Monte Carlo modeling of stiffness of MEMS membrane (original) (raw)
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Application of multiphysics approach to study variation of dynamic properties of MEMS structure
In the paper the results of a study of uncertainty propagation for selected MEMS structure are presented. Both geometric and material properties are considered as uncertain parameters present in performed finite element analyses. Variation of dynamic properties resulting from assumed parameter scatters has been assessed by means of probabilistic technique. Multidisciplinary approach has been applied to model different phenomena present in MEMS structure. To speed up calculations metamodelling technique has been used.
Probabilistic modeling of microelectromechanical systems (MEMS) /
Micro-Electro-Mechanical Systems (MEMS) are a fast-developing technology that have a potential to permeate most engineering and medical applications. For this technology to continue expanding, issues regarding the cost of manufacturing and reliability of the devices have to be addressed. To improve the reliability, probabilistic design methodologies are potent in both the modeling and testing of high-performance MEMS. The benefit of probabilistic design approaches is a more rational basis for making design decisions that balance component or system efficiency with reliability or safety. Probabilistic methods are used to assess uncertainties involved in the manufacturing of MEMS devices. Probabilistic methods guide the design of these devices to achieve reliable design in a most efficient way. The objectives of the research work were to formulate and analyze probabilistic failure criteria on a simplified capacitive accelerometer mode. In this respect, comprehensive probabilistic and deterministic analysis was carried out for the selected model. The scope of work is threefold. First, two probabilistic failure criteria will be investigated on the capacitive structure, namely probabilistic clearance failure criterion and probabilistic fracture toughness failure criterion. Second, four kinds of probabilistic analyses for characterization of MEMS will be used: probability of failure, sensitivity analysis, safety index, and probability-based design. Third, three kinds of finite element analyses, namely static, modal and specfral analysis, will be used to see the deterministic response and will be compared with probabilistic result. VI LIST OF TABLES 2.1 Distribution Type 3.1 Calculation of Mass Center 3.2 Mechanical properties for polysilicon 3.3 Probabilistic values of input variables 3.4 Input Response Spectrums 4. 1 Probability of failure and Reliability Calculation at ZQ = 0 performance level 94 4.2 CPU time for Probabilistic Analyses 4.3 Crifical Displacement and Stress at nodes for Stafic Analysis 4.4 Displacement and stress at node points using Spectral Analysis 97 vii LIST OF FIGURES 1.1 Schematic Design of a Simplified Capacitive Accelerometer 1.2 MEMS material probabilistic analysis procedure 1.3 Damage of MEMS Device due to contact 2.1 Limit State Concept 2.2 Normal Distribution 2.3 Lognormal Distribution 2.3 Weibull Distribution 2.5 Uniform Distribution 2.6 Transformation to Standard Normal Space 37 2.7 Monte Carlo Simulation flow chart 2.8 Transforming a U(0,1) pick to Random Variable 2.9 Probability offailure calculation by AMV method 2.10 AMV iteration algorithm for P-level 41 2.11 AMV+iteration algorithm for P-level 3.1 Free body diagram of simplified accelerometer mode 3.2 Characterization of Random Variables: (a) Critical Stress Intensity Factor, and (b) Yield Sfrength 3.3 Random Variable Characterizations (a) PDF, (b) CDF 3.4 Shock Spectrum for use if measured data are not available 4.1 Probability of failure for clearance failure criterion 4.2 Probability offailure for fracture toughness based response function 70 4.3 Sensitivity analyses for clearance failure criterion 71 4.4 Sensitivity analyses for fracture toughness failure criterion 72 4.5 Comparative Study of Probability offailure by FORM, SORM, AMV, AMV+, Monte Carlo 73 4.6 Cumulative distribution functions in the transformed space 74 4.7 Probability Sensitivity Factor 75 4.8 Probability Sensitivity Factor 76 4.9 Effect of reducing random variation on Probability of Failure 77 4.10 Effect of reducing random variation on Safety Index 78 viii 4.11 Sensitivity Factor with respect to Distribution Parameters (Standard deviation) 4.12 Sensitivity Factor with respect to Distiibution Parameters (mean) 80 4.13 Effect of varying the mean (while keeping standard deviation constant) of beam thickness onProbability of Failure 4.14 Effect of randomness of thickness (standard deviation) on Probability of Failure... 4.15 Effect of variation of total length with fixed coefficient of variation on Probability of Failure 4.16 Effect of randomness of total length (standard deviation) on Probability of Failure 4.17 CDF for the first natural frequency generated by Monte Carlo Simulation 4.18 Solution errors of SORM, FORM and AMV with respect to Monte Cario Simulation 4.19 Front View of Displaced model with respect to undeformed edge 4.20 Contour Plot for Displacement 4.
Mechanical characterization of membrane like microelectronic components
Microelectronic Engineering, 2006
The tools of optical measurement of deformation are increasingly used to characterize both the mechanical and the thermal properties of MEMS components and especially membranes. In the paper the application of optical methods for membranes tension measurement, their thickness variations and vibrational mode shapes identification of membrane like microcomponents is reported. Using of several sophisticated optical techniques is reviewed such as autocollimation observation of the radii of curvature of deflected 6-in. large membranes, Fizeau interferometry of membrane thickness, Laser doppler vibrometry for membrane vibration movement and deformation propagation and also time-average recording of vibrational mode structure. Specific features of the methods, their performances and limitations regarding practical experience of the exploitation are reported, too.
Sensors
In this study, an accurate analytic semi-linear elliptic differential model for a circular membrane MEMS device, which considers the effect of the fringing field on the membrane curvature recovering, is presented. A novel algebraic condition, related to the membrane electromechanical properties, able to govern the uniqueness of the solution, is also demonstrated. Numerical results for the membrane profile, obtained by using the Shooting techniques, the Keller–Box scheme, and the III/IV Stage Lobatto IIIa formulas, have been carried out, and their performances have been compared. The convergence conditions, and the possible presence of ghost solutions, have been evaluated and discussed. Finally, a practical criterion for choosing the membrane material as a function of the MEMS specific application is presented.
A methodology for determining mechanical properties of freestanding thin films and MEMS materials
Journal of the Mechanics and Physics of Solids, 2003
This paper presents a methodology for directly determining macromolecular stiffness parameters from ensemble measurements of interatomic distances. These stiffness parameters can be used to derive empirical statistical potentials which, by definition, have the effects of solvent built in. A Gaussian network model is used together with methods from equilibrium statistical mechanics to formulate the problem. Ensemble distance measurements could come from a number of experimental modalities including FRET or NMR. The computational method presented here relies on the existence of a complete baseline structure (e.g., from crystallography), but no a-priori assumption of interatomic potentials is required.
Modeling and Simulation Software in MEMS Design
Micro-Electro-Mechanical Systems (MEMS) is a process technology that combines mechanical and electrical components to make micro-scale range devices. A considerable cost of the device can be reduced if we simulate the design. There are many available simulation software to choose from, which in turn is one of the major challenge. The paper explores the functional and technical features of some software used in MEMS designing. It further presents the keypoints which we should acknowledge while selecting software. Basic features are available in all MEMS Simulation software. However, if the design involves specific physics, geometry, material or meshing, the search must be done to find the appropriate software. If the user intends to fabricate the device then software with a virtual fabrication tool needs to be selected.
Modeling and Simulation of MEMS Components: Challenges and Possible Solutions
Micro-electro-mechanical systems (MEMS) represent a very important class of systems having applications ranging from small embedded sensors and actuators, passive components in RF and microwave fields, and micro-mirrors in the optical range. The importance of MEMS stems from their many advantages, among which are, their small compact size amendable to integration with other components, low loss and parameter variability. From structural point of view, each MEMS component is, by itself, a very small electromechanical system of heterogeneous structure composed of materials with different chemical composition (dielectric substrate, metal alloys and conducting wire) and different physical (electrical, thermal, mechanical) properties. Moreover, MEMS components may represent static systems or they may contain some moving parts, such as in variable capacitor, moving membranes and cantilevers. The dimensional scale of the different parts of MEMS components may vary from very small (microns or even nanometers) in one dimension, such as thickness of a plate, to comparatively large of few hundred microns in other dimensions, thus resulting in large aspect-ratios. When MEMS components are put into oration, they constitute systems, in which electrical, thermal, mechanical, and other physical phenomena take place and interact with each other. From mathematical modeling and simulation point of view, this calls for multi-physics treatment, in which coupled systems of differential equations of different combinations of electromagnetic, mechanical, fluid, heat transfer and/or transport equations, are formulated then solved depending on the type of boundary conditions imposed by MEMS component under investigation. Mathematical modeling and simulation has been used in all fields and disciplines of engineering for decades, for theoretical characterization of devices and systems before manufacturing, or even before prototyping, for a number of reasons among which are reduction in manufacturing cost and time. However, the heterogeneous nature of MEMS structures, coupled with multi-physics phenomena that take place during their operation, makes modeling and simulation of MEMS components, a complex and challenging task. The main objectives of this chapter are to outline the nature of MEMS componets, from both the structural and physical points of view and identify the difficulties that these
2006
In the paper a new nondestructive quality testing methods for MEMS were presented that can be applied on wafer level in early stage of the manufacturing process. The approach was applied to determine the thickness of KOH etched membranes from measured eigenfrequencies. The dynamic measurements of test specimen were performed by laser Doppler vibrometry. A finite element (FE) model was created to identify the membrane thickness from the measured eigenfrequency values. A good agreement between the measured thicknesses and the calculated thicknesses of membranes was found. Furthermore, a stochastic model was created to describe the influence of different parameters on the calculated thickness of membrane
Predictions of strength in MEMS Components a novel experimental theoretical approach
This paper presents a novel experimental-theoretical method to investigate the strength of structures having complex geometries, which are commonly used in microelectromechanical systems (MEMS). It involves the stretching to failure of freestanding thin-film membranes, in a fixed-fixed configuration, containing micro-fabricated sharp cracks, blunt notches and re-entrant corners. The defects, made by nanoindentation and focused ion beam milling, are characterized by scanning electron microscopy (SEM). MEMS structures made of ultra-nano-crystalline-diamond (UNCD), a material developed at Argonne National Laboratory, were investigated using this methodology. A theory to predict the strength of microstructures with defects is proposed and compared with experimental results. It is shown that fracture mechanics general concepts can be applied with confidence in the design of MEMS. An experimental methodology and formulas to predict strength of MEMS structures possessing defects of various geometries are provided.