Nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrate

Abstract

The invention provides a nonlinear multi-field coupling simulation method for femtosecond laser processing of a glass substrate, and relates to the technical field of femtosecond laser micromachining, and the method comprises the following steps: constructing a substrate physical model corresponding to the glass substrate based on material parameters of the glass substrate; constructing a nonlinear ionization model according to the substrate physical model and a coupled multi-photon absorption and avalanche ionization mechanism; constructing a transient optical response model based on a Dyde model and a nonlinear ionization model so as to obtain a change curve corresponding to the free electron density; an electron-lattice heat transfer model is constructed based on the double-temperature equation, and evolution curves of electron temperature and lattice temperature are obtained respectively; according to a preset critical plasma density condition, a simulation ablation morphology corresponding to the substrate physical model is predicted; and comparing the simulated ablation morphology with the experimental ablation morphology to obtain a simulated comparison result, and adjusting femtosecond laser processing parameters according to the simulated comparison result. According to the method, the accuracy of ablation morphology reconstruction is improved.

Description

Technical Field

[0001] This invention relates to the field of femtosecond laser micromachining technology, and in particular to a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates. Background Technology

[0002] With the rapid development of artificial intelligence, high-performance computing, and 5G / 6G communication technologies, the demand for high-density interconnects and high-frequency performance in electronic devices is increasing daily. Three-dimensional integration technology has become a key path to overcome the limitations of Moore's Law, and glass substrates, with their excellent high-frequency electrical properties, controllable coefficient of thermal expansion, and superior insulation performance, are gradually replacing traditional organic substrates and silicon interposers, becoming the core material for high-end chip packaging in the post-Moore's Law era. Glass substrates play a dual role in high-density packaging: on the one hand, they serve as three-dimensional interconnect interposers through glass vias (TGVs); on the other hand, they act as wiring carriers for ultra-low-loss signal transmission. Among them, borosilicate glass (such as Borofloat® 33) has become an ideal substrate material for high-performance AI chip packaging due to its high thermal stability, tunable dielectric constant, and good mechanical strength.

[0003] Chinese patent CN117236007A discloses a method for predicting femtosecond laser-induced nonequilibrium deformation of metal thin films. This method includes: using a two-temperature equation to describe the energy transfer of the electronic and lattice systems of the metal thin film during femtosecond laser processing; using a linear elastic motion equation to simulate ultrafast lattice deformation during the nonequilibrium process; establishing a multiphysics coupled model of electron-phonon coupled heat transfer and thermo-elastic-plastic deformation; calculating and setting the material physical parameters required by the model; setting the initial and boundary conditions of the multiphysics model; introducing an artificial viscosity term; setting a computational mesh; adding physical field probes and configuring the solver; simulating and predicting the changes in electron and lattice temperatures within the copper material and the stress propagation induced by thermionic explosions during femtosecond laser processing; and analyzing and predicting the ultrafast nonequilibrium deformation of the metal thin film induced by the femtosecond laser. However, the above scheme, under the metal thin film paradigm, employs the small deformation assumption of linear absorption coupled with a two-temperature model and linear elasticity. The model scheduling strategy prioritizes ensuring the numerical stability of the thermal field solution, resulting in insufficient accuracy and transferability in the reconstruction of ablation morphology. Therefore, it is essential to provide a nonlinear multi-field coupling simulation method and system for femtosecond laser processing of glass substrates to improve the accuracy of ablation morphology reconstruction. Summary of the Invention

[0004] In view of this, the present invention proposes a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates.

[0005] This invention provides a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates, the method comprising: Based on the material parameters of the glass substrate, a physical model of the substrate corresponding to the glass substrate is constructed. Based on the physical model of the substrate and the coupled multiphoton absorption and avalanche ionization mechanism, a nonlinear ionization model is constructed. Based on the Drude model and the aforementioned nonlinear ionization model, a transient optical response model is constructed to obtain the variation curve of the free electron density. An electron-lattice heat transfer model was constructed based on the dual-temperature equation to simulate the process by which electrons transfer energy to the physical model of the substrate under the action of electro-acoustic coupling, and the evolution curves of electron temperature and lattice temperature were obtained respectively. Based on the preset critical plasma density condition, the simulated ablation morphology corresponding to the physical model of the substrate is predicted, wherein the preset critical plasma density condition is obtained based on the evolution curve corresponding to the lattice temperature and the change curve corresponding to the free electron density. The simulated ablation morphology is compared with the experimental ablation morphology to obtain the simulation comparison results, and the femtosecond laser processing parameters are adjusted according to the simulation comparison results.

[0006] Based on the above technical solutions, preferably, the step of constructing a nonlinear ionization model according to the substrate physical model and the coupled multiphoton absorption and avalanche ionization mechanism specifically includes: Based on the band gap and laser photon energy of the physical model of the substrate, the lowest order of multiphoton absorption is calculated; Based on historical experimental data, the multiphoton absorption coefficient and avalanche ionization cross section were obtained. Based on the multiphoton absorption coefficient, the avalanche ionization cross section, the unified rate equation is solved to obtain the electron density evolution function of the free electron density, thereby constructing the nonlinear ionization model.

[0007] Based on the above technical solutions, preferably, the construction of the electron-lattice heat transfer model based on the two-temperature equation specifically includes: The electron temperature equation and the lattice temperature equation are solved at a preset initial temperature to construct an electron-lattice heat transfer model and obtain the spatiotemporal evolution curves of electron temperature and lattice temperature. Determine whether the electron-phonon coupling term in the electron-lattice heat transfer model satisfies the preset heat accumulation condition. If the electron-phonon coupling term satisfies the preset heat accumulation condition, then the physical model of the substrate is determined to have a heat accumulation risk.

[0008] More preferably, the preset heat accumulation conditions specifically include: When the highest lattice temperature of the substrate physical model is greater than or equal to the glass transition temperature or melting point of the material, and the pulse interval in the multi-pulse case is less than or equal to the lattice temperature relaxation time, it is determined that the substrate physical model has a risk of heat accumulation. When the highest lattice temperature of the substrate physical model is less than the glass transition temperature or melting point of the material, and the pulse interval is greater than the lattice temperature relaxation time in the case of multiple pulses, it is determined that the substrate physical model does not have a risk of heat accumulation.

[0009] More preferably, the step of predicting the simulated ablation morphology corresponding to the physical model of the substrate based on a preset critical plasma density condition specifically includes: Based on the change curve corresponding to the free electron density, the critical time point and critical spatial distribution of the free electron density reaching the critical value are obtained; Based on the critical time point and the critical spatial distribution, the boundary of the physical model of the substrate at the vaporization time is extracted to obtain ablation morphology parameters and simulated ablation morphology.

[0010] More preferably, the step of comparing the simulated ablation morphology with the experimental ablation morphology to obtain simulation comparison results specifically includes: Determine whether the difference between the ablation depth of the simulated ablation morphology and the experimental ablation morphology and the difference between the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than a first error threshold, and whether the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than a second error threshold. If the difference between the ablation depth of the simulated ablation morphology and the experimental ablation morphology and the difference between the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than the first error threshold, and the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than the second error threshold, then the simulated ablation morphology is determined to be the standard prediction result.

[0011] More preferably, the material parameters include the band gap of the glass substrate, the refractive index of the glass substrate, the thermal conductivity of the glass substrate, the specific heat capacity of the glass substrate, and the initial free electron concentration of the glass substrate.

[0012] A second aspect of this application provides a nonlinear multi-field coupling simulation system for femtosecond laser processing of glass substrates. The nonlinear multi-field coupling simulation system includes a model building module, a data processing module, and a simulation optimization module. The model building module is used to construct a physical model of the substrate corresponding to the glass substrate based on the material parameters of the glass substrate. The data processing module is used to construct a nonlinear ionization model based on the substrate physical model and the coupled multiphoton absorption and avalanche ionization mechanism; construct a transient optical response model based on the Drude model and the nonlinear ionization model to obtain the change curve of the free electron density; construct an electron-lattice heat transfer model based on the dual-temperature equation to simulate the process of electrons transferring energy to the substrate physical model under the action of electroacoustic coupling; and obtain the evolution curves of electron temperature and lattice temperature respectively. The simulation optimization module is used to predict the simulated ablation morphology corresponding to the physical model of the substrate based on the preset critical plasma density condition. The preset critical plasma density condition is obtained based on the evolution curve corresponding to the lattice temperature and the change curve corresponding to the free electron density. The simulated ablation morphology is compared with the experimental ablation morphology to obtain the simulation comparison result, and the femtosecond laser processing parameters are adjusted based on the simulation comparison result.

[0013] A third aspect of this application provides an electronic device including a processor, a memory, a user interface, and a network interface, wherein the memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory.

[0014] A fourth aspect of this application provides a computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the steps of a nonlinear multi-field coupling simulation method for femtosecond laser processing of a glass substrate.

[0015] The nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates provided by this invention has the following advantages over existing technologies: (1) By unifying the nonlinear ionization process of multiphoton absorption and avalanche ionization, the transient optical response based on the Drude model, and the heat transfer coupled by the dual-temperature model into the same framework, the entire chain from laser incident to material response can be simulated, which significantly improves the prediction accuracy of free electron density, reflectivity / absorbency evolution and thermal deposition distribution. It can also output the time-series evolution curves and spatial distribution of free electron density and electron / lattice temperature, revealing the entire process mechanism from nonlinear ionization initiation, carrier accumulation, energy coupling and transfer, plasma formation to material ablation. This helps to distinguish the weights of thermal and non-thermal effects at different time / space scales. By coupling the critical plasma density condition with the lattice temperature threshold, an ablation triggering criterion that is more in line with the actual femtosecond scale can be constructed. Compared with using only temperature or only density threshold, it can more accurately predict key features such as ablation threshold, hole opening size, depth and sidewall morphology, thereby improving the accuracy of ablation morphology reconstruction. By using the comparison between simulated morphology and experimental morphology to form feedback, laser parameters can be quickly corrected, reducing the number of trial and error attempts and significantly saving R&D costs and time.

[0016] (2) Taking the critical plasma density as the core criterion, the time point and spatial distribution of reaching the critical value are accurately located in the spatiotemporal evolution of the free electron density. Then, the boundary of the actual material removal is extracted by combining the time required for material vaporization, thereby obtaining reliable ablation morphology parameters and simulated morphology. This takes into account both ultrafast and thermal processes, improves the accuracy and consistency of aperture, depth and sidewall morphology prediction, and enhances the adaptability to complex beam and multi-pulse working conditions. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates provided by the present invention; Figure 2 This invention provides a modeling and visualization model for a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates. Figure 3 This is a schematic diagram of the nonlinear multi-field coupling simulation system provided by the present invention; Figure 4 This is a schematic diagram of the structure of the electronic device provided by the present invention.

[0019] Explanation of reference numerals in the attached figures: 1. Nonlinear multi-field coupled simulation system; 11. Model building module; 12. Data processing module; 13. Simulation optimization module; 2. Electronic equipment; 21. Processor; 22. Communication bus; 23. User interface; 24. Network interface; 25. Memory. Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] This invention discloses a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates, with reference to... Figure 1 The steps of this method include S1 to S6.

[0022] Step S1: Based on the material parameters of the glass substrate, construct a physical model of the substrate corresponding to the glass substrate.

[0023] Step S2: Based on the physical model of the substrate and the coupled multiphoton absorption and avalanche ionization mechanism, a nonlinear ionization model is constructed.

[0024] In this step, the nonlinear ionization model is constructed using a unified rate equation, namely the modified Fokker-Planck equation, which comprehensively represents the combined contributions of multiphoton absorption and avalanche ionization. The coupling mechanism here does not refer to a single model or equation, but rather to the physical processes in which multiphoton absorption and avalanche ionization coexist and interact within the aforementioned single equation.

[0025] This step also includes steps S21 to S23.

[0026] Step S21: Calculate the lowest order of multiphoton absorption based on the band gap and laser photon energy of the substrate physical model.

[0027] In this step, based on the bandgap characteristics E of the glass substrate... g and femtosecond laser photon energy Theoretically, the minimum order required for multiphoton absorption can be determined. (Rounded up). For the Borofloat® 33 glass (Eg≈4.0 eV) and 1030 nm laser targeted in this embodiment ( Since m = [4.0 / 1.2] = 4, in actual modeling, due to defects and band tails in the amorphous glass state, effective excitation may begin at a lower order, such as m = 3. If experimental fitting results show that lower-order absorption contributes significantly, then corresponding values ​​will be introduced into the rate equation. item( The correction can be made, or it can be described by an effective equivalent order. For this implementation scheme, based on experimental data, the contributions of m=3 and m=4 are mainly considered, and the model is performed with three-photon absorption m=3 as the dominant term.

[0028] Step S22: Based on historical experimental data, obtain the multiphoton absorption coefficient and avalanche ionization cross section.

[0029] Step S23: Based on the multiphoton absorption coefficient, the avalanche ionization cross section, solve the unified rate equation to obtain the electron density evolution function of the free electron density, so as to construct a nonlinear ionization model.

[0030] In this step, the evolution of free electron density is described by the modified Fokker-Planck equation:

[0031] Where, α i I represents the avalanche ionization component, δ m I m α represents the multiphoton absorption portion. i The avalanche ionization coefficient, δ, is determined by the avalanche ionization cross section σ and the band gap. m The multiphoton absorption coefficient is represented by n, where m represents the multiphoton absorption order, τ represents the free electron relaxation time, and n represents the m-th order multiphoton absorption coefficient. e Let I represent the free electron density, and let I represent the avalanche current.

[0032] In this step, the lowest order of multiphotons is determined by the material band gap and photon energy. Combined with the experimentally calibrated multiphoton absorption coefficient and avalanche ionization cross section, a unified rate equation is constructed to obtain the time-series evolution function of free electron density. This significantly enhances the accuracy of ionization modeling in terms of physical constraints, parameter robustness, and mechanism interpretability. The results directly improve the reliability of subsequent transient optical response and ablation threshold / morphology prediction, shorten the process optimization iteration, and expand the stable processing window.

[0033] Step S3: Based on the Drude model and the nonlinear ionization model, construct a transient optical response model to obtain the change curve corresponding to the free electron density.

[0034] In this step, the transient optical response model is based on the Drude model to describe the material's optical response, and the complex refractive index is determined by the plasma frequency and the damping coefficient:

[0035] Where R represents reflectivity, and reflectivity R is calculated using the Fresnel formula, n cr This represents the threshold plasma concentration, n. cr Determined by the laser wavelength λ = 1030 nm, where n represents the refractive index, κ represents the extinction coefficient, and ω p n represents the plasma frequency. e The density of free electrons, m e ε and e represent the mass and charge of an electron, respectively, ε0 ​​represents the dielectric constant in vacuum, and ω L This indicates the frequency of the femtosecond laser.

[0036] Step S4: Construct an electron-lattice heat transfer model based on the dual-temperature equation to simulate the process of electrons transferring energy to the physical model of the substrate under the action of electro-acoustic coupling, and obtain the evolution curves of electron temperature and lattice temperature respectively.

[0037] This step also includes steps S41 to S42.

[0038] Step S41: Solve the electron temperature equation and the lattice temperature equation at a preset initial temperature to construct an electron-lattice heat transfer model and obtain the spatiotemporal evolution curves of electron temperature and lattice temperature.

[0039] In this step, the two-temperature model includes the electronic temperature equation and the lattice temperature equation:

[0040] Among them, C e T represents the electronic specific heat coefficient. e Indicates electron temperature, κ e denoted by κ1, g represents the electron-phonon coupling coefficient, T1 represents the lattice temperature, S represents the laser source term, C1 represents the lattice specific heat, and κ1 represents the lattice thermal conductivity. The mathematical expression for the laser source term S is a Gaussian spatiotemporal distribution.

[0041] Step S42: Solve the electron temperature equation and the lattice temperature equation at a preset initial temperature to construct an electron-lattice heat transfer model and obtain the spatiotemporal evolution curves of electron temperature and lattice temperature.

[0042] In this embodiment, the spatiotemporal evolution of electron and lattice temperatures is solved separately under a dual-temperature framework, realistically reproducing the dynamic process of rapid electron energy absorption and subsequent electron-phonon energy exchange during femtosecond processing. With the help of the preset thermal accumulation criterion of the electron-phonon coupling term, the risk of thermal accumulation can be identified and quantified in a timely manner under multi-pulse, high repetition frequency scenarios, avoiding the generation of failure morphologies such as excessive heat-affected zone, remelting, and microcracks, and significantly improving the simulation's fit to the experiment and its transferability.

[0043] Furthermore, preset heat accumulation conditions specifically include: When the highest lattice temperature of the substrate physical model is greater than or equal to the glass transition temperature or melting point of the material, and the pulse interval in the multi-pulse case is less than or equal to the lattice temperature relaxation time, the substrate physical model is determined to have a risk of heat accumulation. If the highest lattice temperature of the substrate physical model is lower than the glass transition temperature or melting point of the material, and the pulse interval is greater than the lattice temperature relaxation time in the case of multiple pulses, then the substrate physical model is determined to have no risk of thermal accumulation.

[0044] Understandably, the risk of heat accumulation is assessed by analyzing the energy transfer efficiency during electron-phonon coupling. Energy transfer efficiency analysis is performed by calculating the electron-phonon coupling term g(T). e -T l It is realized by the ratio of the integral of the laser source term S in the spatiotemporal domain to the total absorbed energy (the spatiotemporal integral of the laser source term S).

[0045] Heat accumulation risk is assessed using the following criteria: a) Monitor the highest lattice temperature max(T) l Does it exceed the glass transition temperature or melting point of the material? b) Analysis of high-temperature regions (T) l >T glass The duration of ) c) In multi-pulse simulation, compare the pulse interval time with the lattice temperature relaxation time. If the former is shorter than the latter, it is determined that there is a significant risk of heat accumulation.

[0046] Step S5: Based on the preset critical plasma density condition, predict the simulated ablation morphology corresponding to the physical model of the substrate. The preset critical plasma density condition is obtained from the evolution curve corresponding to the lattice temperature and the change curve corresponding to the free electron density.

[0047] In one example, the ablation criterion is that the free electron density reaches the critical plasma concentration n. e ≥n cr .

[0048] This step also includes steps S51 to S52.

[0049] Step S51: Based on the change curve corresponding to the free electron density, obtain the critical time point and critical spatial distribution of the free electron density reaching the critical value; Step S52: Based on the critical time point and critical spatial distribution, extract the boundary of the physical model of the substrate at the vaporization time to obtain ablation morphology parameters and simulated ablation morphology.

[0050] In this step, the ablation initiation point and propagation process are predicted based on the electron density distribution. The prediction of the ablation region is based on the following physical criterion: the spatiotemporal region after time tcr, where the lattice temperature exceeds the material vaporization temperature (approximately 2200°C for borosilicate glass), is defined as the volume of material ultimately ablated and removed. The predicted ablation morphology can be obtained by extracting the boundary of this volume.

[0051] In this embodiment, the critical plasma density is used as the core criterion. First, the time point and spatial distribution of reaching the critical value are precisely located from the spatiotemporal evolution of the free electron density. Then, the boundary of actual material removal is extracted by combining the time required for material vaporization, thereby obtaining reliable ablation morphology parameters and simulated morphology. Compared to methods that rely solely on temperature or fixed energy thresholds, this process unifies ultrafast plasma establishment, transient optical constant changes, and subsequent thermally driven removal within the same spatiotemporal framework, taking into account both ultrafast and thermal processes. This significantly reduces the risk of over-cutting and under-cutting, and improves the accuracy and consistency of aperture, depth, and sidewall morphology predictions. Simultaneously, the output morphology parameters are easily compared quantitatively with experimental data, enabling closed-loop optimization of processing parameters and enhancing adaptability to complex beams and multi-pulse conditions.

[0052] Step S6: Compare the simulated ablation morphology with the experimental ablation morphology to obtain the simulation comparison results, and adjust the femtosecond laser processing parameters according to the simulation comparison results.

[0053] In one example, the optimized femtosecond laser processing parameters include: pulse energy 0.1-10 μJ, pulse width 100-500 fs, repetition rate 1-1000 kHz, focusing numerical aperture 0.1-0.9, and scanning speed 0.1-10 mm / s.

[0054] In this embodiment, it is determined whether the difference between the ablation depth of the simulated ablation morphology and the experimental ablation morphology and the difference between the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than a first error threshold, and whether the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than a second error threshold. If the difference between the ablation depth and the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than the first error threshold, and the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than the second error threshold, then the simulated ablation morphology is determined to be the standard prediction result; otherwise, the simulated ablation morphology is discarded.

[0055] The accuracy of the model is verified by comparing the simulated ablation morphology with the experimental ablation morphology. The verification condition for model accuracy requires that both of the following conditions be met simultaneously: (i) Ablation morphology size error: The relative errors between the predicted ablation depth and diameter / width and the experimental measurements are both less than 15%; (ii) Ablation threshold error: The relative error between the ablation energy density threshold fitted based on simulation data and the experimentally measured ablation threshold is less than 10%. Only when the simulation results simultaneously meet the above requirements for morphology and threshold error can the model prediction be considered accurate and used for process optimization.

[0056] like Figure 2 As shown, Figure 2 The top left corner shows the time-varying curve of reflectivity. This curve rises rapidly in a very short time and plateaus around 0.2 ps, indicating the ultrafast setup process at the sub-picosecond scale, i.e., the rapid increase and saturation of free carrier density, transient reflectivity, or electron temperature. Figure 2 The upper right corner shows the evolution curve of the two-temperature equation. Under pulse action, the electron temperature changes rapidly first, and then gradually approaches the lattice temperature through electron-lattice coupling, reflecting typical two-temperature model (TTM) dynamics, where electrons first absorb energy and then transfer it to the lattice. Figure 2 The six images below are morphological evolution diagrams of the physical model of the substrate. As the order from left to right and from top to bottom is followed, the pits gradually deepen / expand, showing the evolution process of energy deposition, material removal or modification from the initial stage to the stable stage, reflecting the coupling result of nonlinear absorption-thermal conduction-phase change / removal.

[0057] In this implementation, by unifying the nonlinear ionization process of multiphoton absorption and avalanche ionization, the transient optical response based on the Drude model, and the coupled heat transfer of the dual-temperature model into a single framework, the entire chain from laser incidence to material response can be simulated. This significantly improves the prediction accuracy of free electron density, reflectivity / absorbency evolution, and thermal deposition distribution. Furthermore, it can output the temporal evolution curves and spatial distribution of free electron density and electron / lattice temperature, revealing the entire process mechanism from nonlinear ionization initiation, carrier accumulation, energy coupling and transfer, plasma formation to material ablation. This helps to distinguish the weights of thermal and non-thermal effects at different temporal / spatial scales. By coupling the critical plasma density condition with the lattice temperature threshold, an ablation triggering criterion that is more consistent with the reality of the femtosecond scale is constructed. Compared with using only temperature or only density thresholds, it can more accurately predict key features such as ablation threshold, hole opening size, depth, and sidewall morphology, thereby improving the accuracy of ablation morphology reconstruction. By using the comparison between simulated and experimental morphologies to form feedback, laser parameters can be quickly corrected, reducing the number of trial and error attempts and significantly saving R&D costs and time.

[0058] In one example, a simulation flow for femtosecond laser processing of borosilicate glass is given. This embodiment uses Borofloat® 33 borosilicate glass as the processing object and a femtosecond laser with a wavelength of 1030 nm and a pulse width of 100 fs is used for processing simulation. The specific implementation steps are as follows: Material parameter settings: Based on the material properties of Borofloat® 33 glass, set the basic parameters required for simulation: band gap E g =4.0 eV, refractive index n=1.471, thermal conductivity Specific heat of crystal lattice Electron specific heat coefficient The initial free electron concentration n0 = 10 6 cm -3 Electron relaxation time τ = 10 ps, ​​electron-phonon coupling coefficient .

[0059] A nonlinear ionization model is established, and the evolution of free electron density is described using the modified Fokker-Planck equation:

[0060] Among them, the multiphoton absorption coefficient avalanche ionization coefficient α i =σ / (n 2 E g Avalanche ionization cross section σ = 5 × 10 -18 cm -2 The equation was solved using the finite difference method, yielding the evolution curve of the free electron density over time.

[0061] Transient optical response calculation: Calculating the optical response properties of materials based on the Drude model.

[0062] Among them, plasma frequency The reflectivity R is calculated using Fresnel's formula. The threshold plasma concentration is set to n. cr =9.5×10 26 m -3 .

[0063] The two-temperature model is solved using two-temperature equations to describe the energy transfer process:

[0064] Among them, the laser source term S adopts a Gaussian spatiotemporal distribution with a peak power density of 10. 14 W / cm 2 The electron temperature T was obtained by solving the two-temperature equation using the finite element method. e and lattice temperature T l The spatiotemporal evolution.

[0065] Prediction and verification of ablation morphology when the free electron density reaches the critical value n crWhen the ablation occurs, it is determined that ablation has taken place. By monitoring the electron density distribution, the ablation initiation point and propagation process are predicted. The simulation results are compared with experimental data. The predicted ablation depth is 0.95 μm, while the experimental measurement is 1.05 μm, with a relative error of less than 10%, verifying the accuracy of the model.

[0066] Process parameter optimization: Based on simulation results, the femtosecond laser processing parameters were optimized. The pulse energy is 2 μJ, the pulse width is 100 fs, the repetition frequency is 100 kHz, the focusing numerical aperture is 0.5, and the scanning speed is 1 mm / s. Under these parameters, an ablation structure with a depth of approximately 1 μm and a width of approximately 2 μm can be obtained, with a heat-affected zone of less than 0.5 μm.

[0067] In this embodiment, by coupling multi-physics processes such as nonlinear ionization, transient optical response, and nonequilibrium heat transfer, accurate simulation of the entire process of femtosecond laser processing of glass substrates was achieved, solving the problem of insufficient description of the synergistic effect of multiphoton absorption and avalanche ionization in existing models. By introducing a dynamic calibration mechanism for the multiphoton absorption coefficient and an avalanche ionization cross-section model, the prediction accuracy of free electron density was significantly improved, reducing the error from 30% in existing technologies to less than 10%, providing a theoretical basis for accurate prediction of ablation threshold and heat-affected zone. A method combining the two-temperature equation (TTM) and the transient Drude model was used to reveal the unique energy relaxation mechanism of glass, achieving accurate prediction of the nanoscale evolution of the heat-affected zone and effectively avoiding thermal damage and microcrack formation. A critical plasma density gradient criterion was proposed, and a high-precision prediction of submicron ablation morphology was achieved using an electron concentration threshold, with an ablation depth prediction error of less than 10%, providing a reliable theoretical tool for the processing of high aspect ratio TGV structures. This invention provides comprehensive process optimization guidance for femtosecond laser processing of glass substrates. By optimizing processing parameters through simulation results, it significantly reduces experimental trial and error costs and improves processing efficiency and yield. It is especially suitable for the preparation of glass vias in high-density packaging of AI chips.

[0068] Based on the above method, this application discloses a nonlinear multi-field coupling simulation system for femtosecond laser processing of glass substrates, referencing... Figure 3 The nonlinear multi-field coupled simulation system 1 includes a model building module 11, a data processing module 12, and a simulation optimization module 13, wherein... Model building module 11 is used to build a physical model of the substrate corresponding to the glass substrate based on the material parameters of the glass substrate; The data processing module 12 is used to construct a nonlinear ionization model based on the substrate physical model and the coupled multiphoton absorption and avalanche ionization mechanism, construct a transient optical response model based on the Drude model and the nonlinear ionization model to obtain the change curve of the free electron density, construct an electron-lattice heat transfer model based on the dual-temperature equation to simulate the process of electrons transferring energy to the substrate physical model under the action of electro-acoustic coupling, and obtain the evolution curves of electron temperature and lattice temperature respectively. The simulation optimization module 13 is used to predict the simulated ablation morphology corresponding to the physical model of the substrate based on the preset critical plasma density conditions. The preset critical plasma density conditions are obtained from the evolution curve corresponding to the lattice temperature and the change curve corresponding to the free electron density. The simulated ablation morphology is compared with the experimental ablation morphology to obtain the simulation comparison results, and the femtosecond laser processing parameters are adjusted based on the simulation comparison results.

[0069] In one example, the data processing module 12 is used to calculate the lowest order of multiphoton absorption based on the band gap and laser photon energy of the substrate physical model; to obtain the multiphoton absorption coefficient and avalanche ionization cross section based on historical experimental data; and to solve the unified rate equation based on the multiphoton absorption coefficient, the multiphoton absorption coefficient and the avalanche ionization cross section to obtain the electron density evolution function of the free electron density in order to construct a nonlinear ionization model.

[0070] In one example, the data processing module 12 is used to solve the electron temperature equation and the lattice temperature equation at a preset initial temperature to construct an electron-lattice heat transfer model and obtain the spatiotemporal evolution curves of electron temperature and lattice temperature; determine whether the electron-phonon coupling term in the electron-lattice heat transfer model satisfies the preset heat accumulation condition; if the electron-phonon coupling term satisfies the preset heat accumulation condition, it is determined that the substrate physical model has a heat accumulation risk.

[0071] In one example, the preset heat accumulation conditions specifically include: When the highest lattice temperature of the substrate physical model is greater than or equal to the glass transition temperature or melting point of the material, and the pulse interval in the multi-pulse case is less than or equal to the lattice temperature relaxation time, the substrate physical model is determined to have a risk of heat accumulation. If the highest lattice temperature of the substrate physical model is lower than the glass transition temperature or melting point of the material, and the pulse interval is greater than the lattice temperature relaxation time in the case of multiple pulses, then the substrate physical model is determined to have no risk of thermal accumulation.

[0072] In one example, the simulation optimization module 13 is used to obtain the critical time point and critical spatial distribution of the free electron density reaching the critical value based on the change curve corresponding to the free electron density; based on the critical time point and critical spatial distribution, the boundary of the physical model of the substrate at the vaporization time is extracted to obtain the ablation morphology parameters and the simulated ablation morphology.

[0073] In one example, the simulation optimization module 13 is used to determine whether the difference between the ablation depth and the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than a first error threshold, and whether the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than a second error threshold; if the difference between the ablation depth and the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than the first error threshold, and the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than the second error threshold, then the simulated ablation morphology is determined to be the standard prediction result.

[0074] In one example, the material parameters include the band gap of the glass substrate, the refractive index of the glass substrate, the thermal conductivity of the glass substrate, the specific heat capacity of the glass substrate, and the initial free electron concentration of the glass substrate.

[0075] Please see Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 4 As shown, the electronic device 2 may include: at least one processor 21, at least one network interface 24, user interface 23, memory 25, and at least one communication bus 22.

[0076] The communication bus 22 is used to enable communication between these components.

[0077] The user interface 23 may include a display screen and a camera. Optionally, the user interface 23 may also include a standard wired interface and a wireless interface.

[0078] The network interface 24 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0079] The processor 21 may include one or more processing cores. The processor 21 connects to various parts of the server using various interfaces and lines, and performs various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 25, and by calling data stored in the memory 25. Optionally, the processor 21 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 21 may integrate one or a combination of several of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), and modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content required for display; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 21 and may be implemented as a separate chip.

[0080] The memory 25 may include random access memory (RAM) or read-only memory. Optionally, the memory 25 may include a non-transitory computer-readable medium. The memory 25 may be used to store instructions, programs, code, code sets, or instruction sets. The memory 25 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the various method embodiments described above, etc.; the data storage area may store data involved in the various method embodiments described above, etc. Optionally, the memory 25 may also be at least one storage device located remotely from the aforementioned processor 21. Figure 4 As shown, the memory 25, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and an application program for a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates.

[0081] exist Figure 4In the electronic device 2 shown, the user interface 23 is mainly used to provide an input interface for the user and to obtain the user input data; while the processor 21 can be used to call the application program stored in the memory 25 for a nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrate. When executed by one or more processors, the electronic device performs one or more methods as described in the above embodiments.

[0082] A computer-readable storage medium storing instructions that, when executed by one or more processors, cause a computer to perform one or more methods as described in the embodiments above.

[0083] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0084] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0085] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the shown or discussed mutual couplings or direct couplings or communication connections may be through some service interfaces; indirect couplings or communication connections between apparatuses or units may be electrical or other forms.

[0086] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0087] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0088] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates, characterized in that, The method includes: Based on the material parameters of the glass substrate, a physical model of the substrate corresponding to the glass substrate is constructed. Based on the physical model of the substrate and the coupled multiphoton absorption and avalanche ionization mechanism, a nonlinear ionization model is constructed. Based on the Drude model and the aforementioned nonlinear ionization model, a transient optical response model is constructed to obtain the variation curve of the free electron density. An electron-lattice heat transfer model was constructed based on the dual-temperature equation to simulate the process by which electrons transfer energy to the physical model of the substrate under the action of electro-acoustic coupling, and the evolution curves of electron temperature and lattice temperature were obtained respectively. Based on the preset critical plasma density condition, the simulated ablation morphology corresponding to the physical model of the substrate is predicted, wherein the preset critical plasma density condition is obtained based on the evolution curve corresponding to the lattice temperature and the change curve corresponding to the free electron density. The simulated ablation morphology is compared with the experimental ablation morphology to obtain the simulation comparison results, and the femtosecond laser processing parameters are adjusted according to the simulation comparison results.

2. The nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates as described in claim 1, characterized in that, The nonlinear ionization model constructed based on the substrate physical model and the coupled multiphoton absorption and avalanche ionization mechanism specifically includes: Based on the band gap and laser photon energy of the physical model of the substrate, the lowest order of multiphoton absorption is calculated; Based on historical experimental data, the multiphoton absorption coefficient and avalanche ionization cross section were obtained. Based on the multiphoton absorption coefficient, the avalanche ionization cross section, the unified rate equation is solved to obtain the electron density evolution function of the free electron density, so as to construct the nonlinear ionization model.

3. The nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates as described in claim 1, characterized in that, The electron-lattice heat transfer model constructed based on the two-temperature equation specifically includes: The electron temperature equation and the lattice temperature equation are solved at a preset initial temperature to construct an electron-lattice heat transfer model and obtain the spatiotemporal evolution curves of electron temperature and lattice temperature. Determine whether the electron-phonon coupling term in the electron-lattice heat transfer model satisfies the preset heat accumulation condition. If the electron-phonon coupling term satisfies the preset heat accumulation condition, then the physical model of the substrate is determined to have a heat accumulation risk.

4. The nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates as described in claim 3, characterized in that, The preset heat accumulation conditions specifically include: When the highest lattice temperature of the substrate physical model is greater than or equal to the glass transition temperature or melting point of the material, and the pulse interval in the multi-pulse case is less than or equal to the lattice temperature relaxation time, it is determined that the substrate physical model has a risk of heat accumulation. When the highest lattice temperature of the substrate physical model is less than the glass transition temperature or melting point of the material, and the pulse interval is greater than the lattice temperature relaxation time in the case of multiple pulses, it is determined that the substrate physical model does not have a risk of heat accumulation.

5. The nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates as described in claim 1, characterized in that, The step of predicting the simulated ablation morphology corresponding to the physical model of the substrate based on a preset critical plasma density condition specifically includes: Based on the change curve corresponding to the free electron density, the critical time point and critical spatial distribution of the free electron density reaching the critical value are obtained; Based on the critical time point and the critical spatial distribution, the boundary of the physical model of the substrate at the vaporization time is extracted to obtain ablation morphology parameters and simulated ablation morphology.

6. The nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates as described in claim 1, characterized in that, The step of comparing the simulated ablation morphology with the experimental ablation morphology to obtain the simulation comparison results specifically includes: Determine whether the difference between the ablation depth of the simulated ablation morphology and the experimental ablation morphology and the difference between the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than a first error threshold, and whether the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than a second error threshold. If the difference between the ablation depth of the simulated ablation morphology and the experimental ablation morphology and the difference between the diameter of the simulated ablation morphology and the experimental ablation morphology are both less than the first error threshold, and the difference between the ablation energy density of the simulated ablation morphology and the experimental ablation morphology is less than the second error threshold, then the simulated ablation morphology is determined to be the standard prediction result.

7. The nonlinear multi-field coupling simulation method for femtosecond laser processing of glass substrates as described in claim 1, characterized in that, The material parameters include the band gap of the glass substrate, the refractive index of the glass substrate, the thermal conductivity of the glass substrate, the specific heat capacity of the glass substrate, and the initial free electron concentration of the glass substrate.

8. A nonlinear multi-field coupling simulation system for femtosecond laser processing of glass substrates, characterized in that, The nonlinear multi-field coupled simulation system (1) includes a model building module (11), a data processing module (12), and a simulation optimization module (13), wherein, The model building module (11) is used to build a physical model of the substrate corresponding to the glass substrate based on the material parameters of the glass substrate; The data processing module (12) is used to construct a nonlinear ionization model based on the substrate physical model and the coupled multiphoton absorption and avalanche ionization mechanism, construct a transient optical response model based on the Drude model and the nonlinear ionization model to obtain the change curve corresponding to the free electron density, construct an electron-lattice heat transfer model based on the dual-temperature equation to simulate the process of electrons transferring energy to the substrate physical model under the action of electro-acoustic coupling, and obtain the evolution curves of electron temperature and lattice temperature respectively. The simulation optimization module (13) is used to predict the simulated ablation morphology corresponding to the physical model of the substrate according to the preset critical plasma density condition. The preset critical plasma density condition is obtained according to the evolution curve corresponding to the lattice temperature and the change curve corresponding to the free electron density. The simulated ablation morphology is compared with the experimental ablation morphology to obtain the simulation comparison result, and the femtosecond laser processing parameters are adjusted according to the simulation comparison result.

9. An electronic device, characterized in that, The device includes a processor (21), a memory (25), a user interface (23), and a network interface (24). The memory (25) is used to store instructions. The user interface (23) and the network interface (24) are used to communicate with other devices. The processor (21) is used to execute the instructions stored in the memory (25) to cause the electronic device (2) to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

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