飞秒激光烧蚀硅的分子动力学模拟
摘要
本文基于三维“x-分区”模型和SW势,编写了可以处理晶体硅的飞秒激光烧蚀过程的分子动力学程序,在国内首次开展了飞秒激光烧蚀晶体硅的分子动力学模拟;通过与实验结果和其它分子动力学模拟结果的比较,证明了分子动力学模拟是一种很有价值的研究方法。
对比研究了硅的五种经验势函数,考察了原子间距、键角对系统总能量的影响。结果表明,SW势由于截断半径适中、参数较少、形式简单且具有一定的物理基础,因而应用广泛。本文选择了SW势进行分子动力学模拟,并推导出基于SW势的受力计算公式。
模拟了给定系统向NVT系综和NVE系综演化的过程以及系统自由演化的过程,以便调试程序和考察各趋衡过程的性质。其中,FREE过程能很好地保持系统的总能量守恒,并驱动系统很快达到合理的平衡,通常用于动力学加载后的趋衡过程;NVT模拟可以保持温度恒定,适用于描述系统在特定温度下的趋衡过程。在激光烧蚀过程的模拟中,将会用到这两种平衡态分子动力学模拟。
发展了用于描述激光能量沉积过程的三维“x-分区”模型,研究了飞秒激光光斑完全覆盖Si(100)表面和小于Si(100)表面两种情况下的烧蚀现象,得到了飞秒激光烧蚀现象的一般特征。烧蚀过程自材料内部气泡的产生开始,由气泡的发展最终导致。烧蚀材料可分成晶体区、熔化区和烧蚀区三部分,三个区域中原子的运动分别具有固体、液体和气体粒子的运动特征。观察到烧蚀过程中激光诱导应力波的产生与传播。熔化区的应力波是由原子的飞散引起的稀疏波。晶体区的应力波以声速传播。
系统地分析了激光参数和激光加载方式对烧蚀现象的影响。结果表明:对于能通量相同的短脉冲和长脉冲激光,短脉冲的烧蚀现象比长脉冲剧烈,热效应比长脉冲小;脉宽一定的情况下,随着激光能通量的增加,烧蚀现象加剧,存在一个能恰好使材料烧蚀的能通量,即烧蚀阈值;空间谱决定激光能量的空间分布,不同的空间分布将会产生不同的烧蚀现象;随着波长的增加,光子能量降低,相应激光在晶体硅中的吸收系数减小,烧蚀过程的热损伤和热影响区域大大增加。激光加载有长时间加载和瞬时加载两种方式,两者的区别在于激光能量沉积过程是否伴随系统的趋衡过程。瞬时加载和长时间加载对飞秒激光烧蚀现象的影响差别很小,因此可以用瞬时加载代替长时间加载以简化计算。但是瞬时加载在很大程度上夸大了皮秒激光的烧蚀现象,故不能用瞬时加载简化皮秒激光的作用过程,可以采用将长脉冲激光离散为飞秒激光的方法来简化计算。
In this paper, a molecular dynamics program has been written out to handle the femtosecond laser ablation of crystal silicon. The program is written in FORTRAN, parallelized by the mean of decomposing atoms, and optimized by the neighbor-list method to reduce the time expended in the force calculation. The results agree with the experimental and other numerical results, which indicate the molecular dynamics method is valuable for problems of laser ablation.
Comparative study of five empirical potentials for silicon was performed. Influences of bond angles and distances between atoms on the system energy were investigated. The results show SW potential is widely used because of its moderate cutoff radius, less parameters, simpler form and physical foundations. Thus, SW potential was chosen to describe the interactions between atoms in this paper. Equations of force calculation were educed based on SW potential.
Evolutions of initial systems to NVT and NVE ensembles besides the free evolution were simulated in order to debug the program and investigate the characteristics of the balancing processes. The FREE process can conserve the total energy well and drive the system to reach a reasonable equilibrious state quickly, so is usually used in the balancing process after a dynamics loading. The NVT process can keep the temperature constant and is suitable for the balancing process at a given temperature. Both of the two processes were used in the simulations of laser ablation.
A 3-D“x-section”model was developed to describe the deposition process of laser energy. Based on the 3-D“x-section”model, femtosecond laser ablations of Si(100) were simulated under two conditions which were total covering of the laser spot on the target surface and less laser spot than the target surface. Through the simulations, common characteristics of the femtosecond laser ablation were gotten. The ablation begins from the emergence of bubbles and is eventually induced by developments of the bubbles. The ablated material is composed of crystal, melted and ablated regions in which atoms move just like particles in solid, liquid and gas respectively. Moreover, two kinds of laser-induced stress waves were captured. One in the melted region is caused by the dispersion of surface atoms; the other in the crystal region propagates with the sound velocity.
Influences of laser parameters (such as pulse width, intensity, spatial spectrum and wave length) and loading styles on ablation phenomena were analyzed systemically. The results show: with the same energy flux, the short pulse produces more serious ablation phenomena than the long pulse; at a given pulse width, ablation becomes more and more serious with the increase of laser intensity, the least intensity with which the laser can ablate the target is called ablation threshold; the spatial spectrum determines the spatial distribution of laser energy, and will lead specific ablation phenomena; the laser with longer wave length has photons with lower energy and a larger thermal-affected region in the ablation process. There are two loading styles of the incident laser, one is long-time loading and the other is instantaneous loading. The difference between them is whether the deposition process of laser energy is accompanied with the balancing process of the system. The ablation phenomena of femtosecond lasers under the two loading styles are almost same, so the instantaneous loading can be used in femtosecond laser ablations to reduce the simulation time. However, it is not effective to the picoseoncd laser ablation because of magnifying the ablation phenomena. Decomposing the long laser pulse into femtosecond lasers may be used to simplify the simulation.
对比研究了硅的五种经验势函数,考察了原子间距、键角对系统总能量的影响。结果表明,SW势由于截断半径适中、参数较少、形式简单且具有一定的物理基础,因而应用广泛。本文选择了SW势进行分子动力学模拟,并推导出基于SW势的受力计算公式。
模拟了给定系统向NVT系综和NVE系综演化的过程以及系统自由演化的过程,以便调试程序和考察各趋衡过程的性质。其中,FREE过程能很好地保持系统的总能量守恒,并驱动系统很快达到合理的平衡,通常用于动力学加载后的趋衡过程;NVT模拟可以保持温度恒定,适用于描述系统在特定温度下的趋衡过程。在激光烧蚀过程的模拟中,将会用到这两种平衡态分子动力学模拟。
发展了用于描述激光能量沉积过程的三维“x-分区”模型,研究了飞秒激光光斑完全覆盖Si(100)表面和小于Si(100)表面两种情况下的烧蚀现象,得到了飞秒激光烧蚀现象的一般特征。烧蚀过程自材料内部气泡的产生开始,由气泡的发展最终导致。烧蚀材料可分成晶体区、熔化区和烧蚀区三部分,三个区域中原子的运动分别具有固体、液体和气体粒子的运动特征。观察到烧蚀过程中激光诱导应力波的产生与传播。熔化区的应力波是由原子的飞散引起的稀疏波。晶体区的应力波以声速传播。
系统地分析了激光参数和激光加载方式对烧蚀现象的影响。结果表明:对于能通量相同的短脉冲和长脉冲激光,短脉冲的烧蚀现象比长脉冲剧烈,热效应比长脉冲小;脉宽一定的情况下,随着激光能通量的增加,烧蚀现象加剧,存在一个能恰好使材料烧蚀的能通量,即烧蚀阈值;空间谱决定激光能量的空间分布,不同的空间分布将会产生不同的烧蚀现象;随着波长的增加,光子能量降低,相应激光在晶体硅中的吸收系数减小,烧蚀过程的热损伤和热影响区域大大增加。激光加载有长时间加载和瞬时加载两种方式,两者的区别在于激光能量沉积过程是否伴随系统的趋衡过程。瞬时加载和长时间加载对飞秒激光烧蚀现象的影响差别很小,因此可以用瞬时加载代替长时间加载以简化计算。但是瞬时加载在很大程度上夸大了皮秒激光的烧蚀现象,故不能用瞬时加载简化皮秒激光的作用过程,可以采用将长脉冲激光离散为飞秒激光的方法来简化计算。
In this paper, a molecular dynamics program has been written out to handle the femtosecond laser ablation of crystal silicon. The program is written in FORTRAN, parallelized by the mean of decomposing atoms, and optimized by the neighbor-list method to reduce the time expended in the force calculation. The results agree with the experimental and other numerical results, which indicate the molecular dynamics method is valuable for problems of laser ablation.
Comparative study of five empirical potentials for silicon was performed. Influences of bond angles and distances between atoms on the system energy were investigated. The results show SW potential is widely used because of its moderate cutoff radius, less parameters, simpler form and physical foundations. Thus, SW potential was chosen to describe the interactions between atoms in this paper. Equations of force calculation were educed based on SW potential.
Evolutions of initial systems to NVT and NVE ensembles besides the free evolution were simulated in order to debug the program and investigate the characteristics of the balancing processes. The FREE process can conserve the total energy well and drive the system to reach a reasonable equilibrious state quickly, so is usually used in the balancing process after a dynamics loading. The NVT process can keep the temperature constant and is suitable for the balancing process at a given temperature. Both of the two processes were used in the simulations of laser ablation.
A 3-D“x-section”model was developed to describe the deposition process of laser energy. Based on the 3-D“x-section”model, femtosecond laser ablations of Si(100) were simulated under two conditions which were total covering of the laser spot on the target surface and less laser spot than the target surface. Through the simulations, common characteristics of the femtosecond laser ablation were gotten. The ablation begins from the emergence of bubbles and is eventually induced by developments of the bubbles. The ablated material is composed of crystal, melted and ablated regions in which atoms move just like particles in solid, liquid and gas respectively. Moreover, two kinds of laser-induced stress waves were captured. One in the melted region is caused by the dispersion of surface atoms; the other in the crystal region propagates with the sound velocity.
Influences of laser parameters (such as pulse width, intensity, spatial spectrum and wave length) and loading styles on ablation phenomena were analyzed systemically. The results show: with the same energy flux, the short pulse produces more serious ablation phenomena than the long pulse; at a given pulse width, ablation becomes more and more serious with the increase of laser intensity, the least intensity with which the laser can ablate the target is called ablation threshold; the spatial spectrum determines the spatial distribution of laser energy, and will lead specific ablation phenomena; the laser with longer wave length has photons with lower energy and a larger thermal-affected region in the ablation process. There are two loading styles of the incident laser, one is long-time loading and the other is instantaneous loading. The difference between them is whether the deposition process of laser energy is accompanied with the balancing process of the system. The ablation phenomena of femtosecond lasers under the two loading styles are almost same, so the instantaneous loading can be used in femtosecond laser ablations to reduce the simulation time. However, it is not effective to the picoseoncd laser ablation because of magnifying the ablation phenomena. Decomposing the long laser pulse into femtosecond lasers may be used to simplify the simulation.
引文
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