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.     

Characterizing mechanical behaviors of a flexible AMOLED during the debonding process

The stress distribution of a flexible active-matrix organic light-emitting diode (AMOLED) display during the debonding process was investigated using finite element analysis. During the fabrication of an AMOLED display, an AMOLED with a polyimide (PI) substrate is detached from a glass carrier; this is a critical process and generally results in failure of the AMOLED. To enhance the yielding rate of AMOLEDs, their stress states generated during the debonding process must be reduced. The interfacial fracture behavior between the PI substrate and glass carrier was characterized on the basis of bimaterial fracture mechanics, and the fracture toughness associated with mode mixity determined through peeling tests was considered a criterion for detaching the AMOLED from the glass carrier. The stress distribution of the AMOLED at the inception of debonding crack extension was evaluated according to fracture toughness. In addition, the parameters possibly influencing the stress states of the AMOLED in the debonding process are discussed.     

Mechanical properties and fracture analysis of glass substrate for PDPs

Abstract— A thermal shock test was carried out using high‐strain‐point glass substrates for plasma‐display panels. From the fracture analysis, the fracture stress was determined and compared with the initial edge strength. It was observed that the edge strength greatly decreased because of micro cracks that formed on the glass surface during testing. Therefore, it is important to prevent the formation of micro cracks in order to avoid failure as well as to minimize thermal stress in the process. Fatigue is also an important parameter in preventing the failure of the glass substrate when the stress on it lasts for a long period of time.     

Fatigue of directly wafer-bonded silicon under static and cyclic loading

 Fatigue tests were performed to investigate the reliability properties of wafer-bonded single crystalline silicon exposed to static or cyclic mechanical loading. A distinct decrease of strength with increasing load duration or cycle number was found which limited the lifetime of mechanically stressed wafer-bonded components. The occurrence of fatigue is related to siloxane bonds in the bonded interface between the silicon wafers. It was shown that fatigue is absent either if siloxane bonds are not present in the bonded interface or if local areas of pure silicon bonds were formed between the silicon wafers. As a consequence of this fatigue phenomenon, loaded wafer-bonded silicon sensors and actuators may suddenly fail during application. Therefore, appropriate fracture mechanical techniques were developed to predict either the time-to-failure or the cycles-to-failure for a given loading situation. These concepts allow for the optimization of the device layout with respect to long-term reliability, which can reduce the development time and costs.     

The influence of package-induced stresses on moulded Hall sensors

The output signals of moulded Hall sensors show changes in offset and sensitivity when the devices are affected by changing temperatures. This behaviour is a result of the differences in the thermal expansion behaviour of the package materials and is also affected by their time-dependent, viscous material properties. The stresses affected to the sensor’s sensitive layer will become effective via the piezo-Hall-effect as well as via piezo-resistivity which both change the sensitivity and the offset of the sensor’s output voltage. For modelling the stress in the sensitive area correctly it is indispensable to consider the visco-elastic and the visco-plastic behaviour of the materials constituting the package. Especially for very accurate sensors or components operating in harsh environments these effects must be regarded. In this work we investigate the thermo-mechanical stresses, which are induced in the sensitive layer of a moulded Hall sensor during the assembly process, the investigations were based mainly on finite-elements-simulations.     

Investigating fracture strength of poly-silicon membranes using microscopic loading tests and numerical simulation

The fracture strength of poly-silicon as widely used membrane material in micro electro mechanical system applications has a critical impact in respect to design, function and reliability of e.g. pressure sensors or microphones. This circumstance necessitates the investigation of the fracture strength of these poly-silicon membranes. In this study the strength was investigated by experimental tests and numerical simulations. A new fracture test has been developed that applies a well-defined and almost constant stress within a certain region of the membrane and prevent a cracking of the membrane at the edge. The brittle behavior of poly-silicon needs a statistical evaluation of the results. To this end, a set of 45 membranes was tested at each of the three positions on the wafer in order to assure statistical accuracy and to evaluate the strength distribution across the wafer. The experimental loading tests were attended by scanning electron microscopy to examine the microstructure and the crack path. Using finite element simulation, the non-linear deformation behavior during membrane loading was analyzed and the fracture stresses were calculated. In the final step the obtained results were statistically evaluated by means of a two-parametric Weibull distribution. High values were found for the characteristic fracture stresses. They are in the range of 5400–6000 MPa.     

Novel process for cover glass with ideal stress distribution

Abstract — This paper proposes a new process to manufacture cover glass that overcomes a strength trade‐off between the face and the edge. In the process, alkali barrier films are deposited on glass faces before an ion exchange process in order to control face stress properties without inhibiting the edge strengthening. As a demonstration of the process, alkali‐alumino‐silicate glass sheets with sputter‐deposited SiO₂ films were chemically strengthened, and then their stress properties and strengths were investigated. As a result, thicker SiO₂ films cause lower face DOL (depth of strengthened layer), and it is observed that the faces have lower DOL than the edges. In strength tests corresponding to major fracture modes of smartphone cover glass, specimens with 80–100 nm films have more balanced face performance and better edge impact strengths than the no‐film specimen.     

Damage tolerance based design optimisation of a fuel flow vent hole in an aircraft structure

This paper investigates the design optimisation of a fuel flow vent hole (FFVH) located in the wing pivot fitting (WPF) of an F-111 aircraft assuming a damage tolerance design philosophy. The design of the vent hole shape is undertaken considering the basic durability based design objectives of stress, residual (fracture) strength, and fatigue life. Initially, a stress based optimised shape is determined. Damage tolerance based design optimisation is then undertaken to determine the shape of the cutout so as to maximise its residual strength and fatigue life. For stress optimisation, the problem is analysed using the gradient-less biological algorithm and the gradient-based nonlinear programming methods. The optimum designs predicted by the two fundamentally different optimisation algorithms agree well. The optimum shapes of the vent hole are subsequently determined considering residual strength and fatigue life as the distinct design objectives in the presence of numerous 3D cracks located along the vent hole boundary. A number of crack cases are considered to investigate how the crack size affects the optimal shapes. A semi-analytical method is employed for computation of the stress intensity factors (SIF), and an analytical crack closure model is subsequently used to evaluate the fatigue life. The 3D biological algorithm is used for designing the cutout profiles that optimise residual strength and fatigue life of the component. An improved residual strength/fatigue life (depending on the optimisation objective) is achieved for the optimal designs. The variability in SIF/fatigue life around the cutout boundary is reduced, thereby making the shape more evenly fracture/fatigue critical. The vent hole shapes optimised for stress, residual strength, and fatigue life are different from each other for a given nature and size of the flaws. This emphasises the need to consider residual strength and/or fatigue life as the explicit design objective. The durability based optimal vent hole shapes depend on the initial and final crack sizes. It is also shown that a damage tolerance optimisation additionally produces a reduced weight WPF component, which is highly desirable for aerospace industries. The design space near the ‘optimal’ region is found to be flat. This allows us to achieve a considerable enhancement in fatigue performance without precisely identifying the local/global optimum solution, and also enables us to select a reduced weight ‘near optimal’ design rather than the precise optimal shape.     

Fracture Toughness, Fracture Strength, and Stress Corrosion Cracking of Silicon Dioxide Thin Films

The fracture toughness, fracture strength, and stress corrosion cracking behavior of thin-film amorphous silicon dioxide $(hbox{SiO}_{2})$ deposited on silicon wafers via plasma-enhanced chemical vapor deposition have been measured using specimens with length scales comparable to micromachined devices. Clamped–clamped microtensile specimens were fabricated using standard micromachining techniques. These devices exploit residual tensile stresses in the film to create stress intensity factors at precrack tips and stress concentrations at notches, in order to measure fracture toughness and fracture strength, respectively. The fracture toughness of thin-film $hbox{SiO}_{2}$ was $0.77 pm 0.15 hbox{MPa}cdot hbox{m}^{1/2}$, and the fracture strength was $0.81 pm 0.06 hbox{GPa}$. Stress corrosion cracking (slow crack growth) was also measured in the $hbox{SiO}_{2}$ devices with sharp precracks subjected to residual tensile stresses. These data are used to predict lifetimes for a $hbox{SiO}_{2}$-based microdevice. $hfill$[2007-0304]      

Micro crack detection with Dijkstra’s shortest path algorithm

A package based on the free software R is presented which allows the automatic detection of micro cracks and corresponding statistical analysis of crack quantities. It uses a shortest path algorithm to detect micro cracks in situations where the cracks are surrounded by plastic deformations and where a discrimination between cracks and plastic deformations is difficult. In a first step, crack clusters are detected as connected components of pixels with values below a given threshold value. Then the crack paths are determined by Dijkstra’s algorithm as longest shortest paths through the darkest parts of the crack clusters. Linear parts of kinked paths can be identified with this. The new method was applied to over 2,000 images. Some statistical applications and a comparison with another free image tool are given.     

Study of elastic behaviour of plates containing cracks by finite element analysis

This work applies finite element analysis very simply to cracked plates. An infinite plate and a finite plate, both with a central crack, are considered to study their elastic behaviour and some fracture mechanics concepts, such as the geometry factor and the fracture toughness. These magnitudes are calculated by means of finite element methods and the results are in very good agreement with the established theory, which proves that the finite element approach is very appropriate. The fracture toughness fraction is defined and calculated for a finite plate to predict its failure.     

Exploring the applicability of gradient elasticity to certain micro/nano reliability problems

It has long been assessed that continuum mechanics can be used successfully to address a variety of mechanical problems at both macroscopic and microscopic scales. The term “micromechanics”, in particular, has been used in considering elasticity, plasticity, damage, and fracture mechanics problems at the micron scale involving metallic, ceramic and polymeric materials, as well as their composites. Applications to automobile, aerospace, and concrete industries, as well as to chemical and microelectronic technologies have already been documented. The recent developments in the field of nanotechnology have prompted a substantial literature in nanomechanics. While this term was first introduced by the author in the early 90’s to advance a generalized continuum mechanics framework for applications at the nanoscale, it is mainly used today in considering “hybrid” ab-initio/molecular dynamics/finite element simulations, usually based on elasticity theory, to interpret the mechanical response of nano-objects (nanotubes, nanowires, nanoaggregates) and extract information on nano-configurations (dislocation cores, crack tips, interfaces). The modest goal of this article is to show that continuum elasticity can indeed be extended to describe a variety of problems at the micro/nano regime. The resultant micro/nanoelasticity theory includes long-range or nonlocal material point interactions and surface effects in the form of (phenomenological) higher-order stress/strain gradients. Coupled thermo-diffuso-chemo-mechanical processes can also be considered within such a higher-order theory. Size effects on micro/nano holes and micro/nano cracks can conveniently be modeled, and some standard strength of materials formulas routinely used for micro/nano beams can be improved, with potential applications to MEMS/NEMS devices and micro/nano reliability components.     

基于Abaqus柔度标定法的Q235材料断裂韧性仿真

为简便、准确地获得Q235材料的应力强度因子值和J积分值,用Abaqus对Q235材料进行有限元仿真,得到三点弯曲试样及其裂纹尖端区域的应力分布情况;针对裂纹尖端的奇异性,引入折叠单元进行裂纹尖端单元的奇异性建模.不同尺寸试件应力强度因子仿真值与试验值基本一致,表明该方法可以准确预测材料断裂参数.     

Integrated micro Pirani gauge based hermetical package monitoring for uncooled VO x bolometer FPAs

This paper presents the design and fabrication of a micro Pirani gauge using VO _x as the sensitive material for monitoring the pressure inside a hermetical package for micro bolometer focal plane arrays (FPAs). The designed Pirani gauge working in heat dissipating mode was intentionally fabricated using standard MEMS processing which is highly compatible with the FPAs fabrication. The functional layer of the micro Pirani gauge is a VO _x thin film designed as a 100 × 200 μm pixel, suspended 2 μm above the substrate. By modeling of rarefied gas heat conduction using the Extended Fourier’s law, finite element analysis is used to investigate the sensitivity of the pressure gauge. Also the thermal interactions between the micro Pirani gauge and bolometer FPAs are verified. From the fabricated prototype, the measured device TCR is about −0.8% K⁻¹ and the sensitivity about 1.84 × 10⁻³ W K⁻¹ mbar⁻¹.     

MEMS cantilever sensor for non-destructive metrology within high-aspect-ratio micro holes

Tactile metrology with deep and narrow micro holes was addressed using extremely slender piezoresistive micro cantilever sensors. Linear strain–displacement characteristics were observed with this sensor operated under transversal and axial loading. From noise, non-linearity and repeatability measurements the resolution and uncertainty of the cantilever sensors were determined to few nm and few tens of nm, respectively, within a micron displacement span. Under axial loading buckling of the cantilevers was observed after exceeding the critical limit of an Euler beam under the boundary conditions of a clamped-pinned beam. The cantilevers typically survived displacements well above the buckling limit, i.e., fracture of 3-mm long cantilevers was only observed at displacements of more than 200 μm. The feasibility of the cantilever as an active 1D touch probe for high-aspect-ratio blind holes was demonstrated at a dry-etched silicon high-aspect-ratio microstructure. As an application example with a high-volume product we investigated the form and roughness of diesel injector nozzle spray holes.     

Influence of the frequency on fatigue of directly wafer-bonded silicon

Fatigue tests on directly wafer-bonded silicon samples were performed using pre-cracked Micro-Chevron samples applying cycling loading frequencies between 0.3 and 40 Hz. The experimental lifetime results were compared with a theoretical prediction using measured subcritical crack growth parameters under static loading conditions. The experimental investigations revealed that the number of cycles required to break the samples increased with frequency. In contrast, the corresponding time-to-failure values did not depend on frequency. Both the qualitative behavior and the quantitative life-time results agreed very well with a prediction based on a fracture mechanical model. Therefore, it could be concluded that fatigue behavior in the considered frequency range is solely controlled by stress corrosion in the bonded interface. Furthermore, the results demonstrate an available approach for life-time prediction of wafer-bonded micro-electro-mechanical systems components stressed by cycling loading.     

Lifetime modelling for microsystems integration: from nano to systems

Due to the rapid development of IC technology the traditional packaging concepts are making a transition into more complex system integration techniques in order to enable the constantly increasing demand for more functionality, performance, miniaturisation and lower cost. These new packaging concepts (as e.g. system in package, 3D integration, MEMS-devices) will have to combine smaller structures and layers made of new materials with even higher reliability. As these structures will more and more display nano-features, a coupled experimental and simulative approach has to account for this development to assure design for reliability in the future. A necessary “nano-reliability” approach as a scientific discipline has to encompass research on the properties and failure behaviour of materials and material interfaces under explicit consideration of their micro- and nano-structure and the effects hereby induced. It uses micro- and nano-analytical methods in simulation and experiment to consistently describe failure mechanisms over these length scales for more accurate and physically motivated lifetime prediction models. This paper deals with the thermo-mechanical reliability of microelectronic components and systems and methods to analyse and predict it. Various methods are presented to enable lifetime prediction on system, component and material level, the latter promoting the field of nano-reliability for future packaging challenges in advanced electronics system integration.     

A contact-type piezoresistive micro-shear stress sensor forabove-knee prosthesis application

A prototype contact-type micro piezoresistive shear-stress sensor that can be utilized to measure the shear stress between skin of stump and socket of above-knee (AK) prosthesis was designed, fabricated and tested. Micro-electro-mechanical system (MEMS) technology has been chosen for the design because of the low cost, small size and adaptability to this application. In this paper, the finite element method (FEM) package ANSYS has been employed for the stress analysis of the micro shear-stress sensors. The sensors contain two transducers that will transform the stresses into an output voltage. In the developed sensor, a 3000×3000×300 μm³ square membrane is formed by bulk micromachining of an n-type (100) monolithic silicon. The piezoresistive strain gauges were implanted with boron ions with a dose of 10¹⁵ atoms/cm². Static characteristics of the shear sensor were determined through a series of calibration tests. The fabricated sensor exhibits a sensitivity of 0.13 mV/mA-MPa for a 1.4 N full scales shear force range and the overall mean hysteresis error is than 3.5%. In addition, the results simulated by FEM are validated by comparison with experimental investigations     

Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem

A novel computational modelling technique has been developed for the prediction of crack growth in load bearing orthopaedic alloys subjected to fatigue loading. Elastic-plastic fracture mechanics has been used to define a three-dimensional fracture model, which explicitly models the opening, sliding and tearing process. This model consists of 3D nonlinear spring elements implemented in conjunction with a brittle material failure function, which is defined by the fracture energy for each nonlinear spring element. Thus, the fracture energy criterion is implicit in the brittle material failure function to search for crack initiation and crack development automatically. A degradation function is employed to reduce interfacial fracture properties corresponding to the number of cycles; thus fatigue lifetime can be predicted. Unlike other failure modelling methods, this model predicts the failure load, crack path and residual stiffness directly without assuming any pre-flaw condition. As an example, fatigue of a cobalt based alloy (CoCrMo) femoral stem is simulated. Experimental fatigue data was obtained from four point bending tests. The finite element model simulated a fully embedded implant with a constant point load. Comparison between the model and mechanical test results showed good agreement in fatigue crack growth rate.     

Reliability analysis of brittle structures under random loadings

A method for the reliability analysis of brittle structures subjected to random loads is proposed. The method is based on the weakest-link hypothesis and Weibull statistics for brittle materials. Initial flaws with a given expected size are assumed to be distributed at random with a certain density per unit volume. Basic concepts in random vibration theory and fracture mechanics are utilized in evaluating stress statistics, crack propagation and strength degradation. A structure fails when the stress intensity at any flaw reaches a critical value for rapid crack propagation. The failure of the structure is modeled as the first exceedance in random vibration theory. The effects of multi-vibration modes on the failure probability of the structure are included in the formulation. The evaluation of stress distribution and the computation of failure probability can be accomplished in a finite element analysis. Numerical examples on the evaluation of lifetime reliabilities of structures are given to demonstrate the feasibility of the proposed method.