雷射輔助式直接壓印是利用雷射在試片表面瞬間產生高溫而使試片產生熔融，再以預壓力將所需要的圖形轉印到試片上。在本研究中，我們以準分子雷射做為熱源使矽基板的表面產生高溫而發生熔融，經由實驗的方法與模擬的數值比較，探討此加熱機制的所造成的熔融時間與矽基板的熔融深度。
在熔融時間的實驗中以632.8 nm的氦氖雷射當作量測光源，量測矽基板表面的反射率，我們可以發現溫度的變化會造成反射率的改變，並且在熔融層出現時，反射率會維持一個水平，因此可以藉由反射率持平的時間定義出熔融的時間。此一實驗量測結果可以與理論模擬結果進行比對，得到非常一致的結果，間接證明理論模擬對矽基板的熔融時間與熔融深度的估算正確性。
此外，本研究發現以1310 nm的二極體雷射量測矽基板背部的反射率時，反射率會隨著熔融層厚度的不同而有週期性的變化，藉此我們可以由反射率的週期估算出熔融深度的大小。

Laser assisted direct imprinting (LADI) technology is a special kind of nanoimprint technology which applies a preloaded nano-mold and a high-energy laser pulse. The laser pulse can instantaneously melt the sample surface to make the pattern transfer from the mold to the sample. In this study, we will investigate both theoretically and experimentally the melting phenomenon of the silicon substrate subjected to the irradiation of an excimer laser pulse. By comparing the experimental and simulation data we can quantitatively determine the molten time and molten depth of silicon substrate, which play an important role in the LADI process.
Experimentally, the time-resolved reflectivity (TRR) measurements are carried out with a probe He-Ne laser of 632.8 nm in wavelength. From the TRR measurements, we discover that the reflectivity signal as a function of time can be used to re-construct the time-history of substrate melting. Therefore, we could deduce the molten time and melting depth under different laser fluence.
Furthermore, this study discovers that if we measured the back surface reflectivity by a diode laser of wavelength 1310 nm, the reflectivity signal will oscillate cyclically along with the increasing molten depth. With this cyclic signal of back surface reflectivity, the molten depth can also be estimated. Good agreements between experiments and simulation are observed.

[1] S. Y. Chou, P. R. Krauss and P. J. Renstrom, “Nanoimprint
lithography,” J. Vac. Sci. Technol. B, Vol. 14, pp 4129-4133 (1996).
[2] S. Y. Chou, C. Keimel and J. Gu, “Ultrafast and direct imprint of nanostructures in silicon,” Naturl, Vol. 417, pp 835-837 (2002).
[3] W. R. Sooy, M. Geller and D. P. Bortfeld, “Switching of semiconductor reflectivity by a giant pulse laser,” Appl. Phys. Lett., Vol. 5, pp 54-56 (1964).
[4] M. Birnbaum and T. L. Stocker, “Reflectivity enhancement of semiconductors by Q-switched ruby lasers,” J. Appl. Phys., Vol. 39, pp 6032-6036 (1968).
[5] M. O. Lampert, J. M. Koebel and P. Siffert, “Temperature dependence of the reflectance of solid and liquid silicon,” J. Appl. Phys., Vol. 52, pp 4975-4976 (1981).
[6] G. E. Jellison, Jr. and H. H. Burke, “The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths,” J. Appl. Phys., Vol. 60, pp 841-843 (1986).
[7] K. D. Li and P. M. Fauchet, “Picosecond determination of the dielectric function of liquid silicon at 1064nm,” Solid State Commun. Vol. 61, pp 207-209 (1987).
[8] P. Baeri, M. G. Grimaldi and R. Reitano, “Thermal properties of metastable phases studied by nanosecond laser heating,” High temp. High press., Vol. 23, pp 675-683 (1991).
[9] S. Moon, M. Lee, M. Hatano, G. P. Grigoropoulos, “Interpretation of optical diagnostics for the analysis of laser crystallization of amorphous silicon films,” Microscale Thermophysical Engineering, Vol. 4, pp 25-38 (2000).
[10] M. Hatano, S. Moon, M. Lee, K. Suzuki and C. P. Grigoropoulos, “Excimer laser-induced temperature field in melting and resolidification of silicon thin films,” J. Appl. Phys., Vol. 87, pp 36-43 (2000).
[11] J. C. Wang, R. F. Wood and P. P. Pronko, “Theoretical analysis of thermal and mass transport in ion-implanted laser-annealed silicon,” Appl. Phys.Lett., Vol. 33, pp 455-458 (1978).
[12] R. O. Bell, M. Toulemonde and P. Siffert, “Calculated temperature Distribution during laser annealing in silicon and cadmium telluride,” Appl. Phys., Vol. 19, pp 313-319 (1979).
[13] M. Toulemonde, S. Unamuno, R. Heddache, M. O. Lampert, M. Hage-Ali and P. Siffert, “Time-resolved reflectivity and melting depth measurements using pulsed ruby laser on silicon,” Appl. Phys. A, Vol. 36, pp 31-36 (1985).
[14] C. K. Ong, H. S. Tan and E. H. Sin, “Calculations of melting threshold energies of crystalline and amorphous materials due to pulsed-laser irradiation,” Mater. sci. eng., Vol. 79, pp 79-85 (1986).
[15] S. Deunamuno and E. Fogarassy, “Athermal description of the melting of c- and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci., Vol. 36, pp 1-11 (1989).
[16] A. G. Cullis, H. C. Webber, N. G. Chew, J. M. Poate and P. Baeri, “Transitions to defective crystal and the amorphous state induced in elemental Si by laser quenching,” Phys. Rev. Lett., Vol. 49, pp 219-222 (1982).
[17] P. Baeri, “Nanosecond laser-induced phase transitions and metastable phases quenching,” Phil. Mag. B., Vol. 61, pp 587-600 (1990).
[18] F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, N.J., Prentice Hall (1993).
[19] L. E. Kinsler, A. R. Frey, A. B. Coppens and J. V. Sanders, Fundamentals of acoustics, Wiley, New York (1982).
[20] A. Bejan, “Heat Transfer,” John Wiley & Sons, Inc., New York (1993).
[21] F. B. Hsiao, C. P. Jen, D. B. Wang, C. H. Chuang, Y. C. Lee, C. P. Liu and H. J. Hsu, “An analytical modeling of heat transfer for laser-assisted nanoimprinting processes,” Comput. Mech., Vol. 37, pp 173-181(2006).
[22] V. N. Tokarev and A. F. H. Kaplan, “An analytical modeling of time dependent pulsed laser melting,” J. Appl. Phys., Vol. 86, pp 2836-2846 (1999).
[23] E. D. Palik, Handbook of optical constants of solids, Academic Press, Inc.(1985).
[24] Goodfellow Corporation, Material Catalogue, USA (2002).
[25] F. B. Hsiao, D. B. Wang and C. P. Jen, “Numerical investigation of thermal contact resistance between the mold and substrate on laser-assisted imprinting fabrication,” Numer. heat transf., A Appl., Vol. 49, pp 669-682 (2006)
[26] K. M. Shvarev, B. A. Baum and P. V. Gel’d, “Optical properties of liquid silicon,” Sov. Phys. Solid State, Vol. 16, pp 2111-2112 (1975).
[27] B. K. Sun, X. Zhang and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Transfer., Vol. 40, pp 1591-1600 (1997).
[28] P. Tosin, W. Luthy and H. P. Weber, “Liquid carbon observed with reflection measurements on CVD-diamond under UV pulsed-laser irradiation,” Appl. Surf. Sci., Vol. 96-98, pp 384-386 (1996).
[29] G. D. Ivlev and E. I. Gatskevich, “Liquid phase reflectivity under conditions of laser-induced silicon melting,” Semiconductors, Vol. 34, pp 759-762 (2000).
[30] G. E. Jellison, Jr., D. H. Lowndes, D.N. Mashburn and R.F. Wood, “Time-resolved reflectivity measurements on silicon and germanium using a pulsed excimer KrF laser heating beam,” Phys. Rev. B, Vol. 34, pp 2407-2415 (1986).
[31] S. Rubanov and P. R.Munroe, “FIB-induced damage in silicon,” J. microsc., Vol. 214, pp 213-221 (2004).
[32] A. G. Cullis, N. G. Chew, H. C. Webber and D. J. Smith, “Orientation dependence of high speed silicon crystal growth from the melt,” J. cryst. growth., Vol. 68, pp 624-638 (1984).
[33] M. O. Thompson, J. W. Mayer, A. G. Cullis, H. C. Webber, N. G. Chew, J. M. Poate and D. C. Jacobson, “Silicon melt, regrowth, and amorphization velocities during pulsed laser irradiation,” Phys. Rev. Lett., Vol. 50, pp 896-899 (1983).
[34] D. E. Hoglund, M. O. Thompson and M. J. Aziz, “Experimental test of morphological stability theory for a planar interface during rapid solidification,” Phys. Rev. B, Vol. 58, pp 189-199 (1998).
[35] C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation, J. Appl. Phys., Vol. 83, pp 3323-3336 (1998).
[36] 李正中，薄膜光學與鍍膜技術，藝軒圖書出版社，台灣 (2002).
[37] O. S. Heavens, Optical properties of thin solid films, Dover Publications, Inc., New York, (1965).
[38] Z. Knittl, Optics of thin films, John Wiley & Sons, London (1976).