Propagation of material and surface profile uncertainties on MEMS micro‐resonators using a stochastic second‐order computational multi‐scale approach

This paper aims at accounting for the uncertainties because of material structure and surface topology of micro‐beams in a stochastic multi‐scale model. For micro‐resonators made of anisotropic polycrystalline materials, micro‐scale uncertainties exist because of the grain size, grain orientation, and the surface profile. First, micro‐scale realizations of stochastic volume elements are obtained based on experimental measurements. To account for the surface roughness, the stochastic volume elements are defined as a volume element having the same thickness as the microelectromechanical system (MEMS), with a view to the use of a plate model at the structural scale. The uncertainties are then propagated up to an intermediate scale, the meso‐scale, through a second‐order homogenization procedure. From the meso‐scale plate‐resultant material property realizations, a spatially correlated random field of the in‐plane, out‐of‐plane, and cross‐resultant material tensors can be characterized. Owing to this characterized random field, realizations of MEMS‐scale problems can be defined on a plate finite element model. Samples of the macro‐scale quantity of interest can then be computed by relying on a Monte Carlo simulation procedure. As a case study, the resonance frequency of MEMS micro‐beams is investigated for different uncertainty cases, such as grain‐preferred orientations and surface roughness effects. Copyright © 2016 John Wiley & Sons, Ltd.     

Uncertainty in microscale gas damping: Implications on dynamics of capacitive MEMS switches

Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150 V), i.e. the voltage required to actuate 90% of the sample, is about 129 cm/s and increases to 173 cm/s for the 99%-actuation voltage (of about 173 V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness.     

Robust Free‐Standing Nano‐Thin SiC Membranes Enable Direct Photolithography for MEMS Sensing Applications

This work presents fabrication of micro structures on sub–100 nm SiC membranes with a large aspect ratio up to 1:3200. Unlike conventional processes, this approach starts with Si wet etching to form suspended SiC membranes, followed by micro‐machined processes to pattern free‐standing microstructures such as cantilevers and micro bridges. This technique eliminates the sticking or the under‐etching effects on free‐standing structures, enhancing mechanical performance which is favorable for MEMS applications. In addition, post‐Si‐etching photography also enables the formation of metal electrodes on free standing SiC membranes to develop electrically‐measurable devices. To proof this concept, the authors demonstrate a SiC pressure sensor by applying lithography and plasma etching on released ultrathin SiC films. The sensors exhibit excellent linear response to the applied pressure, as well as good repeatability. The proposed method opens a pathway for the development of self‐sensing free‐standing SiC sensors.     

Inkjet‐Printed High‐Q Nanocrystalline Diamond Resonators

Diamond is a highly desirable material for state‐of‐the‐art micro‐electromechanical (MEMS) devices, radio‐frequency filters and mass sensors, due to its extreme properties and robustness. However, the fabrication/integration of diamond structures into Si‐based components remain costly and complex. In this work, a lithography‐free, low‐cost method is introduced to fabricate diamond‐based micro‐resonators: a modified home/office desktop inkjet printer is used to locally deposit nanodiamond ink as ?50–60 µm spots, which are grown into ≈1 µm thick nanocrystalline diamond film disks by chemical vapor deposition, and suspended by reactive ion etching. The frequency response of the fabricated structures is analyzed by laser interferometry, showing resonance frequencies in the range of ≈9–30 MHz, with Q ‐factors exceeding 10⁴, and (f₀ × Q) figure of merit up to ≈2.5 × 10¹¹ Hz in vacuum. Analysis in controlled atmospheres shows a clear dependence of the Q‐factors on gas pressure up until 1 atm, with Q ∝ 1/P. When applied as mass sensors, the inkjet‐printed diamond resonators yield mass responsivities up to 981 Hz fg^?1 after Au deposition, and ultrahigh mass resolution up to 278 ± 48 zg, thus outperforming many similar devices produced by traditional top‐down, lithography‐based techniques. In summary, this work demonstrates the fabrication of functional high‐performance diamond‐based micro‐sensors by direct inkjet printing.     

Heat‐flux‐specified boundary treatment for gas flow and heat transfer in microchannel using direct simulation Monte Carlo method

Direct simulation Monte Carlo (DSMC) method has been widely used to study gaseous flow and heat transfer in micro‐fluidic devices. For flows associated with microelectromechanical systems (MEMS), the heat‐flux‐specified (HFS) boundary condition broadly exists. However, problems with HFS boundary have not been realized in the simulation of microchannel flows with DSMC method. To overcome this problem, a new technique named as inverse temperature sampling (ITS) is developed. This technique provides an approach to calculate the molecular reflective characteristic temperature from the specified heat flux at the wall boundary. Coupling with DSMC method, the ITS technique can treat the HFS boundary condition in DSMC method for both simple gas and gas mixtures. For validation, heat flux obtained from two‐dimensional Poiseuille flows with wall‐temperature‐specified (WTS) boundary condition is employed as the initial thermal boundary condition of our new method. Sampled wall temperature by the ITS method agrees well with the expected value. Pressure, velocity and temperature distributions under these two thermal boundary conditions (WTS and HFS) are compared. Effects of molecule collision model and gas–surface interaction model are also investigated. Results show that the proposed ITS method could accurately simulate gaseous flow and heat transfer in MEMS. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi‐linearity algorithm for wall slip in two‐dimensional gap flow

Wall slip has been observed in a micro/nanometer gap during the past few years. It is difficult to make a mathematical analysis for the hydrodynamics of the fluid flowing in a gap with wall slip because the fluid velocity at the liquid–solid interface is not known a priori. This difficulty is met especially in a two‐dimensional slip flow due to the non‐linearity of the slip control equation. In the present paper we developed a multi‐linearity method to approach the non‐linear control equation of the two‐dimensional slip gap flow. We used an amended polygon to approximate the circle yield (slip) boundary of surface shear stress. The numerical solution does not need an iterative process and can simultaneously give rise to fluid pressure distribution, wall slip velocity and surface shear stress. We analysed the squeeze film flow between two parallel discs and the hydrodynamics of a finite slider gap with wall slip. Our numerical solutions show that wall slip is first developed in the large pressure gradient zone, where a high surface shear stress is easily generated, and then the slip zone is enlarged with the increase in the shear rate. Wall slip dramatically affects generation of the hydrodynamic pressure. Copyright © 2006 John Wiley & Sons, Ltd.     

石英晶振真空度检测系统

随着科研及工业的不断发展, 对真空环境的要求越来越高, 相应的真空测量技术要求也越来越严格, 在精准测量的基础上对传感器的体积提出了更高的要求, 例如MEMS封装的真空设备将需要较小体积的传感器来完成真空度的测量。而目前常见的电阻真空规、液态式真空计、电容真空计、热传导真空计等都无法同时满足小体积、宽范围、高精度的测量要求。本文基于石英晶振在不同气压环境下振荡时其两端阻抗随环境中气压的改变而变化的原理, 设计了石英晶振振荡电路、信号隔离电路、差分放大电路、真有效值转换电路等, 并且将其前端信号利用STM32单片机进行处理, 通过编写对应的软件程序实现不同环境中真空度检测。在石英晶振振荡电路方面与已有研究有所不同, 本文采用石英晶振本身作为激励信号的自振荡电路, 相对于已有研究中的外加激励信号源而言频率稳定, Q值高, 因此能够产生非常稳定的正弦振荡, 可以有效的减小整个系统的测量误差, 提高测量精度。经过实际测试, 实验结果表明, 系统设计合理, 测量精度高, 达到预期测量效果。     

Braking of a “Magnetized” Sphere in a Hypersonic Rarefied Plasma Flow

The dependence of the drag coefficient of a “magnetized” (with a self-generated magnetic field) sphere on the ratio of the magnetic pressure to the gas dynamic pressure in a hypersonic rarefied plasma flow is determined experimentally. The dependences are obtained for a wide range of angles between the vectors of the incident flow velocity and the magnetic field, as well as between the velocity vectors of the incident hypersonic plasma flow and a subsonic plasma jet injected from the surface of the sphere. It is shown that the injection of a subsonic plasma jet from the surface of a “magnetized” sphere in a hypersonic rarefied plasma flow increases its drag coefficient by several times in comparison with an “unmagnetized” sphere.     

Powder‐Based Ceramic Meso‐ and Microscale Fabrication Processes

Processing techniques are reviewed that allow the introduction of ceramic components made from powders into microelectromechanical systems (MEMS). Ceramics have several advantages over other materials also in microsystems, e.g., heat resistance, hardness, corrosion resistivity, or functional properties. The range of available materials in microfabrication technology is being increased beyond those deposited by thin‐film technology. Top–down approaches like mechanical and laser‐based direct writing processes, ink‐jet printing, microextrusion, and lithography‐based methods are presented. They are complemented by some more fundamental work in the field of bottom–up synthesis of micro‐ and nanoscaled ceramic materials.     

On the evaluation of damping in MEMS in the slip–flow regime

The analysis of fluid damping in micro‐electro‐mechanical systems (MEMS) is addressed. A mixed fast multipole boundary element method based on both velocity and traction integral equations is employed and adapted in order to account for slip boundary conditions. The formulation presented is applied to the analysis of a biaxial accelerometer and validated with experimental results. Copyright © 2006 John Wiley & Sons, Ltd.     

Reliability‐based Design for Damping Behavior of Inner Mass Single‐unit Impact Dampers

In this paper, the dynamic response of a vibratory system equipped with a single‐unit impact damper is analyzed. The reliability behavior of this system is investigated when the stress and strength are distributed lognormally. The standard deviation of lognormal stress is realistically calculated by applying external noise and an uncertainty parameter in the simulated model. Variations of the damping inclination and the reliability of the system, with respect to the coefficient of restitution, are obtained. Finally, damping inclination, safety factor and system reliability are presented in a user‐oriented diagram. Such reliable systems equipped with impact dampers can strongly suppress the undesired vibrations. Copyright © 2012 John Wiley & Sons, Ltd.     

Vakuummikro‐ und Vakuumnanoelektronik mit Feldemission

Vacuum microelectronics and nanoelectronics with field emission — features of breakdown voltage in vacuum gaps lower than 10 μm Further miniaturization in vacuum electronics will be possible only with field‐emitter cathodes. However in microscale vacuum gaps in the range 10 μm field emission is a dominant process in gas breakdown process, leading to signif icant deviations from the traditional Paschen's Law. At first a significant reduction of breakdown voltage is observed. The high surface‐to‐volume ratio in microscale dimensions 3 μm and in interactions with gas desorption, outgassing and gas ionization during electron field‐emission give a ignition and stabilization of micro plasmas (glow discharges) or/and micro arcs, which exist largely independent of surrounding vacuum, atmospheric or over pressure. In this range the Paschen's Law is invalid. This is an interesting approach which opens up new dimensions for basic research, field emission‐driven micro plasmas and for novel fieldemitter applications in vacuum electronics and plasma technology.     

Einsatz von Mikroplasmen für die Herstellung von Silizium‐Mehrlagenaufbauten

Micro Plasma Processes for MEMS Packaging The encapsulation of MEMS devices can be difficult, since released micromechanical parts (e.g. membranes, valves, and cantilevers) tend to stick to the surrounding surfaces. Area‐selective surface modification is a new approach, developed by the Fraunhofer‐Institute for Surface Engineering and Thin Films (IST), to overcome these problems. From a more general point of view, area‐selective surface tailoring with microplasmas is an attractive topic for micro systems production. The business transfer of the technique by implementation into the SU SS mask is currently being evaluated.     

基于MEMS技术的SU-8胶被动微阀片的设计与研制

为解决微流体在微流控芯片上的单向流动,进而实现生化反应的片上系统,采用微机电系统（MEMS）技术加工出SU-8胶微型阀片．SU-8胶阀片具有弹性模量和弹性常数低、开启压力小、反向泄漏小、易于加工等特点．从理论上分析了不同厚度（10μm,15μm,20μm,25μm）的微型阀片在不同压力作用下的挠度和应力分布,在相同尺寸和压力下,SU-8微阀片的挠度与传统的硅阀片的挠度相比要大10倍左右．讨论了有阻尼作用下的谐振频率以及过流特性。可知阀臂和阀座的尺寸是影响阀片性能的主要因素．给出了加工工艺,测试了阀片的正反向过流性能,以水作为工作物质,得到3种厚度阀片的过流曲线,其最大正向流速达到7000μL／min．     

A Shape‐Adaptive Thin‐Film‐Based Approach for 50% High‐Efficiency Energy Generation Through Micro‐Grating Sliding Electrification

Effectively harvesting ambient mechanical energy is the key for realizing self‐powered and autonomous electronics, which addresses limitations of batteries and thus has tremendous applications in sensor networks, wireless devices, and wearable/implantable electronics, etc. Here, a thin‐film‐based micro‐grating triboelectric nanogenerator (MG‐TENG) is developed for high‐efficiency power generation through conversion of mechanical energy. The shape‐adaptive MG‐TENG relies on sliding electrification between complementary micro‐sized arrays of linear grating, which offers a unique and straightforward solution in harnessing energy from relative sliding motion between surfaces. Operating at a sliding velocity of 10 m/s, a MG‐TENG of 60 cm² in overall area, 0.2 cm³ in volume and 0.6 g in weight can deliver an average output power of 3 W (power density of 50 mW cm^?2 and 15 W cm^?3) at an overall conversion efficiency of ～50%, making it a sufficient power supply to regular electronics, such as light bulbs. The scalable and cost‐effective MG‐TENG is practically applicable in not only harvesting various mechanical motions but also possibly power generation at a large scale.     

A Murine Oral‐Exposure Model for Nano‐ and Micro‐Particulates: Demonstrating Human Relevance with Food‐Grade Titanium Dioxide

Human exposure to persistent, nonbiological nanoparticles and microparticles via the oral route is continuous and large scale (10¹²–10¹³ particles per day per adult in Europe). Whether this matters or not is unknown but confirmed health risks with airborne particle exposure warns against complacency. Murine models of oral exposure will help to identify risk but, to date, lack validation or relevance to humans. This work addresses that gap. It reports i) on a murine diet, modified with differing concentrations of the common dietary particle, food grade titanium dioxide (fgTiO₂), an additive of polydisperse form that contains micro‐ and nano‐particles, ii) that these diets deliver particles to basal cells of intestinal lymphoid follicles, exactly as is reported as a “normal occurrence” in humans, iii) that confocal reflectance microscopy is the method of analytical choice to determine this, and iv) that food intake, weight gain, and Peyer's patch immune cell profiles, up to 18 weeks of feeding, do not differ between fgTiO₂‐fed groups or controls. These findings afford a human‐relevant and validated oral dosing protocol for fgTiO₂ risk assessment as well as provide a generalized platform for application to oral exposure studies with nano‐ and micro‐particles.     

Hydrogen production from methane in electron-beam-generated plasma

Processes in a rarefied flow of methane activated by a high-energy electron beam have been studied as dependent on the gas pressure and the electron energy and total current. The electron beam initiates reactions leading to the conversion of methane into molecular hydrogen. The conversion coefficient has been determined as a function of the process parameters. By selecting proper parameters, it is possible to provide for a high rate of the conversion reaction.     

Determination and verification of the gap dependent heat transfer coefficient during permanent mold casting of A356 aluminum alloy

In complex castings, the heat transfer across the casting / mold interface depends on the local gap size and contact pressure. Thus, an experimental setup is constructed to measure and evaluate the air‐gap dependent heat transfer coefficient during solidification of an A356 permanent mold casting. In order to evaluate the heat transfer coefficient, the temperature gradient and air gap development is measured at the casting / mold interface. This allows the interface temperatures and the time‐dependent heat flux across the gap to be calculated as a function of the measured gap size. Furthermore, the heat transfer coefficient and gap size are correlated to the interface temperature of the casting. The experimental setup and the evaluation procedure provide consistent and reproducible results. The heat transfer coefficient thus evaluated is employed to simulate the experimental setup. The temperatures measured are well reproduced. The results of the present work are compared to simulations using two heat transfer coefficient functions found in literature. This comparison shows a substantial improvement over the state of the art. This improvement is due to the exact knowledge of gap formation and the corresponding values of the heat transfer coefficient.     

Prüflecks für Schnüffel‐Lecksucher

In the testing of leak tightness and in the localisation of leaks by means of a test gas, proper operation and sensitivity of the employed instrument must be checked by a certified reference leak. In the so‐called sniffer mode of operation, the component under test is filled to overpressure with the test gas, so that in case of a leak there is a gas flow from the component to atmosphere. The atmospheric gas is sucked by the instrument and probed for its test gas content. For checking the instruments performance, commercial test leaks are available for various gas species, which deliver a well‐defined leakage. Construction and properties of such a test leak are described. The leak has an internal gas reservoir and a capillary as leak element. Because the inlet pressure at the capillary is kept constant by a pressure controller, the leakage remains constant over several years despite the gradual pressure decrease in the gas reservoir. The calibration of the leakage via the volume flow rate is described in detail. The volume flow rate can be measured by a liquid drop in a measuring capillary as well as a displacement piston in a dosing syringe.     

Uncertainty and Traceability for the CEESI Iowa Natural Gas Facility

This paper analyzes the uncertainty of a secondary flow measurement facility that calibrates a significant fraction of United States and foreign flow meters used for custody transfer of natural gas. The facility, owned by the Colorado Experimental Engineering Station Incorporated (CEESI), is located in Iowa. This facility measures flow with nine turbine meter standards, each of which is traceable to the NIST primary flow standard. The flow capacity of this facility ranges from 0.7 actual m³/s to 10.7 actual m³/s at nominal pressures of 7174 kPa and at ambient temperatures. Over this flow range the relative expanded flow uncertainty varies from 0.28 % to 0.30 % (depending on flow).CEESI Iowa: natural gas facility, CEESI Iowa uncertainty analysis, CEESI traceability to NIST, correlation coefficient, critical flow venturi uncertainty, traceability, turbine meter uncertainty analysis