Jonathan W. Wittwer

Surface micromachined force gauges: uncertainty and reliability

Surface micromachining of micro-electro-mechanical systems (MEMS), like all other fabrication processes, has inherent variation that leads to uncertain material and dimensional parameters. By considering the effects of these variations during the design of micro force gauges, the gauge uncertainty and reliability can be estimated. Without the means of calibrating micro gauges, these effects are often significant when compared to experimental repeatability. The general force gauge model described in this paper can be used to measure a wide range of forces, and simple design changes can lead to improved accuracy in measurement. A method of probabilistic design is described that is not limited to small beam deflections.

Robust design and model validation of nonlinear compliant micromechanisms

Although the use of compliance or elastic flexibility in microelectromechanical systems (MEMS) helps eliminate friction, wear, and backlash, compliant MEMS are known to be sensitive to variations in material properties and feature geometry, resulting in large uncertainties in performance. This paper proposes an approach for design stage uncertainty analysis, model validation, and robust optimization of nonlinear MEMS to account for critical process uncertainties including residual stress, layer thicknesses, edge bias, and material stiffness. A fully compliant bistable micromechanism (FCBM) is used as an example, demonstrating that the approach can be used to handle complex devices involving nonlinear finite element models. The general shape of the force-displacement curve is validated by comparing the uncertainty predictions to measurements obtained from in situ force gauges. A robust design is presented, where simulations show that the estimated force variation at the point of interest may be reduced from /spl plusmn/47 /spl mu/N to /spl plusmn/3 /spl mu/N. The reduced sensitivity to process variations is experimentally validated by measuring the second stable position at multiple locations on a wafer.

A Novel Fully Compliant Planar Linear-Motion Mechanism

A new fully compliant linear-motion mechanism, called the XBob, is presented. The mechanism is based on the pseudo-rigid-body model (PRBM) of a system of Roberts approximate straight-line mechanisms combined in series and parallel. It can be fabricated in a single plane and has a linear force-displacement relationship. Symmetry and compliance compensate for the structural error inherent in the Roberts mechanism, resulting in precise straight-line motion. The device is designed and its motion and force-displacement relations are predicted by the PRBM. The design is validated using finite element analysis and experimental results.Copyright

Piezoresistive sensing of bistable micro mechanism state

The objective of this work is to demonstrate the feasibility of on-chip sensing of bistable mechanism state using the piezoresistive properties of polysilicon, thus eliminating the need for electrical contacts. Changes in position are detected by observing changes in resistance across the mechanism. Sensing the state of bistable mechanisms is critical for various applications, including high-acceleration sensing arrays and alternative forms of nonvolatile memory. A fully compliant bistable micro mechanism was designed, fabricated and tested to demonstrate the feasibility of this sensing technique. Testing results from two fabrication processes, SUMMiT IV and MUMPs, are presented. The SUMMiT mechanism was then integrated into various Wheatstone bridge configurations to investigate their potential advantages and to demonstrate various design layouts. Repeatable and detectable results were found with independent mechanisms and with those integrated into Wheatstone bridges.

Reliability-Based Design Optimization for Shape Design of Compliant Micro-Electro-Mechanical Systems.

Reliability methods are probabilistic algorithms for quantifying the effect of uncertainties on response metrics of interest. In particular, they compute approximate response function distribution statistics (probability, reliability, and response levels) based on specified probability distributions for input random variables. In conjunction with simulation software, these reliability analysis methods may be employed within reliability-based design optimization (RBDO) algorithms for designing systems subject to probabilistic performance criteria. In this paper, RBDO methods are compared and their effectiveness demonstrated by application to design optimization of microelectromechanical systems (MEMS), devices for which uncertainties in material properties and geometry affect performance and reliability. A new tapered beam topology for a fully compliant bistable mechanism is presented and its geometry optimized with RBDO to reliably achieve a specified actuation force, while simultaneously reducing predicted force variability due to material properties and manufacturing. The optimal designs specified by these optimization processes are predicted to be reliable, but also more robust to manufacturing process variations. Software-based MEMS design illustrates challenges faced when applying RBDO methods in engineering contexts.

Low Vibration Sensitivity MEMS Resonators

It is well known that the stability of crystal oscillator references is undermined in high-g environments [1,2]. This can result in failure of communications systems relying on the crystal as a frequency reference. Lower vibration sensitivity is theoretically achievable by replacing the crystal with a micro electromechanical (MEMS) resonator. In this paper we present an electrostatically actuated Lame resonator that has vibration sensitivity (0.91 ppb/g) comparable to the best high-g insensitive crystal oscillators.

Mitigating the Effects of Local Flexibility at the Built-In Ends of Cantilever Beams

Local distortion at the built-in ends of cantilever beams can lead to significant errors when models assume the support to be perfectly rigid. This paper presents a novel approach for mitigating this effect, using appropriately sized fillets to provide the additional stiffness needed to make simplified models more accurate and reduce stress concentrations. The optimal nondimensional fillet radius, called the optimal fillet ratio, is shown to be nearly constant for a wide range of geometries under predominantly bending loads, making it a useful parameter in the design of planar monolithic flexible mechanisms.

Predicting the Performance of a Bistable Micro Mechanism Using Design-Stage Uncertainty Analysis

Significant reduction in cost and time to market can be realized by implementing design-stage uncertainty analysis to predict whether a device will meet specified requirements. This paper demonstrates a generalized uncertainty analysis method appropriate for surface micromachined devices and uses a micro linear-displacement bistable mechanism as an example. Dimensional variations, joint clearances, material property uncertainty and friction are included as sources of error. Using matrix notation, the model consists of a system of implicit, nonlinear equations. The analysis is performed at multiple deflections to estimate uncertainty bands around the force-deflection curve of the mechanism. These results can then be used to predict the performance of the mechanism. Applying these techniques resulted in a functional first-time prototype of a bistable mechanism that can be actuated using a non-amplified thermal actuator.Copyright

MEMS Passive Latching Mechanical Shock Sensor

This paper presents a novel micro-scale passive-latching mechanical shock sensor with reset capability. The device integrates a compliant bistable mechanism, designed to have a high contact force and low actuation force, with metal-to-metal electrical contacts that provide a means for interrogating the switch state. No electrical power is required during storage or sensing. Electrical power is only required to initialize, reset, self-test, or interrogate the device, allowing the mechanism to be used in low-power and long shelf-life applications. The sensor has a footprint of about 1 mm2 , allowing multiple devices to be integrated on a single chip for arrays of acceleration thresholds, redundancy, and/or multiple sense directions. Modeling and experimental results for a few devices with different thresholds in the 100g to 400g range are given. Centrifuge test results show that the accelerations required to toggle the switches are higher than current model predictions. Resonant frequency measurements suggest that the springs may be stiffer than predicted. Hammer-strike tests demonstrate the feasibility of using the devices as sensors for actual mechanical shock events.Copyright

Solution-Verified Reliability Analysis and Design of Compliant Micro-Electro-Mechanical Systems

An important component of verification and validation of computational models is solution verification, which focuses on the convergence of the desired solution quantities as one refines the spatial and temporal discretizations and iterative controls. Uncertainty analyses often treat solution verification as a separate issue, hopefully through the use of a priori grid convergence studies and selection of models with acceptable discretization errors. In this paper, a tighter connection between solution verification and uncertainty quantification is investigated. In particular, error estimation techniques, using global norm and quantity of interest error estimators, are applied to the nonlinear structural analysis of microelectromechanical systems (MEMS). Two primary approaches for uncertainty quantification are then developed: an error-corrected approach, in which simulation results are directly corrected for discretization errors, and an error-controlled approach, in which estimators are used to drive adaptive h-refinement of mesh discretizations. The former requires quantity of interest error estimates that are quantitatively accurate, whereas the latter can employ any estimator that is qualitatively accurate. Combinations of these error-corrected and error-controlled approaches are also explored. Each of these techniques treats solution verification and uncertainty analysis as a coupled problem, recognizing that the simulation errors may be influenced by, for example, conditions present in the tails of input probability distributions. The most effective and affordable of these approaches are carried forward in probabilistic design studies for robust and reliable operation of a bistable MEMS device. Computational results show that on-line and parameter-adaptive solution verification can lead to uncertainty quantification and design under uncertainty studies that are more accurate, efficient, reliable, and convenient.