材料的雷射剝蝕閾值是研究材料損傷及雷射加工的重要參數。因為雷射光束強度輪廓通常並不是理想的高斯分布，我們研究用更精確的方法推估剝蝕閾值:以雷射光束強度輪廓的各光強強度值對應面積之趨勢去對照剝蝕脈衝能量閾值，用以推算雷射剝蝕閾值。並可以用以驗證實驗中的雷射光強輪廓。為此量測，我們架設一台成像式顯微鏡可直接觀測雷射剝蝕的過程並量測雷射聚焦點光束輪廓。實驗及分析顯示甲基丙烯酸甲酯的單發雷射剝蝕閾值為3.1焦耳每平方公分，多發雷射剝蝕閾值之孵化係數為0.65±0.03。 100奈米厚的氮化鋁的單發雷射剝蝕閾值為6.53焦耳每平方公分，50奈米厚的氮化鋁的單發雷射剝蝕閾值為9.83焦耳每平方公分。

The laser ablation threshold of materials is an important parameter for studying material damage and laser processing. Because the laser beam intensity profile is usually not an ideal Gaussian distribution, we study a more accurate method to estimate the ablation threshold: use the trend of the area corresponding to each intensity value of the laser beam intensity profile to compare the ablation pulse energy threshold with, then calculate the laser ablation threshold. The analysis can also be used to verify the laser intensity profile in the experiment. For this measurement, we set up an imaging microscope to directly observe the laser ablation process and measure the beam profile at the laser focus point. Experiments and analysis show that the single-shot laser ablation threshold of PMMA is 3.1 J/cm^2. Incubation coefficient of multi-shot laser ablation is0.65±0.03. Single shot laser ablation threshold of AlN is 6.53 J\/cm^2 for 100-nm-thick AlN film is , and 9.83 J\/cm^2 for 50-nm-thick AlN film.

[1] S. Baudach, J. Bonse, and W. Krautek, "Ablation experiments on polyimide with femtosecond laser pulses," Applied Physics a-Materials Science & Processing, vol. 69, pp. S395-S398, Dec 1999, doi: 10.1007/s003390051424.
[2] S. Baudach, J. Bonse, J. Kruger, and W. Kautek, "Ultrashort pulse laser ablation of polycarbonate and polymethylmethacrylate," Applied Surface Science, vol. 154, pp. 555-560, Feb 2000, doi: 10.1016/s0169-4332(99)00474-2.
[3] S. Biswas, N. Roy, R. Biswas, and A. Kuar, "Experimental Investigation of Varying Laser Pass on Micro-channel Characteristics of Thick PMMA by Laser Transmission Micro-machining," Materials Today: Proceedings, vol. 18, pp. 3514-3520, 2019.
[4] J. Li, W. Wang, X. Mei, A. Pan, B. Liu, and J. Cui, "Rapid fabrication of microlens arrays on PMMA substrate using a microlens array by rear-side picosecond laser swelling," Optics and Lasers in Engineering, vol. 126, p. 105872, 2020.
[5] J. Li, W. Wang, X. Mei, X. Sun, and A. Pan, "The formation of convex microstructures by laser irradiation of dual-layer polymethylmethacrylate (PMMA)," Optics & Laser Technology, vol. 106, pp. 461-468, 2018.
[6] K. Sakaue et al., "Surface processing of PMMA and metal nano-particle resist by sub-micrometer focusing of coherent extreme ultraviolet high-order harmonics pulses," Optics letters, vol. 45, no. 10, pp. 2926-2929, 2020.
[7] A. Volpe, G. Trotta, U. Krishnan, and A. Ancona, "Prediction model of the depth of the femtosecond laser micro-milling of PMMA," Optics & Laser Technology, vol. 120, p. 105713, 2019.
[8] V. Vozda et al., "Characterization of megahertz X-ray laser beams by multishot desorption imprints in PMMA," Optics express, vol. 28, no. 18, pp. 25664-25681, 2020.
[9] P. P. Rajeev et al., "Memory in nonlinear ionization of transparent solids," (in English), Physical Review Letters, Article vol. 97, no. 25, p. 4, Dec 2006, Art no. 253001, doi: 10.1103/PhysRevLett.97.253001.
[10] N. Sanner et al., "Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics," Applied Physics a-Materials Science & Processing, vol. 94, no. 4, pp. 889-897, Mar 2009, doi: 10.1007/s00339-009-5077-6.
[11] Y. P. Deng et al., "Optical breakdown for silica and silicon with double femtosecond laser pulses," (in English), Optics Express, Article vol. 13, no. 8, pp. 3096-3103, Apr 2005, doi: 10.1364/opex.13.003096.
[12] I. H. Chowdhury, X. Xu, and A. M. Weiner, "Ultrafast two-color ablation of fused silica," Applied Physics a-Materials Science & Processing, vol. 83, no. 1, pp. 49-52, Apr 2006, doi: 10.1007/s00339-005-3476-x.
[13] E. Terasawa et al., "Pulse duration dependence of ablation threshold for fused silica in the visible femtosecond regime," Applied Physics A, vol. 126, pp. 1-5, 2020.
[14] B. Zhou, A. Kar, M. Soileau, and X. Yu, "Reducing feature size in femtosecond laser ablation of fused silica by exciton-seeded photoionization," Optics letters, vol. 45, no. 7, pp. 1994-1997, 2020.
[15] S. Zoppel, R. Merz, J. Zehetner, and G. A. Reider, "Enhancement of laser ablation yield by two color excitation," Applied Physics a-Materials Science & Processing, vol. 81, no. 4, pp. 847-850, Sep 2005, doi: 10.1007/s00339-005-3275-4.
[16] T. J. Derrien, T. Sarnet, M. Sentis, and T. E. Itina, "Application of a two-temperature model for the investigation of the periodic structure formation on Si surface in femtosecond laser interactions," Journal of Optoelectronics and Advanced Materials, vol. 12, no. 3, pp. 610-615, Mar 2010. [Online]. Available: <Go to ISI>://WOS:000277827900039.
[17] M. D. Perry, B. C. Stuart, P. S. Banks, M. D. Feit, V. Yanovsky, and A. M. Rubenchik, "Ultrashort-pulse laser machining of dielectric materials," Journal of Applied Physics, vol. 85, no. 9, pp. 6803-6810, May 1999, doi: 10.1063/1.370197.
[18] B. Chimier et al., "Damage and ablation thresholds of fused-silica in femtosecond regime," Physical Review B, vol. 84, no. 9, Sep 2011, Art no. 094104, doi: 10.1103/PhysRevB.84.094104.
[19] E. Coyne, J. Magee, P. Mannion, G. O’Connor, and T. Glynn, "Characterisation of laser ablation of silicon using a Gaussian wavefront and computer generated wavefront reconstruction," Applied surface science, vol. 229, no. 1-4, pp. 148-160, 2004.
[20] X. Wang, H. Zheng, C. Tan, F. Wang, H. Yu, and K. Pey, "Femtosecond laser induced surface nanostructuring and simultaneous crystallization of amorphous thin silicon film," Optics express, vol. 18, no. 18, pp. 19379-19385, 2010.
[21] X.-P. Zhan, M.-Y. Hou, F.-S. Ma, Y. Su, J.-Z. Chen, and H.-L. Xu, "Room temperature crystallization of amorphous silicon film by ultrashort femtosecond laser pulses," Optics & Laser Technology, vol. 112, pp. 363-367, 2019.
[22] A. J. Antończak, P. E. Kozioł, B. Stępak, P. Szymczyk, and K. M. Abramski, "Direct selective metallization of AlN ceramics induced by laser radiation," in Laser-based Micro-and Nanoprocessing VIII, 2014, vol. 8968: International Society for Optics and Photonics, p. 896814.
[23] Y. Hirayama, H. Yabe, and M. Obara, "Selective ablation of AlN ceramic using femtosecond, nanosecond, and microsecond pulsed laser," Journal of Applied Physics, vol. 89, no. 5, pp. 2943-2949, 2001.
[24] S. H. Kim, I.-B. Sohn, and S. Jeong, "Ablation characteristics of aluminum oxide and nitride ceramics during femtosecond laser micromachining," Applied Surface Science, vol. 255, no. 24, pp. 9717-9720, 2009.
[25] A. Narazaki, H. Takada, D. Yoshitomi, K. Torizuka, and Y. Kobayashi, "Study on nonthermal–thermal processing boundary in drilling of ceramics using ultrashort pulse laser system with variable parameters over a wide range," Applied Physics A, vol. 126, no. 4, pp. 1-8, 2020.
[26] N. Nedialkov, M. Sawczak, R. Jendrzejewski, P. Atanasov, M. Martin, and G. Śliwiński, "Analysis of surface and material modifications caused by laser drilling of AlN ceramics," Applied Surface Science, vol. 254, no. 4, pp. 893-897, 2007.
[27] R. S. Sposili, J. Bovatsek, and R. Patel, "Laser processing of ceramics for microelectronics manufacturing," in Laser Applications in Microelectronic and Optoelectronic Manufacturing (LAMOM) XXII, 2017, vol. 10091: International Society for Optics and Photonics, p. 100910X.
[28] D. Pietroy, Y. Di Maio, B. Moine, E. Baubeau, and E. Audouard, "Femtosecond laser volume ablation rate and threshold measurements by differential weighing," Optics express, vol. 20, no. 28, pp. 29900-29908, 2012.
[29] R. E. Samad and N. Vieira, "Geometrical method for determining the surface damage threshold for femtosecond laser pulses," Laser physics, vol. 16, no. 2, pp. 336-339, 2006.
[30] N. Sanner et al., "Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics," Applied Physics A, vol. 94, no. 4, pp. 889-897, 2009.
[31] J. Liu, "Simple technique for measurements of pulsed Gaussian-beam spot sizes," Optics letters, vol. 7, no. 5, pp. 196-198, 1982.
[32] M. Garcia-Lechuga and D. Grojo, "Simple and robust method for determination of laser fluence thresholds for material modifications: an extension of Liu’s approach to imperfect beams," Open Research Europe, vol. 1, no. 7, p. 7, 2021.
[33] M. Garcia-Lechuga, O. Utéza, N. Sanner, and D. Grojo, "Evidencing the nonlinearity independence of resolution in femtosecond laser ablation," Optics letters, vol. 45, no. 4, pp. 952-955, 2020.
[34] M. Garcia-Lechuga, G. Gebrayel El Reaidy, H. Ning, P. Delaporte, and D. Grojo, "Assessing the limits of determinism and precision in ultrafast laser ablation," Applied Physics Letters, vol. 117, no. 17, p. 171604, 2020.
[35] B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Optical ablation by high-power short-pulse lasers," JOSA B, vol. 13, no. 2, pp. 459-468, 1996.
[36] M. Sparks et al., "Theory of electron-avalanche breakdown in solids," Physical Review B, vol. 24, no. 6, p. 3519, 1981.
[37] Y. Assaf and A.-M. Kietzig, "Optical and chemical effects governing femtosecond laser-induced structure formation on polymer surfaces," Materials Today Communications, vol. 14, pp. 169-179, 2018.
[38] D. J. Krajnovich, "Incubation and photoablation of poly (methyl methacrylate) at 248 nm. New insight into the reaction mechanism using photofragment translational spectroscopy," The Journal of Physical Chemistry A, vol. 101, no. 11, pp. 2033-2039, 1997.
[39] D. Ashkenasi, "The potential of ultrashort laser pulses (< 10ps) in future material processing: mode-locked Ti: sapphire vs. q-switch Nd: YAG applications," in Photon Processing in Microelectronics and Photonics, 2002, vol. 4637: International Society for Optics and Photonics, pp. 378-385.
[40] F. Baset et al., "Femtosecond laser induced surface swelling in poly-methyl methacrylate," Optics express, vol. 21, no. 10, pp. 12527-12538, 2013.
[41] L. Torrisi, A. Lorusso, V. Nassisi, and A. Picciotto, "Characterization of laser ablation of polymethylmethacrylate at different laser wavelengths," Radiation Effects & Defects in Solids, vol. 163, no. 3, pp. 179-187, 2008.
[42] J. Guay, A. Villafranca, F. Baset, K. Popov, L. Ramunno, and V. Bhardwaj, "Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate," New Journal of Physics, vol. 14, no. 8, p. 085010, 2012.
[43] S. Baudach, J. Krüger, and W. Kautek, "Femtosecond laser processing of soft materials," The Review of Laser Engineering, vol. 29, no. 11, pp. 705-709, 2001.
[44] J. R. Nam, K.-S. Lim, and S. C. Jeoung, "Femtosecond laser ablation of polymethylmethacrylate doped with dye molecules and formation of a grating structure," Journal of the Korean Physical Society, vol. 52, no. 5, pp. 1661-1664, 2008.
[45] J. Krüger et al., "Femto-and nanosecond laser treatment of doped polymethylmethacrylate," Applied surface science, vol. 247, no. 1-4, pp. 406-411, 2005.
[46] D. E. Hare, J. Franken, and D. D. Dlott, "Coherent raman measurements of polymer thin‐film pressure and temperature during picosecond laser ablation," Journal of applied physics, vol. 77, no. 11, pp. 5950-5960, 1995.
[47] M. Gedvilas and G. Račiukaitis, "Investigation of UV picosecond laser ablation of polymers," in Workshop on Laser Applications in Europe, 2005, vol. 6157: International Society for Optics and Photonics, p. 61570T.
[48] R. Srinivasan, E. Sutcliffe, and B. Braren, "Ablation and etching of polymethylmethacrylate by very short (160 fs) ultraviolet (308 nm) laser pulses," Applied physics letters, vol. 51, no. 16, pp. 1285-1287, 1987.
[49] H. Zheng, H. M. Phillips, J. L. Tan, and G. C. Lim, "Laser-induced conductivity in aluminum nitride," in Photonic Systems and Applications in Defense and Manufacturing, 1999, vol. 3898: International Society for Optics and Photonics, pp. 280-286.
[50] G. Račiukaitis, S. Jacinavičius, M. Brikas, and S. Balickas, "Picosecond lasers in micromachining," in International Congress on Applications of Lasers & Electro-Optics, 2003, vol. 2003, no. 1: Laser Institute of America, p. M308.
[51] F. Preusch, B. Adelmann, and R. Hellmann, "Micromachining of AlN and Al2O3 using fiber laser," Micromachines, vol. 5, no. 4, pp. 1051-1060, 2014.