The ultrashort pulse laser ablation model of silicon based on the generalized thermoelastic theory with spatio-temporal nonlocal effect

References

• X. C. Wang et al., “Femtosecond laser drilling of alumina ceramic substrates,” Appl. Phys. A, vol. 101, no. 2, pp. 271–278, 2010. DOI: 10.1007/s00339-010-5816-8.
   Web of Science ®Google Scholar
• H. Zhu et al., “An experimental study of micro-machining of hydroxyapatite using an ultrashort picosecond laser,” Precis. Eng., vol. 54, pp. 154–162, 2018. DOI: 10.1016/j.precisioneng.2018.05.012.
   Web of Science ®Google Scholar
• A. Narazaki et al., “Study on nonthermal-thermal processing boundary in drilling of ceramics using ultrashort pulse laser system with variable parameters over a wide range,” Appl. Phys. A, vol. 126, no. 4, pp. 252, 2020. DOI: 10.1007/s00339-020-3410-2.
   Web of Science ®Google Scholar
• S. Tan et al., “A model of femtosecond laser ablation of metal based on dual-phase-lag model,” Acta Phys. Sin, vol. 68, no. 5, pp. 057901, 2019. DOI: 10.7498/aps.68.20182099.
   Web of Science ®Google Scholar
• H. Shen and D. Feng, “Thermal and mechanical behavior in laser trepan drilling of yttria-stabilized zirconia,” J. Heat Transf., vol. 141, no. 4, pp. 042101.1–042101.12, 2019. DOI: 10.1115/1.4042778.
   Web of Science ®Google Scholar
• C. Zheng et al., “Crack behavior in ultrafast laser drilling of thermal barrier coated nickel superalloy,” J. Mater. Process. Technol., vol. 282, no. 1-2, pp. 116678, 2020. DOI: 10.1016/j.jmatprotec.2020.116678.
   Web of Science ®Google Scholar
• R. Kelly and A. Miotello, “Does normal boiling exist due to laser-pulse or ion bombardment,” J. Appl. Phys., vol. 87, no. 6, pp. 3177–3179, 2000. DOI: 10.1063/1.372319.
   Web of Science ®Google Scholar
• X. Y. Tan et al., “Target ablation characteristics of thin films during nanosecond pulsed laser deposition in the ablation process,” Acta Phys. Sin., vol. 54, no. 8, pp. 3915–3921, 2005.
   Web of Science ®Google Scholar
• D. Marla, U. V. Bhandarkar and S. S. Joshi, “A model of laser ablation with temperature-dependent material properties, vaporization, phase explosion and plasma shielding,” Appl. Phys. A, vol. 116, no. 1, pp. 273–285, 2014. DOI: 10.1007/s00339-013-8118-0.
   Web of Science ®Google Scholar
• A. Peterlongo, A. Miotello and R. Kelly, “Laser-pulse sputtering of aluminum: vaporization, boiling, superheating, and gas-dynamic effects,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, vol. 50, no. 6, pp. 4716–4727, 1994. DOI: 10.1103/physreve.50.4716.
   PubMed Web of Science ®Google Scholar
• R. K. Singh and J. Narayan, “Pulsed-laser evaporation technique for deposition of thin films: physics and theoretical model,” Phys. Rev. B Condens. Matter, vol. 41, no. 13, pp. 8843–8859, 1990. DOI: 10.1103/physrevb.41.8843.
   PubMed Web of Science ®Google Scholar
• Q. M. Lu, “Thermodynamic evolution of phase explosion during high-power nanosecond laser ablation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys., vol. 67, no. 1 Pt 2, pp. 016410, 2003. DOI: 10.1103/PhysRevE.67.016410.
   PubMed Web of Science ®Google Scholar
• L-j Huang, G-m Zhang, H. Li, B-j Li, Y-y Wang, and N-f Ren, “Selective laser ablation and patterning on Ag thin films with width and depth control,” J Mater Sci: Mater. Electron., vol. 31, no. 6, pp. 4943–4955, 2020. DOI: 10.1007/s10854-020-03061-y.
   Web of Science ®Google Scholar
• N. Bellini, R. Geremia, and D. Karnakis, “Increasing laser pulse overlap restricts picosecond laser ablation of thin metal films near ablation threshold,” Appl. Phys. A, vol. 123, no. 5, pp. 346, 2017. DOI: 10.1007/s00339-017-0971-9.
   Web of Science ®Google Scholar
• Y. Sun, D. Fang, M. Saka, and A. K. Soh, “Laser-induced vibrations of micro-beams under different boundary conditions,” Int. J. Solids Struct., vol. 45, no. 7-8, pp. 1993–2013, 2008. DOI: 10.1016/j.ijsolstr.2007.11.006.
   Web of Science ®Google Scholar
• C. Cattaneo, “A form of heat conduction equation which eliminates the paradox of instantaneous propagation,” C. R. Phys., vol. 247, pp. 431–433, 1958.
   Google Scholar
• P. Vernotte, “Les paradoxes de la theorie continue de l’equation de la chaleur,” C. R. Acad. Sci., vol. 246, pp. 3154–3155, 1958.
   Google Scholar
• D. Y. Tzou, “Thermal shock phenomena under high-rate response in soils,” Annu. Rev. Heat Transf., vol. 4, no. 4, pp. 111–185, 1992. DOI: 10.1615/AnnualRevHeatTransfer.v4.50.
   Google Scholar
• D. Y. Tzou, “A unified field approach for heat conduction from micro-to-macro-scales,” J. Heat Transf., vol. 117, no. 1, pp. 8–16, 1995. DOI: 10.1115/1.2822329.
   Web of Science ®Google Scholar
• H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids, vol. 15, no. 5, pp. 299–309, 1967. DOI: 10.1016/0022-5096(67)90024-5.
   Web of Science ®Google Scholar
• A. E. Green and K. A. Lindsay, “Thermoelasticity,” J Elasticity, vol. 2, no. 1, pp. 1–7, 1972. DOI: 10.1007/BF00045689.
   Google Scholar
• A. E. Green and P. M. Naghdi, “Thermoelasticity without energy dissipation,” J Elasticity, vol. 31, no. 3, pp. 189–208, 1993. DOI: 10.1007/BF00044969.
   Web of Science ®Google Scholar
• H. M. Youssef, “Theory of two-temperature-generalized thermoelasticity,” J. Appl. Math., vol. 71, no. 3, pp. 383–390, 2006. DOI: 10.1093/imamat/hxh101.
   Web of Science ®Google Scholar
• X. L. Qi and C. S. Suh, “Generalized thermo-elastodynamics for semiconductor material subject to ultrafast laser heating. Part I: model description and validation,” Int. J. Heat Mass Transf., vol. 53, no. 1-3, pp. 41–47, 2010. DOI: 10.1016/j.ijheatmasstransfer.2009.10.010.
   Web of Science ®Google Scholar
• Z. B. Kuang, “Variational principles for generalized dynamical theory of thermopiezoelectricity,” Acta Mech., vol. 203, no. 1-2, pp. 1–11, 2009. DOI: 10.1007/s00707-008-0039-1.
   Web of Science ®Google Scholar
• Y. Z. Wang, X. B. Zhang, and X. N. Song, “A generalized theory of thermoelasticity based on thermomass and its uniqueness theorem,” Acta Mech., vol. 225, no. 3, pp. 797–808, 2014. DOI: 10.1007/s00707-013-1001-4.
   Web of Science ®Google Scholar
• Y. J. Yu, W. Hu, and X. G. Tian, “A novel generalized thermoelasticity model based on memory-dependent derivative,” Int. J. Eng. Sci., vol. 81, no. 811, pp. 123–134, 2014. DOI: 10.1016/j.ijengsci.2014.04.014.
   Web of Science ®Google Scholar
• I. A. Abbas and M. Marin, “Analytical solutions of a two-dimensional generalized thermoelastic diffusions problem due to laser pulse,” Iran. J. Sci. Technol. Trans. Mech. Eng., vol. 42, no. 1, pp. 57–71, 2018. DOI: 10.1007/s40997-017-0077-1.
   Web of Science ®Google Scholar
• Y. Li and T. H. He, “Investigation of a half-space heated by laser pulses based on the generalized thermoelastic theory with variable thermal material properties,” Waves Random Complex Media, vol. 32, no. 1, pp. 120–136, 2022. DOI: 10.1080/17455030.2020.1766157.
   Web of Science ®Google Scholar
• Y. Li and T. H. He, “The transient response of a functionally graded half-space heated by a laser pulse based on the generalized thermoelasticity with memory-dependent derivative,” Mech. Adv. Mater. Struct., vol. 28, no. 22, pp. 2299–2309, 2021. DOI: 10.1080/15376494.2020.1731888.
   Web of Science ®Google Scholar
• Y. Li, P. Zhang, C. Li, and T. He, “Fractional order and memory-dependent analysis to the dynamic response of a bi-layered structure due to laser pulse heating,” Int. J. Heat Mass Transf., vol. 144, pp. 118664, 2019. DOI: 10.1016/j.ijheatmasstransfer.2019.118664.
   Web of Science ®Google Scholar
• M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, “Generalized thermo-viscoelasticity with memory-dependent derivatives,” Int. J. Mech. Sci., vol. 89, pp. 470–475, 2014. DOI: 10.1016/j.ijmecsci.2014.10.006.
   Web of Science ®Google Scholar
• J. L. Wang and H. F. Li, “Surpassing the fractional derivative: concept of the memory-dependent derivative,” Comput. Math. Appl., vol. 62, no. 3, pp. 1562–1567, 2011. DOI: 10.1016/j.camwa.2011.04.028.
   Web of Science ®Google Scholar
• A. C. Eringen and J. Wegner, “Nonlocal continuum field theories,” Appl. Mech. Rev., vol. 56, no. 2, pp. 391–398, 2003.
   Google Scholar
• A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. DOI: 10.1063/1.332803.
   Web of Science ®Google Scholar
• Y. J. Yu, X. G. Tian, and Q. L. Xiong, “Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity,” Eur. J. Mech.-A/Solids, vol. 60, pp. 238–253, 2016. DOI: 10.1016/j.euromechsol.2016.08.004.
   Web of Science ®Google Scholar
• Y. J. Yu, Z.-N. Xue, C.-L. Li, and X.-G. Tian, “Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity,” Compos. Struct., vol. 146, pp. 108–113, 2016. DOI: 10.1016/j.compstruct.2016.03.014.
   Web of Science ®Google Scholar
• C. L. Li, H. L. Guo, and X. G. Tian, “A size-dependent generalized thermoelastic diffusion theory and its application,” J. Therm. Stress., vol. 40, no. 5, pp. 603–626, 2017. DOI: 10.1080/01495739.2017.1300786.
   Web of Science ®Google Scholar
• P. Zhang and T. H. He, “A generalized thermoelastic problem with nonlocal effect and memory-dependent derivative when subjected to a moving heat source,” Waves Random Complex Media, vol. 30, no. 1, pp. 142–156, 2020. DOI: 10.1080/17455030.2018.1490043.
   Web of Science ®Google Scholar
• L. Zhang, M. M. Bhatti, M. Marin and K. S. Mekheimer, “Entropy analysis on the blood flow through anisotropically tapered arteries filled with magnetic zinc-oxide (ZnO) nanoparticles,” Entropy, vol. 22, no. 10, pp. 1070, 2020. DOI: 10.3390/e22101070.
   PubMed Web of Science ®Google Scholar
• L. Brancik, “Programs for fast numerical inversion of Laplace transforms in Matlab language environment,” In Proceedings of the 7th Conference MATLAB’99. Czech Republic, Prague, 1999, pp. 27–39.
   Google Scholar
• I. M. Taye, K. Lotfy, A. A. El-Bary, J. Alebraheem, and S. Asad, “The hyperbolic two temperature semiconducting thermoelastic waves by laser pulses,” Comput. Mater. Contin., vol. 67, no. 3, pp. 3601–3618, 2021. DOI: 10.32604/cmc.2021.015223.
   Web of Science ®Google Scholar
• J. H. Yoo, S. H. Jeong, R. Greif and R. E. Russo, “Explosive change in crater properties during high power nanosecond laser ablation of silicon,” J. Appl. Phys., vol. 88, no. 3, pp. 1638–1649, 2000. DOI: 10.1063/1.373865.
   Web of Science ®Google Scholar