are sensitive to a variety of forces, such as the van der Waals force and body forces. MWCNTs are also incorporated into the MEMSs in this study because of their special mechanical, thermal, and electrical characteristics. The suggested method uses the HPM to model how electrically activated microbeams behave when MWCNTs and the van der Waals force are present. The nonlinear equations controlling the dynamics of the system can be roughly solved thanks to the HPM. The HPM offers a precise and effective way to analyze the microbeam’s reaction to these outside stimuli by converting the nonlinear equations into linear forms. The study’s findings shed important light on how electrically activated microbeams behave in MEMSs. A more thorough examination of the system’s performance is made possible with the addition of MWCNTs and the van der Waals force. With its ability to approximate solutions and characterize system behavior, the HPM is a potent instrument that improves comprehension of the physics at play and facilitates the design and optimization of MEMS devices. The aforementioned method’s accuracy is verified by comparing it with published data that directly aligns with Anjum et al.’s findings. We have faith in this method’s accuracy and its current application.

Extending the Validity of Squeeze Film Damping Models with Lower Aspect Ratios.

Squeeze film air damping is a significant factor in the design of MEMS devices owing to its great impact on the dynamic performance of vibrating structures. However, the traditional theoretical results of squeeze film air damping are derived from the Reynolds equation, wherein there exists a deviation from the true results, especially in low aspect ratios. While expensive efforts have been undertaken to prove that this deviation is caused by the neglect of pressure change across the film, a quantitative study has remained elusive. This paper focuses on the investigation of the finite size effect of squeeze film air damping and conducts numerical research using a set of simulations. A modified expression is extended to lower aspect ratio conditions from the original model of squeeze film air damping. The new quick-calculating formulas based on the simulation results reproduce the squeeze film air damping with a finite size effect accurately with a maximum error of less than 1% in the model without a border effect and 10.185% in the compact model with a border effect. The high consistency between the new formulas and simulation results shows that the finite size effect was adequately considered, which offers a previously unattainable precise damping design guide for MEMS devices.

Design of a large-range rotary microgripper with freeform geometries using a genetic algorithm

This paper describes a novel electrostatically actuated microgripper with freeform geometries designed by a genetic algorithm. This new semiautomated design methodology is capable of designing near-optimal MEMS devices that are robust to fabrication tolerances. The use of freeform geometries designed by a genetic algorithm significantly improves the performance of the microgripper. An experiment shows that the designed microgripper has a large displacement (91.5 μm) with a low actuation voltage (47.5 V), which agrees well with the theory. The microgripper has a large actuation displacement and can handle micro-objects with a size from 10 to 100 μm. A grasping experiment on human hair with a diameter of 77 μm was performed to prove the functionality of the gripper. The result confirmed the superior performance of the new design methodology enabling freeform geometries. This design method can also be extended to the design of many other MEMS devices.

Rapid Prototyping of Inertial MEMS Devices through Structural Optimization.

In this paper, we propose a novel design and optimization environment for inertial MEMS devices based on a computationally efficient schematization of the structure at the a device level. This allows us to obtain a flexible and efficient design optimization tool, particularly useful for rapid device prototyping. The presented design environment—feMEMSlite—handles the parametric generation of the structure geometry, the simulation of its dynamic behavior, and a gradient-based layout optimization. The methodology addresses the design of general inertial MEMS devices employing suspended proof masses, in which the focus is typically on the dynamics associated with the first vibration modes. In particular, the proposed design tool is tested on a triaxial beating-heart MEMS gyroscope, an industrially relevant and adequately complex example. The sensor layout is schematized by treating the proof masses as rigid bodies, discretizing flexural springs by Timoshenko beam finite elements, and accounting for electrostatic softening effects by additional negative spring constants. The MEMS device is then optimized according to two possible formulations of the optimization problem, including typical design requirements from the MEMS industry, with particular focus on the tuning of the structural eigenfrequencies and on the maximization of the response to external angular rates. The validity of the proposed approach is then assessed through a comparison with full FEM schematizations: rapidly prototyped layouts at the device level show a good performance when simulated with more complex models and therefore require only minor adjustments to accomplish the subsequent physical-level design.

The role of etching anisotropy in the fabrication of freestanding oxide microstructures on SrTiO3(100), SrTiO3(110), and SrTiO3(111) substrates

The release process for the fabrication of freestanding oxide microstructures relies on appropriate, controllable, and repeatable wet etching procedures. SrTiO3 (STO) is among the most employed substrates for oxide thin films growth and can be decomposed in HF:water solution. Such a process is strongly anisotropic and is affected by local defects and substrate cut-planes. We analyze the etching behavior of SrTiO3 substrates having (100), (110), and (111) cut-planes during immersion in a 5% HF:water solution. The etching process over the three substrates is compared in terms of pitting, anisotropy, macroscopic etch rate, and underetching effects around HF-resistant (La,Sr)MnO3 thin film micropatterns. The release of targeted structures, such as the reported (La,Sr)MnO3 freestanding microbridges, depends on the substrate crystallographic symmetry and on the in-plane orientation of the structures themselves along the planar directions. By comparing the etching evolution at two different length scales, we distinguish two regimes for the propagation of the etching front: an intrinsic one, owing to a specific lattice direction, and a macroscopic one, resulting from the mixing of different etching fronts. We report the morphologies of the etched SrTiO3 surfaces and the geometries of the underetched regions as well as of the microbridge clamping zones. The reported analysis will enable the design of complex MEMS devices by allowing to model the evolution of the etching process required for the release of arbitrary structures made of oxide thin films deposited on top of STO.

Non-linear dynamic characteristics analysis of multilayer electrostatic micro-beam structure

The dynamic analysis of multi-layer cantilever beam's structure is of great significance to the structural design of MEMS devices. Due to the multi-coupling and non-linearity of the multi-layer cantilever beam, this paper presents a method for modelling and solving multilayer micro-beam. Firstly, the dynamic equation mathematical model of electrostatic multi-layer cantilever beam was established based on the energy principle and fluid film damping effect; second, the dynamic model was transformed to single-layer beam solution model by equivalent parameter method. Thirdly, Galerkin mapping reduction algorithm was used to solve this model. The theoretical computing results and simulation results can provide strong support for the study of the working motion state of the MEMS devices.

A Technique for Estimation of Residual Stress and Young’s Modulus of Compressively Stressed Thin Films Using Microfabricated Beams

Predictive design of MEMS devices and their performance evaluation require post-fabrication measurement of essential material properties, such as Young's modulus and residual stress, as these are usually affected by fabrication process conditions. To our knowledge, few techniques exist for the measurement of residual stress in micromechanical structures fabricated from compressively-stressed amorphous dielectric thin films. Here, we propose a method for estimating residual stress and Young's modulus from the post-buckling dynamic response of fixed-fixed microbeams and frequency response of cantilevers, respectively. Static deflection profiles and first natural frequencies of buckled beams are used in this analysis. Further, the proposed method uses the length of the beams as an unknown to account for the variation in the actual length of a fabricated beam due to the presence of undercut. The effective length is simultaneously determined from the analysis of the measured data using multi-parameter curve fitting. Use of post-buckling analysis makes this technique useful for thin films with high compressive stresses. Since the proposed method does not involve electrostatic actuation, it is applicable for dielectric thin films in addition to crystalline and conducting films. Using the proposed method, residual stress is estimated in amorphous silicon carbide thin films deposited by PECVD and reactive-sputtering. In addition, the modulus values of three materials (PECVD SiNx, PECVD SiC, and sputtered SiC) are estimated and compared with reported results. [2019-0090]

An experimental methodology for the concurrent characterization of multiple parameters influencing nanoscale friction

A structured transdisciplinary method for the experimental determination of friction in the nanometric domain is proposed in this paper. The dependence of nanoscale friction on multiple process parameters on these scales, which comprise normal forces, sliding velocities, and temperature, was studied via the lateral force microscopy approach. The procedure used to characterize the stiffness of the probes used, and especially the influence of adhesion on the obtained results, is thoroughly described. The analyzed thin films were obtained by using either atomic layer or pulsed laser deposition. The developed methodology, based on elaborated design of experiments algorithms, was successfully implemented to concurrently characterize the dependence of nanoscale friction in the multidimensional space defined by the considered process parameters. This enables the establishment of a novel methodology that extends the current state-of-the-art of nanotribological studies, as it allows not only the gathering of experimental data, but also the ability to do so systematically and concurrently for several influencing variables at once. This, in turn, creates the basis for determining generalizing correlations of the value of nanoscale friction in any multidimensional experimental space. These developments create the preconditions to eventually extend the available macro- and mesoscale friction models to a true multiscale model that will considerably improve the design, modelling and production of MEMS devices, as well as all precision positioning systems aimed at micro- and nanometric accuracy and precision.

Temperature effect on pull-off force for gold cantilevers array

This paper focuses on revealing the length influence of a group of gold cantilevers on the mechanical behaviour (i.e. bending stiffness, Young modulus, pull-off force) on the one hand and on the investigation of the temperature influence on the pull-off force of thermally actuated microcantilevers, on the other hand. The length was ranged between 200 μm and 350 μm while the temperature was ranged between 20 °C to 100 °C. The tests were performed using an atomic force microscope. The results obtained in the study are important to enhance the design of MEMS devices and to increase their reliability and their lifetime.

Study of Dynamic Behavior of Magnetostrictively Patterned Flexible Micro-Wings

For the design of magnetostrictive MEMS devices, finite-element modeling (FEM), the determination of the magnetostrictive coefficient, and application examples were examined in this paper. The magnetostrictive coefficients are usually calculated by measuring the bending deflection of the cantilever on which magnetostrictive materials are deposited. In most of the research on the magnetostrictive deposited substrate for the derivation of structural formulas, it is commonly assumed that the flexural rigidities of magnetostrictive materials are negligible because magnetostrictive films are much thinner than substrate materials. In this paper, the effect of magnetostrictive thin film's elastic energy on the magnetostrictive coefficient is investigated. A self-coded and developed finite-element program for magnetostrictive actuators is formulated, where magnetic properties are considered as nonlinear, and elastic properties are assumed as linear. As a result, it is potentially shown that magnetostrictive thin-film micropatterned actuators would be accommodated for targeted actuating behavior through an FEM capability for evaluation and selective micropatterning technique for fabrication.

Probabilistic Physics of Failure (PPOF) Reliability Analysis of RF-MEMS Switches under Uncertainty

MEMS reliability analysis is a challenging area of research which comprises various physics of failure and diverse failure mechanisms. Reliability issues are critical in both design and fabrication phases of MEMS devices as their commercialization is still delayed by these problems. In this research, a hybrid methodology is developed for the reliability evaluation of MEMS devices. Its first step is the identification of dominant failure modes by FMEA, evaluation of failure mechanisms and an updated lifetime estimation by the Bayesian method. The reliability of MEMS devices is studied using probabilistic physics of failure (PPoF) by determining the dominant failure mechanism. Accordingly, a deterministic model is selected for the analysis of the life and reliability of the dominant failure mechanisms. To convert the deterministic model to a probabilistic model, the uncertainty sources affecting the dielectric lifetime are determined. This model is simulated by the utilization of the Monte Carlo method. In the final stage, the results of life estimation are updated using the Bayesian method. Considering wide application and advantages of RF MEMS capacitive switches, it has been selected as a case study. A framework is developed for reliability evaluation of these switches failures due to stiction mechanism. The results contain FMEA table, lifetime estimation in different voltages, number of duty cycles and at the end, updated results of life estimation using the Bayesian method.

Material selection for Micro-Electro-Mechanical-Systems (MEMS) using Ashby's approach

A key aspect in design optimization of a product or a system is the selection of materials that best meet the design needs, ensuring maximum performance and minimum cost. Ashby's approach, originally introduced for macro-systems and products, has been very successfully employed for Micro-Electro-Mechanical-Systems (MEMS)/micromachined sensors, actuators and devices. This paper presents a comprehensive review and critical analysis of MEMS material selection studies using Ashby's approach reported in the literature during the last two decades. Performance and Material Indices derived for various microsystems and MEMS devices have been summarized. Moreover, all MEMS materials reported in the literature and the most suitable materials proposed for a variety of MEMS systems and devices have also been consolidated. A material selection case study utilizing micro-scale properties of 51 MEMS compatible materials has been presented to demonstrate that the use of different materials' bulk properties is not the best choice for MEMS materials selection. This paper will serve as a reference guide and useful resource for researchers and engineers engaged in the design and fabrication of various microsystems and MEMS sensors, actuators and devices.

Mechanical stability of heat-treated nanoporous anodic alumina subjected to repetitive mechanical deformation

We report studies on the mechanical response and deformation behavior of heat-treated nanoporous anodic alumina using a micro-balance test and experimental test equipment especially designed for this purpose. AAO samples were characterized mechanically by a three-point bending test using a micro-analytical balance. The deformation behavior was studied by repetitive mechanical bending of the AAO membranes using an electronically controlled system. The nanoporous AAO structures were prepared electrochemically from Al sheet substrates using a two-step anodizing technique in oxalic acid followed by heat treatment at 700 °C in air. The morphological study of the aluminum oxide layer after the mechanical tests and mechanical deformation was conducted using scanning electron and optical microscopy, respectively. The experimental results showed that the techniques proposed are simple and accurate; they could, therefore, be combined to constitute a method for mechanical stability assessment of nanostructured AAO films, which are important structural components in the design of MEMS devices and sensors.

A design method and its CAD prototype system for surface micromachined MEMS devices

Now the MEMS design method of “bottom–up” (mask-to-shape-to-function) has been adopted widely. However, it is complicated, time-consuming and not straightforward and can’t meet the demand of MEMS development. In this paper, a 3D MEMS aided design method is studied for surface micromachined MEMS devices, which adopts the design procedure of function-to-shape-to-mask. With this method, 3D geometric models of surface micromachined MEMS devices are built by selecting 3D MEMS features from the developed feature database after functional requirement analysis and concept design have been made. After the geometric model is analyzed with FEM analysis tools, 2D candidate masks and process flow are automatically generated by analyzing geometric information and material information of the model. Meanwhile, a 3D MEMS CAD prototype system of this method is developed based on SolidWorks. Finally a torsional micromirror is designed to verify the validity of the design method and its CAD prototype system. The practical example shows that 3D MEMS design method can help designers develop MEMS devices straightforwardly and obtain 2D masks and process flow automatically, and the developed 3D MEMS CAD prototype system based on SolidWorks can make MEMS device design easily.

Surface Roughness of Z-Cut Quartz Etched by Ammonium Bifluoride and Ammonium Bifluoride Mixed with Isopropyl Alcohol Solutions

It is meaningful to study the surface morphology of monocrystalline material, but there are few studies on the surface roughness of quartz. So, surface roughness of Z-cut quartz etched by pure ammonium bifluoride and ammonium bifluoride mixed with isopropyl alcohol (IPA) solution was investigated for the first time in this paper. Firstly, when etching in pure ammonium bifluoride solutions, the surface roughness change with etching time, etching temperature, and solution concentration were studied. Then, the surface roughness improvement given by isopropyl alcohol solution was analyzed carefully. The experimental results indicated that: the surface roughness of Z-cut quartz (0001) plane increased with etching time, but decreased with etching temperature and solution concentration; the adding of isopropyl alcohol in ammonium bifluoride solution could decrease the roughness and improve the surface quality. This is the first systemic research of the evolution of quartz surface roughness when etching in ammonium bifluoride solution, and will benefit the future design and manufacture of quartz MEMS devices.

Modeling and Experimental Validation of Bi-Stable Beam Based Piezoelectric Energy Harvester

Abstract We have previously proposed a bi-stable nonlinear oscillator based piezoelectric energy harvester to address the challenges of low-frequency, low-g vibration energy harvesting at MEMS scale. The compressive residual stress in micro-fabricated thin films could be employed to induce buckling in doubly clamped beams. The buckled beams with two equilibriums can snap through at low frequencies and enhance the power generation. This paper focuses on the modeling of the dynamics of the bi-stable oscillator based energy harvesters. An electromechanical lumped model has been built by Lagrange’s formulation and lumped parameters have been solved explicitly. More particularly, the model considers multi-layer thin films and the residual stress in these films, to be readily applicable to MEMS device design. Harmonic functions as the approximate solutions have been used to analytically solve for the frequency responses of the nonlinear oscillations. Two modes of oscillations predicted by the analytical model have been validated by testing a meso-scale prototype.

A wafer mapping technique for residual stress in surface micromachined films

The design of MEMS devices employing movable structures is crucially dependant on the mechanical behaviour of the deposited materials. It is therefore important to be able to fully characterize the micromachined films and predict with confidence the mechanical properties of patterned structures. This paper presents a characterization technique that enables the residual stress in MEMS films to be mapped at the wafer level by using microstructures released by surface micromachining. These dedicated MEMS test structures and the associated measurement techniques are used to extract localized information on the strain and Young’s modulus of the film under investigation. The residual stress is then determined by numerically coupling this data with a finite element analysis of the structure. This paper illustrates the measurement routine and demonstrates it with a case study using electrochemically deposited alloys of nickel and iron, particularly prone to develop high levels of residual stress. The results show that the technique enables wafer mapping of film non-uniformities and identifies wafer-to-wafer differences. A comparison between the results obtained from the mapping technique and conventional wafer bow measurements highlights the benefits of using a procedure tailored to films that are non-uniform, patterned and surface-micromachined, as opposed to simple standard stress extraction methods. The presented technique reveals detailed information that is generally unexplored when using conventional stress extraction methods such as wafer bow measurements.

Dynamics of hydrogenated amorphous silicon flexural resonators for enhanced performance

Hydrogenated amorphous silicon thin-film flexural resonators with sub-micron actuation gaps are fabricated by surface micromachining on glass substrates. Experimentally, the resonators are electrostatically actuated and their motion is optically detected. Three different configurations for the electrostatic excitation force are used to study the dynamics of the resonators. In the first case, a dc voltage (Vdc) is added to an ac voltage with variable excitation frequency (Vac(ω)) and harmonic, superharmonic, and subharmonic resonances of different orders are observed. The second case consists on mixing the dc voltage (Vdc) with an ac voltage applied at a fixed frequency of twice the natural frequency of the resonator (V(2ω0)). High-amplitude parametric resonance is excited at the natural frequency of the system, ω0. This configuration allows a separation between the frequencies of the excitation and the mechanical motion. Finally, in the third case, the dc voltage (Vdc) is combined with both ac voltages, Vac(ω) and V(2ω0), and parametric resonance is excited and emerges from the fundamental harmonic resonance peak. The single-degree-of-freedom equation of motion is modeled and discussed for each case. The nonlinearity inherent to the electrostatic force is responsible for modulating the spring constant of the system at different frequencies, giving rise to parametric resonance. These equations of motion are simulated in the time and frequency domains, providing a consistent explanation of the experimentally observed phenomena. A wide variety of possible resonance modes with different characteristics can be used advantageously in MEMS device design.

A New Methodology for Uniaxial Tensile Testing of Free-Standing Thin Films at High Strain-Rates

The investigation of strain-rate effects on the mechanical response and characteristics of thin free-standing films is crucial for the design and fabrication of more reliable MEMS devices. It is also of high interest from the scientific and materials engineering views. In this paper we present a novel apparatus and a procedure for tensile testing of thin free-standing films under a wide range of strain rates from quasistatic to high, almost comparable with those obtained in Hopkinson bar tests. To provide this capability, a unique displacement measurement method is applied and a micro device which meets several strict requirements is implemented. We describe recent results of quasistatic experiments performed on pure aluminum free-standing thin films. A high rate experiment which demonstrates the setup capabilities is also presented. The micro-device measured properties are compared with finite element analysis results.

Design, Modeling and Simulation of MEMS Devices on Si, SiC, and Diamond for Harsh Environment Applications

Set of micromechanical (MEMS) test structures designed for fabrication on silicon, silicon carbide and diamond substrates has been successfully designed. A dedicated mask-set development has been carried along with numerical simulations performed with assistance of a dedicated design and modelling CoventorWare toolset by Coventor. A set of sample simulations presented in this paper has been performed for speci c simulation domains focused on silicon-alternative material reality to proof the usefulness of proposed substrates. The aim was to verify its applicability for MEMS design and con rm an outstanding performance of the resulting device which e ectively opens a new area of interest for subsequent research and development e orts.