The Thermal Damage Theoretical Research Of Solid Materials Under Femtosecond Pulse Laser Irradiations

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 metalThe 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 materialsMetals 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.