Study on the effect of focal position change on the expansion velocity and propagation mechanism of plasma generated by millisecond pulsed laser-induced fused silica

Lixue WANG (王立雪) and Jixing CAI (蔡繼興)

Jilin Key Laboratory of Solid-state Laser Technology and Application, School of Physics, Changchun University of Science and Technology, Changchun 130022, People’s Republic of China

Abstract In this work,by controlling the positional relationship between the target and the focal point,the surface damage, shock wave phenomenon and propagation mechanism involved in the plasma generation of fused silica by millisecond pulsed laser irradiation at different focal positions were studied.Laser energy is an important experimental variable.The dynamic process of plasma was detected by optical shadow method, and the influence of surface film damage on plasma propagation and the propagation mechanism at different focal positions were discussed.The study found that the plasma induced by the pulsed laser at the focus position within 0-20 μs exploded,the micro-droplets formed around 20 μs.At the same time,a shock wave is formed by the compressed air,the micro-droplets are compressed under the action of the shock wave recoil pressure, and the micro-droplets channel phenomenon is observed in the micro-droplets.The peak velocities of plasma and combustion wave appear earlier in the pre-focus position than in the post-focus position.This research provides a reference for the field of laser processing using fused silica as the substrate.

Keywords: relationship of different focal positions, plasma, combustion wave, shock wave,dynamic mechanism, damage morphology

1.Introduction

Fused silica has been widely used in various fields due to its good optical properties [1, 2].In the field of semiconductor manufacturing, fused silica is widely used as a substrate in photolithography [3-5].During the interaction between the laser and the fused silica, damage to the material is unavoidable, and once the damage occurs, it will cause the formation of plasma.Plasma absorbs laser energy to form lasersupported absorption waves [6, 7].When the speed of the absorption wave exceeds the speed of sound, it is called a laser-supported detonation wave[8,9],and when the speed is lower than the speed of sound, it is called a laser-supported combustion wave [10, 11].This work mainly studies the influence of different focal position relationship on the propagation law of plasma and combustion wave.

The material damage properties of laser-induced fused silica have been extensively reported [12-14].V P Efremov et al studied the dynamic process inside fused silica due to laser action[15].Wei Zhang et al studied the evolution law of laser-supported absorption waves induced by millisecond lasers [16].Aurelia Alonso-Medina ablated lead samples and studied the expansion kinetics of the resulting lead plasma[17].Haley Kerrigan et al studied the laser-plasma interaction during the superposition of femtosecond and nanosecond pulses ablating solid materials [18].Jixing Cai et al used the optical shadow method to study the dynamics of the plasma and the expansion velocity of the combustion wave[19].The above related works are mainly carried out at fixed focal positions.There are differences in laser-induced plasma damage and propagation phenomena at different focal positions.Laser-supported absorption and shock waves are observed throughout the physical process in studies of plasma-induced plasma generation in combination lasers[20-23].Jingyi Li et al studied the phenomenon of absorption wave induced by combined pulses in single crystal silicon,and found the phenomenon of double wave [24].Zefeng Yang et al studied the interaction between aluminum plasma and shock induced by double short pulses [25].The above phenomenon still occurs when the combined laser is replaced by a millisecond pulsed laser,provided that the material is on the beam waist of the laser focus.

Laser-induced breakdown spectroscopy is an important research direction, and related research has been reported[26-29].This paper only briefly introduces the feasibility of subsequent LIBS studies at different focal positions in the conclusion.

In this paper, the damage dynamics of fused silica at different focal positions are studied through experiments and simulations.The damage morphology and propagation mechanism involved in the physical process of laser-induced plasma and combustion wave are discussed, and a comparative analysis is carried out.The shock wave phenomenon generated when the target is in the focal position is analyzed.

2.Numerical model and experiment

2.1.Numerical model

Figure 1 shows the schematic diagram of the physical model of laser-induced plasma.The initial plasma is caused by laser ablation and generated on the surface of the target,propagates in the opposite direction of the laser under the action of the laser.

Figure 1.Initial plasma generation area.

In the simulation process, it needs to be clear: (1) the propagation speed of the plasma is much lower than the speed of sound, and it can be regarded as a subsonic laminar flow.(2)The time span of plasma generation is very small,there is no heat exchange with the outside world, and the interior is locally thermally balanced.

In the whole physical process, the total mass of matter remains unchanged,which satisfies the law of conservation of mass, the equation of conservation of momentum, and the equation of conservation of energy:

In the formula:uis the fluid velocity,ρis the density,pis the pressure,μis the material viscosity,Cpis the specific heat capacity,λis the thermal conductivity,QLaseris the laser heat source,QLossis the heat loss source,δ(φ) represents the level set function.The level set function can be defined as:

The mass loss on the surface of the fused silica material will provide a mass source for the generation of plasma, and the quantity that affects the mass loss is the mass mobility[30]:

In the formula:βis the diffusion coefficient, which is assumed to be 1 at the beginning of evaporation, 0 after stabilization,kBis the Boltzmann constant, andPsat(T) is the saturated vapor pressure of the target steam,the expression is[31]:

In the formula:Pambis the atmospheric pressure,Lvis the latent heat of evaporation,Tvis the evaporation temperature,MSiO2and is the molar mass of fused silica.

When the laser is focused, diffraction inevitably occurs near the focus, andξis given by the Fraunhofer diffraction formula:

In the formula:fis the focal length,ais the light transmission radius of the lens, andUis the dimensionless coordinate of the laser propagation direction

zis the distance from the surface of the target material to the focal point, if the pre-focus position is positive and the postfocus position is negative,rqis the radius of the spot before the focus,rhis the radius of the spot after the focus,θis the focusing numerical aperture of 1 2:

In the energy conservation equation,QLaseras the main term of the laser source, it can be described by the Gaussian function related to time and temperature:

whereQL,QRare the power density of the heat source in the plasma, the plasma radiation transmission energy,Jis the laser intensity,Ksis the plasma inverse bremsstrahlung absorption coefficient,χe=is the equilibrium electron density,peis the electron pressure,Um,Ueq,mare the volume absorption coefficient, medium thermal radiation energy density and ideal black body radiation density of the first group of radiation, respectively, andNmis the number of groups of thermal radiation in the multi-group diffusion approximation.

2.2.Experiment

In terms of experimental research, we use the optical shadow method to detect the phenomenon of the propagation process of the plasma combustion wave in real time.The construction of the experimental optical path is shown in figure 2.

Figure 2.Schematic diagram of the experimental setup.(a) Pre-focus position, (b) focus position, (c) post-focus position.

The entire combustion wave detection system consists of a laser energy output part, a plasma detection part, and the two parts can be synchronized together by a synchronous detection system.The laser energy output system consists of a high-energy millisecond pulse laser (energy range output:20-100 J adjustable, repetition frequency 10 Hz), focusing lens (focal length 500 nm), spectroscope, energy meter; the synchronous detection system is connected in series by the DG645 delay trigger.The detection system consists of a 532 nm green laser(green light source in the detection part),a laser beam expander (to expand the 532 nm laser beam), a focusing lens 2 (to focus the expanded parallel laser beam),and a high-speed camera(acquisition of dynamic processes of plasma and combustion waves).The laser parameters involved in the study are shown in table 1.

Figure 3.Simulation results of laser-induced combustion wave when the laser energy is 2.548 × 103 J cm-2.(a)Pre-focus results,(b)postfocus results.

Table 1.Laser parameters.

3.Research results and analysis

In order to better analyze the propagation characteristics and mechanisms of plasma and combustion waves.It is necessary to analyze the propagation process of plasma and combustion wave.The velocity fields of plasma and combustion waves can be calculated from equation (14)

where the expanding plasma front is detected at a distanceL(t)at timet,andΔtis usually a small time interval,the unit we use here is μs.

3.1.Flow field simulation at pre- and post-focus positions

In the simulation research,the laser energy we choose is 20 J,the pulse width is 1 ms, and the laser radius is 0.5 mm.The simulation results of the flow field are as follows:

Figure 3 shows the evolution of the combustion wave velocity with time under the condition that the laser energy is 20 J and the pulse width is 1 ms.In the time range of 0-120 μs, the speed of the combustion wave suddenly increased and the peak speed appeared,and then the expansion speed of the combustion wave decreased abruptly and continued to expand outward at a constant speed around 300 μs.When the velocity reaches the maximum value, the plasma formed by the ionization of the steam is saturated, and the thermal radiation of the plasma is greater than the absorption of the laser energy.Due to the difference between the spatial distribution of laser energy in the pre-focus position and the energy distribution in the post-focus position, the maximum velocity of the combustion wave at the post-focal position is delayed.It can be seen from figure 4 that as the pulse width increases, the peak velocity of the combustion wave appears later, and the peak velocity decreases gradually.

3.2.Flow field experiments at pre- and post-focus positions

When the laser pulse width is 1 ms, the plasma and combustion wave flow field distributions at the 2.548 ×103J cm-2,3.145 × 103J cm-2pre-focus position are shown in figure 5.The distributions of plasma and combustion wave flow field at 2.105 × 103J cm-2, 2.652 × 103J cm-2postposition are shown in figure 6.

The speed trend can be seen from figures 5 and 6.When the laser irradiates the surface of the target, the surface film layer is first exposed to the energy of the laser and undergoes a rapid phase transition.The mass lost by the film provides the primary mass source for the plasma.The plasma generated at about 20 μs is mainly generated by the ionization of the vaporized film layer,and is accompanied by a plasma flash in the visible light band.At this time, the combustion wave supported by the laser is ignited, and the expansion speed increases rapidly.A thin film with a thickness of the nm order,which is rapidly phase-transformed under the action of a millisecond pulsed laser to generate a plasma(the time span of which is in the order of μs).After the expansion rate reaches the maximum value, the film layer on the surface of the fused silica material has been completely vaporized and partially ionized into plasma.At this time,the surface film layer of the material has been ablated by the laser, and the internal energy of the plasma continues to be converted into the kinetic energy of the combustion wave,which causes a sudden drop in the speed of the combustion wave,and the expansion speed of the combustion wave begins to drop rapidly to about 5 m s-1.Due to the different spatial distributions of laser energy in the pre- and post-focus positions, the peak velocity of the combustion wave at the post-focal position is different.When the laser energy is 2.548 × 103J cm-2, the back surface of the material at the post-focal position does not have a combustion wave phenomenon.

Figure 4.Simulation results of the variation of speed with pulse width when the laser energy density is 2.548 × 103 J cm-2.(a)Pulse width 1.5 ms, (b) pulse width 2.0 ms.

Figure 5.Plasma velocity field at the pre-focus position.(a) 2.548 × 103 J cm-2, (b) 3.145 × 103 J cm-2.

When the high-energy millisecond pulse laser irradiates the target surface,the laser irradiation area on the target surface will melt,vaporize,etc.At this time,the target vapor formed by the laser irradiation will absorb the incident laser energy,so that the material surface vapor ionization forms high temperature and high density plasma.When the millisecond pulsed laser irradiates the surface of the fused silica target, there are two main mechanisms for the vapor on the surface of the material to absorb the laser energy to form a plasma: one is multiphoton absorption, and the other is avalanche ionization.

Multiphoton absorption is a nonlinear optical phenomenon generated during the interaction between strong laser light and medium.That is, when a strong laser acts on a target, a molecule of the target may absorb several or more photons at the same time.This process can be considered as multiple photons absorbed by a molecule of the target at the same time,then passes through an imaginary virtual intermediate state,and finally transitioning to the excited state.When the total energy of photons absorbed by the molecule is greater than the ionization potential of the atom itself, it ionizes itself.

Another mechanism is avalanche ionization, in which free electrons in the focal region can generate accelerated motion in the optical field by inverse bremsstrahlung absorption of photon energy.The accelerated electron collides with other atoms and ionizes it to form two free electrons of low kinetic energy.The newly generated free electrons absorb the incident photons and repeat the above process, which eventually leads to a sharp increase in the density of free electrons and forms avalanche ionization.This process mainly depends on the competition between the gain and loss of electron number and electron energy.Avalanche breakdown occurs when the electron density in the focal region exceeds the critical density required to form the plasma.

Figure 6.Plasma velocity field at the post-focus position.(a) 2.105 × 103 J cm-2, (b) 2.652 × 103 J cm-2.

Figure 7.260-460 μs combustion wave flow field distribution at 3.145 × 103 J cm-2.

Figure 8.Comparison of the expansion state of the combustion wave between the experiment (a) and the simulation (b) at 100 μs.

In this paragraph,the physical mechanism of laser-induced plasma will be discussed in more depth in combination with the above-mentioned laser plasma generation mechanism and physical process.The first is that in the 0-20 μs stage,the target vapor generates more free electrons under the action of the multiphoton absorption mechanism, and the region where the initial plasma is generated can be seen in the high-speed camera at this time.Then in about 0-60 μs, the generated plasma absorbs the laser energy through inverse bremsstrahlung[32]to become high-energy electrons, and rapidly propagates outward to form a combustion wave.When the velocity reaches the peak, the surface film layer is completely lost, and the plasma loses its mass source.Under the combined action of heat conduction and convection, the plasma gradually cools down, and the expansion velocity of the combustion wave drops rapidly.

In the data analysis of the experiment, in order to better discuss the trend presented by the overall data,we took 10 ms as the data collection point.In this energy range, the main source of mass for plasma formation is mainly provided by the mass lost from the surface film, and the surface film thickness of the target we use is the same(the film thickness will fluctuate by a few microns).Due to the presence of the film (the phenomenon described in the paper was not observed when the fused silica substrate was damaged), there is a difference between the experimental results of non-coated materials(such as silicon [24]) in the trend of velocity over time.

In figure 7, the expansion velocity of the combustion wave fluctuates between 200 and 500 μs,which is due to the short-term ionization of a small part of the target vapor under the action of the laser after the plasma is cooled,resulting in a brief increase in the velocity of the combustion wave, which is reflected in a smaller peak fluctuation on the curve of the velocity change.As the combustion wave expands farther and farther, the amount of target vapor that can be ionized becomes less and less, and the expansion speed of the combustion wave gradually becomes stable.Figure 8 shows the comparison between the simulation and experimental results at the time of 100 μs, when the laser energy is 3.145 × 103J cm-2.

Figure 9.Surface morphology damage of pre-focus with laser energies of 2.548 × 103 J cm-2 (a), 3.145 × 103 J cm-2 (b),3.821 × 103 J cm-2 (c).

Figure 10.Surface morphology damage of post-focus with laser energies of 2.105 × 103 J cm-2 (a), 2.652 × 103 J cm-2(b), 3.161 × 103 J cm-2 (c).

Figure 11.Surface morphology damage of focus with laser energies of 1.194 × 104 J cm-2 (a), 1.592 × 104 J cm-2(b), 1.990 × 104 J cm-2 (c).

3.3.Surface damage experiment

Damage experiments at different focal positions were carried out under the condition of 1 ms pulse width, and the surface damage morphology results are as follows.

Figures 9 and 10 show the front and back surface damage morphologies of fused silica induced by millisecond pulsed laser.From the results of surface damage morphology, there is no large-area heat-affected zone outside the damaged area,the boundary between the damaged area and the undamaged area is obvious, and there are obvious ablation marks at the damaged boundary.When the laser energy wave forms a Gaussian distribution of millisecond pulsed laser irradiation on the surface of fused silica, the antireflection coating layer on the surface of the fused silica inherently absorbs the energy of the laser light.In the initial stage of action,the film on the surface of the material is rapidly ablated in the range of μs,and the damage area is proportional to the laser energy.

Figure 11 shows the surface damage experiment at the focal position.Comparing the damage morphology on the surface of the pre-focus position, it can be seen that the damage morphology of the focus group has obvious laser ablation zone and heat-affected zone, and a darker central ablation zone appears in the middle of the ablation zone.Cracks appeared at the interface of the heat-affected zone and the laser ablation zone, which were believed to be caused by thermal stress.The focal point has a smaller irradiation area under the same laser energy,so it has a higher energy density,resulting in the formation of a central ablation region caused by a large amount of laser accumulation in the central region of the damage morphology.When the laser focus is located on the surface of the material, the energy and heat are accumulated in a fault, so that the irradiation center radiates energy to the surrounding area,resulting in the appearance of the laser ablation area,and the heat-affected zone is caused by the secondary ablation of the material surface by the plasma.

Figure 12.Plasma and shock wave flow field at the focus position with laser energies of 1.194 × 104 J cm-2 (a), 1.592 × 104 J cm-2 (b),1.990 × 104 J cm-2 (c).

3.4.Flow field experiment at focus position

From the optical shadow map of the laser-induced plasma at the focal position under different laser energies in figure 12,it can be seen that its dynamic behavior is different from the kinetic experimental results of the pre-focus group.In the range of 0-30 μs,the plasma expansion speed rapidly reaches its peak value.At this time,the plasma has completely cooled to form droplets.At the same time, a strong shock wave is generated.The experimental results of the front and post-focal groups do not show strong shock waves.At 20 μs, a shock wave appeared above the plasma and rapidly propagated outward.At 80 μs, the shock wave had already exceeded the field of view of the high-speed camera.

When the laser focus is irradiated to the surface of fused silica, a large amount of laser energy is gathered at the laser focus, so that the laser energy can only be absorbed near the focus of the material surface,forming a high temperature and high-pressure area that is insulated from the outside world.Due to the high temperature and high pressure in this area,the particles in this region are fully ionized by the avalanche ionization mechanism, and the generation of a large amount of plasma will cause its explosive overflow, and the compressed air will form a shock wave that propagates rapidly at the speed of supersonic speed.It can be seen from the figure that at 20 μs,the plasma has exploded and compressed air to generate shock waves.Due to the explosive overflow of the plasma, the cooling rate of the plasma is much greater than that of the plasma pro- and post-focus position.The rapidly cooling plasma forms micro-droplets, which cause a sudden drop in velocity due to greatly reduced absorption of laser energy by the micro-droplets.

In figure 12(c),the plasma has mostly cooled by 30 μs,at which point it begins to be compressed under the effect of shock wave recoil pressure [33].The time came to 40 μs because the plasma was completely cooled and the laser was no longer absorbed strongly (80-100 μs), and at the same time,as the shock wave recoiled,a clear channel of laser light micro-droplets in the droplet was observed.

4.Conclusion

In this paper,the plasma and combustion waves generated by fused silica induced by millisecond pulsed laser at different focal positions are studied,and the propagation mechanism of laser-induced plasma and combustion waves is obtained.The mechanism of different focus positions is as follows.

When the front surface of the target is in the pre- and post-focal positions, the target vapor generates more free electrons under the action of the multiphoton absorption mechanism.Under the action of inverse bremsstrahlung, the free electrons collide with each other and ionize into plasma,and the combustion wave is formed under the continuous action of the reverse bremsstrahlung mechanism.

When the front surface of the target is at the focal position, the laser energy density is large enough.At this time, avalanche ionization is the main mechanism of plasma formation.Under the action of the avalanche ionization mechanism, a large amount of plasma overflows in a short time, and the compressed air forms a shock wave phenomenon.

The damage of the surface film layer provides the main mass source for the plasma.The plasma rapidly forms a combustion wave under the action of the subsequent laser, a physical process occurs on the microsecond scale.The mass loss of the surface film affects the entire combustion wave propagation process.The peak expansion velocity of the combustion wave in front of the coke occurs at about 60 μs,and when the laser energy density is 2.548 × 103J cm-2and 3.145 × 103J cm-2, the peak velocities are 19.7 m s-1and 28.3 m s-1, respectively; when the laser energy density is 2.105 × 103J cm-2and 2.652 × 103J cm-2, the peak expansion velocity of the combustion wave at the post-focus position appears around 110 μs, and the peak velocities are 18 m s-1and 22.1 m s-1, respectively.

The research results of the focus group are obviously different.The high energy density at the focus position causes the explosive overflow of the plasma,and the compressed air forms a shock wave.After 40 μs, the plasma has been completely cooled due to the explosive overflow, and the formed droplets no longer strongly absorb the laser energy.The droplets are compressed under the action of shock recoil pressure, and the phenomenon of micro-droplets channels appears.

Compared with the results before and after the coke,there are obvious differences in the damage test results at the focal position.The main reason is that the surface damages before and after the coke are caused by direct laser ablation;the surface damage at the focal position is caused by the excessive accumulated energy in the central ablation area and the secondary ablation of the material surface by the plasma.This work expands the field of laser-induced plasma, and provides the corresponding simulation and experimental basis, which has important reference significance for the research on the field of laser processing with fused silica as the substrate.

As an important elemental analysis technique, the development of laser-induced breakdown spectroscopy is very important to natural sciences.In the elemental analysis of long-distance matter, it is necessary to consider how the element spectrum changes at different focal positions.This is the insufficiency of this paper, and related research will be carried out in the follow-up work.

Acknowledgments

This study is supported by Natural Science Foundation of Jilin Province, China (No.20220101032JC).We really appreciate Jilin Key Laboratory of Solid-state Laser Technology and Application for supporting our experiment.