飞秒脉冲激光对固体材料热损伤的研究
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摘要
随着调Q、锁模等技术的不断发展,人们已经成功地将超短脉冲激光的时间尺度从ns和ps量级压缩到了fs量级;随着啁啾脉冲放大技术的不断完善,人们已经把激光脉冲的峰值功率提高了若干个数量级,从而使激光与物质相互作用这一研究领域进入了一个全新的阶段。
同连续激光和其他时间尺度脉冲激光器一样,在超短脉冲激光器的使用过程中,所面临的一个主要问题就是激光器的长期连续稳定运转问题。而这必然涉及到激光系统中的工作物质、谐振腔镜和输出光路等几个环节及其组成元件的激光损伤问题。其中的元件主要指的是激光器系统中的光学元件,如各种反射镜、透镜和窗口等,当然也可以是整个激光检测系统中所包含的各种光电元器件。除具体结构上的差别之外,构成各种元件的材料主要可以分为透明介质、金属和半导体等三大类。
以往的大量实验研究已经表明,在入射激光的脉冲宽度(FWHM)τ大于约10皮秒的情况下,大多数光学元件及材料的激光损伤阈值均较好地符合著名的τ1/ 2标度律,即各类元件或材料的激光损伤阈值通量密度均大致与τ1/ 2成正比。而这一标度律是与经典傅立叶热传导理论相一致的,或者说是经典傅立叶热传导理论的必然结果。而当脉宽降至约几个皮秒以下后,激光损伤阈值通量密度Fth不再遵从τ1/2标度律。或者说,以往用来处理ns以上脉冲宽度激光损伤问题的经典的傅立叶热传导方程以及经典的热应力分析理论已经失效,不再适用于飞秒激光条件下相关问题的研究。
有鉴于此,在本论文中,我们针对飞秒脉冲激光作用下的透明介质、金属和半导体三类主要材料的损伤机制等国际上的热点和难点问题,利用理论分析和数值模拟计算等方法,进行了以下的基础性研究工作:
1.飞秒脉冲激光对透明介质的损伤方面
在对材料的本征吸收和非本征吸收、杂质和缺陷吸收、电子雪崩电离和多光子电离等损伤机制进行了比较详细的分析后,介绍了Stuart等人所给出的描述透明介质材料体内自由电子密度变化过程的速率方程理论,并在光束尺寸远大于自由电子的扩散长度和激光脉宽可比拟于自由电子弛豫时间的双重条件下,分别就指数形式和双曲正割形式两种超短激光脉冲,对上述速率方程进行了数学解析求解,求解的过程及对结果的数学表达形式,在国际上均未见相关的类似报道。
之后,针对波长为1053nm的飞秒脉冲激光,利用得到的一系列解析表达式,对不同时刻透明材料体内的电子密度、损伤阈值与入射激光的脉冲宽度、峰值功率等诸多参数之间的关系,进行了模拟计算和分析。具体结论如下:
(1)当用入射激光的峰值功率密度描述透明介质的损伤阈值时,入射激光的脉冲宽度越短,则其所对应的损伤阈值越高。如:300fs脉冲激光对熔石英的损伤阈值约为3.5TW/cm2,而100fs脉冲激光的损伤阈值则约7.5TW/cm2,而这与前人所得的结果符合得比较好。
(2)当激光脉冲的特征宽度小于1000fs时,介质损伤阈值辐照通量与入射激光脉宽之间具有较好的线性关系。而这也与前人的实验结果相吻合。
在此基础上,我们还考查了材料中的初始电子密度对其损伤阈值的影响。其中的初始电子密度,可以认为主要是来源于材料中的杂质或缺陷。从我们的计算结果中可以看出:当初始电子密度高于一定值时(约为1011/cm3),其对损伤阈值具有较大的影响;而当初始电子密度低于一定程度时(约为109/cm3),其对损伤阈值的影响可以忽略。这也从一个角度揭示了材料的纯净度及其加工质量对其损伤阈值的影响。而这也与国际上的理论和实验研究结果具有较好的一致性。
2.飞秒脉冲激光对金属材料的损伤方面
在第四章中我们将基于有限差分的数值模拟计算方法,对超短脉冲激光辐照条件下金属材料的损伤机理及其过程等展开比较详细的理论研究。基于内容连续性的考虑,在第三章中,我们利用了整章的篇幅,先以成功描述了纳秒以上脉宽激光对各类材料损伤过程的经典的傅立叶热传导方程为例,对偏微分方程有限差分数值分析方法中的一些基本问题展开了必要的讨论,以为第四章中将要进行的物理问题的研究奠定必要的数学基础。
在第三章中,我们首先对微分之差商的近似表达的数学基础、误差、稳定性、收敛性、差分格式的精确度等进行了初步的介绍,并展开了必要的讨论。其次,给出了在一维和高维空间中数值求解经典傅立叶热传导方程的Crank-Nicolson隐式格式和D’Yakonov交替方向格式。最后,对用以描述熔融和汽化过程的、傅立叶热传导理论中的界面移动问题等,作了理论描述和公式推导,得出了界面位置的离散化方程。
而在第四章中,我们在对非Fourier热传导模型的发展历程及其几个有代表性的阶段性理论,如:CV波理论、双相迟滞模型、广义时间迟滞模型、抛物两步模型、双曲两步模型等进行了简要的介绍,在对非Fourier热传导的理论分析方法(如Boltzmann输运理论和量子分子动力学方法等)进行了系统的介绍之后,又对微观热传导模型的数学求解方法,如解析法和数值法的内涵及发展历程等进行了必要的归纳和总结。
在此基础上,并基于Qiu,Chen和Kaiser等人的工作,我们提出了自己的双温双曲模型。并详细地介绍了该模型的建立过程及数值求解方法—具有人工粘性和时间步长自适应调节能力的前向差分算法。利用标准C语言编制了计算程序,在普通个人计算机上进行了模拟计算。对特定参数条件下的特定金属材料薄膜—金膜表面及体内的电子温度、晶格温度、电子热流、晶格热流等参量随时间和空间的变化规律等,进行了详细的计算与分析,所作的工作内容在国际上均未见过类似的报道。具体的研究结论如下:
(1)在tp=0.14ps,J0=4700J/m2激光辐照下,我们计算所得到的厚度为200nm的金膜的损伤阈值为4700J/m2,而Al-Nimr等人在相同参数条件下所得到的实验值为0.43±0.04J/cm2。两者之间符合得相当好,也就验证了我们所提出的理论模型的合理性和程序的正确性。
(2)在我们的理论模型中,电子热容这一参数选择得是否合理,对电子的最大温度及电子与晶格的热平衡时间等,均会产生较大的影响,而电子热导率对自由电子温度的影响并不显著。此外,电子—晶格之间的能量耦合过程对晶格温度分布的影响,明显低于晶格间热传导过程的影响。
(3)电子热流与电子温度一样,都具有明显的尖峰结构;而除了薄膜前表面以外,其他位置的热流还都具有明显的双峰结构。
(4)电子热流达到最大值比电子温度达到最大值的时间稍微早一些:而在同一深度处,电子温度较高时,所对应的电子热流也比较大。
此外,尽管与电子热流相比,晶格热流的结构相对比较简单,但需要注意的是:在材料的光学吸收深度范围内,在越深的地方晶格的热流也越大。而这也是单纯的经典傅立叶热传导理论所根本无法解释的。其主要原因在于体系高度的复杂性,如电子温度概念的引入、电子与晶格相互作用过程的高度非线性等,具体原因的揭示也有待更加深入的理论分析和数值模拟计算等工作。
3.飞秒脉冲激光对半导体材料的损伤方面
由于无论是从电学特性还是从光学特性上讲,金属材料和透明介质材料都应该看作是半导体材料的一种极限情况——当半导体材料中的自由载流子仅仅为电子而并非包含空穴的成分时,并且当自由电子这种单纯载流子的浓度趋近于材料中的晶格原子的浓度时,半导体材料的电学特性和光学特性就会强烈地体现出一种金属材料的性质;而当半导体材料中的自由载流子的浓度趋近于无穷小或者远远低于材料晶格原子的浓度时,半导体材料的电学特性和光学特性就会强烈地体现出一种透明介质材料的性质。
在第五章中,对已有的半导体材料的激光损伤机制等进行了比较深入的分析、归纳和总结。具体内容包括:
(1)各类激光系统中用到的半导体材料可以分为无源光学材料和有源光学材料这样两类。无源光学材料的光学强度由激光损伤阈值(laser-induced damage threshold-LIDT)来决定,通常用能量密度(J/cm2)或功率密度(W/cm2)等来描述。而有源光学材料对应的光学强度是由自损伤(Self-damage)现象的判断来获得,其对应的是灾变光学损伤(Catastrophic optical damage-COD)发生时所对应的功率密度或能量密度。
(2)在LIDT的测量过程中,采用的判断标准既可以是光学损伤,也可以是电学损伤,还可以是表面形貌损伤。而有关COD的检测,最早是以其电光曲线的突然非可逆性变化的测量来实现的,并在此之后附以表面损伤形貌的检测来完成的。
(3)与半导体材料的COD现象密切相关的一个问题就是LD系统的输出功率与其寿命之间的关系问题:尽管材料的COD通常是采用逐渐增加激光系统输出功率的测试方法获得的。然而COD对LD系统的寿命也会产生一种必然的影响,其结果也是导致LD工作系统的突然失效。
此外,在本章中,还对半导体材料COD的机制和过程,以及改善半导体激光材料抗损伤阈值的方法等,作了概括性的说明。为下一章“飞秒脉冲激光对半导体材料损伤过程的理论分析”打下了必要的理论基础。
而在第六章中,基于对前一章内容的总结,并在深入查阅大量相关文献的基础上,对各类半导体材料的激光损伤机制及其过程等有了更深一步的认识:当亚皮秒超短脉冲激光与材料相互作用时,入射激光可以将材料价带中的电子激发到导带上去,并可以使激发出的电子具有非常高的密度(1021~1022/cm3)和温度(>=1000K)。同时使大量的共价键遭到破损,产生一个以等离子体为中介的相变过程。在晶格声子加热产生之前,晶格的稳定性就已遭到了破坏,这就是所谓的非热熔化过程。
基于上述的认识以及Chen等人于2005年公开发表的工作内容,我们在本章中给出了一个比较完全的自恰场模型,其基于的是弛豫时间近似的Boltzmann方程,所考查的参量有电子和空穴等两类载流子的密度、密度流、能流密度、载流子和晶格的温度等之间的关系。
利用上述的自恰场模型及包含粘滞项的有限差分解法,即可完成超短脉冲激光辐照过程中,相应半导体材料的载流子浓度、载流子温度、晶格温度等的计算。若结合热-弹塑性等动力学模型,还可完成超短脉冲激光冲击波及超声波的传播特性及相关超声检测技术的分析。而若结合前一章的内容,还可考查半导体激光材料在超短脉冲激光条件下的光学强度等。
我们在第二章有关飞秒脉冲激光对透明介质的损伤阈值的解析分析过程中,所利用的是单变量的速率方程理论,所考查的仅仅是材料体内自由电子密度随时间的变化过程,而忽略了自由电子温度和晶格温度对自由电子密度的影响。而在第四章有关飞秒脉冲激光对金属材料损伤机理的理论研究过程中,所提出的是双温双曲模型,所考查的主要是自由电子温度和晶格温度随时间的变化过程,而忽略了自由电子密度的变化过程及其所产生的各种影响。
而我们在第六章中所给出的自恰场模型,所考查的参量有电子和空穴等两类载流子的密度、两类载流子的温度和晶格的温度等随时间的变化规律,并且在模型的理论分析过程中还考查了以上诸多变量之间的相互制约关系。当然对上述诸多制约关系的深入研究还需要经历一个过程。
Along with the continuous progress of the Q-switching and model-locking technologies, the durations of ultra-short optical pulses have been compressed successfully from ns and ps to the order of fs. And supported by the amplifier technologies of the chirp pulses, the peak power of laser pulses have been successfully increased by several orders. As a result, the research on the interaction between laser and materials has been advanced to completely new stage.
Generally, for ns and ps lasers, the major problem is how to keep the lasers working steadily for a long time. On other words, people have to deal with the problem of damages of various optical by laser radiations etc. The optical components may include many kinds of reflectors, lens and windows, which are very useful in the laser systems. Of course, the components may also include various optoelectronics components. Except for the differences in the forms of individual components, the materials of the components may be composed of transparent medium, metal and semiconductors.
It has been proved by many experimental researches that the damage threshold of most optical components and materials obeys the famousτ1/2 law when the laser pulse width (FWHM)τis lager than 10ps, which means that the laser damage threshold of the materials, in unit of J/cm2, is approximately proportional toτ1/2. It has been conformed that this scaling law is the natural result of the classical Fourier thermal conduction theory. However, when the FWHM of the laser pulse becomes shorter than about 10ps, the laser damage threshold of the materials disobeys theτ1/ 2 law. This suggests that fs laser damage of materials can not be treated by the classical Fourier thermal conduction theory.
On this dissertation, the damage mechanisms of transparent media, metal and semiconductors are researched by theory analysis and numerical simulation method. As a result, in this dissertation, the damage mechanism of the three main materials, which are transparent dielectric, metal and semiconductor, are investigated through theoretical analysis and numerical simulation. The basic research works are as follows.
1. femtosecond pulse damage of transparent dielectrics The damage mechanisms, including intrinsic absorption, extrinsic absorption, impurity/defect absorption, avalanche and multiphoton ionization, are analyzed in details; and the rate equations describing the changes of free electron density inside the transparent medium given by Stuart et al are introduced. Under the conditions that beam dimension is well above the diffusion extent of free electrons and laser pulse width is of the same comparable to the free electron life time, the above rate equations for exponential and hyperbolic secant envelopes are investigated analytically, which are not found in international reports to our knowledge. Afterwards, based on a series of analytical expressions obtained from the above femtosecond laser pulse with a wavelength of 1053 nm and, the relations between the electron density, damage threshold, incident pulse width, and pulse peak power etc. are analyzed leading to a closed form expression of damage threshold in terms of the pulse parameters. The conclusions are listed as follows.
(1) When using the parameter of incident pulse peak power density to describe the damage threshold of the transparent dielectric, the shorter the pulse width, the higher the damage threshold intensity is. For example, the damage threshold for the pulse with a width of 300 fs to fused silica is about 3.5TW/cm2, while the threshold of the width is about 7.5TW/cm2 for pulse with a width of 100fs, which confirms the previously reported results.
(2) When the characteristic time of the pulse width is less than 1000fs, damage threshold fluence of the dielectrics varies with the incident laser pulse width linearly, which also confirms the previously reported experimental results.
Based on the above discussion, the influence of the initial electron density inside the material to its damage threshold is also investigated. The initial electron can be considered to be generated due to material impurity or defect. According to our calculation results, the influence of the initial electron density to damage threshold becomes more prominent, when the density is higher than a certain numerical value(about 1011/cm3); while the influence of the initial electron density to damage threshold can be neglected, when the density is lower than a certain value(about 109/cm3). This indicates the influences of material purity and machining quality to damage threshold, which is in accordance with the previously reported theoretical and experimental results.
2. femtosecond pulse damage to metal
The analytical simulation based on the finite differential method will be discussed in chapter 4 to study the ultrashort pulse ablation mechanism for metal materials. We start from the Fourier thermal conduction equations for laser pulse width longer than nanosecond, and basic questions about numerical analysis methods of partial-differential equations are discussed the in the whole chapter 3, which provides essential mathematical basis for the physical problems to be discussed in chapter 4.
In chapter 3, the mathematical issues of finite differential approximate expressions of continuous differential equations, such as errors, stability, stringency and definitions, are introduced and discussed. Secondly, the one and multiple dimensional latent Crank-Nicolson formulas and D’Yakonov alternant directional formulas for numerical calculations of classics Fourier thermal conduction are given. Finally, the theoretical descriptions and expressions deduction of the melting and vaporization processes, such as interfacial movement problems in the Fourier thermal conduction theories are made, and the dispersed equations of the interface is also educed. In chapter 4, several representative theories in the development course, such as CV model , dual-phase-lag model , general-time-lag model、parabolic two-step model and hyperbolic two-step model, are recommended briefly. And then, a systemic introduction of Un-Fourier thermal conduction theories, such as Boltzmann transportation theories and the quantum theory of molecule dynamics, are introduced systemically. The mathematical solving methods of microcosmic thermal conduction models, such as analysis and numerical methods, are reviewed and concluded. And then, based on the earlier jobs of Qiu, Chen and Kaiser, a new dual-hyperbolic two temperature model is established. One self-adaptive forward finite differential numerical solving method with artificial-viscosity-treatment is utilized. A calculation program is written based on standard C language and run in an ordinary PC. The spatio-temporal temperatures and heat flux distributions of electrons and lattices, in the specified metal films, are calculated and discussed. The chief conclusions may be shown as follows:
(1) irradiated by the laser pulse with parameters of tp=0.14ps and J0=4700J/m2, the damage threshold of golden films with 200nm thickness, calculated by us, is about 4700J/m2, and the experimental result got by Al-Nimr et al, in the same parameters, is 0.43±0.04J/cm2. The agreement between the theory prediction and experiment result verifies the validity of our model.
(2) Our further calculations have verified that the influence of capacity of electrons, on the electron temperature distributions and the electron-lattice balance time,is very strong. But the influence of the thermal conduction is very little and may be neglected. And the influence of energy coupling procedure of electron-lattice, to the temperature distributions of lattice, is much lets important than that of thermal conduction procedure to the lattice.
(3) There are obvious sharp peak structures in the curves of heat flux and temperature of electrons. And except for the front surface, there are tow-sharp-peak structures in the heat flux curves.
(4) The time when the heat flux of electrons reaches its maximum is a little bit earlier than that of temperature of electrons. And in the same depth, the heat flux of the electrons is lager while its temperature is higher.
In addition, although the structure of heat flux in the lattice is simpler than that in the electrons, one should pay more attention to that, in the range of the optical absorption depth, the heat flux is larger if the depth is larger. This phenomenon can not be explained by the classic Fourier thermal conduction theories. The main reason is arise from the complexity of the system, such as the large non-linearity of the interaction behaved electrons and lattices. The reveal of the concrete reasons is waiting for deeper theory analysis and numerical calculation research.
3. Femtosecond pulse damage to semiconductor materials
Metals and transparent dielectrics can be regarded as marginal condition of the semiconductor materials, that is the electrical and optical characteristics of semiconductor materials are similar to metal characteristics when free carrier comprises of only electrons and the free electrons density is close to the crystal lattice atom density. While the electrical and optical characteristics of semiconductor materials are close transparent dielectric characteristics when the free electrons density becomes much lower than that of the crystal lattice atom density. The above laser damage mechanisms of the semiconductor materials are analyzed, concluded and summarized in chapter 5. The main contents are as follows.
(1) The semiconductors used in the different kinds of laser systems may be divided into active optical materials and passivity optical materials. The optical strength required passivity materials dictated by the laser-induced damage threshold (LIDT), and is described by energy density (J/cm2) or power density (W/cm2). And the optical strength imposed on active materials is decided by the judgment on the Self-damage phenomenon, and is evaluated by the energy density (J/cm2) or power density (W/cm2) while catastrophic optical damage (COD) is happened.
(2) In the test of LIDT, the determine standard may be based on optical damage, electrical damage, confirmed by a comparing surface configuration damage. In earliest tests, the COD is obtained by observing the abrupt and irreversible variation happened on electrical-optical curves, and then confirmed by a test of the surface damage configuration.
(3) One problem correlated to the COD phenomenon of semiconductor materials is that the dependence of the output power of LD system on its lifetime. Although the COD of the materials is usually obtained by the test methods of gradually increasing the output power of the laser systems, COD of the materials inevitably influences the lifetime of LD systems. And the consequence is the sudden invalidation of the LD systems.
Furthermore, the mechanism and process of the semiconductor material COD and the methods to improve semiconductor material ablation threshold characteristics are explained synoptically, which is essential theoretical basis for the next chapter– theoretical analysis of the femtosecond pulse ablation to semiconductor materials. Based on the conclusions of the previous chapter and referred to lots of relevant literatures, the laser damage mechanisms and process to various semiconductor materials are understood more profoundly.
When sub-picosecond ultra-short laser pulses irradiated on materials, electrons can be excitated from valence band to conductive band by the incident laser pulse, and the electron density can reach vary high level (1021~1022/cm3). At the same time, the covalent bond is broken, and the plasma is generated. The stability of the crystal lattice is destroyed before the crystal lattice phonon heated, which is the so-called non-thermal fusion process.
Based on the above understanding, and referencing the job of Chen et al, a self-consistent field model is established in this chapter. The theory fundamental of the model is relaxed timing approximation of Boltzmann equations. The parameters we take care of in the model mainly are the densities and currents of electrons and holes, energy currents and energy densities, the temperature of electrons and lattices. And the relations of the parameters above is simulated and calculated in the dissertation.
Utilizing the self-coincided field model described above and an artificial-viscosity-treated finite differential numerical method, the densities and temperatures of electrons and holes, and the temperatures of lattices can be calculated. Further if the relations of thermal-elastic dynamics are introduced, the shock waves and/or ultrasonic waves introduced by ultrashort pulses lasers may be studied. In addition if the content of the preceding chapters are combined, the optical strength of semiconductor materials irradiated by ultrashort pulses lasers may also be tested.
In the analytical analysis of the damage threshold of the femtosecond pulse to transparent dielectrics, the single-variable rate equation theory is used, which is to investigate the changes of the free electron density inside the material at different time, however, the influences of the temperatures of free electron and crystal lattice to free electron density is neglected. While in the theoretical analysis of the ablation mechanisms of femtosecond pulse to metal materials in the chapter 4, the dual-hyperbolic two temperature model is used to, and the changes of the temperatures of free electron and crystal lattice with different time is investigated, however, the changes of the free electron density and its influences are neglected.
And finally, one self-consistent field model is given in chapter 6. The parameters to be considered in the model are densities and temperatures of electrons and holes, and the temperatures of crystal lattice. And the principal assignment is to discuss the spatio and temporal and inter-dependence between of the parameters.
同连续激光和其他时间尺度脉冲激光器一样,在超短脉冲激光器的使用过程中,所面临的一个主要问题就是激光器的长期连续稳定运转问题。而这必然涉及到激光系统中的工作物质、谐振腔镜和输出光路等几个环节及其组成元件的激光损伤问题。其中的元件主要指的是激光器系统中的光学元件,如各种反射镜、透镜和窗口等,当然也可以是整个激光检测系统中所包含的各种光电元器件。除具体结构上的差别之外,构成各种元件的材料主要可以分为透明介质、金属和半导体等三大类。
以往的大量实验研究已经表明,在入射激光的脉冲宽度(FWHM)τ大于约10皮秒的情况下,大多数光学元件及材料的激光损伤阈值均较好地符合著名的τ1/ 2标度律,即各类元件或材料的激光损伤阈值通量密度均大致与τ1/ 2成正比。而这一标度律是与经典傅立叶热传导理论相一致的,或者说是经典傅立叶热传导理论的必然结果。而当脉宽降至约几个皮秒以下后,激光损伤阈值通量密度Fth不再遵从τ1/2标度律。或者说,以往用来处理ns以上脉冲宽度激光损伤问题的经典的傅立叶热传导方程以及经典的热应力分析理论已经失效,不再适用于飞秒激光条件下相关问题的研究。
有鉴于此,在本论文中,我们针对飞秒脉冲激光作用下的透明介质、金属和半导体三类主要材料的损伤机制等国际上的热点和难点问题,利用理论分析和数值模拟计算等方法,进行了以下的基础性研究工作:
1.飞秒脉冲激光对透明介质的损伤方面
在对材料的本征吸收和非本征吸收、杂质和缺陷吸收、电子雪崩电离和多光子电离等损伤机制进行了比较详细的分析后,介绍了Stuart等人所给出的描述透明介质材料体内自由电子密度变化过程的速率方程理论,并在光束尺寸远大于自由电子的扩散长度和激光脉宽可比拟于自由电子弛豫时间的双重条件下,分别就指数形式和双曲正割形式两种超短激光脉冲,对上述速率方程进行了数学解析求解,求解的过程及对结果的数学表达形式,在国际上均未见相关的类似报道。
之后,针对波长为1053nm的飞秒脉冲激光,利用得到的一系列解析表达式,对不同时刻透明材料体内的电子密度、损伤阈值与入射激光的脉冲宽度、峰值功率等诸多参数之间的关系,进行了模拟计算和分析。具体结论如下:
(1)当用入射激光的峰值功率密度描述透明介质的损伤阈值时,入射激光的脉冲宽度越短,则其所对应的损伤阈值越高。如:300fs脉冲激光对熔石英的损伤阈值约为3.5TW/cm2,而100fs脉冲激光的损伤阈值则约7.5TW/cm2,而这与前人所得的结果符合得比较好。
(2)当激光脉冲的特征宽度小于1000fs时,介质损伤阈值辐照通量与入射激光脉宽之间具有较好的线性关系。而这也与前人的实验结果相吻合。
在此基础上,我们还考查了材料中的初始电子密度对其损伤阈值的影响。其中的初始电子密度,可以认为主要是来源于材料中的杂质或缺陷。从我们的计算结果中可以看出:当初始电子密度高于一定值时(约为1011/cm3),其对损伤阈值具有较大的影响;而当初始电子密度低于一定程度时(约为109/cm3),其对损伤阈值的影响可以忽略。这也从一个角度揭示了材料的纯净度及其加工质量对其损伤阈值的影响。而这也与国际上的理论和实验研究结果具有较好的一致性。
2.飞秒脉冲激光对金属材料的损伤方面
在第四章中我们将基于有限差分的数值模拟计算方法,对超短脉冲激光辐照条件下金属材料的损伤机理及其过程等展开比较详细的理论研究。基于内容连续性的考虑,在第三章中,我们利用了整章的篇幅,先以成功描述了纳秒以上脉宽激光对各类材料损伤过程的经典的傅立叶热传导方程为例,对偏微分方程有限差分数值分析方法中的一些基本问题展开了必要的讨论,以为第四章中将要进行的物理问题的研究奠定必要的数学基础。
在第三章中,我们首先对微分之差商的近似表达的数学基础、误差、稳定性、收敛性、差分格式的精确度等进行了初步的介绍,并展开了必要的讨论。其次,给出了在一维和高维空间中数值求解经典傅立叶热传导方程的Crank-Nicolson隐式格式和D’Yakonov交替方向格式。最后,对用以描述熔融和汽化过程的、傅立叶热传导理论中的界面移动问题等,作了理论描述和公式推导,得出了界面位置的离散化方程。
而在第四章中,我们在对非Fourier热传导模型的发展历程及其几个有代表性的阶段性理论,如:CV波理论、双相迟滞模型、广义时间迟滞模型、抛物两步模型、双曲两步模型等进行了简要的介绍,在对非Fourier热传导的理论分析方法(如Boltzmann输运理论和量子分子动力学方法等)进行了系统的介绍之后,又对微观热传导模型的数学求解方法,如解析法和数值法的内涵及发展历程等进行了必要的归纳和总结。
在此基础上,并基于Qiu,Chen和Kaiser等人的工作,我们提出了自己的双温双曲模型。并详细地介绍了该模型的建立过程及数值求解方法—具有人工粘性和时间步长自适应调节能力的前向差分算法。利用标准C语言编制了计算程序,在普通个人计算机上进行了模拟计算。对特定参数条件下的特定金属材料薄膜—金膜表面及体内的电子温度、晶格温度、电子热流、晶格热流等参量随时间和空间的变化规律等,进行了详细的计算与分析,所作的工作内容在国际上均未见过类似的报道。具体的研究结论如下:
(1)在tp=0.14ps,J0=4700J/m2激光辐照下,我们计算所得到的厚度为200nm的金膜的损伤阈值为4700J/m2,而Al-Nimr等人在相同参数条件下所得到的实验值为0.43±0.04J/cm2。两者之间符合得相当好,也就验证了我们所提出的理论模型的合理性和程序的正确性。
(2)在我们的理论模型中,电子热容这一参数选择得是否合理,对电子的最大温度及电子与晶格的热平衡时间等,均会产生较大的影响,而电子热导率对自由电子温度的影响并不显著。此外,电子—晶格之间的能量耦合过程对晶格温度分布的影响,明显低于晶格间热传导过程的影响。
(3)电子热流与电子温度一样,都具有明显的尖峰结构;而除了薄膜前表面以外,其他位置的热流还都具有明显的双峰结构。
(4)电子热流达到最大值比电子温度达到最大值的时间稍微早一些:而在同一深度处,电子温度较高时,所对应的电子热流也比较大。
此外,尽管与电子热流相比,晶格热流的结构相对比较简单,但需要注意的是:在材料的光学吸收深度范围内,在越深的地方晶格的热流也越大。而这也是单纯的经典傅立叶热传导理论所根本无法解释的。其主要原因在于体系高度的复杂性,如电子温度概念的引入、电子与晶格相互作用过程的高度非线性等,具体原因的揭示也有待更加深入的理论分析和数值模拟计算等工作。
3.飞秒脉冲激光对半导体材料的损伤方面
由于无论是从电学特性还是从光学特性上讲,金属材料和透明介质材料都应该看作是半导体材料的一种极限情况——当半导体材料中的自由载流子仅仅为电子而并非包含空穴的成分时,并且当自由电子这种单纯载流子的浓度趋近于材料中的晶格原子的浓度时,半导体材料的电学特性和光学特性就会强烈地体现出一种金属材料的性质;而当半导体材料中的自由载流子的浓度趋近于无穷小或者远远低于材料晶格原子的浓度时,半导体材料的电学特性和光学特性就会强烈地体现出一种透明介质材料的性质。
在第五章中,对已有的半导体材料的激光损伤机制等进行了比较深入的分析、归纳和总结。具体内容包括:
(1)各类激光系统中用到的半导体材料可以分为无源光学材料和有源光学材料这样两类。无源光学材料的光学强度由激光损伤阈值(laser-induced damage threshold-LIDT)来决定,通常用能量密度(J/cm2)或功率密度(W/cm2)等来描述。而有源光学材料对应的光学强度是由自损伤(Self-damage)现象的判断来获得,其对应的是灾变光学损伤(Catastrophic optical damage-COD)发生时所对应的功率密度或能量密度。
(2)在LIDT的测量过程中,采用的判断标准既可以是光学损伤,也可以是电学损伤,还可以是表面形貌损伤。而有关COD的检测,最早是以其电光曲线的突然非可逆性变化的测量来实现的,并在此之后附以表面损伤形貌的检测来完成的。
(3)与半导体材料的COD现象密切相关的一个问题就是LD系统的输出功率与其寿命之间的关系问题:尽管材料的COD通常是采用逐渐增加激光系统输出功率的测试方法获得的。然而COD对LD系统的寿命也会产生一种必然的影响,其结果也是导致LD工作系统的突然失效。
此外,在本章中,还对半导体材料COD的机制和过程,以及改善半导体激光材料抗损伤阈值的方法等,作了概括性的说明。为下一章“飞秒脉冲激光对半导体材料损伤过程的理论分析”打下了必要的理论基础。
而在第六章中,基于对前一章内容的总结,并在深入查阅大量相关文献的基础上,对各类半导体材料的激光损伤机制及其过程等有了更深一步的认识:当亚皮秒超短脉冲激光与材料相互作用时,入射激光可以将材料价带中的电子激发到导带上去,并可以使激发出的电子具有非常高的密度(1021~1022/cm3)和温度(>=1000K)。同时使大量的共价键遭到破损,产生一个以等离子体为中介的相变过程。在晶格声子加热产生之前,晶格的稳定性就已遭到了破坏,这就是所谓的非热熔化过程。
基于上述的认识以及Chen等人于2005年公开发表的工作内容,我们在本章中给出了一个比较完全的自恰场模型,其基于的是弛豫时间近似的Boltzmann方程,所考查的参量有电子和空穴等两类载流子的密度、密度流、能流密度、载流子和晶格的温度等之间的关系。
利用上述的自恰场模型及包含粘滞项的有限差分解法,即可完成超短脉冲激光辐照过程中,相应半导体材料的载流子浓度、载流子温度、晶格温度等的计算。若结合热-弹塑性等动力学模型,还可完成超短脉冲激光冲击波及超声波的传播特性及相关超声检测技术的分析。而若结合前一章的内容,还可考查半导体激光材料在超短脉冲激光条件下的光学强度等。
我们在第二章有关飞秒脉冲激光对透明介质的损伤阈值的解析分析过程中,所利用的是单变量的速率方程理论,所考查的仅仅是材料体内自由电子密度随时间的变化过程,而忽略了自由电子温度和晶格温度对自由电子密度的影响。而在第四章有关飞秒脉冲激光对金属材料损伤机理的理论研究过程中,所提出的是双温双曲模型,所考查的主要是自由电子温度和晶格温度随时间的变化过程,而忽略了自由电子密度的变化过程及其所产生的各种影响。
而我们在第六章中所给出的自恰场模型,所考查的参量有电子和空穴等两类载流子的密度、两类载流子的温度和晶格的温度等随时间的变化规律,并且在模型的理论分析过程中还考查了以上诸多变量之间的相互制约关系。当然对上述诸多制约关系的深入研究还需要经历一个过程。
Along with the continuous progress of the Q-switching and model-locking technologies, the durations of ultra-short optical pulses have been compressed successfully from ns and ps to the order of fs. And supported by the amplifier technologies of the chirp pulses, the peak power of laser pulses have been successfully increased by several orders. As a result, the research on the interaction between laser and materials has been advanced to completely new stage.
Generally, for ns and ps lasers, the major problem is how to keep the lasers working steadily for a long time. On other words, people have to deal with the problem of damages of various optical by laser radiations etc. The optical components may include many kinds of reflectors, lens and windows, which are very useful in the laser systems. Of course, the components may also include various optoelectronics components. Except for the differences in the forms of individual components, the materials of the components may be composed of transparent medium, metal and semiconductors.
It has been proved by many experimental researches that the damage threshold of most optical components and materials obeys the famousτ1/2 law when the laser pulse width (FWHM)τis lager than 10ps, which means that the laser damage threshold of the materials, in unit of J/cm2, is approximately proportional toτ1/2. It has been conformed that this scaling law is the natural result of the classical Fourier thermal conduction theory. However, when the FWHM of the laser pulse becomes shorter than about 10ps, the laser damage threshold of the materials disobeys theτ1/ 2 law. This suggests that fs laser damage of materials can not be treated by the classical Fourier thermal conduction theory.
On this dissertation, the damage mechanisms of transparent media, metal and semiconductors are researched by theory analysis and numerical simulation method. As a result, in this dissertation, the damage mechanism of the three main materials, which are transparent dielectric, metal and semiconductor, are investigated through theoretical analysis and numerical simulation. The basic research works are as follows.
1. femtosecond pulse damage of transparent dielectrics The damage mechanisms, including intrinsic absorption, extrinsic absorption, impurity/defect absorption, avalanche and multiphoton ionization, are analyzed in details; and the rate equations describing the changes of free electron density inside the transparent medium given by Stuart et al are introduced. Under the conditions that beam dimension is well above the diffusion extent of free electrons and laser pulse width is of the same comparable to the free electron life time, the above rate equations for exponential and hyperbolic secant envelopes are investigated analytically, which are not found in international reports to our knowledge. Afterwards, based on a series of analytical expressions obtained from the above femtosecond laser pulse with a wavelength of 1053 nm and, the relations between the electron density, damage threshold, incident pulse width, and pulse peak power etc. are analyzed leading to a closed form expression of damage threshold in terms of the pulse parameters. The conclusions are listed as follows.
(1) When using the parameter of incident pulse peak power density to describe the damage threshold of the transparent dielectric, the shorter the pulse width, the higher the damage threshold intensity is. For example, the damage threshold for the pulse with a width of 300 fs to fused silica is about 3.5TW/cm2, while the threshold of the width is about 7.5TW/cm2 for pulse with a width of 100fs, which confirms the previously reported results.
(2) When the characteristic time of the pulse width is less than 1000fs, damage threshold fluence of the dielectrics varies with the incident laser pulse width linearly, which also confirms the previously reported experimental results.
Based on the above discussion, the influence of the initial electron density inside the material to its damage threshold is also investigated. The initial electron can be considered to be generated due to material impurity or defect. According to our calculation results, the influence of the initial electron density to damage threshold becomes more prominent, when the density is higher than a certain numerical value(about 1011/cm3); while the influence of the initial electron density to damage threshold can be neglected, when the density is lower than a certain value(about 109/cm3). This indicates the influences of material purity and machining quality to damage threshold, which is in accordance with the previously reported theoretical and experimental results.
2. femtosecond pulse damage to metal
The analytical simulation based on the finite differential method will be discussed in chapter 4 to study the ultrashort pulse ablation mechanism for metal materials. We start from the Fourier thermal conduction equations for laser pulse width longer than nanosecond, and basic questions about numerical analysis methods of partial-differential equations are discussed the in the whole chapter 3, which provides essential mathematical basis for the physical problems to be discussed in chapter 4.
In chapter 3, the mathematical issues of finite differential approximate expressions of continuous differential equations, such as errors, stability, stringency and definitions, are introduced and discussed. Secondly, the one and multiple dimensional latent Crank-Nicolson formulas and D’Yakonov alternant directional formulas for numerical calculations of classics Fourier thermal conduction are given. Finally, the theoretical descriptions and expressions deduction of the melting and vaporization processes, such as interfacial movement problems in the Fourier thermal conduction theories are made, and the dispersed equations of the interface is also educed. In chapter 4, several representative theories in the development course, such as CV model , dual-phase-lag model , general-time-lag model、parabolic two-step model and hyperbolic two-step model, are recommended briefly. And then, a systemic introduction of Un-Fourier thermal conduction theories, such as Boltzmann transportation theories and the quantum theory of molecule dynamics, are introduced systemically. The mathematical solving methods of microcosmic thermal conduction models, such as analysis and numerical methods, are reviewed and concluded. And then, based on the earlier jobs of Qiu, Chen and Kaiser, a new dual-hyperbolic two temperature model is established. One self-adaptive forward finite differential numerical solving method with artificial-viscosity-treatment is utilized. A calculation program is written based on standard C language and run in an ordinary PC. The spatio-temporal temperatures and heat flux distributions of electrons and lattices, in the specified metal films, are calculated and discussed. The chief conclusions may be shown as follows:
(1) irradiated by the laser pulse with parameters of tp=0.14ps and J0=4700J/m2, the damage threshold of golden films with 200nm thickness, calculated by us, is about 4700J/m2, and the experimental result got by Al-Nimr et al, in the same parameters, is 0.43±0.04J/cm2. The agreement between the theory prediction and experiment result verifies the validity of our model.
(2) Our further calculations have verified that the influence of capacity of electrons, on the electron temperature distributions and the electron-lattice balance time,is very strong. But the influence of the thermal conduction is very little and may be neglected. And the influence of energy coupling procedure of electron-lattice, to the temperature distributions of lattice, is much lets important than that of thermal conduction procedure to the lattice.
(3) There are obvious sharp peak structures in the curves of heat flux and temperature of electrons. And except for the front surface, there are tow-sharp-peak structures in the heat flux curves.
(4) The time when the heat flux of electrons reaches its maximum is a little bit earlier than that of temperature of electrons. And in the same depth, the heat flux of the electrons is lager while its temperature is higher.
In addition, although the structure of heat flux in the lattice is simpler than that in the electrons, one should pay more attention to that, in the range of the optical absorption depth, the heat flux is larger if the depth is larger. This phenomenon can not be explained by the classic Fourier thermal conduction theories. The main reason is arise from the complexity of the system, such as the large non-linearity of the interaction behaved electrons and lattices. The reveal of the concrete reasons is waiting for deeper theory analysis and numerical calculation research.
3. Femtosecond pulse damage to semiconductor materials
Metals and transparent dielectrics can be regarded as marginal condition of the semiconductor materials, that is the electrical and optical characteristics of semiconductor materials are similar to metal characteristics when free carrier comprises of only electrons and the free electrons density is close to the crystal lattice atom density. While the electrical and optical characteristics of semiconductor materials are close transparent dielectric characteristics when the free electrons density becomes much lower than that of the crystal lattice atom density. The above laser damage mechanisms of the semiconductor materials are analyzed, concluded and summarized in chapter 5. The main contents are as follows.
(1) The semiconductors used in the different kinds of laser systems may be divided into active optical materials and passivity optical materials. The optical strength required passivity materials dictated by the laser-induced damage threshold (LIDT), and is described by energy density (J/cm2) or power density (W/cm2). And the optical strength imposed on active materials is decided by the judgment on the Self-damage phenomenon, and is evaluated by the energy density (J/cm2) or power density (W/cm2) while catastrophic optical damage (COD) is happened.
(2) In the test of LIDT, the determine standard may be based on optical damage, electrical damage, confirmed by a comparing surface configuration damage. In earliest tests, the COD is obtained by observing the abrupt and irreversible variation happened on electrical-optical curves, and then confirmed by a test of the surface damage configuration.
(3) One problem correlated to the COD phenomenon of semiconductor materials is that the dependence of the output power of LD system on its lifetime. Although the COD of the materials is usually obtained by the test methods of gradually increasing the output power of the laser systems, COD of the materials inevitably influences the lifetime of LD systems. And the consequence is the sudden invalidation of the LD systems.
Furthermore, the mechanism and process of the semiconductor material COD and the methods to improve semiconductor material ablation threshold characteristics are explained synoptically, which is essential theoretical basis for the next chapter– theoretical analysis of the femtosecond pulse ablation to semiconductor materials. Based on the conclusions of the previous chapter and referred to lots of relevant literatures, the laser damage mechanisms and process to various semiconductor materials are understood more profoundly.
When sub-picosecond ultra-short laser pulses irradiated on materials, electrons can be excitated from valence band to conductive band by the incident laser pulse, and the electron density can reach vary high level (1021~1022/cm3). At the same time, the covalent bond is broken, and the plasma is generated. The stability of the crystal lattice is destroyed before the crystal lattice phonon heated, which is the so-called non-thermal fusion process.
Based on the above understanding, and referencing the job of Chen et al, a self-consistent field model is established in this chapter. The theory fundamental of the model is relaxed timing approximation of Boltzmann equations. The parameters we take care of in the model mainly are the densities and currents of electrons and holes, energy currents and energy densities, the temperature of electrons and lattices. And the relations of the parameters above is simulated and calculated in the dissertation.
Utilizing the self-coincided field model described above and an artificial-viscosity-treated finite differential numerical method, the densities and temperatures of electrons and holes, and the temperatures of lattices can be calculated. Further if the relations of thermal-elastic dynamics are introduced, the shock waves and/or ultrasonic waves introduced by ultrashort pulses lasers may be studied. In addition if the content of the preceding chapters are combined, the optical strength of semiconductor materials irradiated by ultrashort pulses lasers may also be tested.
In the analytical analysis of the damage threshold of the femtosecond pulse to transparent dielectrics, the single-variable rate equation theory is used, which is to investigate the changes of the free electron density inside the material at different time, however, the influences of the temperatures of free electron and crystal lattice to free electron density is neglected. While in the theoretical analysis of the ablation mechanisms of femtosecond pulse to metal materials in the chapter 4, the dual-hyperbolic two temperature model is used to, and the changes of the temperatures of free electron and crystal lattice with different time is investigated, however, the changes of the free electron density and its influences are neglected.
And finally, one self-consistent field model is given in chapter 6. The parameters to be considered in the model are densities and temperatures of electrons and holes, and the temperatures of crystal lattice. And the principal assignment is to discuss the spatio and temporal and inter-dependence between of the parameters.
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