原子力顯微鏡(Atomic Force Microscopy，AFM)為奈米時代的一項重要量測工具。其主要的操作機制是利用光槓桿方式來量測一微小探針與樣品之間各種作用力的變化，藉以獲得高解析度的表面形貌圖。雖然此種光槓桿感測方式的靈敏度高，但是卻有調整與校正程序繁瑣的缺點，因此本研究主要的目的是利用可以同時執行致動與感測功能的壓電音叉式探針來取代光槓桿的感測方法，建立一簡便的原子力顯微鏡。在本論文中，吾人利用對壓電音叉式探針的模型建構，來探討音叉式探針的操作動態；並利用系統等效彈簧係數的改變來探討原子力的影響，最後設計具有強健性的控制器取代需要參數調整的PI控制器。

1.G. Binnig, C. F. Quate and Ch. Gerber, ‘Atomic Force Microscope’, Phys. Rev. Lett 56 (1986), 930.
2.Paul K. Hansma and Jerry Tersoff, ‘Scanning tunneling microscopy’, J. Appl. Phys. 61(2) (1987), R1.
3.Y. Martin, C.C. Williams and H. K. Wickramasinghe, ‘Atomic force microscope-force mapping and profiling on a sub 100- scale’, J. Appl. Phys. 61(10) (1987), 4723.
4.S. R. Manalis, S. C. Minne and C. F. Quate, ‘Atomic force microscopy for high speed imaging using cantilevers with an integrated actuator and sensor’, Appl. Phys. Lett. 68(6) (1996), 871.
5.T. Itoh and T. Suga, ‘Development of a force sensor for atomic force microscopy using piezoelectric thin films’, Nanotechnology 4 (1993), 218.
6.Khaled Karrai and Robert D. Grober, ‘Piezoelectric tip-sample distance control for near field optical microscopes’, Appl. Phys. Lett. 66 (1995), 1842.
7.V.Blank, M.Popov, N.Lvova, K.Gogolinsky and V.Reshetov, ‘Nano-sclerometry measurements of superhard materials and diamond hardness using scanning force microscope with the ultrahard fullerite C60 tip’, J. Mater. Res., 12 (1997), 3109.
8.Q. Zhong, D. Inniss, K. Kjoller and V.B. Elings, ‘Fractured polymer / silica fiber surface studied by tapping mode atomic force microscopy’, Surface Science Letters 290 (1993), L688.
9.Ricardo Garcia and Ruben Perez, ‘Dynamic atomic force microscopy methods’, Surface Science Reports 47 (2002), 197.
10.S.N. Magonov, V. Elings, and M.-H Whangbo, ‘Phase imaging and stiffness in tapping mode atomic force microscopy’, Surface Science 375 (1997), L385.
11.http://www.nanosensors.com.
12.Dror Sarid, ‘Scanning force microscopy : with applications to electric, magnetic,and atomic forces’, Oxford University Press, 1994.
13.Gibson, Ronald F. ‘Principles of composite material mechanics’, McGraw-Hill, 1994
14.Ikeda, Takuro, ‘Fundamentals of piezoelectricity’, Oxford University Press, 1990.
15.C. K. Lee, ‘Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I : Governing equations and reciprocal relationships’, J. Acoust. Soc. Am. 87 (1990), 1144.
16.Hibbeler, R. C., ‘Mechanics of materials’, Prentice Hall, 1997.
17.Singiresu S., ‘Mechanical vibrations’, Addison-Wesley, 1990.
18.Jan G. Smits and Arthur Ballato, ‘Dynamic Admittance Matrix of Piezoelectirc Cantilever Bimorphs’, Journal of microelectro- mechanical systems, 3(3) (1994), 105.
19.Meirovitch, Leonard, ‘Analytical methods in vibrations’, Macmillan, 1967.
20.Ricardo Garcia and Alvaro San Paulo, ‘Attractive and repulsive tip-sample interaction regimes in tapping-mode atomic force microscopy’, Physical Review B, 60(7) (1999), 4961.
21.T. R. Albrecht, P. Grutter, D. Horne, and D. Rugar, ‘Frequency modulation detection using high-Q cantilevers for enhanced force microscope sensitivity’, J. Appl. Phys. 69(2) (1991), 668.
22.A.G.T. Ruiter, K.O. van der Werf, J.A. Veerman, M.F. Garcia-Parajo, W.H.J. Rensen and N.F. van Hulst, ‘Tuning fork shear-force feedback’, Ultramicroscopy 71 (1998), 149.
23.Charles Kitchin and Lew Counts, ‘RMS TO DC CONVERSION APPLICATION GUIDE’, Analog Devices, 1986.
24.Zhou, Kemin, ’Robust and optimal control’, Prentice Hall, 1996.
25.Michael Athans, ‘A TUTORIAL ON THE LQG/LTR METHOD’, Proc. American Control Conference, Seattle, WA, June 1986.
26.Ting-Jen Yeh, ‘Modeling, Analysis and Control of Magnetically Levitated Rotating Machines.’ Ph.D. dissertation, Massachusetts Institute of Technology (1996).
27.Hal Edwards, Larry Taylor, Walter Duncan and Allan J. Melmed, ‘Fast, high-resolution atomic force microscopy using a quartz tuning fork as actuator and sensor’, J. Appl. Phys. 82(3) (1997), 980.