A Numerical Fatigue Damage Model for Life Scatter of MEMS Devices

This paper presents a fatigue damage model to estimate fatigue lives of microelectromechanical systems (MEMS) devices and account for the effects of topological randomness of material microstructure. For this purpose, the damage mechanics modeling approach is incorporated into a new Voronoi finite-element model (VFEM). The VFEM developed for this investigation is able to consider both intergranular crack initiation (debonding) and propagation stages. The model relates the fatigue life to a damage parameter "D" which is a measure of the gradual material degradation under cyclic loading. The fatigue damage model is then used to investigate the effects of microstructure randomness on the fatigue of MEMS. In this paper, three different types of randomness are considered: (1) randomness in the microstructure due to random shapes and sizes of the material grains; (2) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus; and (3) the randomness in the material properties considering a normally distributed resistance stress, which is the experimentally determined material property controlling the ability of a material to resist the damage accumulation. Thirty-one numerical models of MEMS specimens are considered under cyclic axial and bending loading conditions. It is observed that the stress-life results obtained are in good agreement with the experimental study. The effects of material inhomogeneity and internal voids are numerically investigated.     

Silicon MEMS components: a fatigue life assessment approach

A fatigue damage approach for life assessment of silicon micro-components is proposed. The components of this model have been developed based on the physics of crack initiation and damage progress on the most damaging planes. This approach may be of great importance in durability assessment of silicon-based MEMS components while the complexity of testing equipment, micro-sized specimen preparation, and the high expenses associated with the fatigue tests of micro-components are of great concern. Fatigue damage accumulation of silicon micro-components is accompanied with the formation of inclined micro-critical planes of {111} on the fracture surface as a means of dissipating energy during fatigue damage progress, which coincides with the theory of fatigue damage accumulation in Varvanis approach (2000). Predicted fatigue lives based on the damage model were found in good agreement with experimental fatigue life data of these components reported in the literature. Correlations are within a factor of ±2.5 for short and long lives, which are within the limits of acceptance.The financial support of Natural Science and Engineering Research Council (NSERC) of Canada is greatly appreciated.Phone: 416-979-5000 Ext. 7707     

Low cycle fatigue of single crystal silicon thin films

Silicon will continue to be the critical structure material for micromechanical components for years to come so that reliability must be a key concern. Consequently, in order to ensure reliability design approaches must account for fatigue behavior. This work is aimed at studying the fatigue of single crystal silicon (SCS) thin films by a specially designed method. The films were tested using cantilever microbeam deflection with respect to the effect of loading conditions. To conduct a fatigue test under cyclic strain would be more realistic because many MEMS applications, such as micro-accelerometers and micro-filters, consist of beams vibrating in the same mode. A micro-force testing machine with a micro-probe and specially designed fixtures is used to contact and load the beams under the cyclic strain. Before the fatigue test, the failure strain _f of beams in the flexural test is achieved as the testing criterion. In fatigue testing, various percentages of failure strain _f, two times of the strain amplitude, are adopted. First of all, fatigue strain–life cycle (S/N) curve is achieved. Further, the curve of fatigue force detected on the SCS versus fatigue life is measured. SEM is also employed to observe the fracture modes of films under fatigue. Based on the SEM observation and force/life curve, the failure mechanism of the fatigued SCS films under the cyclic strain is proposed. This provides a viable method to evaluate the reliability of the SCS.     

A Study for the Effect of the PCB Motion on the Dynamics of MEMS Devices Under Mechanical Shock

We present a theoretical and experimental investigation into the effect of the motion of a printed circuit board (PCB) on the response of microelectromechanical systems (MEMS) devices to shock loading. For the theoretical part, a 2-DOF model is used, where the first degree of freedom accounts for the PCB. The second degree of freedom represents the motion of the MEMS microstructure. Low-g acceleration pulses are applied to the MEMS–PCB assembly base to simulate shock pulses generated from a drop-table test. Simulation data are presented to show the effects of the natural frequency of the PCB, the natural frequency of the microstructure, and the shock pulse duration. Universal 3-D spectra representing the effect of these parameters are presented. It is found that neglecting the PCB effect on the design of MEMS devices under shock loads can lead to undesirable motion of their microstructures. The effects of electrostatic force and squeeze film damping are investigated. It is found that the amplification of motion due to the PCB can cause early pull-in instability for MEMS devices implementing electrostatic forces. The effect of higher order modes of a microbeam is studied through a continuous beam model coupled with a lumped model of the PCB. The limitations of the 2-DOF model are discussed. An experimental investigation is conducted to verify the theoretical results using a capacitive accelerometer. Experimental data for the response of the accelerometer while it is mounted on two representative PCBs due to different low-g shock conditions are shown.$hfill$[2008-0026]      

多晶硅双端固支梁高周循环下疲劳特性的分析

多晶硅固支梁是MEMS器件中较常见的可动部件,通过静电激励的方式对其进行疲劳振动加载;所用结构为面外运动结构,为了测试样品的加速疲劳特性,通过在固支梁面内引入缺陷的方式来增大应力水平值;器件在经历了1.72×1011次循环之后,微梁的谐振频率、振动幅度发生了较大偏移,其谐振频率的偏移量达到14.531 kHz,器件性能发生了严重的退化.研究结果表明,利用谐振频率的改变来表征材料性能的退化是一种准确、可行的方法,同时本文进一步分析指出,器件上引入凹槽缺陷的方法确实可起到加速疲劳的作用;可利用此方法制作不同应力水平幅度的结构进行振动载荷疲劳加载实验,从而得到固支梁结构疲劳加速因子.     

复合材料层板结构疲劳失效数值仿真研究

研究疲劳载荷作用下复合材料层板结构的疲劳失效问题,由于复合材料损伤演化和破坏机理十分复杂,传统方法依赖大量的试验数据,不仅耗费大,而且适用性有限。为了提高复合材料在疲劳载荷下疲劳失效的准确预测,提出了一种改进的疲劳失效分析方法。得到一个与损伤相关联的刚度-强度关联退化模型,利用复合材料刚度退化的连续性将损伤等效累积,使之能够适用于复杂载荷下的疲劳失效分析。利用Ansys软件开发了相应的复合材料层板结构参数化疲劳分析程序,能够仿真不同几何参数下复合材料层板结构在疲劳载荷下的疲劳失效过程。通过不同类型的算例比较,结果令人满意,证明改进方法及相应程序的正确性,具有工程应用价值。     

Fatigue reliability analysis for structures with known loading trend

Variations, such as those in product operation environment and material properties, result in random fatigue life. Variations in material fatigue properties depend on stochastic stress responses due to their nonlinear relationships with other random variables such as stochastic loading and dimensions. In this work, an efficient fatigue reliability analysis method is developed to accommodate those uncertainties for structures under cyclic loads with known loading trend. To reduce the computational cost, the method incorporates the fatigue life analysis model and the saddlepoint approximation method with the fast integration method. The new method is applied to the fatigue reliability analysis of a cantilever beam and a door cam. The results show high accuracy and efficiency of the proposed method benchmarked with Monte Carlo Simulations.     

Planning accelerated life tests with three constant stress levels

This paper presents two alternative ways of planning for constant stress accelerated tests (CSALT) with three stress levels that not only optimize the stress levels but also optimize the sample allocations. In the first method, we consider limiting the chances of inconsistency arising from non-parallel lines when data from different stress levels are plotted on the same probability plot. For the second method, we consider minimizing both the variance of some estimate and the influence arising from the addition of middle stress when the assumed stress–life relation is true. The test plan generated using the first approach is useful when one needs to establish beyond reasonable doubt that the shape parameters of the assumed Weibull distributions (or other parameters that are related to the slope of the probability plot for other distributions) at different stress levels are different. The second approach is useful when one needs to validate a particular stress–life relationship. Both approaches are formulated as constrained non-linear programs.     

Statistical analysis and predictions of fracture and fatigue of micro-components

A number of materials typically used in MEMS technology exhibit brittle fracture behaviour which leads to a scatter in strength and a size effect as a consequence. Furthermore, some of these materials, e.g. polycrystalline silicon, show fatigue effects which limit the lifetime under cyclic loading conditions. Probabilistic methods based on the Weibull theory have been established successfully in predicting the strength of micro-components under static loading. However, the consequence of fatigue on reliability predictions has not yet been studied extensively. We present strength as well as lifetime predictions for poly-silicon components with stress concentrations based on experimental data published in the literature. Our results show that while strength predictions for components with stress concentrations based on scaling procedures works well, lifetime prediction is a challenging task associated with large prediction uncertainties. Finally, we relate the crack propagation approach used for our lifetime predictions with micro-mechanical fatigue models that are discussed for poly-silicon.     

多晶硅梁疲劳损坏特性的研究

针对多晶硅的疲劳失效机理,人们已经提出了一些解释的模型.然而,到目前为止没有一种模型能够全面地阐述疲劳失效机理.本文旨在采用参量的渐变,如平均杨氏模量E,来反映MEMS多晶硅梁的疲劳.通过测试周期性载荷下双端固支梁结构的pull-in电压变化,确定杨氏模量E的变化,进而表征梁的疲劳失效状态.     

Cyclic plasticity models and application in fatigue analysis

An analytical procedure for prediction of the cyclic plasticity effects on both the structural fatigue life to crack initiation and the rate of crack growth is presented. The crack initiation criterion is based on the Coffin-Manson formulae extended for multiaxial stress state and for inclusion of the mean stress effect. This criterion is also applied for the accumulated damage ahead of the existing crack tip which is assumed to be related to the crack growth rate. Three cyclic plasticity models, based on the concept of combination of several yield surfaces, are employed for computing the crack growth rate of a cracked plane stress panel under several cyclic loading conditions.     

Fatigue-life estimation of functionally graded materials using XFEM

The present work deals with the fatigue crack growth simulation of alloy/ceramic functionally graded materials (FGMs) using extended finite element method (XFEM). Various cases of FGM containing multiple inhomogeneities/discontinuities along with either a major edge or a center crack are taken for the purpose of simulation. The fatigue life of the FGM plate is calculated using Paris law of fatigue crack growth under cyclic loading. The effect of multiple inhomogeneities/discontinuities (minor cracks, holes/voids, and inclusions) on the fatigue life of cracked FGM plate is studied in detail. These simulations show that the presence of inhomogeneities/discontinuities in the domain significantly influences the fatigue life of the components.     

压力传感器引线键合金线的振动疲劳研究

本文对一种汽车用MEMS压力传感器中的键合金线,在加速振动试验时的疲劳情况进行了研究.首先简单介绍了MEMS压力敏感芯片引线键合以及引线的基本情况,然后利用有限元方法对引线在20g的加速振动下的疲劳和寿命进行了分析,并利用了概率上的冗余理论对键合工艺提出了改进,最后给出了实际的结果,证实了模拟和改进工艺的合理性.     

The critical role of environment in fatigue damage accumulation in deep-reactive ion-etched single-crystal silicon structural films

The importance of service environment to the fatigue resistance of n/sup +/-type, 10 /spl mu/m thick, deep-reactive ion-etched (DRIE) silicon structural films used in microelectromechanical systems (MEMS) was characterized by testing of electrostatically actuated resonators (natural frequency, f/sub 0/, /spl sim/40 kHz) in controlled atmospheres. Stress-life (S-N) fatigue tests conducted in 30/spl deg/C, 50% relative humidity (R.H.) air demonstrated the fatigue susceptibility of silicon films. Further characterization of the films in medium vacuum and 25% R.H. air at various stress amplitudes revealed that the rates of fatigue damage accumulation (measured via resonant frequency changes) are strongly sensitive to both stress amplitude and, more importantly, humidity. Scanning electron microscopy of high-cycle fatigue fracture surfaces (cycles to failure, N/sub f/>1/spl times/10/sup 9/) revealed clear failure origins that were not observed in short-life (N/sub f/<1/spl times/10/sup 4/) specimens. Reaction-layer and microcracking mechanisms for fatigue of silicon films are discussed in light of this empirical evidence for the critical role of service environment during damage accumulation under cyclic loading conditions.     

Selection of high strength encapsulant for MEMS devices undergoing high-pressure packaging

Deflection behavior of several encapsulant materials under uniform pressure was studied to determine the best outer encapsulant for MEMS device. Encapsulation is needed to protect movable parts of MEMS devices during high-pressure transfer molded packaging process. The selected outer encapsulant material has to have surface deflection of less than 5 μm under 100 atm vertical loading. Deflection was simulated using Coventorware ver.2005 software and verified with calculation results obtained using shell bending theory. Screening design was used to construct a systematic approach for selecting the best encapsulant material and thickness under uniform pressure up to 100 atm. Materials considered for this study were SMC polyimide, liquid crystal polymer (LCP) carbon fiber and polyphenylene sulfide (PPS) high modulus carbon fiber. It was observed that PPS high modulus carbon fiber has deflection of less than 5 μm for all thickness and pressure variations. LCP carbon fiber is acceptable and SMC polyimide is unsuitable as high strength encapsulant. PPS high modulus carbon fiber is considered the best encapsulation material for MEMS under high-pressure packaging process due to its high strength. The generalized mathematical model and equations developed for predicting deflection of encapsulation under uniform loading could be used to determine the suitability of any candidate material and encapsulation design with similar domed shaped structure.     

Fatigue Life Prediction Criterion for Micro–Nanoscale Single-Crystal Silicon Structures

This paper describes fatigue damage evaluation for micro–nanoscale single-crystal silicon (SCS) structures toward the reliable design of microelectromechanical systems subjected to fluctuating stresses. The fatigue tests, by using atomic force microscope (AFM), nanoindentation tester, and specially developed uniaxial tensile tester, have been conducted under tensile and bending deformation modes for investigating the effects of specimen size, frequency, temperature, and deformation mode on the fatigue life of SCS specimens. Regardless of frequency and temperature, the fatigue life has correlated with specimen size. For example, nanoscale SCS specimens with 200 nm in width and 255 nm in thickness have showed a larger number of cycles to failure, by a factor of $10^{5}$, at the same stress level, as compared to microscale specimens with 48 $muhbox{m}$ in width and 19 $muhbox{m}$ in thickness. Deformation mode has also affected the lifetime; however, no frequency and temperature dependences have been observed unambiguously in the $S{-}N$ curves. The stress ratio parameter corresponding to the ratio of peak stress to average fracture strength has enabled us to estimate the lifetime for each deformation mode. To predict the fatigue life of SCS structures regardless of deformation mode and specimen size, we have proposed an empirical parameter that includes the resolved shear stress. The mechanism of fatigue failure of SCS structures is discussed from the viewpoint of dislocation slip, crack nucleation, growth, and failure through observations using AFM and scanning electron microscope.$hfillhbox{[2008-0072]}$      

Prediction of constant amplitude fatigue crack growth life of 2024 T3 Al alloy with R-ratio effect by GP

The objective of this study is to develop a genetic programming (GP) based model to predict constant amplitude fatigue crack propagation life of 2024 T3 aluminum alloys under load ratio effect based on experimental data and to compare the results with earlier proposed ANN model. It is proved that genetic programming can effectively interpret fatigue crack growth rate data and can efficiently model fatigue life of the material system under investigation in comparison to ANN model.     

Topology optimization with finite-life fatigue constraints

This work investigates efficient topology optimization for finite-life high-cycle fatigue damage using a density approach and analytical gradients. To restrict the minimum mass problem to withstand a prescribed finite accumulated damage, constraints are formulated using Palmgren-Miner’s linear damage hypothesis, S-N curves, and the Sines fatigue criterion. Utilizing aggregation functions and the accumulative nature of Palmgren-Miner’s rule, an adjoint formulation is applied where the amount of adjoint problems that must be solved is independent of the amount of cycles in the load spectrum. Consequently, large load histories can be included directly in the optimization with minimal additional computational costs. The method is currently limited to proportional loading conditions and linear elastic material behavior and a quasi-static structural analysis, but can be applied to various equivalent stress-based fatigue criteria. Optimized designs are presented for benchmark examples and compared to stress optimized designs for static loads.     

A Microfabricated Planar Electrospray Array Ionic Liquid Ion Source With Integrated Extractor

This paper reports the design, fabrication, and experimental characterization of a fully microfabricated planar array of externally fed electrospray emitters that produces heavy molecular ions from the ionic liquids $hbox{EMI-BF}_{4}$ and EMI-Im. The microelectromechanical systems (MEMS) electrospray array is composed of the following two microfabricated parts: 1) an emitter die with as many as 502 emitters in 1.13 $hbox{cm}^{2}$ and 2) an extractor component that provides assembly alignment, electrical insulation, and a common bias voltage to the emitter array. The devices were created using Pyrex and silicon substrates, as well as microfabrication techniques such as deep reactive ion etching, low-temperature fusion bonding, and anodic bonding. The emitters are coated with black silicon, which acts as a wicking material for transporting the liquid to the emitter tips. The extractor electrode uses a 3-D MEMS packaging technology that allows hand assembly of the two components with micrometer-level precision. Experimental characterization of the MEMS electrospray array includes current–voltage characteristics, time-of-flight mass spectrometry, beam divergence, and imprints on a collector. The data show that with both ionic liquids and in both polarities, the electrospray array works in the pure ionic regime, emitting ions with as little as 500 V of bias voltage. The data suggest that the MEMS electrospray array ion source could be used in applications such as coating, printing, etching, and nanosatellite propulsion. $hfill$[2008-0270]