Specific numerical simulation method for femtosecond laser ablation removal

Abstract

The invention discloses an elephant-only numerical simulation method for femtosecond laser ablation removal, and belongs to the technical field of femtosecond laser processing. The implementation method comprises the following steps of: dividing the surface of a target material into nodes at equal intervals along the horizontal direction by adopting a discretization numerical method; on the surface of the target material, under single pulse irradiation with the position (x0, y0) as the center, the incident flux at the given point is calculated according to an incident flux formula; describing the surface topography change and incubation effect caused by laser irradiation by using a manifestation method; according to the included angle between the laser incidence direction and the local normal vector, net ablation flux is obtained through calculation, and numerical simulation of the ablation removal process is carried out; and data cycle calibration is performed based on experiments, a material removal coefficient xi is obtained, displacement of any point on the surface of the material is calculated, and surface topography simulation prediction of femtosecond laser single pulse or multi-pulse machining is realized. According to the method, the numerical simulation result of the machining process can be quickly generated according to different laser flux parameters, and the experiment cost is remarkably reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of femtosecond laser processing, and relates to a numerical simulation and prediction method for simulating a femtosecond laser ablation and removal target material processing scene. Background Art

[0002] In materials science, dielectric materials have become an indispensable component in many technical fields such as electronics, optics, and energy due to their unique electrical insulation properties and ability to polarize under the action of an electric field, and have important applications in many industries. However, the processing of dielectric materials often faces challenges. For example, for hard and brittle materials such as fused quartz, traditional mechanical processing methods are prone to cause cracks and fractures in the material; for materials such as resin materials that are thermally sensitive and chemically unstable, the large amount of heat generated by traditional processing methods will cause a decrease in processing quality. The emergence of femtosecond laser technology provides a new solution for the precision processing of dielectric materials. The ultrashort pulse and high peak power characteristics of femtosecond lasers enable high-precision micron-level processing of materials in extremely small heat-affected zones. This processing method is particularly important for heat-sensitive materials such as fused quartz and resins, because it effectively reduces deformation and damage caused by thermal stress. In addition, the high positioning accuracy of femtosecond laser processing makes it particularly suitable for the manufacture of microstructures on the surface of target materials.

[0003] Although femtosecond laser processing technology has made significant progress in theory and practice, the precise control of material removal in multiple pulse processing is still a challenge, so numerical simulation is particularly important. Existing physical models such as the two-temperature equation and plasma model can accurately describe the physical principles of the interaction between femtosecond laser and dielectric materials, but when dealing with multiple pulse processing, the model is too complex and the calculation is large and slow, which leads to the problem of bloated models, high time and resource costs in the method of simulating femtosecond laser ablation removal using these models. The present invention develops a phenomenological numerical simulation method to accurately simulate the surface morphology changes of dielectric materials after femtosecond laser irradiation. The phenomenological method collects and analyzes experimental data, simplifies and assumes to achieve the description and statistical analysis of experimental results. This method will consider the influence of ablation surface morphology and hatching effect on material removal, and is suitable for single pulse and multiple pulse processing scenarios. Through this method, the cross-sectional profile of the ablation pit under different laser parameters, as well as the key parameters such as the radius, depth and volume of the ablation pit can be accurately predicted. In addition, the invention can also simulate the morphology of microgrooves and three-dimensional microstructures produced by multiple laser pulse processing, providing effective guidance for parameter selection and experimental design of high-precision micromachining. Summary of the invention

[0004] In order to solve the problem that the traditional modeling process for simulating femtosecond laser processing is too complicated, the model is bloated, the amount of calculation is large, and the speed is slow, which leads to high time and resource costs for actual deployment and application, the purpose of the present invention is to provide a phenomenological numerical simulation method for femtosecond laser processing. The phenomenological method is used to efficiently and accurately simulate the surface morphology of single or multiple pulses of femtosecond laser processing, thereby realizing the numerical simulation of femtosecond laser micro-nano processing. The present invention combines the changes in the surface morphology of fused quartz and the influence of the incubation effect prediction on subsequent laser pulse processing. The key parameters of the present invention are determined by comparison with experimental data, so that the present invention is suitable for simulating the cross-sectional profile of laser pulse ablation under different energy densities, and predicting the depth and radius of the pit. The present invention can also be used to simulate microgrooves and three-dimensional microstructures formed by multi-pulse ablation, which helps to improve the accuracy and efficiency of femtosecond laser processing parameter selection. The key parameter is the material removal thickness caused by unit laser energy density,

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The present invention discloses a phenomenological numerical simulation method for femtosecond laser ablation removal, comprising the following steps:

[0007] Step 1: Use a discretized numerical method to divide the target surface into equally spaced nodes in the horizontal direction. The node coordinates (x, y, z) are used to represent the coordinates of the material point and the laser light source. Under a single pulse irradiation centered at position (x0, y0) on the target surface, the incident flux at a given point is calculated by the following formula:

[0008]

[0009] Where J is the incident laser flux. ω0 is 1 / e of the laser spot. 2 Nominal radius, that is, the laser intensity decays to 1 / e of the central peak intensity 2 The corresponding radius value. When simulating a single laser pulse ablation, (x0, y0) is the center of the single laser pulse, which is a set of fixed coordinate values; when simulating multiple laser pulse ablation, (x0, y0) is the center of multiple laser pulses, which is a set of independent coordinate values ​​that may or may not overlap (when the centers of multiple laser pulses overlap, multiple pulses are used to punch holes at fixed points, and when the centers of multiple laser pulses do not overlap, microgrooves or other microstructures are processed on the target surface using a pulse sequence). For multiple laser pulse ablation, the incident laser flux at a certain point is the sum of the fluxes of all pulses at that point.

[0010] In formula (1), J max is the peak flux of the laser pulse, and the calculation formula is

[0011]

[0012] E is the energy of a single pulse.

[0013] Step 2: Simulate the interaction between femtosecond laser and target material, and use phenomenological method to describe the surface morphology changes and incubation effects caused by laser irradiation:

[0014]

[0015] Initial ablation threshold J th,1 , stable ablation threshold J th,∞ , laser spot radius ω0; N refers to the number of pulses irradiated to the material; the absorption coefficient of the material is represented by α, and Δα is the absorption coefficient from the initial value α0 to the maximum value α max β and γ are fitting coefficients.

[0016] Step 3: Numerical simulation of the ablation removal process; according to the laser incident direction and the local normal vector The angle α between ag The net ablation flux J is calculated as net

[0017] J ab =Jcosα ag (2)

[0018]

[0019] Where J is the incident laser flux, J ab is the laser flux absorbed by the target.

[0020] Step 4: Perform data cycle calibration according to formula (5), obtain the material removal coefficient ξ, and calculate the displacement (Δr, Δz) of any point (r, z) on the material surface.

[0021]

[0022] where n r Represents the unit normal vector in the radial direction, n z represents the unit normal vector in the vertical direction of laser incidence, and r is the radial direction.

[0023] Step 5. Save Δz to a CSV file. When N=1, the z obtained in step 4 is the surface morphology processed by a single pulse of a femtosecond laser, and the simulation of a single pulse is completed; when N>1, return to step 1 to step 3 for iterative simulation, and the z obtained in step 4 is the surface morphology processed by multiple pulses of a femtosecond laser, completing the simulation of multiple pulse ablation processes, thereby simulating the femtosecond laser ablation removal results corresponding to different laser processing processes.

[0024] Beneficial effects:

[0025] 1. The present invention discloses a phenomenological numerical simulation method for femtosecond laser ablation removal, which can quickly generate numerical simulation results of the processing process for different laser flux parameters, significantly reducing the time and cost required for experimental trial and error.

[0026] 2. The present invention discloses a phenomenological numerical simulation method for femtosecond laser ablation removal, which adopts an incubation model to describe the phenomenon that the ablation threshold gradually decreases with the increase of the number of pulses. By simulating the incubation effect and the material removal process, it can avoid the uncertainties in the experiment and better realize the accurate description of the incubation effect in the femtosecond laser processing process.

[0027] 3. The present invention discloses a phenomenological numerical simulation method for femtosecond laser ablation removal, which uses a phenomenological method to describe the influence of laser energy removal on a straight or inclined target surface and the hatching effect on the processing effect. It can not only characterize the phenomenon and trend of the processing results, but also improve the accuracy and efficiency of femtosecond laser ablation removal simulation.

[0028] 4. The present invention discloses a phenomenological numerical simulation method for femtosecond laser ablation removal, which comprehensively considers the changes in surface morphology caused by coupling with previous pulses and the influence of incubation effect on subsequent pulses, and realizes numerical simulation of laser ablation morphology and threshold. It is suitable for simulating the cross-sectional profile of laser pulse ablation under different energy densities, and predicting the depth and radius of pits, and then used to simulate microgrooves and three-dimensional microstructures formed by multi-pulse ablation, which helps to improve the accuracy and efficiency of femtosecond laser processing parameter selection and reduce production time and labor costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Genetic algorithm operation flow chart;

[0030] Figure 2 A flow chart of a phenomenological numerical simulation method for femtosecond laser ablation removal disclosed in the present invention;

[0031] Figure 3 (a) Laser flux is 6.2 J / cm 2 (a) The profile of the ablation crater in the femtosecond laser processing experiment; (b) The comparison between the cross-sectional profile obtained by simulation and the experimental cross-sectional profile;

[0032] Figure 4 The simulated laser flux is 6.2 J / cm 2 Cross-sectional profile of multiple pulse ablation of static laser spot;

[0033] Figure 5 Oblique views of the target surface profile obtained by laser scanning (a) along the y-axis and (b) at a 45° angle to the x-axis and y-axis;

[0034] Figure 6 Oblique view of the target surface profile obtained by (a) laser scanning of two intersecting microgrooves and (b) the "field" - shaped grid obtained by processing six groups of pulse sequences. Detailed implementation manners

[0035] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0036] Embodiment 1

[0037] As Figure 2 shown, it is a flow chart of a phenomenological numerical simulation method for femtosecond laser ablation removal. The embodiments of the present invention require: under specified femtosecond laser parameter conditions, that is, the laser wavelength is 800 nm, the laser pulse width is 120 fs, the incident laser fluence is 6.2 J / cm 2 , and the 1 / e 2 nominal radius of the laser spot is 6 μm. In the exemplary material, that is, a single - side polished fused silica wafer with dimensions of 10 mm × 10 mm × 1 mm, simulate and predict the ablation removal induced by femtosecond laser, and output the cross - sectional profile, ablation pit depth and radius after ablation to characterize the corresponding process.

[0038] As Figure 2 shown, a phenomenological numerical simulation method for femtosecond laser ablation removal disclosed in this embodiment is specifically implemented as follows:

[0039] Step 1: Adopt a discretized numerical method. The target surface is divided into equally - spaced nodes along the horizontal direction, and the node coordinates (x, y, z) are used to represent the coordinates of material points and the laser light source. Specifically, the target surface is divided into 3000 equally - spaced nodes along the horizontal direction to simulate a 30 - μm - long region. The interval of each simulation node is 10 nm.

[0040] Under the irradiation of a single pulse centered at the position (x0, y0) on the target surface, the incident fluence at a given point can be calculated by the following formula:

[0041]

[0042] where J is the incident laser fluence. ω0 is the 1 / e 2 nominal radius of the laser spot, that is, the laser intensity decays to 1 / e 2The corresponding radius value. When simulating a single laser pulse ablation, (x0, y0) is the center of the single laser pulse, which is a set of fixed coordinate values; when simulating multiple laser pulse ablation, (x0, y0) is the center of multiple laser pulses, which is a set of independent coordinate values ​​that may or may not overlap (when they overlap, multiple pulses are used to punch holes at fixed points, and when they do not overlap, microgrooves or other microstructures are processed on the target surface using a pulse sequence). For multiple laser pulse ablation, the incident laser flux at a point is the sum of the fluxes of all pulses at that point.

[0043] In formula (1), J max is the peak flux of the laser pulse, and the calculation formula is

[0044]

[0045] E is the energy of a single pulse.

[0046] Step 2: Simulate the interaction between the femtosecond laser and the target. The incubation effect in dielectric materials is caused by the accumulation of laser-induced defects, such as color centers and Frenkel defects. The incubation effect makes the material more susceptible to ablation, which in turn leads to a reduction in the ablation threshold. In order to accurately simulate this effect, the present invention adopts a generic incubation model, which can more accurately describe the trend of the ablation threshold gradually decreasing with the increase in the number of pulses compared to the traditional exponential incubation model:

[0047]

[0048] Initial ablation threshold J th,1 , stable ablation threshold J th,∞ , laser spot radius ω0; N refers to the number of pulses irradiated to the material; the absorption coefficient of the material is represented by α, and Δα is the absorption coefficient from the initial value α0 to the maximum value α max The change of; β and γ are fitting coefficients. The material property of fused silica is the initial ablation threshold J th,1 =3.7J / cm 2 , stable ablation threshold J th,∞ =0.74J / cm 2 The undetermined parameters of the general hatching model were fitted by genetic algorithm. The calculation parameters of the genetic algorithm were configured as follows: the population size was set to 100 individuals, the crossover probability was set to 80%, the mutation probability was set to 0.5%, the convergence accuracy of the algorithm was set to 1e-6, and the maximum number of iterations was set to 2000 rounds. In this embodiment, the values ​​of Δα / α, β and γ calculated by the algorithm were 0.533, 0.00190 cm, respectively. 2 / J and 0.0544cm2 / J.

[0049] Step 3: Numerical simulation of the ablation removal process. When the femtosecond laser pulse acts on the surface of the target material, only when the laser flux exceeds the ablation threshold J th,N In the present invention, the portion of the laser flux exceeding the ablation threshold is defined as the net ablation flux J net In the simulation of multi-pulse ablation, the influence of subsequent pulses on the inclined ablation crater surface is particularly considered. The influence will cause the laser energy J absorbed by the material surface to ab The reduction depends on the laser incident direction and the local normal vector The angle α between ag Specifically, the reduction in absorbed energy is related to the angle α ag The cosine value of cosα ag is proportional to

[0050] J ab =Jcosα ag (2)

[0051]

[0052] Where J is the incident laser flux, J ab is the laser flux absorbed by the target. In order to obtain the partial derivative of the surface morphology and Usually, it is necessary to differentiate the surface height data. In the present invention, since the calculation is performed on discrete nodes, a numerical differentiation method is adopted, and numerical derivatives between adjacent nodes are used for approximation.

[0053] Step 4: Calculate the displacement of any point on the material surface based on the material removal coefficient ξ. Based on the assumption that the local ablation depth of the material is proportional to the local net ablation flux, a material removal coefficient ξ is introduced to be determined. This coefficient is used to quantify the unit net ablation flux along the local normal vector. Therefore, after a single pulse ablation, the displacement (Δr, Δz) of any point (r, z) on the target surface is expressed as

[0054]

[0055] where n r Represents the unit normal vector in the radial direction, n z represents the unit normal vector in the vertical direction of laser incidence, and r is the radial direction.

[0056] The material removal coefficient ξ is cyclically calibrated. First, ξ is randomly initialized to 10.00nm / (J / cm 2) to 50.00nm / (J / cm 2 ), which is related to the parameters of the laser and can be obtained based on experience and experiments. Set the coefficient iteration step to 0.1nm / (J / cm 2 ), import the experimental data, and then start iterative calculation. exp With z sim The absolute deviation between z When the minimum value is not reached, ξ is updated by a step size, and the update direction is such that δ z The cycle iterates until δ z In this embodiment, the value of ξ is finally updated to 22.45nm / (J / cm 2 ), which means that a laser pulse per unit net flux can ablate to a depth of 22.45nm.

[0057] Step 5. Save Δz to a CSV file. When N=1, the simulation of a single pulse is completed; when N>1, the simulation of multiple pulse ablation processes is completed, thereby simulating different laser processing techniques and application scenarios.

[0058] When N = 1, the simulation results can be visualized using Python open source graphics. Figure 3 , where the solid line Sim. in Figure (b) represents the ablation profile simulated by the phenomenological method of the present invention, the dashed line Ave.Exp. represents the statistical average of multiple sets of experimental ablation pit profile data, and the dotted line Sing.Exp. represents the ablation pit profile obtained from a single experiment. After extracting and processing the data, it is obtained that the laser flux in this embodiment is 6.2 J / cm 2 The radius of the single pulse ablation crater is 4.39 μm, the depth is 183.26 nm, and the volume is 5.71 μm 3 The entire single pulse ablation simulation takes only about 2 seconds, compared to more than 10 minutes for the single pulse ablation examples of the two-temperature equation and plasma model.

[0059] When N>1, the scene of femtosecond laser multiple pulse ablation is simulated. Keeping the center coordinates of the laser spot unchanged, the simulated single-point multiple pulse ablation results are as follows: Figure 4 As shown, 1, 2, 3, 5, 8, and 10 pulses are used for punching operations. The center of the laser spot is moved at a constant rate. In this embodiment, Figure 5The top view and auxiliary view of the microgroove profile on the target surface obtained by laser pulse sequence ablation along the y-axis direction and at a 45° angle to both the x-axis and the y-axis are shown. The length of the microgroove is 12 μm and is processed by 30 pulses with a spatial interval of 0.4 μm. The ablation depth is distinguished by color. Furthermore, in addition to microgrooves, the present invention can also be used to simulate more complex three-dimensional cross microstructures. Figure 6 (a) shows two spatially intersecting microgrooves machined parallel to the x-axis and y-axis, and (b) shows an oblique view of a grid-shaped microstructure machined by a sequence of six pulses parallel to the x-axis and y-axis. Each edge of the machined pattern is 21 μm long and is distributed with 30 evenly spaced pulses.

[0060] The above embodiments are only used to illustrate rather than limit the method solutions of the present invention. Any equivalent replacement or change of the technical solutions and inventive concepts of the present invention should be included in the protection scope of the present invention.

Claims

1. A phenomenological numerical simulation method for femtosecond laser ablation removal, characterized in that: The following steps are included: Step 1: Use a discretized numerical method to divide the target surface into equally spaced nodes in the horizontal direction. The node coordinates (x, y, z) are used to represent the coordinates of the material point and the laser light source. Under a single pulse irradiation centered at position (x0, y0) on the target surface, the incident flux at a given point is calculated by the following formula: Where J is the incident laser flux; ω0 is 1 / e of the laser spot 2 Nominal radius, that is, the laser intensity decays to 1 / e of the central peak intensity 2 The corresponding radius value; when simulating a single laser pulse ablation, (x0, y0) is the center of the single laser pulse, which is a set of fixed coordinate values; when simulating multiple laser pulse ablation, (x0, y0) is the center of multiple laser pulses, which is a set of independent coordinate values; for multiple laser pulse ablation, the incident laser flux at a certain point is the sum of the flux of all pulses at that point; In formula (1), J max is the peak flux of the laser pulse, and the calculation formula is E is the energy of a single pulse; Step 2: Simulate the interaction between femtosecond laser and target material, and use phenomenological method to describe the surface morphology changes and incubation effects caused by laser irradiation: Initial ablation threshold J th,1 , stable ablation threshold J th,∞ , laser spot radius ω0; N refers to the number of pulses irradiated to the material; the absorption coefficient of the material is represented by α, and Δα is the absorption coefficient from the initial value α0 to the maximum value α max The change in β and γ are the fitting coefficients; Step 3: Numerical simulation of the ablation removal process; according to the laser incident direction and the local normal vector The angle α between ag The net ablation flux J is calculated as net J ab =Jcosα ag (2) Where J is the incident laser flux, J ab is the laser flux absorbed by the target; Step 4: Perform data cycle calibration according to formula (5), obtain the material removal coefficient ξ, and calculate the displacement (Δr, Δz) of any point (r, z) on the material surface. where n r Represents the unit normal vector in the radial direction, n z represents the unit normal vector in the vertical direction of laser incidence, and r is the radial direction; Step 5. When N=1, the z obtained in step 4 is the surface morphology processed by a single pulse of femtosecond laser, and the simulation of a single pulse is completed; when N>1, return to step 1 to step 3 for iterative simulation, and the z obtained in step 4 is the surface morphology processed by multiple pulses of femtosecond laser, and the simulation of multiple pulse ablation processes is completed, thereby simulating the femtosecond laser ablation removal results corresponding to different laser processing processes.

2. A phenomenological numerical simulation method for femtosecond laser ablation removal according to claim 1, characterized in that: When the centers of multiple laser pulses coincide, multiple pulses are used to drill holes at fixed points. When the centers of multiple laser pulses do not coincide, microgrooves or other microstructures are processed on the surface of the target material using a pulse sequence.

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