基于双相延迟模型的飞秒激光烧蚀金属模型

谭胜; 吴建军; 黄强; 张宇; 杜忻洳

doi:10.7498/aps.68.20182099

摘要

为了分析飞秒激光烧蚀过程, 在双相延迟模型的基础上建立了双曲型热传导模型. 模型中考虑了靶材的加热、蒸发和相爆炸, 还考虑了等离子体羽流的形成和膨胀及其与入射激光的相互作用, 以及光学和热物性参数随温度的变化. 研究结果表明: 等离子体屏蔽对飞秒激光烧蚀过程有重要的影响, 特别是在激光能量密度较高时; 两个延迟时间的比值对飞秒激光烧蚀过程中靶材的温度特性和烧蚀深度有较大的影响; 飞秒激光烧蚀机制主要以相爆炸为主. 飞秒激光烧蚀的热影响区域较小, 而且热影响区域的大小受激光能量密度的影响较小. 计算结果与文献中实验结果的对比表明基于双相延迟模型的飞秒激光烧蚀模型能有效对飞秒激光烧蚀过程进行模拟.

关键词:

Abstract

Femtosecond laser ablation possesses a variety of applications due to its better control, high power density, smaller heat-affected zone, minimal collateral material damage, lower ablation thresholds, and excellent mechanical properties. The non-Fourier effect in heat conduction becomes significant when the heating time becomes extremely small. In order to analyze the femtosecond laser ablation process, a hyperbolic heat conduction model is established based on the dual-phase-lag model. Taken into account in the model are the effect of heat source, laser heating of the target, the evaporation and phase explosion of the target material, the formation and expansion of the plasma plume, and interaction of the plasma plume with the incoming laser. Temperature-dependent optical and thermophysical properties are also considered in the model due to the fact that the properties of the target will change over a wide range in the femtosecond laser ablation process. The effects of the plasma shielding, the ratio of the two delay times, and laser fluence are discussed and the effectiveness of the model is verified by comparing the simulation results with the experimental results. The results show that the plasma shielding has a great influence on the femtosecond laser ablation process, especially when the laser fluence is high. The ratio between the two delay times (the ratio B) has a great influence on the temperature characteristic and ablation characteristic in the femtosecond laser ablation process. The augment of the ratio B will increase the degree of thermal diffusion, which will lower down the surface temperature and accelerate the ablation rate after the ablation has begun. The ablation mechanism of femtosecond laser ablation is dominated by phase explosion. The heat affected zone of femtosecond laser ablation is small, and the heat affected zone is less affected by laser fluence. The comparison between the simulation results and the experimental results in the literature shows that the model based on the dual-phase-lag model can effectively simulate the femtosecond laser ablation process.

Keywords:

作者及机构信息

国防科技大学空天科学学院, 长沙　410073

通信作者: 谭胜, tsh201201401007@163.com

基金项目: 国家自然科学基金(批准号: 11772354)资助的课题.

Authors and contacts

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

Corresponding author: Tan Sheng, tsh201201401007@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11772354).

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施引文献

图 1 蒸发开始前激光与靶材相互作用示意图

Fig. 1. Schematic of laser interaction with target before the initiation of the evaporation.

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图 2 蒸发开始后激光与靶材相互作用示意图

Fig. 2. Schematic of laser interaction with target after the initiation of the evaporation.

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图 3 激光强度与最大激光强度的比值随时间的变化(t_p = 170 fs (FWHM))

Fig. 3. The variation of the ratio of laser intensity to maximum laser intensity with time (t_p = 170 fs (FWHM)).

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图 4 计算网格示意图

Fig. 4. Schematic of computational grids.

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图 5 激光强度和烧蚀深度的对比(F_fluence = 20.0 J/cm²)

Fig. 5. Comparison of laser intensity and ablation depth (F_fluence = 20.0 J/cm²).

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图 6 等离子体屏蔽比例随着激光能量密度的变化

Fig. 6. Variation of plasma shielding proportions with laser fluence.

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图 7 不同比值B (${\tau _q}$不变)时, 温度沿靶材深度的分布(F_fluence = 0.2 J/cm²)

Fig. 7. Distribution of temperature along the target depth at different ratios B (${\tau _q}$ is constant) (F_fluence = 0.2 J/cm²).

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图 8 比值B (${\tau _q}$不变)对表层温度的影响(F_fluence = 10.0 J/cm²)

Fig. 8. The effect of ratios B (${\tau _q}$ is constant) on temperature of surface layer (F_fluence = 10.0 J/cm²).

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图 9 比值B (${\tau _q}$不变)对表面温度的影响(F_fluence = 10.0 J/cm²)

Fig. 9. The effect of ratios B (${\tau _q}$ is constant) on surface temperature (F_fluence = 10.0 J/cm²).

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图 10 比值B (${\tau _q}$不变)对烧蚀深度的影响(F_fluence = 10.0 J/cm²)

Fig. 10. The effect of ratios B (${\tau _q}$ is constant) on ablation depth (F_fluence = 10.0 J/cm²).

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图 11 比值B ($\tau _{\rm{T}}$不变)对表面温度的影响(F_fluence = 10.0 J/cm²)

Fig. 11. The effect of ratios B ($\tau _{\rm{T}}$ is constant) on surface temperature (F_fluence = 10.0 J/cm²).

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图 12 比值B($\tau _{\rm{T}}$不变)对烧蚀特性的影响(F_fluence = 10.0 J/cm²)

Fig. 12. The effect of ratios B ($\tau _{\rm{T}}$ is constant) on ablation depth (F_fluence = 10.0 J/cm²).

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图 13 不同激光能量密度下, 表面温度随时间的变化($\tau _{\rm{T}}$ = 12.0 ps, ${\tau _q}$ = 1.0 ps)

Fig. 13. Surface temperature changes with time at different laser fluence ($\tau _{\rm{T}}$ = 12.0 ps, ${\tau _q}$ = 1.0 ps).

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图 14 不同激光能量密度下, 烧蚀深度随时间的变化($\tau _{\rm{T}}$ = 12.0 ps, ${\tau _q}$ = 1.0 ps)

Fig. 14. Ablation depth changes with time at different laser fluence ($\tau _{\rm{T}}$ = 12.0 ps, ${\tau _q}$ = 1.0 ps).

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图 15 不同能量密度下, 烧蚀深度、超热液体层、融化层和热影响的固体层随时间的变化($\tau _{\rm{T}}$ = 12.0 ps, ${\tau _q}$ = 1.0 ps)

Fig. 15. The ablation depth, the superheated liquid layer, melting layer and heat affected solid layer as a function of time at different laser fluence ($\tau _{\rm{T}}$ = 12.0 ps, ${\tau _q}$ = 1.0 ps).

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图 16 烧蚀深度的计算结果与文献[90]的实验结果对比(t_p = 170 fs (FWHM))

Fig. 16. Comparison of simulation results of ablation depth with the experimental results from Ref. [90] (t_p = 170 fs (FWHM)).

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图 17 烧蚀深度的计算结果与文献[91]的实验结果对比(t_p = 70 fs (FWHM))

Fig. 17. Comparison of simulation results of ablation depth with the experimental results from Ref. [91] (t_p = 70 fs (FWHM)).

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表 1 模型中用到的Cu的参数

Table 1. Parameters of Cu used in the model.

参数	符号	取值	文献
熔点/K	${T_{\rm{m}}}$	1357.77	[83]
沸点/K	${T_{\rm{b}}}$	2835.15	[83]
蒸发潜热/J·kg^–1	${L_{{\rm{hv}}}}$	4.79937 × 10⁶	[83]
第一电离能/eV	$I{P_1}$	7.72638	[83]
临界温度/K	${T_{{\rm{cr}}}}$	8500.00	[81]
蒸发系数	${C_{\rm{s}}}$	0.82	[85]
热流矢量延迟时间/ps	${\tau _q}$	0.56—5.4	[66]
温度梯度延迟时间/ps	${\tau _{\rm{T}}}$	6.0—63.0	[66]

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[3]	Amoruso S, Ausanio G, Bruzzese R, Vitiello M, Wang X 2005 Phys. Rev. B 71 033406
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[7]	Herman P R, Oettl A, Chen K P, Marjoribanks R S 1999 Proceedings of SPIE - The International Society for Optical Engineering California, USA, January 4, 1999 p148
[8]	Derrien T J, Krüger J, Itina T E, Höhm S, Rosenfeld A, Bonse J 2014 Opt. Express 117 77
[9]	谭胜, 吴建军, 张宇, 程玉强, 李健, 欧阳 2018 推进技术 39 2415 Tan S, Wu J J, Zhang Y, Cheng Y Q, Li J, Ou Y 2018 J. Propuls. Technol. 39 2415
[10]	Piñon V, Fotakis C, Nicolas G, Anglos D 2008 Spectrochim. Acta Part B 63 1006 Google Scholar
[11]	Miyamoto I, Horn A, Gottmann J, Wortmann D, Yoshino F 2007 J. Laser Micro/Nanoeng. 2 57 Google Scholar
[12]	Zhang Y, Tzou D Y, Chen J K 2009 High-Power and Femtosecond Lasers: Properties, Materials and Applications (1st Ed.) (New York: Nova Science Publisher) pp1–11
[13]	Eidmann K, Meyer-ter-Vehn J, Schlegel T, Hüller S 2000 Phys. Rev. E 62 1202 Google Scholar
[14]	Vidal F, Johnstion T W, Laville S, Barthélemy, Chaker M, Drogoff B L, Margot J, Sabsabi M 2001 Phys. Rev. Lett. 86 2573 Google Scholar
[15]	Ding P J, Hu B T, Li Y H 2011 NDT E Int. 29 53
[16]	Perez D, Lewis L J 2003 Phys. Rev. B 67 184102 Google Scholar
[17]	Nedialkov N N, Imamova S E, Atanasov P A, Berger P, Dausinger F 2005 Appl. Surf. Sci. 247 243 Google Scholar
[18]	Liu X, Zhou W, Chen C, Zhao L, Zhang Y 2008 J. Mat. Proc. Technol. 203 202 Google Scholar
[19]	Chichkov B N, Momma C, Nolte S, von Alvensleben F, Tünnermann A 1996 Appl. Phys. A 63 109 Google Scholar
[20]	Hu W, Shin Y C, King G 2010 Appl. Phys. A 98 407
[21]	王文亭, 张楠, 王明伟, 何远航, 杨建军, 朱晓农 2013 物理学报 62 210601 Google Scholar Wang W T, Zhang N, Wang M W, He Y H, Yang J J, Zhu X N 2013 Acta Phys. Sin. 62 210601 Google Scholar
[22]	Wu B, Shin Y C 2007 Appl. Surf. Sci. 253 4079 Google Scholar
[23]	Wu B, Shin Y C 2009 Appl. Surf. Sci. 255 4996 Google Scholar
[24]	Qiu T Q, Tien C L 1994 Int. J. Heat Mass Transf. 37 2789 Google Scholar
[25]	Tzou D Y, Chen J K, Beraun J E 2005 J. Therm. Stress. 28 563 Google Scholar
[26]	Singh N 2010 Int. J. Mod. Phys. B 24 1141 Google Scholar
[27]	Qiu T Q, Tien C L 1993 J. Heat Tranf. 115 835 Google Scholar
[28]	Chen J K, Beraun J E 2001 Numer. Heat Transf. Part A: Appl. 40 1
[29]	Jiang L, Tsai H L 2005 J. Heat Transf. 127 1167 Google Scholar
[30]	Chen J K, Tzou D Y, Beraun J E 2006 Int. J. Heat Mass Transf. 49 307 Google Scholar
[31]	Carpene E 2006 Phys. Rev. B 74 024301
[32]	Fang R, Wei H, Li Z, Zhang D 2012 Solid State Commun. 152 108 Google Scholar
[33]	Zhang J, Chen Y, Hu M, Chen X 2015 J. Appl. Phys. 117 063104 Google Scholar
[34]	Shin T, Teitelbaum S W, Wolfson J, Kandyla M, Nelson K A 2015 J. Chem. Phys. 143 194705 Google Scholar
[35]	Sonntag S, Roth J, Gaehler F, Trebin H R 2009 Appl. Surf. Sci. 255 9742 Google Scholar
[36]	Ji P, Zhang Y 2017 Appl. Phys. A 123 671 Google Scholar
[37]	Colombier J P, Combis P, Bonneau F, Le Harzic R, Audouard E 2005 Phys. Rev. B 71 165406 Google Scholar
[38]	Zhao X, Shin Y C 2012 J. Phys. D: Appl. Phys. 45 105201 Google Scholar
[39]	Taylor L L, Scott R E, Qiao J 2018 Opt. Mater. Express 8 648 Google Scholar
[40]	Fann W S, Storz R, Tom H W K, Bokor J 1992 Phys. Rev. Lett. 68 2834 Google Scholar
[41]	Groeneveld R H M, Sprik R, Lagendijk A 1995 Phys. Rev. B 51 11433 Google Scholar
[42]	Schmidt V, Husinsky W, Betz G 2002 Appl. Surf. Sci. 197 145
[43]	Byskov-Nielsen J, Savolainen J M, Christensen M S, Balling P 2011 Appl. Phys. A 103 447 Google Scholar
[44]	Christensen B H, Vestentoft K, Balling P 2007 Appl. Surf. Sci. 253 6347 Google Scholar
[45]	Abdelmalek A, Bedrane Z, Amara E 2018 J. Phys. Conf. Ser. 987 012012 Google Scholar
[46]	Qi H T, Xu H Y, Guo X W 2013 Comput. Math. Appl. 66 824 Google Scholar
[47]	Rahideh H, Malekzadeh P, Haghighi M R G 2011 ISRN Mech. Eng. 321605
[48]	Catteneo C 1958 Compte Rendus 247 431
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