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In this paper, we present an inversion estimation method of thin film parameters based on thermal effects induced by laser irradiation. Firstly, the theoretical model of classical Fourier heat conduction of thin film irradiated by laser is established, and the analytical solutions of temperature fields are obtained by using Laplace transform. Then, the inversion model and the iteration algorithm are established based on the nonlinear conjugate gradient method on condition that the thermal conductivities of the film and the substrate are selected as inversion parameters and the temperature fields of the thin film surface in different irradiation times are selected as measured data. In view of the fact that the sensitivity coefficient plays a decisive role in determining the accuracy and efficiency of the nonlinear conjugate gradient iteration inversion algorithm, we derive the closed form expressions of the sensitivity coefficients for the thermal conductivities of the film and the substrate based on the above analytical solutions of the temperature fields, and this closed form expressions can improve the accuracy and efficiency of the thin film parameter inversion significantly. Taking four kinds of metal films (aluminum, silver, copper and gold) with glass substrate for example, the accuracies of the analytical solutions of temperature fields are verified by comparing with the numerical results from the finite element method in the existing literature, and it can ensure the accuracies of the sensitivity coefficients in the process of iteration inversion. Finally, the thermal conductivities of the above four kinds of thin films are estimated by using the presented iteration inversion method. The accuracy and efficiency of the parameter inversion are verified by investigating and analyzing the inversion results of the parameters for different random noises and different iterative initial values. The inversion results show that this method has a high accuracy and efficiency, and it only needs less than 20 iteration times to convergence when the iteration stop error is 10-7. The smaller random noise is added in the measured data, and the less iteration times to convergence are needed. It can achieve higher convergence efficiency even in the iterative initial values from the inversion results that differ greatly for the case of 5% random noise. This inversion method of thin film parameters is not only applicable to the inversion of the thermal conductivity, but can also be used to inverse the parameters such as the reflection coefficient or the absorption coefficient. The presented method has a certain guiding significance for the parameters inversion and the parameters optimization in the process of the laser processing or the laser damage.
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Keywords:
- parameter inversion /
- laser irradiation /
- thermal effects /
- nonlinear conjugate
[1] Wang Y, Liu X, Zhang Y G, Gu P F, Li Y Y, Li M Y 2007 Acta Phys. Sin. 56 2382 (in Chinese) [王颖, 刘旭, 章岳光, 顾培夫, 厉以宇, 李明宇 2007 56 2382]
[2] Zhao Y A, Wang T, Zhang D P, He H B, Shao J D, Fan Z X 2005 Acta Phot. Sin. 34 1372 (in Chinese) [赵元安, 王涛, 张东平, 贺洪波, 邵建达, 范正修 2005 光子学报 34 1372]
[3] Wang B 2012 Ph. D. Dissertation (Nanjing: Nanjing University of Science and Technology) (in Chinese) [王斌 2012 博士学位论文(南京: 南京理工大学)]
[4] Wang B, Dai G, Zhang H C, Ni X W, Shen Z H, Lu J 2011 Appl. Surf. Sci. 257 9977
[5] Wang B, Zhang H C, Qin Y, Wang X, Ni X W, Shen Z H, Lu J 2011 Appl. Opt. 50 3435
[6] Sun J Y 2007 M. S. Dissertation (Nanjing: Nanjing University of Science and Technology) (in Chinese) [孙金英 2007 硕士学位论文 (南京: 南京理工大学)]
[7] Ozisik M N, Orlande H R B 2000 Inverse Heat Transfer: Fundamentals and Applications (New York: Taylor Francis) pp115-125
[8] Yang C Y 1999 Appl. Math. Model. 23 469
[9] Pedro H A N, Helcio R B O, Jean L B 2011 Int. Commun. Heat Mass Trans. 38 1172
[10] Zhuang Q, Yu B, Jiang X Y 2015 Physica B 456 9
[11] El-Adawi M K, Abdel-Naby M A, Shalaby S A 1995 Int. J. Heat Mass Transfer 38 947
[12] Feng L X 2011 The Computational Methods and Applications of Inverse Problems (Harbin: Harbin Institute Technology Press) p9 (in Chinese) [冯立新 2011 反问题的计算方法及应用 (哈尔滨: 哈尔滨工业大学出版社) 第9页]
[13] Abramowitz M, Stegun I 1964 Handbook of Mathematical Functions (New York: Dover Publications) pp297-299
[14] Bi J, Zhang X H, Ni X W 2011 Acta Phys. Sin. 60 114210 (in Chinese) [(in Chinese) 毕娟, 张喜和, 倪晓武 2011 60 114210]
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[1] Wang Y, Liu X, Zhang Y G, Gu P F, Li Y Y, Li M Y 2007 Acta Phys. Sin. 56 2382 (in Chinese) [王颖, 刘旭, 章岳光, 顾培夫, 厉以宇, 李明宇 2007 56 2382]
[2] Zhao Y A, Wang T, Zhang D P, He H B, Shao J D, Fan Z X 2005 Acta Phot. Sin. 34 1372 (in Chinese) [赵元安, 王涛, 张东平, 贺洪波, 邵建达, 范正修 2005 光子学报 34 1372]
[3] Wang B 2012 Ph. D. Dissertation (Nanjing: Nanjing University of Science and Technology) (in Chinese) [王斌 2012 博士学位论文(南京: 南京理工大学)]
[4] Wang B, Dai G, Zhang H C, Ni X W, Shen Z H, Lu J 2011 Appl. Surf. Sci. 257 9977
[5] Wang B, Zhang H C, Qin Y, Wang X, Ni X W, Shen Z H, Lu J 2011 Appl. Opt. 50 3435
[6] Sun J Y 2007 M. S. Dissertation (Nanjing: Nanjing University of Science and Technology) (in Chinese) [孙金英 2007 硕士学位论文 (南京: 南京理工大学)]
[7] Ozisik M N, Orlande H R B 2000 Inverse Heat Transfer: Fundamentals and Applications (New York: Taylor Francis) pp115-125
[8] Yang C Y 1999 Appl. Math. Model. 23 469
[9] Pedro H A N, Helcio R B O, Jean L B 2011 Int. Commun. Heat Mass Trans. 38 1172
[10] Zhuang Q, Yu B, Jiang X Y 2015 Physica B 456 9
[11] El-Adawi M K, Abdel-Naby M A, Shalaby S A 1995 Int. J. Heat Mass Transfer 38 947
[12] Feng L X 2011 The Computational Methods and Applications of Inverse Problems (Harbin: Harbin Institute Technology Press) p9 (in Chinese) [冯立新 2011 反问题的计算方法及应用 (哈尔滨: 哈尔滨工业大学出版社) 第9页]
[13] Abramowitz M, Stegun I 1964 Handbook of Mathematical Functions (New York: Dover Publications) pp297-299
[14] Bi J, Zhang X H, Ni X W 2011 Acta Phys. Sin. 60 114210 (in Chinese) [(in Chinese) 毕娟, 张喜和, 倪晓武 2011 60 114210]
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