Special Issue "Modeling, Testing and Reliability Issues in MEMS Engineering - 2009"
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A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Physical Sensors".
Deadline for manuscript submissions: closed (31 December 2009)
Special Issue Editor
Guest Editor
Dr. Stefano Mariani
Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano, Italy
Website: http://www.stru.polimi.it
E-Mail: stefano.mariani@polimi.it
Phone: +39 02 2399 4279
Fax: +39 02 2399 4220
Interests: MEMS; structural sensors; kalman filtering
Special Issue Information
Dear Colleagues,
Micro-electro-mechanical-systems (MEMS) are devices on a millimeter scale, with micro-resolution. Each MEMS is given by the integration of mechanical elements, sensors, actuators and electronics on a common silicon substrate, obtained through micro-fabrication technology.
MEMS are often designed to work in mobile devices, and are therefore subject during their life to accidental mechanical loadings. Because of the MEMS size, multi-scale analyses are sometimes required in reliability analysis. Furthermore, also thermal, electrical, magnetic and environmental actions should be accounted for in a fully coupled multi-physics modelling of the devices.
As for packaging, some technical problems caused to the devices are not yet thoroughly understood and solved. Since standards do not necessarily apply to packaged MEMS, new knowledge-based testing methodologies need to be proposed.
The aim of this special issue is to collect high quality research results on all these aspects of MEMS engineering.
Dr. Stefano Mariani
Guest Editor
Submission
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Sensors is an international peer-reviewed Open Access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs).
Keywords
- micro-electro-mechanical-systems
- multi-scale and multi-physics modelling
- micro-fluidics
- failure analysis
- reliability analysis
- package engineering
Published Papers (22 papers)
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Received: 19 February 2009; in revised form: 14 March 2009 / Accepted: 18 March 2009 / Published: 18 March 2009
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Abstract: This study presents the fabrication and characterization of a micromechanical tunable in-plane resonator. The resonator is manufactured using the commercial 0.35 µm complementary metal oxide semiconductor (CMOS) process. The resonator is made of aluminum, and the sacrificial layer is silicon dioxide. The post-process involves only one maskless etching step using an etchant to remove the sacrificial layer. The resonator includes three parts: a driving part to provide a driving force, a sensing part that is used to detect a change in capacitance when the resonator is vibrating, and a tuning part that changes the resonant frequency of the resonator. The main advantages of the tunable resonator are a low driving voltage and compatibility with the CMOS process. The resonant frequency of the resonator can be changed upon applying a dc voltage to the tuning part. To reduce the driving voltage, the driving part is designed as comb-finger rows. Experimental results show that the resonator has a resonant frequency of about 183 kHz and a driving voltage of 10 V; the resonant frequency increases 14 kHz when a tuning voltage of 30 V is applied. The resonator has a maximum frequency–tuning ratio of 7.6%.
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Received: 27 March 2009; in revised form: 23 April 2009 / Accepted: 13 May 2009 / Published: 20 May 2009
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Abstract: In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.
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Received: 30 June 2009; in revised form: 27 July 2009 / Accepted: 3 August 2009 / Published: 5 August 2009
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Abstract: A novel plastic packaging of a piezoresistive pressure sensor using a patterned ultra-thick photoresist is experimentally and theoretically investigated. Two pressure sensor packages of the sacrifice-replacement and dam-ring type were used in this study. The characteristics of the packaged pressure sensors were investigated by using a finite-element (FE) model and experimental measurements. The results show that the thermal signal drift of the packaged pressure sensor with a small sensing-channel opening or with a thin silicon membrane for the dam-ring approach had a high packaging induced thermal stress, leading to a high temperature coefficient of span (TCO) response of -0.19% span/°C. The results also show that the thermal signal drift of the packaged pressure sensors with a large sensing-channel opening for sacrifice-replacement approach significantly reduced packaging induced thermal stress, and hence a low TCO response of -0.065% span/°C. However, the packaged pressure sensors of both the sacrifice-replacement and dam-ring type still met the specification -0.2% span/°C of the unpackaged pressure sensor. In addition, the size of proposed packages was 4 × 4 × 1.5 mm3 which was about seven times less than the commercialized packages. With the same packaging requirement, the proposed packaging approaches may provide an adequate solution for use in other open-cavity sensors, such as gas sensors, image sensors, and humidity sensors.
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Received: 29 June 2009; in revised form: 25 July 2009 / Accepted: 3 August 2009 / Published: 6 August 2009
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Abstract: In this study we used the commercial 0.35 µm CMOS (complementary metal oxide semiconductor) process and simple maskless post-processing to fabricate an array of micromirrors exhibiting high natural frequency. The micromirrors were manufactured from aluminum; the sacrificial layer was silicon dioxide. Because we fabricated the micromirror arrays using the standard CMOS process, they have the potential to be integrated with circuitry on a chip. For post-processing we used an etchant to remove the sacrificial layer and thereby suspend the micromirrors. The micromirror array contained a circular membrane and four fixed beams set symmetrically around and below the circular mirror; these four fan-shaped electrodes controlled the tilting of the micromirror. A MEMS (microelectromechanical system) motion analysis system and a confocal 3D-surface topography were used to characterize the properties and configuration of the micromirror array. Each micromirror could be rotated in four independent directions. Experimentally, we found that the micromirror had a tilting angle of about 2.55° when applying a driving voltage of 40 V. The natural frequency of the micromirrors was 59.1 kHz.
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Received: 5 August 2009; in revised form: 22 September 2009 / Accepted: 24 September 2009 / Published: 12 October 2009
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Abstract: Wireless sensor networks equipped with various gas sensors have been actively used for air quality monitoring. Previous studies have typically explored system issues that include middleware or networking performance, but most research has barely considered the details of the hardware and software of the sensor node itself. In this paper, we focus on the design and implementation of a sensor board for air pollutant monitoring applications. Several hardware and software issues are discussed to explore the possibilities of a practical WSN-based air pollution monitoring system. Through extensive experiments and evaluation, we have determined the various characteristics of the gas sensors and their practical implications for air pollutant monitoring systems.
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Received: 30 July 2009; in revised form: 15 September 2009 / Accepted: 16 September 2009 / Published: 12 October 2009
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Abstract: In this paper, the reliability of capacitive shunt RF MEMS switches have been investigated using three dimensional (3D) coupled multiphysics finite element (FE) analysis. The coupled field analysis involved three consecutive multiphysics interactions. The first interaction is characterized as a two-way sequential electromagnetic (EM)-thermal field coupling. The second interaction represented a one-way sequential thermal-structural field coupling. The third interaction portrayed a two-way sequential structural-electrostatic field coupling. An automated substructuring algorithm was utilized to reduce the computational cost of the complicated coupled multiphysics FE analysis. The results of the substructured FE model with coupled field analysis is shown to be in good agreement with the outcome of previously published experimental and numerical studies. The current numerical results indicate that the pull-in voltage and the buckling temperature of the RF switch are functions of the microfabrication residual stress state, the switch operational frequency and the surrounding packaging temperature. Furthermore, the current results point out that by introducing proper mechanical approaches such as corrugated switches and through-holes in the switch membrane, it is possible to achieve reliable pull-in voltages, at various operating temperatures. The performed analysis also shows that by controlling the mean and gradient residual stresses, generated during microfabrication, in conjunction with the proposed mechanical approaches, the power handling capability of RF MEMS switches can be increased, at a wide range of operational frequencies. These design features of RF MEMS switches are of particular importance in applications where a high RF power (frequencies above 10 GHz) and large temperature variations are expected, such as in satellites and airplane condition monitoring.
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Received: 29 July 2009; in revised form: 28 August 2009 / Accepted: 21 September 2009 / Published: 21 October 2009
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Abstract: In the analysis of the effects of temperature on the performance of microgyroscopes, it is found that the resonant frequency of the microgyroscope decreases linearly as the temperature increases, and the quality factor changes drastically at low temperatures. Moreover, the zero bias changes greatly with temperature variations. To reduce the temperature effects on the microgyroscope, temperature compensation-control methods are proposed. In the first place, a BP (Back Propagation) neural network and polynomial fitting are utilized for building the temperature model of the microgyroscope. Considering the simplicity and real-time requirements, piecewise polynomial fitting is applied in the temperature compensation system. Then, an integral-separated PID (Proportion Integration Differentiation) control algorithm is adopted in the temperature control system, which can stabilize the temperature inside the microgyrocope in pursuing its optimal performance. Experimental results reveal that the combination of microgyroscope temperature compensation and control methods is both realizable and effective in a miniaturized microgyroscope prototype.
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Received: 6 August 2009; in revised form: 12 September 2009 / Accepted: 12 October 2009 / Published: 27 October 2009
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Abstract: In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at −40 °C, −20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.
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Received: 30 July 2009; in revised form: 19 October 2009 / Accepted: 26 October 2009 / Published: 30 October 2009
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Abstract: In this study, we fabricated a wireless micro FET (field effect transistor) pressure sensor based on the commercial CMOS (complementary metal oxide semiconductor) process and a post-process. The wireless micro pressure sensor is composed of a FET pressure sensor, an oscillator, an amplifier and an antenna. The oscillator is adopted to generate an ac signal, and the amplifier is used to amplify the sensing signal of the pressure sensor. The antenna is utilized to transmit the output voltage of the pressure sensor to a receiver. The pressure sensor is constructed by 16 sensing cells in parallel. Each sensing cell contains an MOS (metal oxide semiconductor) and a suspended membrane, which the gate of the MOS is the suspended membrane. The postprocess employs etchants to etch the sacrificial layers in the pressure sensor for releasing the suspended membranes, and a LPCVD (low pressure chemical vapor deposition) parylene is adopted to seal the etch holes in the pressure. Experimental results show that the pressure sensor has a sensitivity of 0.08 mV/kPa in the pressure range of 0–500 kPa and a wireless transmission distance of 10 cm.
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Received: 26 August 2009; in revised form: 4 November 2009 / Accepted: 5 November 2009 / Published: 17 November 2009
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Abstract: In fuel cells flow configuration and operating conditions such as cell temperature, humidity at each electrode and stoichiometric number are very crucial for improving performance. Too many flow channels could enhance the performance but result in high parasite loss. Therefore a trade-off between pressure drop and efficiency of a fuel cell should be considered for optimum design. This work focused on numerical simulation of the effects of operating conditions, especially cathode humidity, with simple micro parallel flow channels. It is known that the humidity at the cathode flow channel becomes very important for enhancing the ion conductivity of polymer membrane because fully humidified condition was normally set at anode. To investigate the effect of humidity on the performance of a fuel cell, in this study humidification was set to 100% at the anode flow channel and was changed by 0–100% at the cathode flow channel. Results showed that the maximum power density could be obtained under 60% humidified condition at the cathode where oxygen concentration was moderately high while maintaining high ion conductivity at a membrane.
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Received: 4 August 2009; in revised form: 8 October 2009 / Accepted: 12 November 2009 / Published: 19 November 2009
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Abstract: In this paper, a novel portable hard-disk encryption/decryption system with a MEMS coded lock is presented, which can authenticate the user and provide the key for the AES encryption/decryption module. The portable hard-disk encryption/decryption system is composed of the authentication module, the USB portable hard-disk interface card, the ATA protocol command decoder module, the data encryption/decryption module, the cipher key management module, the MEMS coded lock controlling circuit module, the MEMS coded lock and the hard disk. The ATA protocol circuit, the MEMS control circuit and AES encryption/decryption circuit are designed and realized by FPGA(Field Programmable Gate Array). The MEMS coded lock with two couplers and two groups of counter-meshing-gears (CMGs) are fabricated by a LIGA-like process and precision engineering method. The whole prototype was fabricated and tested. The test results show that the user’s password could be correctly discriminated by the MEMS coded lock, and the AES encryption module could get the key from the MEMS coded lock. Moreover, the data in the hard-disk could be encrypted or decrypted, and the read-write speed of the dataflow could reach 17 MB/s in Ultra DMA mode.
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Received: 9 November 2009; in revised form: 7 December 2009 / Accepted: 10 December 2009 / Published: 16 December 2009
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Abstract: This paper reports on numerical modeling and simulation of a generalized contact-type MEMS device having large potential in various micro-sensor/actuator applications, which are currently limited because of detrimental effects of the contact bounce phenomenon that is still not fully explained and requires comprehensive treatment. The proposed 2-D finite element model encompasses cantilever microstructures operating in a vacuum and impacting on a viscoelastic support. The presented numerical analysis focuses on the first three flexural vibration modes and their influence on dynamic characteristics. Simulation results demonstrate the possibility to use higher modes and their particular points for enhancing MEMS performance and reliability through reduction of vibro-impact process duration.
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Received: 21 October 2009; in revised form: 14 December 2009 / Accepted: 22 December 2009 / Published: 28 December 2009
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Abstract: Portable electronic devices such as notebook computers, PDAs, cellular phones, etc., are being widely used, and they increasingly need cheap, efficient, and lightweight power sources. Fuel cells have been proposed as possible power sources to address issues that involve energy production and the environment. In particular, a small type of fuel-cell system is known to be suitable for portable electronic devices. The development of micro fuel cell systems can be achieved by the application of microchannel technology. In this study, the conventional method of chemical etching and the mechanical machining method of micro end milling were used for the microfabrication of microchannel for fuel cell separators. The two methods were compared in terms of their performance in the fabrication with regards to dimensional errors, flatness, straightness, and surface roughness. Following microchannel fabrication, the powder blasting technique is introduced to improve the coating performance of the catalyst on the surface of the microchannel. Experimental results show that end milling can remarkably increase the fabrication performance and that surface treatment by powder blasting can improve the performance of catalyst coating.
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Received: 10 December 2009; in revised form: 24 December 2009 / Accepted: 28 December 2009 / Published: 7 January 2010
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Abstract: The diffusion of micro electro-mechanical systems (MEMS) technology applied to navigation systems is rapidly increasing, but currently, there is a lack of knowledge about the reliability of this typology of devices, representing a serious limitation to their use in aerospace vehicles and other fields with medium and high requirements. In this paper, a reliability testing procedure for inertial sensors and inertial measurement units (IMU) based on MEMS for applications in vibrating environments is presented. The sensing performances were evaluated in terms of signal accuracy, systematic errors, and accidental errors; the actual working conditions were simulated by means of an accelerated dynamic excitation. A commercial MEMS-based IMU was analyzed to validate the proposed procedure. The main weaknesses of the system have been localized by providing important information about the relationship between the reliability levels of the system and individual components.
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Received: 24 December 2009; in revised form: 28 January 2010 / Accepted: 1 February 2010 / Published: 9 February 2010
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Abstract: This work presents a thermoelectric micro generator fabricated by the commercial 0.35 μm complementary metal oxide semiconductor (CMOS) process and the post-CMOS process. The micro generator is composed of 24 thermocouples in series. Each thermocouple is constructed by p-type and n-type polysilicon strips. The output power of the generator depends on the temperature difference between the hot and cold parts in the thermocouples. In order to prevent heat-receiving in the cold part in the thermocouples, the cold part is covered with a silicon dioxide layer with low thermal conductivity to insulate the heat source. The hot part of the thermocouples is suspended and connected to an aluminum plate, to increases the heat-receiving area in the hot part. The generator requires a post-CMOS process to release the suspended structures. The post-CMOS process uses an anisotropic dry etching to remove the oxide sacrificial layer and an isotropic dry etching to etch the silicon substrate. Experimental results show that the micro generator has an output voltage of 67 μV at the temperature difference of 1 K.
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Received: 29 December 2009; in revised form: 21 January 2010 / Accepted: 1 February 2010 / Published: 11 February 2010
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Abstract: Pressure measurement in high temperature environments is important in many applications to provide valuable information for performance studies. Information on pressure patterns is highly desirable for improving performance, condition monitoring and accurate prediction of the remaining life of systems that operate in extremely high temperature environments, such as gas turbine engines. A number of technologies have been recently investigated, however these technologies target specific applications and they are limited by the maximum operating temperature. Thick and thin films of SiCN can withstand high temperatures. SiCN is a polymer-derived ceramic with liquid phase polymer as its starting material. This provides the advantage that it can be molded to any shape. CERASET™ also yields itself for photolithography, with the addition of photo initiator 2, 2-Dimethoxy-2-phenyl-acetophenone (DMPA), thereby enabling photolithographical patterning of the pre-ceramic polymer using UV lithography. SiCN fabrication includes thermosetting, crosslinking and pyrolysis. The technology is still under investigation for stability and improved performance. This work presents the preparation of SiCN films to be used as the body of a sensor for pressure measurements in high temperature environments. The sensor employs the phenomenon of drag effect. The pressure sensor consists of a slender sensitive element and a thick blocking element. The dimensions and thickness of the films depend on the intended application of the sensors. Fabrication methods of SiCN ceramics both as thin (about 40–60 µm) and thick (about 2–3 mm) films for high temperature applications are discussed. In addition, the influence of thermosetting and annealing processes on mechanical properties is investigated.
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Received: 31 December 2009; in revised form: 19 February 2010 / Accepted: 25 February 2010 / Published: 1 March 2010
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Abstract: The aim of this study was to test the user performance, satisfaction and acceptability of the Helping Hand™ (B&O Medicom) electronic medication adherence monitor. Using a mixed-method design, we studied 11 kidney transplant patients and 10 healthy volunteers during three weeks. Although testing showed positive usability aspects, several areas requiring technical improvement were identified: the most important obstacles to usability and acceptability were the weak sound signal, problems loading the medication, and the fact that only one medication could be used at a time.
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Received: 31 December 2009; in revised form: 2 February 2010 / Accepted: 25 February 2010 / Published: 2 March 2010
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Abstract: In a prospective descriptive laboratory study, 25 Helping Hand™ (HH) (10 without and 15 with reminder system) and 50 Medication Event Monitoring Systems (MEMS) (25 with 18-month and 25 with 2-year battery life) were manipulated twice daily following a predefined protocol during 3 consecutive weeks. Accuracy was determined using the fixed manipulation scheme as the reference. Perfect functioning (i.e., total absence of missing registrations and/or overregistrations) was observed in 70% of the HH without, 87% of the HH with reminder, 20% MEMS with 18 months, and 100% with 2-year battery life respectively.
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Received: 22 February 2010; in revised form: 17 March 2010 / Accepted: 6 April 2010 / Published: 14 April 2010
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Abstract: A bulk micromachined inertial measurement unit (MIMU) is presented in this paper. Three single-axis accelerometers and three single-axis gyroscopes were simultaneously fabricated on a silicon wafer using a bulk micromachining process; the wafer is smaller than one square centimeter. In particular, a global area optimization method based on the relationship between the sensitivity and layout area was proposed to determine the layout configuration of the six sensors. The scale factors of the X/Y-axis accelerometer and Z-axis accelerometer are about 213.3 mV/g and 226.9 mV/g, respectively. The scale factors of the X/Y-axis gyroscope and Z-axis gyroscope are about 2.2 mV/o/s and 10.8 mV/o/s, respectively. The bias stability of the X/Y-axis gyroscope and the Z-axis gyroscope are about 2135 deg/h and 80 deg/h, respectively. Finally, the resolutions of X/Y-axis accelerometers, Z-axis accelerometers, X/Y-axis gyroscopes, and Z-axis gyroscopes are 0.0012 g/ √Hz, 0.0011 g/ √Hz, 0.314 °/s/ √Hz, and 0.008 °/s/ √Hz, respectively.
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Received: 5 January 2010; in revised form: 8 March 2010 / Accepted: 22 March 2010 / Published: 20 April 2010
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Abstract: This paper discusses the assembly challenges considering the design and manufacturability of a Wafer Level Thin Film Package in MEMS applications. The assembly processes are discussed. The loads associated with these processes are illustrated and evaluated. Numerical calculations are combined with experimental observations in order to estimate the assembly risks. Our results emphasize the need for concurrent design for assembly.
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Received: 31 December 2009; in revised form: 8 April 2010 / Accepted: 13 April 2010 / Published: 17 May 2010
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Abstract: In this paper a methodology for the three dimensional (3D) modeling and simulation of the profile evolution during anisotropic wet etching of silicon based on the level set method is presented. Etching rate anisotropy in silicon is modeled taking into account full silicon symmetry properties, by means of the interpolation technique using experimentally obtained values for the etching rates along thirteen principal and high index directions in KOH solutions. The resulting level set equations are solved using an open source implementation of the sparse field method (ITK library, developed in medical image processing community), extended for the case of non-convex Hamiltonians. Simulation results for some interesting initial 3D shapes, as well as some more practical examples illustrating anisotropic etching simulation in the presence of masks (simple square aperture mask, convex corner undercutting and convex corner compensation, formation of suspended structures) are shown also. The obtained results show that level set method can be used as an effective tool for wet etching process modeling, and that is a viable alternative to the Cellular Automata method which now prevails in the simulations of the wet etching process.
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Received: 9 March 2010; in revised form: 18 May 2010 / Accepted: 24 May 2010 / Published: 21 June 2010
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Abstract: Electrostatic-driven microelectromechanical systems devices, in most cases, consist of couplings of such energy domains as electromechanics, optical electricity, thermoelectricity, and electromagnetism. Their nonlinear working state makes their analysis complex and complicated. This article introduces the physical model of pull-in voltage, dynamic characteristic analysis, air damping effect, reliability, numerical modeling method, and application of electrostatic-driven MEMS devices.
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Planned Papers
The below list represents only planned manuscripts. Some of these
manuscripts have not been received by the Editorial Office yet. Papers
submitted to MDPI journals are subject to peer-review.
Type of Paper: Review
Title: Mathematical Modeling of Electrostatic MEMS
Authors: Jordan Berg et al.; E-Mail: jordan.berg@ttu.edu
Abstract: Electrostatic MEMS are used in many applications, including optical switches, microrelays, digital displays, micromotors, micropumps, microgrippers, and RF switches. Understanding and predicting the performance of these devices relies on proper modeling of electrostatic fields, charge flow, and mechanical response, including consideration of fringing fields and parasitic capacitances. The interactions between these elements may result in phenomena such as pull-in that profoundly influence device behavior. Mathematical models of electrostatic MEMS serve a variety of purposes, from conceptual design to detailed simulation. This review surveys and discusses models reported in the literature. Special attention is paid to model validation. The intention is to inform readers of the range of results available for mathematical modeling of electrostatic MEMS, and to aid in the selection of the most suitable approach for a particular task.
Papers Published in 2007 and 2008
Last update: 5 April 2011
