一种基于激光辐照热效应的薄膜参数反演方法

本文研究并建立了一种基于激光辐照热效应的薄膜参数反演方法.首先给出激光辐照薄膜产生温升问题的热传导理论模型,并利用拉普拉斯变换得到了膜层和基底温度场的解析解;然后以膜层和基底的导热系数为反演参数,基于非线性共轭梯度算法给出反演基本原理及流程,并推导得到了反演过程中灵敏度系数的解析表达式;以aluminum,silver,copper和gold四种金属薄膜为例,通过与有限元法的计算结果对比验证了温度场解析解的正确性;最后结合四种金属薄膜进行了参数反演,通过考察分析不同随机噪声等条件下的参数反演结果,验证了本文方法在薄膜参数反演精度与反演效率等方面的有效性.反演结果显示:本文方法具有较高的反演精度和效率,在迭代截止误差为10~(-7)时只需用少于20次迭代就能收敛;在测量数据中加入的随机噪声越小,反演的迭代收敛次数就越少,即使是在迭代初值与反演结果相差较大时,用包含5%随机噪声的测量数据反演也能快速收敛.本文提出的薄膜参数反演方法不仅适用于反演导热系数,也可扩展用于反演膜层反射系数或吸收率等参数,具有一定的适用性.本文方法对于激光加工或激光损伤过程中的参数反演及优化具有一定的指导意义.

A parameter inversion method of film based on thermal effects induced by laser irradiation

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.