应用于扫描探针显微镜的石英音叉机械模型研究

华宝成; 钱建强; 王曦; 姚骏恩

doi:10.7498/aps.60.040702

摘要

石英音叉作为力传感器广泛地应用于各种扫描探针显微镜,主要涉及石英音叉的同相振动和反相振动两种振动模式.通过实验方法和有限元仿真方法对石英音叉的两种振动模式进行研究,发现石英音叉的双臂之间以及双臂与音叉的基部之间都存在耦合作用,双臂之间的耦合使音叉的反相共振频率升高,双臂与基部之间的耦合使音叉的同相共振频率降低.针对两种振动模式的动态特性建立了石英音叉的机械模型并进行合理简化.简化模型是一个四弹簧三质点系统,计算了简化模型的参数.通过一个音叉臂等效质量变化与音叉反相共振频率变化之间的定量关系证明了简化机械模

关键词:

Abstract

Quartz tuning forks have been widely used as force sensors in scanning probe microscopes. The anti-phase and in-phase eigenmodes of a tuning fork are involved during microscope operations. Dynamic characteristics of both eigenmodes are studied by experiments and finite element analysis simulations. It is demonstrated that elastic couplings exist between not only both the prongs but also two prongs and the base of the tuning fork. Experimental results show that the coupling between both the prongs increases the anti-phase mode eigenfrequency while the coupling between two prongs and the base of the tuning fork decreases the in-phase mode eigenfrequency. A mechanical model of the tuning fork is introduced and simplified. Parameters of the simplified model are calculated, which is described as a four-springs-three-point-masses system. The quantitative relation between the effective mass of one prong and the eigenfrequency of the anti-phase mode of the mechanical model is in good agreement with that of finite element simulations.

Keywords:

作者及机构信息

(1)北京航空航天大学仪器科学与光电工程学院,北京 100191; (2)北京航空航天大学应用物理系,北京 100191

基金项目: 国家高技术研究发展计划(批准号:2007AA12Z128)和国家自然科学基金(批准号:11074019)资助的课题.

Authors and contacts

(1)Department of Applied Physics, Beihang University, Beijing 100191, China; (2)School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing 100191, China

参考文献

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施引文献

[1]	Günther P, Fischer U C, Dransfeld K 1989 Appl. Phys. B 48 89
[2]	Edwards H, Taylor L, Duncan W, Melmed A J 1997 J. Appl. Phys. 82 980
[3]	Naitou Y, Ookubo N 2004 Appl. Phys. Lett. 85 2131
[4]	Kim K, Seo Y, Jang H, Chang S, Hong M H, Jhe W 2006 Nanotechnology 17 S201
[5]	Labardi M, Allegrini M 2006 Appl. Phys. Lett. 89 174104
[6]	Sandoz P, Friedt J M, Carry E 2008 Rev. Sci. Instrum. 79 086102
[7]	Naber A 1999 J. Microsc. 194 307
[8]	Seo Y, Jhe W, Hwang C S 2002 Appl. Phys. Lett. 80 4324
[9]	Karrai K, Grober R D 1995 Appl. Phys. Lett. 66 1842
[10]	Qin Y, Reifenberger R 2007 Rev. Sci. Instrum. 78 063704
[11]	Giessibl F J 2000 Appl. Phys. Lett. 76 1470
[12]	Seo Y, Choe H, Jhe W 2003 Appl. Phys. Lett. 83 1860
[13]	Giessibl F J, Reichling M 2005 Nanotechnology 16 S118
[14]	Liu J, Callegari A, Stark M, Chergui M 2008 Ultramicroscopy 109 81
[15]	Ruiter A G T, Veerman J A, van der Werf K O,van Hulst N F 1997 Appl. Phys. Lett. 71 28
[16]	Grober R D, Acimovic J, Schuck J, Hessman D, Kindlemann P J, Hespanha J, Morse A S, Karrai K, Tiemann I, Manus S 2000 Rev. Sci. Instrum. 71 2776
[17]	Rensen W H J, van Hulst N F, Ruiter A G T, West P E 1999 Appl. Phys. Lett. 75 1640
[18]	Seo Y, Cadden-Zimansky P, Chandrasekhar V 2005 Appl. Phys. Lett. 87 103103
[19]	Wang X P, Liu L, Hu H L, Zhang K 2004 Acta Phys. Sin. 53 1008 (in Chinese) [王晓平、刘磊、胡海龙、张琨 2004 53 1008]
[20]	Rechen J 2001 Ph.D. Dissertation (Zurich: Swiss Federal Institute of Technology)
[21]	Simon G H, Heyde M, Rust H P 2007 Nanotechnology 18 255503
[22]	Castellanos-Gomez A, Agrait N, Rubio-Bollinger G 2009 Nanotechnology 20 215502
[23]	García R, Pérez R 2002 Surf. Sci. Rep. 47 197

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