A continuum-based modeling of MEMS devices for estimating their resonant frequencies

A continuum-based modeling of coupled electrostatics-structure interactions is presented for the frequency computations of MEMS devices. The present general formulation of electrostatics accounting for free space is validated first by specializing it to one-dimensional uniform motion of conducting surfaces and comparing the resulting electrostatics to conventional lumped models. The general coupled electrostatics-structure interactions are then applied for the prediction of resonant frequencies of MEMS devices due to bias-voltage changes and temperature variations. Comparisons of predicted resonant frequencies obtained by the present coupled electrostatics-structure interaction models with experimental results available in the literature demonstrate that the proposed continuum-based interaction modeling yields high-confidence predictions of resonant frequencies of MEMS devices.     

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.     

Real-time etch-depth measurements of MEMS devices

An in situ, real-time process control tool was developed for MEMS deep reactive-ion etch (DRIE) fabrication. DRIE processes are used to manufacture high-aspect-ratio silicon structures up to several hundred microns thick, which would be difficult or impossible to produce by other methods. DRIE MEMS technologies promise to deliver new devices with increased performance and functionality at lower cost. A major difficulty with DRIE is the control of etch depth. Our research shows that it is possible to monitor the etch depth of various MEMS structures (holes, pillars, trenches, etc.) through measurement and analysis of the infrared reflectance spectrum. Depths as large as 150 μm have been measured. Excellent correlation is found between the etch depths determined by analysis of these measurements and those measured with an SEM. In addition to etch depth, other parameters such as the photoresist thickness (e.g., mask erosion) can be simultaneously extracted. Based on these results, an infrared-reflectance etch monitor was integrated onto a reactive ion etcher at the Berkeley Sensor and Actuator Center for real-time monitoring and end-point determination. The integrated optical metrology system demonstrated accurate real-time monitoring of the etch depth and photoresist mask erosion     

Electrothermoelastic modeling of MEMS gripper

The design of many thermal Microelectromechanical (MEMS) actuators is often based on finite element analysis, but lacks analytical insight. In this paper we report a novel electro-thermal microgripper and a comprehensive thermal modeling of a general 5 lineshape microbeam’s actuator using 1-D steady state heat equations. Because of the variety of microgripper fabrication technologies and their applications, different thermal boundary conditions are considered for lifted off and attached grippers. Parametric and nonparametric electrothermomechanical identification models for silicon on insulator microgripper, fabricated on 100 μm device layer, are obtained.     

Characterization and modeling of electro-thermal MEMS structures

Thermal functional circuits are an interesting group of the MEMS elements with high a potential. A practical realisation is called Quadratic Transfer Characteristics (QTC) element of which driving principle is the Seebeck effect. Such devices can be applied e.g. as RMS meters. In this paper we are dealing with the analyses of a QTC element from different perspectives. A family of compact models is presented. These models are suitable to use in network simulation programs. To investigate the detailed behaviour of the device, we measured a few secondary properties of the structure, such as temperature dependence, cut-off frequency and non-quadratic error.

---

MEMS器件真空封装模型模拟

结合典型的MEMS器件真空封装工艺,应用真空物理的相关理论,建立了MEMS器件真空封装的数学物理模型,确定了其数值模拟算法。据此,对一封装示例进行了计算,获得了真空回流炉内干燥箱及密封腔体真空度的变化情况,实现了MEMS器件真空封装工艺过程的参数化建模与模拟。     

Evaluation of low-acceleration MEMS piezoelectric energy harvesting devices

Microelectromechanical systems-based piezoelectric energy harvesting device research is continuing to increase due to high demands in powering wireless sensor networks. This paper compares three different cantilever structures that have been the most widely used designs in MEMS energy harvesting devices. The cantilever structures consist of a wide beam, narrow beam, and trapezoidal beam structure. Aluminium nitride was used as the piezoelectric material because of its CMOS compatibility. Finite element modelling was used to investigate the theoretical outputs of the devices prior to fabrication. The three different structures were fabricated using standard micro-fabrication techniques on SOI wafers in order to verify the results experimentally. The finite element modelling results agree with the experimental results. The AlN deposited on the experimental wafers had a (002) FWHM rocking curve value of 1.7°. The power density based on the volume of space needed to fabricate the structures was 2.5, 0.78, and 0.65 mW/cm³/g² at resonant frequency for the wide, trapezoidal, and narrow beam structures respectively. The bandwidth of the devices is also an important parameter when selecting the cantilever structure. An array of the cantilevers over a 4 cm² area resulted in a bandwidth of was 4.8, 9, and 26.4 Hz for the wide, trapezoidal, and narrow beam structures respectively.     

Damage and failure in silicon-glass-metal microfluidic joints for high-pressure MEMS devices

The design, fabrication, and testing of microfluidic joints consisting of Kovar metal tubes attached to silicon using borosilicate glass for high pressure microelectromechanical systems devices are presented. The MIT microrocket, which requires microfluidic joints to sustain pressures of at least 12.7 MPa and temperatures in excess of 700 K, is used to demonstrate the feasibility of the glass sealing methodology. A key concern in such joints is the occurrence of cracks due to residual stresses during fabrication, which can affect the load-carrying capability. To obtain a better understanding of the damage and failure characteristics, a hierarchical approach was taken. First, two types of joint configurations with several glass compositions and geometries were considered at the joint-level. Axial tension and pressure tests were performed, and finite element models were used to obtain the residual stress field and to predict failure loads based on linear elastic fracture mechanics. Subsequently, tests were performed on actual and dummy microrockets to validate the methodology at the device-level. Key observations include the importance of bonding between the Kovar tube and the silicon sidewall, which can help increase joint strength, and the detrimental effects of joint proximity under differential pressure loading and manufacturing defects in multiple joint specimens. In addition to specific experimental and analyses results that allow a physical understanding of the damage and failure mechanisms, another key contribution of this work is the overall insight of the design and analysis of reliable glass-sealed microfluidic packages. This insight will help one make better design and process selections for packages in other high-pressure silicon-based MEMS applications.     

MEMS陀螺随机误差模型研究

对MEMS陀螺随机误差进行了实验测试及研究,选取状态方程模型,基于近年来发展起来的随机系统子空间辨识方法,对MEMS陀螺随机误差进行建模,结果与Allan方差方法分析的噪声特性相符合,经与ARMA等模型比较,在同等性能下,所建模型具有阶次低的优点,更加适合于实时在线优化估计器.所提方法可以不加修改直接应用于对多轴陀螺的处理.     

Uncertainty quantification of MEMS devices with correlated random parameters

The concern about process deviations rises because that the performance uncertainty they cause are strengthened with the miniaturization and complication of Microelectromechanical System (MEMS) devices. To predict the statistic behavior of devices, Monte Carlo method is widely used, but it is limited by the low efficiency. The recently emerged generalized polynomial chaos expansion method, though highly efficient, cannot solve uncertainty quantification problems with correlated deviations, which is common in MEMS applications. In this paper, a Gaussian mixture model (GMM) and Nataf transformation based polynomial chaos method is proposed. The distribution of correlated process deviations is estimated using GMM, and modified Nataf transformation is applied to convert the correlated random vectors of GMM into mutually independent ones. Then polynomial chaos expansion and stochastic collection can be implemented. The effectiveness of our proposed method is demonstrated by the simulation results of V-beam thermal actuator, and its computation speed is faster compared with the Monte Carlo technique without loss of accuracy. This method can be served as an efficient analysis technique for MEMS devices which are sensitive to correlated process deviations.

     

Opto-nanomechanical test instrument in mechanical characterization of DLC coated MEMS devices

Nanomechanical test instruments can precisely measure force and displacement and produce repeatable load-unload curves that can be used in characterizing mechanical behaviour at the nanoscale. In this study, a newly developed translucent nanomechanical test instrument was used in deriving reproducible stiffness values for ultra nano crystalline diamond (UNCD)-made atomic force microscope (AFM) cantilevers that are used for mechanical properties characterization of DLC films. The instrument which is calibrated according to the ISO-14577 standard is integrated with nano/micropositioners and multi-view optical microscopes to facilitate precise manipulation of those AFM cantilevers that were dozens of micrometers in size. Experimental results on UNCD-made AFM cantilever stiffness measurements are provided and compared with theoretical and batch production values.

     

MEMS器件中多层金属薄膜溅射工艺研究

溅射工艺是制作微机电系统(MEMS)器件金属薄膜的主要方式,金属薄膜作为MEMS器件中的掩模层和功能层,要求薄膜应力小,粘附性、均匀性和可焊性好.通过对常用金属薄膜材料特性、多层金属薄膜溅射工艺和质量评价方法的研究得出了优化工艺的的方法,提高了多层金属薄膜的质量.     

Supporting casual interactions between board games on public tabletop displays and mobile devices

As more interactive surfaces enter public life, casual interactions from passersby are bound to increase. Most of these users can be expected to carry a mobile phone or PDA, which nowadays offers significant computing capabilities of its own. This offers new possibilities for interaction between these users’ private displays and large public ones. In this paper, we present a system that supports such casual interactions. We first explore a method to track mobile phones that are placed on a horizontal interactive surface by examining the shadows which are cast on the surface. This approach detects the presence of a mobile device, as opposed to any other opaque object, through the signal strength emitted by the built-in Bluetooth transceiver without requiring any modifications to the devices’ software or hardware. We then go on to investigate interaction between a Sudoku game running in parallel on the public display and on mobile devices carried by passing users. Mobile users can join a running game by placing their devices on a designated area. The only requirement is that the device is in discoverable Bluetooth mode. After a specific device has been recognized, a client software is sent to the device which then enables the user to interact with the running game. Finally, we explore the results of a study which we conducted to determine the effectiveness and intrusiveness of interactions between users on the tabletop and users with mobile devices.     

Experimental validation of compact damping models of perforated MEMS devices

Measured damping coefficients of six different perforated micromechanical test structures are compared with damping coefficients given by published compact models. The motion of the perforated plates is almost translational, the surface shape is rectangular, and the perforation is uniform validating the assumptions made for compact models. In the structures, the perforation ratio varies from 24 to 59%. The study of the structure shows that the compressibility and inertia do not contribute to the damping at the frequencies used (130–220 kHz). The damping coefficients given by all four compact models underestimate the measured damping coefficient by approximately 20%. The reasons for this underestimation are discussed by studying the various flow components in the models.     

Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.     

Preparation of sacrificial layer for MEMS devices by lift-off technology

To simplify the preparation of sacrificial layer in micro-electromechanical system structure, new processes have been developed. By using lift-off technology, sacrificial layer was selectively deposited into the pit that prepared for sacrificial layer releasing. Then a short time polishing process was used to remove the burrs around the pit. This method offers several advantages including reducing the difficulty of polishing and hence processing cost. Methods and apparatuses to provide a continuously smoothly sacrificial layer surface in the pit were disclosed. However, it is important to control the homogeneity of filling and avoid the shadow effect at the corner of the pit. The unpadded regions would form a steep step and cause the cracking of structure layer. This problem was discussed and solved by rotating the tilted wafer during sacrificial material deposition. The surface roughness after the preparation process of sacrificial layer was measured. The root mean square roughness of sacrificial layer was 1.247 nm and reduced to 0.861 nm after a short time polishing process. Finally, a film bulk acoustic wave resonator with stacked Mo/AlN/Mo films had been fabricated on the sacrificial layer based on this method.     

Fabrication of microfluidic devices for packaging CMOS MEMS impedance sensors

This work presents a polydimethylsiloxane (PDMS) microfluidic device for packaging CMOS MEMS impedance sensors. The wrinkle electrodes are fabricated on PDMS substrates to ensure a connection between the pads of the sensor and the impedance instrument. The PDMS device can tolerate an injection speed of 27.12 ml/h supplied by a pump. The corresponding pressure is 643.35 Pa. The bonding strength of the device is 32.44 g/mm². In order to demonstrate the feasibility of the device, the short circuit test and impedance measurements for air, de-ionized water, phosphate buffered saline (PBS) at four concentrations (1, 2 × 10⁻⁴, 1 × 10⁻⁴, and 6.7 × 10⁻⁵ M) were performed. The experimental results show that the developed device integrated with a sensor can differentiate various samples.     

MEMS惯性器件的主要失效模式和失效机理研究

针对微机电系统(MEMS)器件的可靠性问题,通过大量的历史资料调研和失效信息收集等方法,针对微机电系统(MEMS)器件的可靠性问题,对冲击、振动、湿度、温变、辐照和静电放电(ESD)等不同环境应力条件下的MEMS惯性器件典型失效模式及失效机理进行了深入分析和总结,研究结果有利于指导未来MEMS惯性器件的失效分析和可靠性设计.