Simulation of SiO2-based piezoresistive microcantilevers

This article uses finite element design for optimization of piezoresistive Si covered SiO₂ microcantilevers. The maximum resistance changes were systematically investigated by varying piezoresistor geometries and doping concentration. Our simulation results show that both cantilever deflection displacement and ΔR/R change decrease when the thickness of piezoresistors increases; the highest sensitivity can be obtained when the piezoresistor length is approximately 2/5 of the SiO₂ cantilever length; increase of both Si width and leg width result in decrease in cantilever deflection and sensitivity; the sensitivity of cantilevers with lower doping concentrations is more significant than those with higher doping concentrations. Temperature control is critical for thin piezoresistor in lowering the S/N ratio and increasing the sensitivity.     

The mechanics of polymer swelling on microcantilever sensors

This paper investigates the swelling mechanics of polymer capture layers integrated into piezoresistive cantilever biochemical sensors. A finite element model investigates mechanical deformations in a polymer layer affixed to a silicon microcantilever. The polymer swells during analyte absorption, inducing deformations in the silicon cantilever which are sensed by a piezoresistive sensor integrated into the cantilever. The highest sensitivity is predicted for short and wide cantilevers that are coated with stiff polymer whose thickness is twice that of the cantilever. While the polymer swelling induces the deformations, the silicon carries most of the load. When portions of the silicon beam are removed to introduce stress concentrations, the system sensitivity can increase by 18% compared to the cantilever without stress concentrations. This study of stress distributions in the cantilever system allows sensor optimization that considers the full 3D effects of polymer swelling mechanics.     

Piezoresistive Cantilever Performance—Part II: Optimization

Piezoresistive silicon cantilevers fabricated by ion implantation are frequently used for force, displacement, and chemical sensors due to their low cost and electronic readout. However, the design of piezoresistive cantilevers is not a straightforward problem due to coupling between the design parameters, constraints, process conditions, and performance. We systematically analyzed the effect of design and process parameters on force resolution and then developed an optimization approach to improve force resolution while satisfying various design constraints using simulation results. The combined simulation and optimization approach is extensible to other doping methods beyond ion implantation in principle. The optimization results were validated by fabricating cantilevers with the optimized conditions and characterizing their performance. The measurement results demonstrate that the analytical model accurately predicts force and displacement resolution, and sensitivity and noise tradeoff in optimal cantilever performance. We also performed a comparison between our optimization technique and existing models and demonstrated eight times improvement in force resolution over simplified models.$hfill$ [2009-0105]      

Piezoresistive Cantilever Performance—Part I: Analytical Model for Sensitivity

An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors. $hfill$[2009-0104]      

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.     

The effect of piezoresistive microcantilever geometry on cantilever sensitivity during surface stress chemical sensing

We have designed, fabricated, and tested five piezoresistive cantilever configurations to investigate the effect of shape and piezoresistor placement on the sensitivity of microcantilevers under both point loading and surface stress loading. The experimental study reveals that: (1) high aspect ratio cantilevers that are much longer than they are wide are optimal for point-loading applications such as microscopy and force measurements; (2) low aspect ratio cantilevers that are short and wide are optimal for surface stress-loading scenarios such as those that occur in biological and chemical sensor applications. The sensitivity data for both point loads and surface stress are consistent with previously developed finite-element models.     

An optimised silicon piezoresistive microcantilever sensor for surface stress studies

Surface stress is a versatile and efficient means to study various physical, chemical, biochemical and biological processes. This work focuses on developing high sensitive piezoresistive microcantilever designs to study surface stress. The cantilevers are made of silicon with rectangular holes at their base that also circumscribe a piezoresistor sensing element. To find the optimum design, the effects of change in cantilever width, rectangular hole length and type of dopant on mechanical properties like deflection, frequency and maximum stress are characterised using finite element analysis software. The surface stress sensitivity characteristics of the different cantilever designs is ascertained by applying a surface stress on their top surfaces. Results show that the sensitivity is increased by increasing the cantilever width as well as the length of the hole and the sensitivity of p-type designs is more than two times the n-type.     

Design and optimization of laminated piezoresistive microcantilever sensors

Microcantilevers-based sensors (MCSs) are a new approach to detecting and measuring physical, chemical, and biological signals in the nano- to femto-range level. Piezoresistive readout systems for MCSs have the advantages of full integration, low cost, ease of use, and the capability of manipulating large arrays. This paper presents a design method for laminated piezoresistive MCSs to obtain optimal performance by optimizing the dimensions of the microcantilevers and the doping concentration of the piezoresistors. Laminated theory was employed to deduce the closed-form solutions to static stress and natural frequency. Expressions for predicting sensitivity and resolution were derived by combining stress distribution with power densities of 1/f noise and Johnson noise. Finite element method (FEM) was performed to verify the theoretical results. The thickness of the laminated MCSs and the doping concentration were optimized by using static analyses and power densities of noise to generate the best sensitivity and resolution. A method based on non-linear programming is given to facilitate the solving process. These methods and some conclusions are also applicable to developing other types of piezoresistive sensors that use laminated structures.     

Design and Analysis of Microcantilevers for Biosensing Applications

We have analyzed the detection of microcantilevers utilized in biosensing chips. First, the primary deflection due to the chemical reaction between the analyte molecules and the receptor coating, which produces surface stresses on the receptor side is analyzed. Oscillating flow conditions, which are the main source of turbulence in cantilever based biosensing chips, are found to produce substantial deflections in the microcantilever at relatively large frequency of turbulence. Then mechanical design and optimization of piezoresistive cantilevers for biosensing applications is studied. Models are described for predicting the static behavior of cantilevers with elastic and piezoresistive layers. Chemo-mechanical binding forces have been analyzed to understand issues of saturation over the cantilever surface. Furthermore, the introduction of stress concentration regions during cantilever fabrication has been discussed which greatly enhances the detection sensitivity through increased surface stress, and novel microcantilever assemblies are presented for the first time that can increase the deflection due to chemical reaction. Finally an experiment was made to demonstrate the shift of resonant frequency of cantilever used as biosensor. The relation between resonant frequency shift and the surface stress was analyzed.     

叠加电桥检测的加速度传感器设计

基于压阻效应的叠加电桥检测法加速度传感器采用超对称"八悬臂梁—质量块"结构,构成惠斯通电桥的力敏电阻器布放在悬臂梁的两端,4个惠斯通电桥的输出电压叠加后作为传感器的最终输出,有效提高了加速度传感器的灵敏度。通过数学建模仿真分析验证了方案的可行性。性能测试结果表明:该加速度计的灵敏度为1.1381mV/gn,频响范围为0～1000Hz,灵敏度约为单电桥检测法和串联电桥检测法加速度传感器灵敏度的4倍。叠加电桥检测法为压阻式传感器提高灵敏度提供了一种新思路。     

Design, fabrication and testing of a high performance silicon piezoresistive Z-axis accelerometer with proof mass-edge-aligned-flexures

This paper presents design, fabrication and testing of a quad beam silicon piezoresistive Z-axis accelerometer with very low cross-axis sensitivity. The accelerometer device proposed in the present work consists of a thick proof mass supported by four thin beams (also called as flexures) that are connected to an outer supporting rim. Cross-axis sensitivity in piezoresistive accelerometers is an important issue particularly for high performance applications. In the present study, low cross-axis sensitivity is achieved by improving the device stability by placing the four flexures in line with the proof mass edges. Various modules of a finite element method based software called CoventorWare^™ was used for design optimization. Based on the simulation results, a flexure thickness of 30 μm and a diffused resistor doping concentration of 5 × 10¹⁸ atoms/cm³ were fixed to achieve a high prime-axis sensitivity of 122 μV/Vg, low cross-axis sensitivity of 27 ppm and a relatively higher bandwidth of 2.89 kHz. The designed accelerometer was realized by a complementary metal oxide semiconductor compatible bulk micromachining process using a dual doped tetra methyl ammonium hydroxide etching solution. The fabricated accelerometer devices were tested up to 13 g static acceleration using a rate table. Test results of fabricated devices with 30 μm flexure thickness show an average prime axis sensitivity of 111 μV/Vg with very low cross-axis sensitivities of 0.652 and 0.688 μV/Vg along X-axis and Y-axis, respectively.     

非致冷双材料红外探测器模拟分析

非制冷双材料红外探测器具有高响应率和低噪声的特点,噪声等效温差接近理论极限。其灵敏度高的基本原理是基于一个比较大的双层材料热膨胀系数和杨氏模量差,通过双材料悬臂结构可以把热转换成机械运动。经过采用ANSYS软件进行有限元模拟,得出材料厚度比与灵敏度、极板位移与电容变化的关系曲线。同时,模拟分析了不同悬臂尺寸的几何模型,得出了相应的优化结构。     

Elastic–plastic modeling of heat-treated bimorph micro-cantilevers

This paper models the residual stress distributions within micro-fabricated bimorph cantilevers of varying thickness. A contact model is introduced to calculate the influence of contact on the residual stress following a heat treatment process. An analytical modeling approach is adopted to characterize bimorph cantilevers composed of thin Au films deposited on thick poly-silicon or silicon-dioxide beams. A thermal elastic–plastic finite element model (FEM) is utilized to calculate the residual stress distribution across the cantilever cross-section and to determine the beam tip deflection following heat treatment. The influences of the beam material and thickness on the residual stress distribution and tip deflections are thoroughly investigated. The numerical results indicate that a larger beam thickness leads to a greater residual stress difference at the interface between the beam and the film. The residual stress established in the poly-silicon cantilever is greater than that induced in the silicon-dioxide cantilever. The results confirm the ability of the developed thermal elastic–plastic finite element contact model to predict the residual stress distributions within micro-fabricated cantilever structures with high accuracy. As such, the proposed model makes a valuable contribution to the development of micro-cantilevers for sensor and actuator applications.     

Quality factors in micron- and submicron-thick cantilevers

Micromechanical cantilevers are commonly used for detection of small forces in microelectromechanical sensors (e.g., accelerometers) and in scientific instruments (e.g., atomic force microscopes). A fundamental limit to the detection of small forces is imposed by thermomechanical noise, the mechanical analog of Johnson noise, which is governed by dissipation of mechanical energy. This paper reports on measurements of the mechanical quality factor Q for arrays of silicon-nitride, polysilicon, and single-crystal silicon cantilevers. By studying the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into dissipation mechanisms has been obtained. For submicron-thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicating surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700°C heat treatment in either N₂ Or forming gas. At low temperatures, silicon cantilevers exhibit a minimum in Q at approximately 135 K, possibly due to a surface-related relaxation process. Thermoelastic dissipation is not a factor for submicron-thick cantilevers, but is shown to be significant for silicon-nitride cantilevers as thin as 2.3 μm     

A 2-D microcantilever array for multiplexed biomolecular analysis

An accurate, rapid, and quantitative method for analyzing variety of biomolecules, such as DNA and proteins, is necessary in many biomedical applications and could help address several scientific issues in molecular biology. Recent experiments have shown that when specific biological reactions occur on one surface of a microcantilever beam, the resulting changes in surface stress deflect the cantilever beam. To exploit this phenomenon for high-throughput label-free biomolecular analysis, we have developed a chip containing a two-dimensional (2-D) array of silicon nitride cantilevers with a thin gold coating on one surface. Integration of microfluid cells on the chip allows for individual functionalization of each cantilever of the array, which is designed to respond specifically to a target analyte. An optical system to readout deflections of multiple cantilevers was also developed. The cantilevers exhibited thermomechanical sensitivity with a standard deviation of seven percent, and were found to fall into two categories-those whose deflections tracked each other in response to external stimuli, and those whose did not due to drift. The best performance of two "tracking" cantilevers showed a maximum difference of 4 nm in their deflections. Although "nontracking" cantilevers exhibited large differences in their drift behavior, an upper bound of their time-dependent drift was determined, which could allow for rapid bioassays. Using the differential deflection signal between tracking cantilevers, immobilization of 25mer thiolated single-stranded DNA (ssDNA) on gold surfaces produced repeatable deflections of 80 nm or so on 0.5-/spl mu/m-thick and 200-/spl mu/m-long cantilevers.     

Precision In-Plane Hand Assembly of Bulk-Microfabricated Components for High-Voltage MEMS Arrays Applications

This paper reports the design and experimental validation of an in-plane assembly method for centimeter-scale bulk-microfabricated components. The method uses mesoscaled deep-reactive-ion-etching (DRIE)-patterned cantilevers that deflect and lock into small v-shaped notches as a result of the hand-exerted rotation between the two components of the assembly. The assembly method is intended for MEMS arrays that necessitate a 3-D electrode structure because of their requirement for low leakage currents and high voltages. The advantages of the assembly method include the ability to decouple the process flow of the components, higher overall device yield, modularity, reassembly capability, and tolerance to differential thermal expansion. Both tapered and untapered cantilevers were studied. Modeling of the cantilever set shows that the springs provide low stiffness while the assembly process is in progress and high stiffness once the assembly is completed, which results in a robust assembly. In addition, analysis of the linearly tapered cantilever predicts that the optimal linearly tapered beam has a cantilever tip height equal to 37% of the cantilever base height, which results in more than a threefold increase in the clamping force for a given cantilever length and deflection, compared to the untapered case. The linear taper profile achieves 80% of the optimal nonlinear taper profile, which would be impractical to fabricate. Analysis of the experimental data reveals a biaxial assembly precision of 6.2-mum rms and a standard deviation of 0.6 mum for assembly repeatability. Electrical insulation was investigated using both thin-film coatings and insulating substrates. Leakage currents less than 1 nA at 2 kV were demonstrated. Finally, this paper provides selected experimental data of a gated MEMS electrospray array as an example of the application of the assembly method.     

Elastic–plastic modeling of heat-treated bimorph micro-cantilevers

This paper models the residual stress distributions within micro-fabricated bimorph cantilevers of varying thickness. A contact model is introduced to calculate the influence of contact on the residual stress following a heat treatment process. An analytical modeling approach is adopted to characterize bimorph cantilevers composed of thin Au films deposited on thick poly-silicon or silicon-dioxide beams. A thermal elastic–plastic finite element model (FEM) is utilized to calculate the residual stress distribution across the cantilever cross-section and to determine the beam tip deflection following heat treatment. The influences of the beam material and thickness on the residual stress distribution and tip deflections are thoroughly investigated. The numerical results indicate that a larger beam thickness leads to a greater residual stress difference at the interface between the beam and the film. The residual stress established in the poly-silicon cantilever is greater than that induced in the silicon-dioxide cantilever. The results confirm the ability of the developed thermal elastic–plastic finite element contact model to predict the residual stress distributions within micro-fabricated cantilever structures with high accuracy. As such, the proposed model makes a valuable contribution to the development of micro-cantilevers for sensor and actuator applications.

     

Low-stiffness silicon cantilevers with integrated heaters andpiezoresistive sensors for high-density AFM thermomechanical datastorage

Single-crystal silicon cantilevers 1 μm thick have been demonstrated for use in high-density atomic-force microscopy (AFM) thermomechanical data storage. Cantilevers with integrated piezoresistive sensors were fabricated with measured sensitivities ΔR/R up to 7.5×10^-7 per Å in close agreement with theoretical predictions. Separate cantilevers with integrated resistive heaters were fabricated using the same basic process. Electrical and thermal measurements on these heating devices produced results consistent with ANSYS simulations. Geometric variants of the cantilever were also tested in order to study the dependence of the thermal time constant on device parameters. Depending on the design, time constants as low as 1 μs were achieved. A thermodynamic model was developed based on the cantilevers geometry and material properties, and the model was shown to predict device behavior accurately. A comprehensive understanding of cantilever functionality enabled us to optimize the cantilever for high-speed thermomechanical recording     

Temperature-insensitive accelerometer based on a strain-chirped FBG

A novel accelerometer based on a strain-chirped optical fiber Bragg grating (FBG) is proposed. The FBG is glued in a slanted direction onto the lateral side of a right-angled triangle cantilever beam with a mass bonded on its free end. Vertical acceleration applied to the cantilever beam leads to a uniform bending along the beam length. As a result, the FBG is chirped and its reflection bandwidth changes linearly with the applied acceleration. A high sensitivity of 0.679 nm/g has been achieved in the experiment. This sensor is temperature insensitive, owning to the temperature-independence nature of reflection bandwidth of the FBG.     

A method to etch undoped silicon cantilever beams

A simple method has been designed to etch cantilever beams oriented in the <100> direction on (100) silicon wafers without back-etching, heavily doped boron etch stop, or anodic oxidation etch stop. The scheme requires only two levels of masking. Silicon dioxide and evaporated gold film are used as passivation materials. Anisotropic etching is performed in a sodium hydroxide bath. Silicon cantilevers with background doping concentration levels and having vertical edges are produced