用于气体测量的压电微悬臂梁力学建模与实验研究
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摘要
微悬臂梁作为最简单的一种MEMS器件,最早应用于扫描探针显微镜进行微小力和表面形貌的检测。近年来,由于其结构尺寸小、灵敏度高、响应速度快和成本低等优点,微悬臂梁在微纳传感器方面得到了广泛的应用。微悬臂梁传感器有两种独立的工作模式:静态工作模式和动态工作模式,通过测量表面功能化处理的微悬臂梁的静态弯曲量或者固有频率变化,可以实现多种检测,因此本文对微悬臂梁气体传感器开展了研究。
虽然微悬臂梁传感器因其众多的优点得到了广泛的研究和应用,但是微悬臂梁的基础研究目前还远不够深入;此外,作为目前广泛应用于微悬臂梁信号检测的光杠杆法虽然具有较高的精度,但其结构复杂,成本高,不利于系统的微型化。本文基于压电材料的压电效应,将压电材料与微悬臂梁相结合,对压电微悬臂梁气体传感器进行了研究。由于压电微悬臂梁集驱动与传感于一身,很好地解决了微悬臂梁传感系统的微型化问题。
通过对压电微悬臂梁气体传感器进行研究,本文建立了压电微悬臂梁用于气体检测的理论模型。首先,在静力学建模过程中引入由于表面吸附应力引起的微悬臂梁中性层位置的变化,建立了压电微悬臂梁静力学弯曲模型,并以水分子吸附为例分析了压电微悬臂梁的静态弯曲特性,得到了压电微悬臂梁的静态弯曲变形量与微悬臂梁厚度、气体吸附量之间的关系。
其次,基于拉格朗日函数和Hamilton原理建立了不考虑吸附条件和压电效应、只考虑吸附条件、只考虑压电效应以及同时考虑压电效应和吸附条件下四种压电微悬臂梁的动力学模型。研究了压电效应以及气体吸附对压电微悬臂梁固有频率的影响,利用所建立的压电微悬臂梁的动力学模型,对镀铝压电微悬臂梁湿度传感器进行了仿真分析。
最后,搭建了一个基于DMASP系列压电微悬臂梁、安捷伦4294A阻抗分析仪和CHL-156型防潮柜的压电微悬臂梁湿度测量实验平台。利用该平台对湿度进行了测量实验,并将实验结果与动力学模型分析结果进行了比较,验证了压电微悬臂梁动力学模型的正确性。
As a kind of the simplest MEMS devices, microcantilever was firstly used in SPM as a tool to measure surface morphology or small force. Recently, microcantilever has also been widely used as micro/nano sensors due to their advantages of reduced size, high sensitivity, fast response and low costs. Microcantilever has two kinds of operational mode: static mode and dynamic mode. The microcantilever can be used to kinds of detections by detecting its static deflection or change of resonant frequency.
Though microcantilever has been widely used and researched because of its some significant advantages, the mechanism of biological and chemical microcantilever sensor hasn’t been fully understood. Additionally, optical leverage is highly sensitive, but it is complicated and not feasible for the miniaturization of the sensing system. Base on the piezoelectric effect of piezoelectric materials, the piezoelectric microcantilever gas sensors are researched in this paper. Because the piezoelectricity can not only be used for microcantilever actuation but also for detection of microcantilever signals, it can effectively solve the problem of miniaturization of the sensing system.
In this paper, the piezoelectric microcantilever gas sensors are studied and the theoretical models are established. First, the change of neutral layer position caused by adsorption-induced surface stress is introduced in the modeling and the static bending model of piezoelectric microcantilever gas sensors is established, and piezoelectric microcantilever adsorbed with water molecules is used to analyze the static bending performancies and investigate the relationship of static deflection of piezoelectric microcantilever gas sensor with thickness of microcantilever and adsorbed gas.
Second, the dynamic models of piezoelectric microcantilever gas sensor without considering the piezoelectric effect and gas adsorption, only considering the adsorption,only considering the piezoelectric effect and considering both the piezoelectric effect and gas adsorption are established, then the effect of piezoelectric effect and adsorption on resonant frequency of microcantilever is analyzed.The piezoelectric microcantilever adsorbed with water molecules is also used to analyze the dynamic performancies and investigate the relationship of resonant frequency of piezoelectric microcantilever gas sensor with driven voltage and adsorbed gas. In the end, an experimental platform including Agilent 4294A impedance analyzer, DMASP piezoelectric microcantilever and CHL-156 dry box is built to detect humidity. The experimental results show that the theoretical model is in good agreement with the experimental results.
虽然微悬臂梁传感器因其众多的优点得到了广泛的研究和应用,但是微悬臂梁的基础研究目前还远不够深入;此外,作为目前广泛应用于微悬臂梁信号检测的光杠杆法虽然具有较高的精度,但其结构复杂,成本高,不利于系统的微型化。本文基于压电材料的压电效应,将压电材料与微悬臂梁相结合,对压电微悬臂梁气体传感器进行了研究。由于压电微悬臂梁集驱动与传感于一身,很好地解决了微悬臂梁传感系统的微型化问题。
通过对压电微悬臂梁气体传感器进行研究,本文建立了压电微悬臂梁用于气体检测的理论模型。首先,在静力学建模过程中引入由于表面吸附应力引起的微悬臂梁中性层位置的变化,建立了压电微悬臂梁静力学弯曲模型,并以水分子吸附为例分析了压电微悬臂梁的静态弯曲特性,得到了压电微悬臂梁的静态弯曲变形量与微悬臂梁厚度、气体吸附量之间的关系。
其次,基于拉格朗日函数和Hamilton原理建立了不考虑吸附条件和压电效应、只考虑吸附条件、只考虑压电效应以及同时考虑压电效应和吸附条件下四种压电微悬臂梁的动力学模型。研究了压电效应以及气体吸附对压电微悬臂梁固有频率的影响,利用所建立的压电微悬臂梁的动力学模型,对镀铝压电微悬臂梁湿度传感器进行了仿真分析。
最后,搭建了一个基于DMASP系列压电微悬臂梁、安捷伦4294A阻抗分析仪和CHL-156型防潮柜的压电微悬臂梁湿度测量实验平台。利用该平台对湿度进行了测量实验,并将实验结果与动力学模型分析结果进行了比较,验证了压电微悬臂梁动力学模型的正确性。
As a kind of the simplest MEMS devices, microcantilever was firstly used in SPM as a tool to measure surface morphology or small force. Recently, microcantilever has also been widely used as micro/nano sensors due to their advantages of reduced size, high sensitivity, fast response and low costs. Microcantilever has two kinds of operational mode: static mode and dynamic mode. The microcantilever can be used to kinds of detections by detecting its static deflection or change of resonant frequency.
Though microcantilever has been widely used and researched because of its some significant advantages, the mechanism of biological and chemical microcantilever sensor hasn’t been fully understood. Additionally, optical leverage is highly sensitive, but it is complicated and not feasible for the miniaturization of the sensing system. Base on the piezoelectric effect of piezoelectric materials, the piezoelectric microcantilever gas sensors are researched in this paper. Because the piezoelectricity can not only be used for microcantilever actuation but also for detection of microcantilever signals, it can effectively solve the problem of miniaturization of the sensing system.
In this paper, the piezoelectric microcantilever gas sensors are studied and the theoretical models are established. First, the change of neutral layer position caused by adsorption-induced surface stress is introduced in the modeling and the static bending model of piezoelectric microcantilever gas sensors is established, and piezoelectric microcantilever adsorbed with water molecules is used to analyze the static bending performancies and investigate the relationship of static deflection of piezoelectric microcantilever gas sensor with thickness of microcantilever and adsorbed gas.
Second, the dynamic models of piezoelectric microcantilever gas sensor without considering the piezoelectric effect and gas adsorption, only considering the adsorption,only considering the piezoelectric effect and considering both the piezoelectric effect and gas adsorption are established, then the effect of piezoelectric effect and adsorption on resonant frequency of microcantilever is analyzed.The piezoelectric microcantilever adsorbed with water molecules is also used to analyze the dynamic performancies and investigate the relationship of resonant frequency of piezoelectric microcantilever gas sensor with driven voltage and adsorbed gas. In the end, an experimental platform including Agilent 4294A impedance analyzer, DMASP piezoelectric microcantilever and CHL-156 dry box is built to detect humidity. The experimental results show that the theoretical model is in good agreement with the experimental results.
引文
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[2]刘新,李淑娥.气体传感器的应用与发展[J].中国西部科技,2008,14:13-15.
[3] http://baike.baidu.com/view/37086.htm.
[4]唐洁.压电微悬臂梁传感技术的研究[D].天津:天津大学学位论文,2005:1-3.
[5] Binning G, Quate C F, Gerber C. Atomic force microscope[J]. Phys.Rev.Lett,1986,56(9):930-933.
[6] Anja Boisen, S?ren Dohn, Stephan Sylvest Keller, Silvan Schmid, Maria Tenje. Cantilever-like micromechanical sensors[J].Rep.Prog.Phys , 2011 , 74(3) :036101.
[7] G.Y.Chen, T.Thundat, E.A.Wachter, R.J.Warmack. Adsorption-induced surface stress and its effects on resonance frequency of microcantilevers[J]. J.Appl.Phys,1995,7(8):3618-3622.
[8] A Kooser, R.L.Gunter, W.D.Delinger, T.L.Porter, M.P.Eastman. Gas sensing using Embedded piezoresistive microcantilever sensors[J].Sensors and Actuators B,2004,99(2-3):474-479.
[9] Zhou Jia,Li Po, Zhang Song et al.Zeolite-modified microcantilever gas sensors for indoor air quality control[J].Sensors and Actuators B,2003,94(3):337-342.
[10] Li Peng, Li Xinxin.A single-sided micromachined piezoresistive SiO2 cantilever sensor for ultra-sensitive detection of gaseous chemicals[J]. J.Micromech. Microeng,2006,16(12):2539.
[11] Ilic B, Czaplewski D, Zalalutdinov M, Craighead H G, Neuzil P, Campagnolo C and Batt C. Single cell detection with micromechanical oscillators[J].J. Vac. Sci.Technol. B,2011,19 (6):2825.
[12] Weeks B L, Camarero J, Noy A, Miller A E, Stanker L and De Yoreo J J.A microcantilever-based pathogen detector[J]. Scanning,2003,25(6):297-299.
[13] Ramos D, Tamayo J, Mertens J, Calleja M and Zaballos A. Origin of the response of nanomechanical resonators to bacteria adsorption[J]. J.Appl.Phys,2006,100 (10):106105.
[14] Burg T P, Godin M, Knudsen S M, Shen W, Carlson G,Foster J S, Babcock K and Manalis S R.Weighing of biomolecules, single cells and single nanoparticles in ?uid[J]. Nature,2007,446(7139):1066-1069.
[15] Wu Guanghua, Datar R H, Hansen K M, Thundat T, Cote R J and Majumdar A.Bioassay of prostate-speci?c antigen(PSA) using microcantilevers[J]. Nature Biotechnol,2001,19:856-860.
[16] Zhang J, Lang H P, Huber F, Bietsch A, Grange W, Certa U,McKendry R, Guntgerodt H J, Hegner M and Gerber C. Rapid and label-free nanomechanical detection of biomarker transcripts in human RNA[J]. Nature Nanotechnol,2006,1:214-220.
[17] Braun T, Ghatkesar M K, Backmann N, Grange W,Boulanger P, Letellier L, Lang H P, Bietsch A, Gerber C and Hegner M. Quantitative time-resolved measurement of membrane protein–ligand interactions using microcantilever array sensors[J]. Nature Nanotechnol.,2009,4(18):179-185.
[18] Ndieyira J W et al. Nanomechanical detection of antibiotic mucopeptide binding in a model for superbug drug resistance[J]. Nature Nanotechnol,2008,3:691-702.
[19] Pinnaduwage L A, Boiadjiev V, Hawk J E and Thundat T.Sensitive detection of plastic explosives with self-assembled monolayer-coated microcantilevers[J].J. Phys. Lett,2008,83(7):1471-1473.
[20] Zuo G M, Li X X, Zhang Z X, Yang T T, Wang Y L, Cheng Z X and Feng S L. Dual-SAM functionalization on integrated cantilevers for speci?c trace-explosive sensing and non-speci?c adsorption suppression[J]. Nanotechnology,2007,18(25):5501.
[21] Yi Decheng, Greve A, Hales J H, Senesac L R, Davis Z J, Nicholson D M, Boisen A and Thundat T. Detection of adsorbed explosive molecules using thermal response of suspended microfabricated bridges[J]. Appl. Phys. Lett,2008,93(15):4102-4104.
[22] Naik A K, Hanay M S, Hiebert W K, Feng XL and Roukes M L.Towards single-molecule nanomechanical mass spectrometry[J].Nature Nanotechnol,2009,4:445-450.
[23] G.G.Stoney. The tension of metallic films deposited by electrolysis[J]. Proc.R. Soc.Lond,1909,82:172-179.
[24] D.W. Dareing, T. Thundat. Simulation of adsorption induced stress of a microcantilever sensor[J]. J. Appl .Phys,2005,97:043526.
[25] G.Y. Chen, T. Thundat, E.A.Wachter, R.J.Warmack. Adsorption-induced surface stress and its effects on resonance frequency of microcantilevers[J].J.Appl. Phys,1995,77 (8):3618–3622.
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