本文的目的在以分子動力學理論，研究奈米鎳基材在雷射輔助下的壓印行為，並進行實際壓印實驗與之比較。以FCC結構之鎳基材作為分子動力學數值模擬之壓印工件。本文數值方法則採用Gear五階預測修正法來計算微系統原子受位移條件後的位置、速度與加速度，並以Verlet鄰近表列與Morse勢能函數的演算法則來處理分子間的相互作用力。
　　數值模擬的主要內容分為三部份：第一部份在於探討以鎳金屬為壓印基材、銅金屬為壓印模具的奈米壓印過程中，模具受到系統溫度的影響所呈現的施力狀況。第二部分則探討系統溫度的高低對壓印過程中，工件應力分布之影響。第三部份再探討系統溫度對壓印結束後工件原子回彈情形的影響。經過以上的數值模擬發現：(1) 模具脫離加工件之後會將工件原子帶離，這與真實的奈米壓印製程的情況一致。(2) 在壓印的過程，系統溫度較高會使得模具受力的負荷較小。(3) 工件受到較大壓應力的地方在圖案底端以及表面原子靠近沖頭的地方。(4) 系統溫度越高以及工件塑變量較大的地方，其回彈量均較大。

　　The object of this thesis is to study the imprint phenomena of nano-scale nickel substrate using molecular dynamics theory, and the results are explained and compared with actual experiments. The imprint workpiece in the numerical simulation is the material of nickel of the construction of FCC. The Gear’s fifth order predictor-corrector algorithms is adapted to calculate the positions, velocities, and accelerations of atoms under various displacement condition, while the interactions of atoms are dealt with Verlet’s neighbor lists and Morse’s potential.

　　The numerical simulations contain three parts. The first part is to study the difference of force on the compressing molds with various system temperatures. The imprint substrate is made of nickel and the mold is copper. The second part is to study the stress on the imprint substrates with various system temperatures. And the third part is to study the spring-back of substrate atoms under different temperature after imprint. From the numerical simulations, it can be found: (1) the mold will bring substrate atoms away from the workpiece, (2) the loading force is lower while system temperature is higher at the imprint process (3) the high compressing stress can be found at the bottom of the mold and in the corner of imprint area, (4) the spring-back phenomenon was obtained while the deformation and temperature are increased.

[1]Dirac P. A. M., The Principles of Quantum Mechanics, Oxford, 1958.
[2]吳大猷, 量子力學(甲部、乙部), 聯經出版社, 台灣, 民國六十八年.
[3]楊衛, 宏微觀斷裂力學, 國防工業出版社, 北京, 1995.
[4]物質結構的探索, 凡異出版社, 台灣, 民國八十年.
[5]李怡嚴, 大學物理學第二冊, 東華書局, 台灣, 民國七十二年.
[6]Dove M. T., Introduction to Lattice Dynamics, Cambridge University
Press,USA, 1993.
[7]Irving J. H. and Kirkwood J. G., “The Statistical Mechanical Theory of
Transport Properties. IV. The Equations of Hydrodynamics,” J. Chem. Phys.,
Vol. 18, pp. 817-823, 1950.
[8]Metropolis N., Rosenbluth A. W., Rosenblluth M. N., Teller A. H., and Teller
E., “Equation of State Calculations by Fast Computing Machines,” J. Chem.
Phys., Vol. 21, pp. 1087-92, 1953.
[9]Allen M. P. and Tildesley D. J., Computer Simulation of Liquids, Oxford
University Press, New York, 1987.
[10]Alder B. J. and Wainwright T. E., “Phase Transition for A Hard Sphere
System,” J. Chem. Phys., Vol. 27, pp. 1208-9, 1957.
[11]Alder B. J. and Wainwright T. E., “Studies in Molecular Dynamics. I.
General Method,” J.Chem. Phys., Vol. 31, pp. 459-466, 1959.
[12]Girifalco L. A. and Weizer V. G., “Application of the Morse Potential
Function to Cubic Metals,” Phys. Rev., Vol. 114, No. 3, 1959.
[13]Rahman A., “Correlations in the Motions of Atoms in Liquid Atom,” Phys.
Rev., 136A, pp. 405-11, 1964.
[14]Verlet L., “Computer ‘Experiments’ on Classical Fluids Ⅱ, Equilibrium
Correlation Function,” Phys. Rev, Vol. 165, pp. 201~14, 1968.
[15]Quentrec B. and Brot C., “New Method for Searching for Neighbors in
Molecular Dynamics Computations,” J. Comput. Phys. Vol. 13, pp. 430, 1975.
[16]Rapaport D. C., “Large-scale Molecular Dynamics Simulation Using Vector
and Parallel Computers,” Comput. Phys. Rep. Vol. 9, pp. 1-53, 1988.
[17]Grest G. S., Dünweg B. and Kremer K., “Vectorrized Link Cell Fortran Code
for Molecular Dynamics Simulations for a Large Number of Particles,”
Comput. Phys. Comm. Vol. 55(3), pp. 269-285, 1989.
[18]Chou S. Y., Krauss P. R., and Renstrom P. J., “Imprint of sub-25 nm vias
and trenches in polymers”, Appl. Phys. Lett., Vol. 67, No. 21, pp.3114-
3116, 20 November, 1995.
[19]Chou S. Y., Krauss P. R., and Renstrom P. J., “Nanoimprint lithography”,
J. Vac. Sci. Technol. B, Vol. 14, No. 6, pp.4129-4133, 1996.
[20]Chou S. Y., Krauss P. R., “Imprint Lithography with Sub-10 nm Feature Size
and high Throughput”, Microelectronic Engineering, 35, pp.237-240, 1997.
[21]Chou S. Y., Krauss P. R., Zhang W., Guo L., and Zhuang L., “Sub-10 nm
imprint lithography and applications”, J. Vac. Sci. Technol. B, Vol. 15,
No. 6, pp.2897-2904, 1997.
[22]Sun X., Zhuang L., Zhang W., and Chou S. Y., “Multilayer resist methods
for nanoimprint lithography on nonflat surfaces”, J. Vac. Sci. Technol. B,
Vol. 16, No. 6, pp.3922-3925, 1998.
[23]Schulz H., Scheer H. C., Hoffmann T., and Torres C. M. S., ”New polymer
materials for nanoimprinting”, J. Vac. Sci. Technol. B, Vol. 18, No. 4,
pp.1861-1865, 2000.
[24]Taniguchi J., Tokano Y., Miyamoto I., Komuro M., and Hiroshima H., ”
Diamond nanoimprint lithography”, Nanotechnology, 13, pp.592-596, 2002.
[25]Chou S. Y., Keimel C., and Gu J., “Ultrafast and direct imprint of
nanostructures in silicon”, Nature, Vol. 417, 20, pp.835-837, 2002.
[26]Fang T. H., Weng C. I., Chang J. G., ”Nano-lithography with atomic force
Microscopy”, Surface Science, 501, pp.138-147, 2002.
[27]吳政達、方得華、許光城, “奈米壓印的成形機制與模具錐度效應之分子動力學研
究”, 中華民國第二十七屆全國力學會議
[28]Jeng Y. R. and Tan Ch. M., “On the Mechanical Behavior of Nanoindentation：
An Atomics Statics Approach”, Journal of the Chinese Society of Mechanical
Engineers, Vol.24, No.4, pp.377-384, 2003.
[29]Arsenault R. J. and Beeler J. R., Computer Simulation in Material Science,
Asm INTERNATIONAL, USA, 1988.
[30]Smith R. and Jakas M., Atomic and Ion Collisions in Solids and at Surfaces：
Theory, Simulation, and Applications, Cambridge University Press, USA, 1997.
[31]Haile J. M., Molecular Dynamics Simulation: Elementary Methods, John Wiely
& Sons, Inc., USA, 1992.
[32]Allen M. P. et al., “Computer Simulation in Chemical Physics,” Series C:
Mathematical and Physical Science, Vol. 397, Kluwer Academic, Dordrecht,
1992.
[33]Allen M. P. et al., “Computer Simulation in Material Science,” Series E:
Applied Sciences, Vol. 205, Kluwer Academic, Dordrecht, 1991.
[34]林青楠, 分子動力學研究銅薄膜之準分子雷射燒蝕, 國立成功大學 機械工程學系 碩士
論文, 台灣, 民國九十二年.
[35]Lennard-Jones J. E., “The Determination of Molecular Fields. I. From the
Variation of the Viscosity of a Gas with Temperature,” Proc. Roy. Soc.
(Lond.), 106A, 441, 1924; “The Determination of Molecular Fields. II. From
the Variation of the Viscosity of a Gas with Temperature,” Proc. Roy. Soc.
(Lond.), 106A, 463, 1924.
[36]陳道隆, 以分子動力學研究奈米級微結構之拉伸、壓縮、扭轉變形機制, 國立成功大
學 機械工程學系 碩士論文, 台灣, 民國九十年.
[37]Iwaki T., “Molecular Dynamics Study on Stress-Strain in Very Thin Film
(Size and Location of Region for Defining Stress and Strain),” JSME Int.
J., Ser. A, Vol. 39, No. 3, pp. 346-353, 1996.
[38]小竹進, 熱流體之分子動力學, 丸善株式會社, 日本, 1998.
[39]Miyazaki N. and Shiozaki Y., “Calculation of Mechanical Properties of
Solids Using Molecular Dynamics Method,” JSME, Series A, Vol. 39, No. 4,
1996.
[40]Imafuku M., Sasajima Y., Yamamoto R., and Doyama M., “Computer simulations
of the structures of the metallic superlattices Ad/Ni and Cd/Ni and their
elastic moduli,” Journal of Physics F: Metal Physics, v 16, n 7, p 823-
829, Jul, 1986.
[41]Wakabayashi H., Shimazu Y., Furuta T., Makino T., “Numerical Simulation on
Melting Behavior of an Atomic Layer Irradiated by Thermal Radiation,” 日本
機械協會論文集 (B編) 59卷563號(1993-7).
[42]Ralph L. D. et al., “METALS HANDBOOK,” American Society for Metals, 7301
Euclid Ave., Cleveland, Ohio, USA, 1939.
[43]Rappaport, D. C., “The art of molecular dynamics simulation,” Cambridge
University Press, Cambridge, UK, 1995.
[44]Verlet L., “Computer ‘Experiments’ on Classical Fluids Ⅱ, Equilibrium
Correlation Function,” Phys. Rev, Vol. 165, pp. 201~14, 1968.
[45]Rapaport D. C., “The Art of Molecular Dynamics Simulation,” Cambridge
University Press, London, 1997.
[46]Goodfellow J. M. et al., “Molecular dynamics,” CRC Press, Boston, 1990.
[47]Allen M. P. and Tildesley D. J., “Computer Simulation of Liquids,” Oxford
Science, London, 1991.
[48]Frenkel D. and Smit B., “Understanding Molecular Simulation,” Academic
Press, San Diego, 1996.
[49]張振燦, 雷射與加工, 亞太圖書出版社, 1985年.
[50]劉國雄，林樹均，李勝隆，鄭晃忠，葉均蔚, “工程材料科學,” 全華圖書公司, 台
北, 1996年.
[51]丁勝懋, 雷射工程導論─第四版, 中央圖書公司, 台北, 1995年.

[52]Bauerle D., “Laser Processing and Chemistry,” Springer-Verlag, Berlin
Heidelberg, 2000.
[53]Ikeda N., Akaba T., Inoue F., Takahashi S., and Noda O. “Diode-Pumped
Solid-State Ultraviolet Laser Micro Processing System”, Mitsubishi Heavy
Industries, Ltd. Technical Review Vol.40 Extra No.2 (Jan. 2003)
[54]Johnson R. A., “Analytic Nearest-Neighbor Model for FCC Metals,” Phy.
Rev. B, Vol. 37(8), pp. 3924-3931, 1987.
[55]Häkkinen H. and Manninen M., “The Effective-Medium Theory beyond the
Nearest-Neighbour Interaction,” J. Phys. Condens. Matter 1 (1989) 9765-
9777.
[56]Jacobsen K. W., “Bonding in Metallic Systems: An Effective-Medium
Approach,” Comments Cond. Mat. Phys. 1988, Vol. 14, No. 3, pp. 129-161.
[57]Justo J. F., Bazant M. Z., Kaxiras E., Bulatov V. V. and Yip S.,
“Interatomic Potential for Silicon Defects and Disordered Phases,” Phys.
Rev. B, Vol. 58, No. 5, pp. 2539-2550, 1998
[58]Stillinger F. H. and Weber T. A., Phys. Rev. B31, pp.5262, 1985.