飞秒激光烧蚀金箔机理及模拟分析

femtosecond laser]J]. Machine Tool & Hydraulics,2019,47(6) ：92 —97.Mechanism and simulation analysis of gold foil ablated by femtosecond laserWen-yu DING, Bang-fu WANG ** , Zhong-wang WANG

(School of Mechanical Engineering, Suzhou University of Science and Technology, Suzhou 215009, China)Abstract: In this paper, the process of ablative gold foil at different energy densities of single pulse femtosecond

laser is studied. The interaction between electro-acoustic interaction and femtosecond laser ablation under different energy density is discussed, and the correlation of the energy density with the femtosecond laser ablation is derived from the simulated data of the two-temperature model under the finite difference method. Combining the simula­tion results with the experimental results, the femtosecond laser energy density is the main factor for the processing efficiency and processing quality of the gold foil, which indicates that the femtosecond laser energy density has great significance for the study of femtosecond laser ablation materials.Key words: Femtosecond laser, Non-equilibrium ablation, Two-temperature model, Cold processing doi: 10.3969/j. issn. 1001-3881.2019.06.016 Document code： A CLC number： TN24als ,which make the femtosecond laser' s physical

function during ablation of certain materials complicat・ ed [ 2 ]. Researchers have been studying these com・ plex mechanisms of action to learn more about the femtosecond laser micromachining, so that the process of femtosecond laser processing can be studied deeply. Because the time of femtosecond laser interaction with material is so fast, the whole ablation process can' t be observed well. However, with the development in the field of computer, the computational technology can be applied to the ablation of femtosecond laser, and the related simulation can be carried out, which has a theoretical support for the experimental process. This paper carries out a single-factor experiment. Un­der the same pulse width conditions, the energy densi­ty of the femtosecond laser is used as a variable, and the whole ablation process of gold foil irradiated by femtosecond laser is simulated by the two-temperature model. The entire ablation process was studied to ana­lyze the evolution of electron and lattice temperature

1 IntroductionFemtosecond laser can process a variety of materi- als. The heat affected zone produced by the material processing area is very small, which can minimize the micro cracks. Due to the extremely short pulse width of the femtosecond laser pulse, a very high peak pow­er density can be obtained at low pulse energy after fo­cusing. This feature determines that its processing mechanism is different from the traditional long pulse and continuous laser processing. It also determines its unique advantages and characteristics in the field of processing: the heat affected zone is very small, the damage threshold is accurate and low, it can break through the diffraction limit, and can process all kinds of materials [ 1 ]. So the application of femtosecond laser in the processing of materials has attracted wide attention. There are some differences in the interac・ tion between femtosecond lasers and different materi­

Received date： 2018 -01 -23Foundation item: Study on the mechanism and properties of micro-nano-connection based on Femtosecond laser ( XKZ201605)* Corresponding author: Bang-fu WANG, Lecturer. E-mail: 1985039687@ qq. comMechanism and simulation analysis of gold foil ablated by femtosecond laser93on the surface of the gold foil under the non-equilibri­um ablation, and the correlation between ablation-in­duced surface topography, depth morphology and fem­tosecond laser energy density [ 3 ]. The research can improve the efficiency and quality of femtosecond laser processing [4].2 Theoretical analysis2. 1 Femtosecond laser machining principleThe key of the ablation is the coupling of electrons and crystal lattices. The electrons in the equilibrium state absorb the photons and disperse them in phase so that they can be converted into excited states. This process will not change the electron energy distribution process. At this time, the lattice system has not changed yet, it is still in its original state, and the temperature remains low relatively. The initial excited state electron distribution corresponds to the laser transition energy state. Then the collision between e- lectrons and electrons changes the initial state rapidly, and the quasi-equilibrium state between electrons will be established. In this quasi -equilibrium state, the surrounding lattice temperature is lower than the elec­tron temperature obviously. The initial non-equilibri­um state of the electronic system achieves thermal e- quilibrium by collision relaxation. The electronic sys­tem uses electro-acoustic coupling to transfer energy to the surrounding lattice to reduce its own energy and decrease the electron temperature during this period. The process of electronically accepting the laser energy to quasi -equilibrium is called the process of electrons, and the process of transferring energy to the lattice by electrons is called the cooling process of electrons [5 ]. After several picoseconds, the process of elec­tron temperature and lattice temperature reaching an equilibrium state is called the process of energy ex­change between electrons and lattices. When the elec・ tron and lattice temperature are in the thermal equilib­rium state, the energy of the laser will be transmitted to the deep layer of the processed material.The laser ablation can be divided into two categories by the time of electroacoustic relaxation and the width of laser pulse. The electronic heating is in the pulse width, during which the electron absorbs the laser en­ergy to heat up ； and the lattice heating is at the end of the pulse mainly. The electrons and the lattice are coupled so that the lattice temperature goes up to the

ablation temperature and it erupts out to finish the ab­lation during this period. It is the thermal equilibrium ablation if the pulse width of laser is greater than the electro-acoustic coupling time, and it is non-equilibri- um ablation if the pulse width of laser pulse is smaller than the electro acoustic coupling time, which is relat­ed to the ablation of femtosecond lasers closely [6].In the case of femtosecond lasers, the laser irradia­tion has been completed before the electron and lattice energy transfer occurs. At this time, the dominance of the ablation process is the lattice. The two-tempera- ture model can describe the non-equilibrium ablation.2. 2 Femtosecond laser processing systemThe experimental equipment is the Origami-10XP femtosecond laser system ( as shown in Fig. 1). The

device outputs a wavelength of 1 028 nm with a pulse width of 400 fs and a single pulse of laser energy. The incident laser is reflected through the polarizer, prism and reflector, then enters the surface of the sample through a flat convex lens.Fig. 1 Femtosecond laser micro-processing system diagram2. 3 Computational modelThe theory of the two-temperature model was pro・ posed by Anisimov in 1974 [ 7 ] , which describes the theoretical model of the thermal conductance of the la­ser acting on the metal. When the femtosecond laser ablates material, the material absorbs laser energy fore ablation. The energy absorbed by the electrons reaches a very high temperature during the pulse ac­tion. At the end of the pulse, the lattice is almost still in the 'cold' state. When the pulse is over, the elec­trons and lattice are coupled rapidly and the lattice reaches the ablation temperature to complete the abla­tion. As a result of that, electrons and lattices can be considered as two separate systems for analysis during94the process of femtosecond laser and metal interaction.The two-temperature model model is based on the one-dimensional unsteady heat conduction equation [8 ]. As the mechanism of the laser pulse and materi・ al matter should be taken into consideration, the dif­ferential equation of the temperature change between the electron temperature and the lattice is listed for the two processes of electron and lattice, photon and elec- tron [9]:Cte (Tee ) —dt = —dx (Ktr —dx ) - G(TIn the formula, G = 10 x 1016 W/ m3K represents the

characteristic parameter of energy interaction between electrons and lattice, which is called the coupling co・ efficient of electron and lattice. Te and Tt are the vari­ables and the electron and lattice temperature. Ce and Cz are the electron and lattice heat capacity. S Tepre・ sents the heat source term corresponding to the laser pulse:So =0.94—1 一 R•丿・exp( -手-4 ・ log(2) - (y- - 2)2) (3)& tpThe electron thermal conductivity k0 is considered as a constant generally, but there is a more general expression [ 10]：K _ (厨+ 0・16)扌(“；+ 0・44)儿 ⑷\"X (加 + 0. 092)1/2

+ 如)In the above formula,Me 二 Ty, Ai = Tt/TF (5)Tf is the Fermi temperature. In this experiment, the Fermi temperature of gold is： 6. 42 x 104 K, and the parameters^ are the material-related constants, \\ 二 353 W ・ K\"・ m_1,叶二0. 16.In this paper, the evolution of the electron and lat­tice temperatures over time and the depth of ablation increases in the two-temperature model can be derived by using the finite difference method [11]. It is pos­sible to ignore the S item in the above equation (1 ) when the depth of the laser ablation is close to the thickness of the processed material. At this point it can be assumed that the entire piece is uniformly heat­ed. For simplicity, the initial and adiabatic boundary conditions are used as:7；&,o)= rz(%,0) = To (6)Wen-yu DING, et al.

=叫 dxdx字(d,t)=散d,t) =0

(8)dx dxIn the formula, TQ is the initial room temperature, To = 300 K.Other relevant parameters of processed gold foil are Ce = 70 J/m3k2, & = 2.7 xlO6 J/m3k2, g= 2.2 x

1016 W/M3K. The parameter of the laser is tp = 400 fs.3 Numerical analystIn this paper, three types of laser energy density are

selected for the given pulse width = 1 540 J/m2,

J2 =3 080 J/m2,J3 =5 380 J/m2. The two-dimension­al diagram (Fig. 2) of electron temperature and lattice temperature which changes with ablation time is ob­tained by using the two-temperature model. According to the simulation, the energy absorbed by the electrons can make the temperature reach the peak temperature of 8 105 K when the laser energy density 人=1 540 J/ni2, and both systems are in thermal equilibrium af­ter 13. 68 ps. The temperature is 510. 7 K, the tem­perature difference between the two systems is 7 594. 3 K. Then according to the simulation, the energy ab­sorbed by the electrons can make the temperature reach the peak temperature of 13 020 K when the laser energy density J2 = 3 080 J/m2. The two systems reach the thermal equilibrium state after 17. 64 ps； the equilibrium state of the temperature is 746. 6 K, and the difference between the system is 12 273.4 K. Be­sides ,if 丿3 二 5 380 J/m2, the simulation of the elec­

tronic temperature peak is 18 650 K and the two tem­

peratures in the heat balance will reach 1 125 K after 22.47 ps. The temperature difference is 17 525 K. The above data shows that the time of the electron temperature reaching the peak becomes longer when the energy density of the femtosecond laser increases. As a result, the ablation time increases, and the abla­tion time is the sum of the electron temperature rise time and the lattice temperature rise to the ablation temperature time. It can be seen from Fig. 2 (a) and (b) that the peak of the electron temperature grows after the increase of the energy density of the femto­second laser. The coupling process of the electrons and the phonons is enhanced. By combining the elec・ tron temperature with the lattice temperature, it can be concluded that the ablation temperature increases

Mechanism and simulation analysis of gold foil ablated by femtosecond laserand the ablation intensity increases. According to the above analysis values, the lattice ablative temperature rises with the increase of energy density, and there is a direct relationship between them [ 12].95radiation, the electron temperature decreases from the peak slowly, and the energy of the electrons is trans­ferred to the lattice system slowly. At this time, the gold foil is ablated. The lattice temperature will de­crease slowly after it has been at a maximum value for some time. Since the propagation speed of thermal ergy in electrons is much faster than the propagation velocity in the lattice, the electron temperature in the equilibrium state will be lower than the lattice temper­ature.Fig. 3 Distribution of electron and lattice temperature changes over time with J = 5 380 J/m2 laser irradia・ tion(b) Lattice temperatureFig. 2 Evolution of electron and lattice temperature in the surface of femtosecond laser ablation of gold foil slices with different energy densitiesIn Fig. 3, the lattice and electron temperature curves are observed under the energy density of J = 5 380 J/ml Unlike the electron temperature, the lat­

tice temperature reaches the maximum state in the re­gion where the electron and lattice are coupled, which means that the lattice temperature is about to be or is at maximum value when the system is in equilibrium again. The electron temperature rises rapidly and is much higher than the lattice temperature after the la­ser irradiated the gold foil. With the end of the laser

Fig. 4 shows the three-dimensional distribution of lattice temperature with different depths of ablation depth and ablation time during the process of gold foil processing. First of all, the lattice temperature is re­lated to time and depth. Besides, the temperature ris­ing speed of the lattice will become faster with the in­crease of the energy density of the femtosecond laser, and the temperature of the lattice will be consumed with the increase of the laser irradiation depth gradual・ ly. Therefore, it is concluded that in the case of a sta­ble lattice temperature, the energy density of the laser is increased, and the final stable temperature is also higher.⑻ J=1 540 J/m2(b) J=3 080 J/m2(c) J=5 380 J/m2Fig. 4 Three-dimensional distribution of lattice temperature in three kinds of laser energy96In order to verify the simulated values, the ablation experiment on the gold foil with a thickness of 0. 05 mm is carried out in the case of the femtosecond laser energy density of ]x = 1 540 J/m2, J2 =3 080 J/m2,

J3 =5 380 J/m2. The processed gold foil was placed in an ultrasonic cleaner and washed with ethanol for 20 minutes to remove ablation splatter on the gold foil surface. After the cleaning is completed, the sample is dried to facilitate observation. In Fig. 5 (a) ( b) (c) , the ablation surface and the depth topography of the femtosecond laser ablation with corresponding en­ergy density were observed under ultra-depth micro­scope. It is obvious that when the energy density of the femtosecond laser rises, the surface morphology of the ablated material and the quality of the depth under the ablation are higher, and the overall quality of the processed material is better.(a) J=\\ 540 J/m: (300 times)lOO.Oum(c) J=5 380 J/m' (300 times)Fig. 5 The surface and depth topography of three en­ergy density lasers under ultra depth microscope4 ConclusionIn this paper, the gold foil is taken as an example, and the two-temperature model is simulated under the finite・diffeie*nce method to analyze the two・dimension­al and three・diniensional distribution diagrams of elec­tron temperature and lattice temperature in femtosec­ond laser processing under three energy densities. When J =5 380 J/m2, the depth of laser ablation in­creases significantly. The results show that the abla・ tion time and lattice temperature in the process of gold

Wen-yu DING, et al.foil with a thickness of 0.05mm will increase with the energy density of the femtosecond laser obviously, and the ablative intensity in the non-equilibrium state will increase, which can improve the ablation quality of the femtosecond laser effectively. Therefore, the in­crease of femtosecond laser energy density can improve the morphology and quality of materials greatly, which is of great significance for the research of femtosecond laser ablation materials.References[1 ] WANG Zhijun. Interaction of femtosecond laser pulses with metal materials[ D]. Tianjin：Tianjin University ,2007.[2] LI Zhiming, NIE Jinsong, HU Yuze, et al. Heat accumula­tion effects on the ablation of silicon with high frequency femto­second laser [J]. Laser & Infrared, 2017,47(4) ：410415.[3] HU Mengning, GE Licheng, ZHANG Jinping, et al. Hole-

Drilling with High Depth-Diameter Ratio Using Multi-Pulse Femtosecond Laser [J]. Chinese Journal of Lasers, 2016,43[4] :1-7.[4]B S YILBAS, A F M ARIF. Material response to thermal loading due to short pulse laser heating [ J ]. Int J Heat Mass

Trans,2001,44(20) ：3787-379&[5 ] GU Jiafang. Research of ultrafast dynamics in copper thin films by femtosecond laser [ D]. Zhenjiang： Jiangsu University,

2010.[6] WU He. Mechanism and numerical simulation of femtosec­

ond laser ablating metals and alloy [ D]. Hengyang: University

of South China,2010.[7] S I ANISIMOV, B L KAPELIOVICH,T L PERELMAN. E・

lectron emission from metal surfaces exposed to ultrashort laser pulses[ J]. Soviet Physics, 1974,39：375 - 3力.[8 ] WU Xuefeng. Studies on Theories and Experiments in Fem­

tosecond Laser Ablation of Metal [ D]. Harbin: Harbin Institute

of Technology ,2006.[9 ] ZHAO Shiqiang, LI Ling. Numerical Investigation of Phase Change during Thermal Ablation of Gold Films Induced by

Femtosecond Laser [ J ]. Acta Optica Sinica, 2015,35 ( 12 )：

1-6.[10]CHEN Anmin, JIANG Yuanfei, LIU Hang, et al. Numeri­cal simulation of femtosecond laser ablation by two-temperature model [J]. Laser & Infrared, 2012,42(8) ：847-851.[11 ] NI Xiaochang, WANG Qingyue. Finite difference method

for thermal analysis of femtosecond-picosecond pulse laser abla・

tion on metal surface [ J ]. Chinese J Lasers, 2004,31 ( 3 )： 277-280.[12] WANG Wenting, ZHANG Nan, WANG Mingwei, et al.

Shock temperature of femtosecond laser ablation of solid target [J]. Acta Physica Sinica, 2013,60(21) ： 1-9.Mechanism and simulation analysis of gold foil ablated by femtosecond laser97飞秒激光烧蚀金箔机理及模拟分析丁雯锤，汪帮富*，王中旺苏州科技大学机械工程学院，江苏苏州215009

摘要:研究了在不同能量密度的单脉冲飞秒激光下烧蚀金箔的过程。讨论在不同能量密度的飞秒激光烧蚀下对电声相互

作用，结合双温模型在有限差分法下模拟出的数据图，从模拟结果中得出能量密度与飞秒激光烧蚀的关联，进一步结合实

验结果，分析飞秒激光能量密度是金箔的加工效率以及加工质量的主要因素，从而表明飞秒激光能量密度对于飞秒激光 烧蚀材料的研究具有很大意义。关键词：飞秒激光;非平衡烧蚀；双温模型；冷加工基金项目：苏州科技大学科研基金项目(XKZ201605 )本文引用格式:丁雯饪,汪帮富，王中旺.飞秒激光烧蚀金箔机理及模拟分析[J].机床与液压,2019,47(6) ：92 -97.(Continued from 16 page)面向液体力学的基质板烘干三维流场仿真研究丁建梅\"，李想J姜鹏S郑学宝I1. 东北林业大学机电工程学院，哈尔滨1500402. 哈尔滨东宇农业工程机械有限公司，哈尔滨150090摘要：水稻育秧基质板是用废弃秸秆粉碎后压制而成，可以有效减少因其焚烧而造成的环境污■染。但由于基质板在烘干

过程中，存在烘干效率低,且烘干不均匀的现象，所以现提取局部干燥空间，采用CFD技术模拟基质板周围空气的运动规

律，探讨不同出风口的形状及摆放对空气速度分布的影响，通过详细对比选取不同出风口时基质板周围空气的速度分布

云图，得到当出风口尺扌为8 x230 mm且与基质板长方向垂直时，基质板周围空气速度分布最好，几乎无零速区，分析证

明了本研究技术能够节省研究成本，提高基质板的干燥质量。关键词：基质板；三维流场；CFD；出风口；速度»-»0« » y xx »0« »0«

xx Y » y »xx

y »o«c « »”

x x « »<、v；基金项目：黑龙江省科技攻关资助项目(GC03A523)i本文引用格式：丁建梅，李想，郑学宝.面向液体力学的基质板烘干三维流场仿真研究[J].机床与液压,2019,47(6):13 -16,97.