Effect of Die-Bonding Process on MEMS Device Performance: System-Level Modeling and Experimental Verification

This paper presents a distributed nodal method (DNM) for compact modeling of the package-device interaction of microelectromechanical systems (MEMS). MEMS devices have movable structures that are sensitive to structural stresses and easily influenced by package structures and environmental parameters. Hence, it is necessary to include the packaged behavior of MEMS into a compact simulation tool with acceptable precision. The conventional nodal method is therefore modified to achieve this purpose. A node with distributed nodal quantities is defined to describe the distributed interactions among the device, package, and environmental temperature. Based on the definition, the related processes of element partition, nodal matrix formation, and element assembly have been demonstrated. The case of a die-bonded microbridge has been used as an example, since the microbridge is not only a typical MEMS structure but also is influenced easily by structural stresses. The DNM model is validated first by a finite-element method (FEM) simulation, then by two individual experiments, including the measurement of die warpage using a digital image correlation system and the detection of shifted natural frequencies of surface-micromachined bridges using a laser Doppler vibrometer system, both after die bonding. The FEM and test results agree with those evaluated by the model with a relative error of less than 10%. Stress alleviation of the test structure has been unintentionally achieved by die bonding, leading to relative shifts of 12%-26% and 19%-26% of the first and third natural frequencies of the microbridges. The packaged behavior also exhibits an evident distributed feature along the die surface as expected. Although, at current stage, the application of the DNM is still limited to static domain, it shows potential in developing hierarchical models of MEMS devices including the package.     

Three-qubit Grover’s algorithm using superconducting quantum interference devices in cavity-QED

We present a scheme for the implementation of three-qubit Grover’s algorithm using four-level superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. The scheme is based on resonant, off-resonant interaction of the cavity field with SQUIDs and application of classical microwave pulses. We show that adjustment of SQUID level spacings during the gate operations, adiabatic passage, and second-order detuning are not required that leads to faster implementation. We also show that the marked state can be searched with high fidelity even in the presence of unwanted off-resonant interactions, level decay, and cavity dissipation.     

Structural modelling and integrative analysis of microelectromechanical systems product using graph theoretic approach

Micro-electromechanical systems (MEMS) as an enabling technology is seen to play a more and more important role for the main stream of industry of the future by broadening its applications to information, communications and bio technologies. Development of MEMS devices, however, still relies on knowledge and experience of MEMS experts due to the design and fabrication process complexity. It is difficult to understand the trade-offs inherent in the system and achieve an optimal structure without any MEMS-related insight. An attempt is made to develop an integrated systems model for the complete structure of the MEMS product system in terms of its constituents and interactions between the constituents. The hierarchical tree structures of the MEMS system and its subsystems are presented up to component level. For characterization, analysis and identification of MEMS product system, three different mathematical models say graph theoretic model, matrix model and permanent model are presented. These models are associated with graph theory, matrix method and variable permanent function by considering the various subsystems, subsubsystems up to component level, their connectivity and interdependency of the MEMS product system. The developed methodology is explained with an example. The proposed modeling and analysis is extendable to the subsystems and the component level. An overall structural analysis can be carried out by following a ‘top-down’ approach or ‘bottom-up’ approach. Understanding of MEMS product structure will help in the improvement of performance, cost, design time, and so on.     

Accurate Assessment of Packaging Stress Effects on MEMS Sensors by Measurement and Sensor–Package Interaction Simulations

In this paper, packaging-induced stress effects are assessed for microelectromechanical systems (MEMS) sensors. A packaged MEMS sensor may experience output signal shift (offset) due to the thermomechanical stresses induced by the plastic packaging assembly processes and external loads applied during subsequent use in the field. Modeling and simulation to minimize the stress-induced offset shift are essential for high-precision accelerometers, gyroscopes, and many other MEMS devices. Improvement of plastic package modeling accuracy is accomplished by correlating finite-element analysis package models using measured material properties and package warpage. Using a refined reduced-order MEMS sensor and package interaction model, device offset is simulated, optimized, and compared with data collected from a unique three-axis accelerometer, which uses a single mass for all three axes sensing. As a result, this accelerometer has achieved very low offset in all axes over device operation temperature range of to . Device offset performance was improved by at least five times after the MEMS design optimization as compared with the one prior to the optimization.     

Modeling of gold microbeams as strain and pressure sensors for characterizing MEMS packages

This work presents the modeling of gold microbeams for characterizing Micro-electro-mechanical systems (MEMS) packages in terms of both strains induced to the MEMS devices and hermetic sealing capability. The proposed test structures are based on arrays of rectangular-shaped clamped-free and clamped–clamped beams, to be realized with a film of electroplated gold by surface micromachining technology. The resonant frequency of the microbeams is modeled by FEM simulations as a function of substrate deformations, which could be induced by the package. Clamped–clamped bridges show a linear change of the square of the resonant frequency in case of in-plane deformations, in fairly good agreement with an approximate analytical model. Cantilever beams are modeled as variable capacitors to detect out-of-plane deformations. Finally, an analytical model to study cantilever beams as resonators for detecting pressure changes is discussed and compared with preliminary experimental results, showing an impact on the quality factor in a range from 10^?2 mbar to 1?bar.     

Piezoelectric control of composite plate vibration: Effect of electric potential distribution

The paper deals with the vibration analysis of active rectangular plates. The plates considered are composites containing piezoelectric sensor/actuator layers, which operate in a velocity feedback control to achieve transverse vibration suppression. The piezoelectric layers are poled through the thickness and equipped with traditional surface electrodes. In order to satisfy the Maxwell electrostatics equation the widely used simplification of the electric potential distribution in the actuator layer (linear across the thickness) is replaced by a combination of a half-cosine and linear distribution in the transverse direction. The in-plane spatial variation of the potential instead of applying uniform distribution is determined by the solution of the coupled electromechanical governing equations with the natural boundary conditions corresponding to both the flexural and electric potential fields. The analysis is performed for simply supported plates. Two models of the plate are considered. In the first case the displacement field is based on the Kirchhoff hypothesis. For the second the Mindlin plate model is applied. The governing coupled equations describing the active plate behaviour are derived. The influence of the electric potential distribution and also the thickness of piezoelectric layers on the plate dynamics including the natural frequencies modification is numerically investigated and discussed.     

Hybrid MEMS optical scanner for volumetric 3‐D displays

Abstract— A fabrication technique and characteristics of high‐power‐handling microelectromechanical systems (MEMS) optical scanners for laser 3‐D volumetric‐image display application is reported. The MEMS scanner is designed to control the reflection of high‐power YAG‐laser beam by using the optomechanical combination of a dielectric‐film‐coated mirror cube and an electrostatic‐MEMS‐scanner platform. These hybrid‐type MEMS optical scanners have a stroke of about 20° at resonant frequencies of 600 Hz when a 45‐V pulse voltage is applied.     

Reduced-order modeling of weakly nonlinear MEMS devices with Taylor-series expansion and Arnoldi approach

In this paper, we present a new technique by combining the Taylor series expansion with the Arnoldi method to automatically develop reduced-order models for coupled energy domain nonlinear microelectromechanical devices. An electrostatically actuated fixed-fixed beam structure with squeeze-film damping effect is examined to illustrate the model-order reduction method. Simulation results show that the reduced-order nonlinear models can accurately capture the device dynamic behavior over a much larger range of device deformation than the conventional linearized model. Compared with the fully meshed finite-difference method, the model reduction method provides accurate models using orders of magnitude less computation. The reduced MEMS device models are represented by a small number of differential and algebraic equations and thus can be conveniently inserted into a circuit simulator for fast and efficient system-level simulation.     

Implementation of phase-locked loop control for MEMS scanning mirror using DSP

The present study has employed the phase-locked loop control method to ensure the operating of MEMS actuators at their resonant frequency. In this study, the control algorism was simulated by the MATLAB. Further, the digital signal processing (DSP) technique was adopted to implement the concept of phase-locked loop control algorithm. Thus, a wide VCO lock-in dynamic range was achieved. In applications, the optical scanners fabricated using the SOI wafer and MOSBE process were respectively employed to demonstrate the present technique. The test show that the resonant frequency was tracked for various driving voltages, loop gains, and initial frequency offsets. Thus, the variation of the scanning angle resulted from the offset of the resonant frequency of the devices can be prevented.     

RF MEMS压控振荡器的研制及相位噪声特性研究

利用RF MEMS可变电容作为频率调节元件,制备了中心频率为2 GHz的MEMS VCO器件.RF MEMS可变电容采用凹型结构,其控制极板与电容极板分离,并采用表面微机械工艺制造,在2 GHz时的Q值最高约为38.462.MEMS VCO的测试结果表明,偏离2.007 GHz的载波频率100kHz处的单边带相位噪声为-107 dBc/Hz,此相位噪声性能优于他们与90年代末国外同频率器件.并与采用GaAs超突变结变容二极管的VCO器件进行了比较,说明由于集成了RF MEMS可变电容,使得在RF MEMS可变电容的机械谐振频率近端时,MEMS VCO的相位噪声特性发生了改变.     

Two-Dimensional MEMS Scanner for Dual-Axes Confocal Microscopy

In this paper, we present a novel 2-D microelectromechanical systems (MEMS) scanner that enables dual-axes confocal microscopy. Dual-axes confocal microscopy provides high resolution and long working distance, while also being well suited for miniaturization and integration into endoscopes for in vivo imaging. The gimbaled MEMS scanner is fabricated on a double silicon-on-insulator (SOI) wafer (a silicon wafer bonded on a SOI wafer) and is actuated by self-aligned vertical electrostatic combdrives. Maximum optical deflections of plusmn4.8deg and plusmn5.5deg are achieved in static mode for the outer and inner axes, respectively. Torsional resonant frequencies are at 500 Hz and 2.9 kHz for the outer and inner axes, respectively. The imaging capability of the MEMS scanner is successfully demonstrated in a breadboard setup. Reflectance images with a field of view of are achieved at 8 frames/s. The transverse resolutions are 3.94 mum and 6.68 mum for the horizontal and vertical dimensions, respectively.     

An investigation into the electrostatic force representation for electrically actuated microelectromechanical systems

The ever-increasing demand for microelectromechanical systems (MEMS) in modern electronics has reinforced the need for extremely accurate analytical and reduced-order models to aid in the design of MEMS devices. Many MEMS designs consist of cantilever beams with a tip mass attached at the free end to act as a courter electrode for electrical actuation. One critical modeling aspect of electrically actuated MEMS is the electrostatic force that drives these systems. The two most used representations in the literature approximate the electrostatic force between two electrodes as a point force. In this work, the effects of the representation of the electrostatic force for electrically actuated microelectromechanical systems are investigated. The system under investigation is composed of a beam with an electrode attached to its end. The distributed force, rigid body, and point mass electrostatic force representations are modeled, studied, and their output results are compared qualitatively. Static and frequency analyses are carried out to investigate the influences of the electrostatic force representation on the static pull-in, fundamental natural frequency, and mode shape of the system. A nonlinear distributed-parameter model is then developed in order to determine and characterize the response of electrically actuated systems when considering various representation of the electrostatic forces. The results show that the size of the electrode may strongly affect the natural frequencies and static pull-in when the point mass, rigid body, and plate representations are considered. From nonlinear analysis, it is also proven that the representation may affect the hardening behavior of the system and its dynamic pull-in. This modeling and analysis give guidelines about the usefulness of the electrostatic force representations and possible erroneous assumptions that can be made which may result in inaccurate design and optimal performance detection for electrostatically actuated systems.

     

Design considerations for an acoustic MEMS filter

Microelectromechanical system (MEMS) devices exhibit characteristics that make them ideal for use as filters in acoustic signal processing applications. In this study, a MEMS filter is constructed from multiple mechanical structures (e.g. cantilever beams) and a differential amplifier. The outputs of the structures are then processed by the differential amplifier to achieve the filter functionality. The important parameters of the mechanical structures and the MEMS filters are investigated using a simulation approach, including the structural damping factors, the normalized frequency ratios (NFR) of the MEMS filters, the number of mechanical structures required to construct individual MEMS filter, and the spatial arrangement of the multiple mechanical structures relative to the differential amplifier. Furthermore, the mutual coupling effects among these parameters are evaluated by detailed simulations. The simulation results show that a plot of the NFR versus the damping factors can be used to determine the optimal parameters for the mechanical structures. The number of mechanical structures required to construct a MEMS filter must equal 2ⁿ, with n as an integer, and these mechanical structures should be arranged as a geometric series with increasing resonant frequencies and with specific connections to the differential amplifier.This material is based (in part) upon work supported by the National Science Council (Taiwan) under Grant NSC 91–2213-E-010-008 and Delta Electronics Foundation. The authors would like to express their appreciation to the NSC Central Regional MEMS Center, Semiconductor Research Center of National Chiao Tung University (Taiwan), and the NSC National Nano Device Laboratories (Taiwan) in providing experimental facilities.     

Microelectromechanical resonators for radio frequency communication applications

Over the past few years, microelectromechanical system (MEMS) based on-chip resonators have shown significant potential for sensing and high frequency signal processing applications. This is due to their excellent features like small size, large frequency-quality factor product, low power consumption, low cost batch fabrication, and integrability with CMOS IC technology. Radio frequency communication circuits like reference oscillators, filters, and mixers based on such MEMS resonators can be utilized for meeting the increasing count of RF components likely to be demanded by the next generation multi-band/multi-mode wireless devices. MEMS resonators can provide a feasible alternative to the present-day well-established quartz crystal technology that is riddled with major drawbacks like relatively large size, high cost, and low compatibility with IC chips. This article presents a survey of the developments in this field of resonant MEMS structures with detailed enumeration on the various micromechanical resonator types, modes of vibration, equivalent mechanical and electrical models, materials and technologies used for fabrication, and the application of the resonators for implementing oscillators and filters. These are followed by a discussion on the challenges for RF MEMS technology in comparison to quartz crystal technology; like high precision, stability, reliability, need for hermetic packaging etc., which remain to be addressed for enabling the inclusion of micromechanical resonators into tomorrow??s highly integrated communication systems.     

A UML-based object-oriented approach for design and simulation of a drug delivery system

Given complexity of the design and manufacturing processes of microelectromechanical system (MEMS) products, we present a unified modeling language (UML) based design approach for multi-domain products or systems like MEMS to designing and evaluating possible solutions at the early design stage to shorten their development time. Specifically, the proposed approach is used to model and analyze a novel drug delivery system combining MEMS devices and integrated circuit (IC) units. This drug delivery system aims to be used for safer and more effective therapy of the diabetics. Two design models about the whole drug delivery system and its micropump subsystem are established using UML diagrams; in particular a composition diagram with components and ports describes the topology of the system. Through design and simulation on the micropump subsystem, it is found that the variations of geometrical dimension and excitation voltage affect the characterization of the micropump. The simulation results demonstrate and validate the proposed approach, and can be used as a significant reference for the designer to design the optimal micropump.