本文以量子分子動力學探討奈米碳管做為AFM探針頭，並以輕敲式的量測技術量測樣品表面時，在碳管端部所可能產生的變形機制及彈性係數。此彈性係數對於敲輕式來說是非常重要的，因為輕敲式工作原理即探針剛好敲到樣品，較不會損壞樣品表面。若輕敲時碳管未產生局部挫曲（Local buckling），則此彈性係數在解析度及量測樣品之剛性上，會有一定程度之影響。本文之模擬採用Tight-Binding 多體勢能，所探討的主要參數為碳管直徑。結果發現管徑小於8.2Å ，凹陷之臨界力呈線性上升；碳管直徑大於8.2Å 之後，平均以0.3nN 可使端部凹陷；碳管端部受力曲線斜率會隨著幾何結構的變化而變化；管徑大於10Å ，端部之彈性
係數平均值約為0.38nN/Å 。最後提出量子分子動力學的瓶頸及可能改進的方向，作為今後努力的方針。

We present a detailed investigation of the deformation mechanism and the spring constants of carbon nanotube probe for AFM tapping mode using
Quantum Molecular Dynamics. The working principle of AFM tapping mode is the probe touch precisely to sample surface, less damage to sample surface than contact mode. This spring constants is significant when the probe does not occur local buckling during cap compression. The diameter of tube is discussed in this article. The simulation show that force which make the cap convex to concave is rise linear if diameters less than 8.2Å . On the other hand,
the average value is 0.3 nN. The slope of force curve of cap vary with geometry of cap. If diameters greater than 10Å , average value of spring constant of cap of carbon nanotube probe is 0.38nN/Å independent of diameter of tube. Finally, we point out the hard of Quantum Molecular Dynamics and feasibility improve way for our future work.

1. G. Binnig, C. F. Quate, and C. Gerber, ²Atomic Force Microscope², phys.
2. 林鶴南, 李龍正, 劉克迅, 科儀新知, 17 (3) , 29 (1995).
3. H. Dai, J. H. Hafner, A. G. Rinzler, D. T. Colbert, and R. E. Smalley,
"Nanotubes as nanoprobes in scanning probe microscopy", Nature 384, 147
4. J. H. Hafner, C. L. Cheung, and C. M. Lieber, "Growth of nanotubes for
probe microscopy tips", Nature 398, 761 (1999).
5. C. L. Cheung, J. H. Hafner, and C. M. Lieber, "Carbon nanotube atomic
force microscopy tips：Direct growth by chemical vapor deposition and
application to high resolution imaging", Proc. Natl. Acad. Sci. USA 97, 3809
6. J. H. Hafner, C. L. Cheung, and C. M. Lieber, "Direc growth of
single-walled carbon nanotube scanning probe microscopy tips", J. Am. Chem.
7. C. L. Cheung,J. H. Hafner, T. W. Odom, K. Kim, and C. M. Lieber,
"Growth and fabrication with single-walled carbon nanotube probe
microscopy tips", Appl. Phys. Lett. 76, 3136 (2000).
8. S. Iijima, Nature 354, 56 (1991).
9. C. F. Cornwell and L.T. Wille, "Elastic Properties of Single-Walled Carbon
Nanotubes in Compression", Solid State Comm. 101,555 (1997).
10. J. A. Harrison and S. J. Stuart, "Properties of Capped Nanotubes When
Used as SPM Tips", J. Phys. Chem. B 101, 9682 (1997).
11. Y. Nan and L. Vincenzo, "Carbon nanotube caps as springs：Molecular
dynamics simulations", Phys. Rev. B 58 (19), 12649 (1998).
12. G. Ajay, H. Jie and B. S. Susan, "Interactions of Carbon-Nanotube
Proximal Probe Tips with Diamond and Graphene", Phys. Rev. Lett. 81 (11),
2260 (1998).
13. J. C. Slater, and G. F. Koster, "Simplified LCAO method for periodic
potential problem" , Physical Review Vol. 94 No. 6 1498-1524 (1954).
14. C. Kittle, Introduction to Solid State Physics, John Wiley and Sons, New
York, (1996).
15. 劉東昇編譯， 化學量子力學，徐氏基金會出版，台北，1992。
16. 江元生， 結構化學，五南圖書出版，台北，1998。
17. L. Colombo, "A source code for tight-binding molecular dynamics
simulation", Computational Materials Science Vol. 12 278-287 (1998).
18. J. Z. H. Zhang, Theory and Application of Quantum Molecular Dynamics,
World Scientific Publishing Company, Singapore, (1999).
19. 江逢霖， 量子化學原理，復旦大學出版社，上海，1990。
20. C. H. Xu, C. Z. Wang, C. T. Chan, and K. M. Ho, "A transferable
tight-binding potential for carbon", J. Phys.: Condens. Matter Vol. 4
6047-6054 (1992).
21. I. Kwon, R. Biswas, C. Z. Wang, K. M. Ho, and M. Soukoulis,
"Transferable tight-binding models for silicon", Physical Review B Vol. 49
No. 11 7242-7250 (1994).
22. R. Saito, G. Dresselhaus, M. S. Dresselhaus, Physical Properties of
Carbon Nanotubes , Imperial College Press , (1998).
23. M. S. Dresselhaus , G. Dresselhaus , P. C. Eklund , Science of Fullerenes
and Carbon Nanotubes , Academic Press , (1996).
24. M. P. Allen et al., Computer Simulation in Chemical Physics, SeriesC:
Mathematical and Physical Sciences Vol. 397, Kluwer Academic, Dordrecht,
(1992).
25. M. Meyer et al., Computer Simulation in Material Science, Series E:
Applied Sciences Vol. 205, Kluwer Academic , Dordrecht, (1991).
26. S. Erkoc, "Annual Reviews of Computational IX", World Scientific
Publishing Company, Singapore, 1-103 (2001).
27. H. Rafii-Tabar, "Modelling the nano-scale phenomena in condensed
matter physics via computer-Based numerical simulations", Physics Reports
Vol. 325 239-310 (2000).
28. R. Smith et al., Atomic & Ion Collisions in Solids and at Surfaces,
Cambridge University Press, London , (1997).
29. G. C. Maitland, M. Rigby, E. B. Smith, and W. A. Wakeham,
Intermolecular Forces, Oxford University Press, London , (1987).
30. P. L. Huyskens et al., Intermolecular Forces , Springer-Verlag, Berlin ,
(1991).
31. M. Rigby, E. B. Smith, W. A. Wakeham, and G. C. Maitland, The Forces
between Molecules, Oxford University Press, London, (1986).
32. R. P. Gupta, "Lattice relaxation at a metal surface", Physical Review B
Vol. 23 No. 12 6265-6270 (1981).
33. J. M. Haile, Molecular dynamics simulation：elementary methods, A
Wiley-interscience publication, New York (1992).
34. D. C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge
University Press, London, (1997).
35. J. M. Goodfellow et al., Molecular dynamics, CRC Press, Boston, (1990).
36. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford
Science, London, (1991).
37. D. Frenkel and B. Smit, Understanding Molecular Simulation, Academic
Press, San Diego, (1996).
38. D. W. Heermann, Computer Simulation Method, Springer-Verlag, Berlin,
(1990).
39. G. Galli, R. M. Martin, R. Car and M. Parrinello, "Carbon：The nature of
the liquid state", Phys. Rev. Lett. 63, 988, (1989).
40. M. S. Dresselhaus, G. Dresselhaus, R. Saito, "Physics of carbon
nanotubes", Carbon 33, 883-891 (1995).
41. L. C. Qin, X. Zhao, K. Hirahara, Y. Miyamoto, Y. Ando, S. Iijima, "The
smallest carbon nanotube", Nature 408, 50 (2000).