Microscopic etching model development method for wafer wet etching

Abstract

The invention relates to a microcosmic etching model development method for wafer wet etching, which is characterized by comprising the following steps of: establishing a multi-scale seepage model to describe the migration rule of etching liquid in the etching process of an etching substrate, and comprehensively considering the seepage characteristic of the etching liquid in the etching substrate, the dynamic evolution of a pore structure and other factors by the model; calculating the migration direction and speed distribution of the etching liquid in different etching stages; a lattice Boltzmann method is adopted to simulate dynamic evolution of a pore structure in the decomposition process of an etching base material, pore network models at different moments are obtained, the migration speed and pressure distribution of the etching liquid under the pore scale are obtained through fluid mechanics calculation, and quantitative correlation between the migration mechanism of the etching liquid under the pore scale and the macroscopic seepage law is established.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wafer etching, in particular to a micro-etching model development method for wafer wet etching. BACKGROUND

[0002] In the process of etching the substrate of the wafer by using etching liquid, the etching liquid used for decomposing the etching substrate will migrate in the etching layer and interact with the etching substrate in a complex manner; the migration law of the etching liquid directly affects the etching effect of the etching substrate. Firstly, the seepage characteristics of the etching liquid at the contact position of the etching substrate are difficult to accurately grasp, and the uncertainty of the flow direction and speed brings challenges to the prediction of the migration of the etching liquid; secondly, the migration law of the etching liquid at the contact position of the etching substrate is not clear, and the etching liquid may form a saturated area in the local area, which hinders the effective seepage of the etching liquid; thirdly, the etching structure evolves dynamically during the decomposition of the etching substrate, and the correlation between the etching liquid migration mechanism at the pore scale and the macroscopic seepage law needs to be further studied; finally, the coupling effect between the decomposition kinetics characteristics of the etching layer under different etching substrate conditions and the migration law of the etching liquid has not been fully elucidated, which brings challenges to accurately describing the migration law of the etching liquid, and further affects the prediction of the etching effect. Therefore, it is of great significance to deeply study the migration law of the etching liquid in the etching substrate, establish the etching liquid migration model at the fine scale, and elucidate the coupling mechanism between the decomposition kinetics of the etching substrate and the migration of the etching liquid, which can guide the efficient and accurate etching of the etching substrate. SUMMARY

[0003] The present application provides a micro-etching model development method for wafer wet etching, mainly comprising: S1: establishing a multi-scale etching model to describe the etching law of the etching liquid in the etching process, which comprehensively considers the seepage characteristics of the etching liquid at the contact surface with the etching substrate and the dynamic evolution factors of the etching structure, and calculates the migration direction and velocity distribution of the etching liquid at different etching stages; S2: using X-ray CT scanning technology to obtain the microstructure image of the etching substrate decomposition interface, using image segmentation algorithm to extract the etching liquid distribution area, combining with the seepage simulation to calculate the local etching liquid saturation degree, judging the influence degree of the high etching liquid saturation area on the etching substrate seepage, when the etching liquid saturation degree exceeds the preset threshold, introducing the capillary force to correct the permeability in the area, the specific implementation method is to calculate the capillary force through the capillary pressure curve, and introduce it into the Darcy law to correct the effective permeability, so as to improve the seepage ability of the etching liquid; S3: Using the lattice Boltzmann method to simulate the dynamic evolution of the pore structure in the decomposition process of the etching substrate, obtain the pore network model at different times, obtain the migration speed and pressure distribution of the etching liquid at the pore scale through fluid mechanics calculation, and establish the quantitative correlation between the etching liquid migration mechanism at the pore scale and the macroscopic seepage law; S4: In order to further improve the multi-scale model, a multi-scale coupling method combining molecular dynamics simulation and continuum mechanics model is used to study the coupling effect of etching substrate decomposition dynamics and etching liquid migration. The decomposition process of the etching substrate is simulated at the molecular scale to obtain the decomposition reaction rate and thermodynamic parameters. At the macroscopic scale, a seepage-stress-thermal coupling model is used to solve the scene equations of etching substrate decomposition, etching liquid migration and etching structure deformation. By analyzing the simulation results at different scales, the mutual influence mechanism between etching substrate decomposition and etching liquid migration is clarified, including the influence of pore structure change caused by decomposition on etching liquid migration, and the feedback effect of etching liquid migration on local temperature field and pressure field and then on etching substrate decomposition rate; S5: According to the decomposition kinetics model of the etching substrate, the decomposition rate under different temperature and pressure conditions is calculated, combined with the numerical simulation results of etching liquid migration, a machine learning algorithm is used to establish the quantitative relationship between the decomposition rate and the etching liquid migration parameters, forming a set of intelligent evaluation model for predicting the etching liquid migration induced by etching substrate decomposition, providing decision basis for on-site etching scheme optimization; S6: Based on the three-dimensional model of the etching substrate, the etching layer is meshed by using the finite element method, and the key parameters such as permeability and porosity of the etching layer are obtained by inverse calculation according to the on-site etching data, and the etching liquid migration range under different etching schemes is calculated by numerical simulation; S7: Using data assimilation method to real-time correct the numerical model of etching substrate decomposition and etching liquid migration, introducing the real-time monitoring data to dynamically correct the model parameters, improving the prediction accuracy of the model, at the same time, using optimization algorithm to real-time adjust the etching model development scheme, taking the most accurate etching degree as the target, taking the etching liquid consumption and the etching substrate change as the constraint condition, through adjusting the temperature, pressure and flow of the injected etching liquid, minimizing the negative impact of the etching liquid, realizing the efficient and accurate etching of the etching liquid to the etching substrate.

[0004] The advantages of the present application are: 1) This invention establishes a multi-scale seepage model, combines X-ray CT scanning and image segmentation techniques to obtain the microstructure, employs the lattice Boltzmann method to simulate the evolution of the pore structure, and utilizes the coupling of molecular dynamics and continuum mechanics to simulate the decomposition kinetics of the etched substrate. Based on machine learning algorithms, it establishes the relationship between the decomposition rate and the etching fluid migration parameters to form an intelligent evaluation model. It uses data assimilation methods to correct the numerical model in real time, optimizes the etching scheme, and achieves efficient and precise etching of the etched substrate. This invention can accurately predict the migration law of the etching fluid, providing a basis for optimizing the development scheme of wet etching of etched substrates. Attached Figure Description

[0005] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0006] Fig. 1 This is a flowchart of a method for developing a micro-etching model for wet etching of wafers according to the present invention.

[0007] Fig. 2 This is a schematic diagram of a method for developing a micro-etching model for wet etching of wafers according to the present invention.

[0008] Fig. 3 This is another schematic diagram of a method for developing a micro-etching model for wet etching of wafers according to the present invention. Detailed Implementation

[0009] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0010] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0011] like Figs. 1 to 3 The method for developing a micro-etching model for wafer wet etching, as shown, includes: S101: Establish a multi-scale etching model to describe the etching law of the etching solution during the etching process. This model comprehensively considers the seepage characteristics of the etching solution at the contact surface with the etched substrate and the dynamic evolution factors of the etching structure, and calculates the migration direction and velocity distribution of the etching solution at different etching stages. According to the multi-scale seepage model, a mathematical model is established to describe the migration of etching liquid in the etching process, which includes the etching liquid seepage equation in the etching substrate and the etching structure dynamic evolution equation; the finite element method is used to discretize the established mathematical model, and the discretized etching liquid seepage control equation and the etching structure dynamic evolution equation are obtained; according to the known etching process parameters and boundary conditions, the discretized etching liquid seepage control equation is solved to obtain the pressure distribution and velocity distribution of the etching liquid at different etching stages; according to the solved etching liquid pressure distribution, the Darcy law is used to calculate the migration direction and migration flux of the etching liquid at different etching stages; the calculated etching liquid migration flux is taken as the input parameter of the etching structure dynamic evolution equation, and the etching structure dynamic evolution equation is solved to obtain the variation law of the etching structure parameters with time; according to the dynamic variation of the etching structure parameters, the permeability and other parameters in the etching liquid seepage control equation are updated, and the etching liquid seepage control equation is solved again to obtain the etching liquid pressure distribution and velocity distribution considering the influence of the dynamic evolution of the etching structure; the calculation results of the migration direction, migration flux and velocity distribution of the etching liquid at different etching stages are comprehensively analyzed to reveal the migration law of the etching liquid in the etching process, which provides a basis for optimizing the etching process parameters of the etching liquid in the etching process.

[0012] For example, according to the multi-scale seepage model, a mathematical model of etching liquid migration in the etching process of etching substrate is established, including the etching liquid seepage equation in the porous medium with pore size of 1-10 μm and the pore structure dynamic evolution equation based on Kozeny-Carman equation. Tetrahedral mesh division and Galerkin weighted residual method are used for finite element discretization of the mathematical model, and a set of discretized etching liquid seepage control equations and pore structure evolution equations containing 105 nodes are obtained. Under the etching conditions of temperature 283 K, pressure 0.1 MPa and constant pressure and flow rate boundary conditions, the etching liquid seepage equation is solved by Newton iteration method to obtain the pressure distribution and Darcy seepage velocity distribution of the etching liquid at different displacement stages. Based on Darcy's law, the migration direction and flux of the etching liquid in different regions are calculated, and the migration flux is in the order of 0.1-0.5 cm / s. The etching liquid migration flux is input into the pore structure evolution equation, which is solved by Euler forward difference format to obtain the nonlinear variation law of parameters such as porosity and specific surface area with time, and the porosity change rate is in the order of 8-10 mD. The dynamic pore structure parameters are updated in the seepage equation, and the etching liquid pressure and seepage velocity distribution considering the influence of pore evolution are obtained by re-solution, with pressure change of 1-5% and velocity change of 5-15%. Comprehensive analysis of the etching liquid migration calculation results at different etching stages shows that the etching liquid mainly migrates to the unetched region in the early stage, and migrates to the low permeability region in the later stage due to the influence of pore structure change, and the migration flux first increases and then decreases, which provides a quantitative basis for optimizing the etching process parameters such as etching liquid temperature, pressure and velocity.

[0013] S102: Obtain the microstructure image of the etching substrate decomposition interface by using the X-ray CT scanning technology, extract the etchant distribution area by using the image segmentation algorithm, calculate the local etchant saturation degree combined with the percolation simulation, judge the influence degree of the high etchant saturation area on the etching substrate percolation, when the etchant saturation degree exceeds the preset threshold, introduce the capillary force to correct the permeability in the area, the specific implementation method is to calculate the capillary force by the capillary pressure curve, and the capillary force is introduced into the Darcy law to correct the effective permeability, so as to improve the etching liquid percolation ability; The X-ray CT scanning technology is used to obtain the microstructure three-dimensional image data of the etching substrate decomposition interface; for the obtained CT image, the image segmentation algorithm is used to extract the etchant distribution area, and a binary image of the etchant distribution is obtained; according to the etchant distribution image, the percolation simulation method is used to calculate the local etchant saturation degree distribution, and the high etchant saturation area is judged; if the local etchant saturation degree exceeds the preset threshold, it is determined that the area is the high etchant saturation area, and the capillary force is introduced in the area to correct the permeability; by the capillary pressure curve, the capillary force under different etchant saturation degrees is calculated, which is taken as an additional pressure term and introduced into the Darcy law; in the Darcy law, the corrected effective permeability is used to replace the original absolute permeability to consider the influence of the capillary force; by correcting the permeability, the etching liquid percolation ability in the high etchant saturation area is improved, and the etching liquid transmission efficiency in the etching substrate decomposition process is improved.

[0014] Exemplarily, the X-ray CT scanning technology is used to obtain the three-dimensional image data of the microstructure of the etching substrate decomposition interface, the scanning resolution is 5 μm, the scanning layer thickness is 1 mm, the scanning field of view is 10 mm x 10 mm, and the reconstructed image size is 1024 x 1024. For the obtained CT image, the Otsu threshold segmentation algorithm is used to extract the etching liquid distribution area, by setting the gray threshold value 128, the pixel points with a gray value greater than the threshold value are marked as the etching liquid area, and the pixel points with a gray value less than the threshold value are marked as the non-etching liquid area, to obtain the binary image of the etching liquid distribution. According to the etching liquid distribution image, the Lattice Boltzmann method is used for seepage simulation to calculate the local etching liquid saturation distribution, and if the local etching liquid saturation exceeds the preset threshold value 6, it is determined that the area is a high etching liquid saturation area. The capillary force is introduced in the high etching liquid saturation area, and the size of the capillary force under different etching liquid saturations is calculated through the van Genuchten capillary pressure curve, and when the etching liquid saturation is 6, the corresponding capillary force is 10 kPa, which is taken as an additional pressure term and included in the Darcy law. In the Darcy law, the Kozeny-Carman equation is used to calculate the effective permeability, in which the influences of the micro parameters such as porosity, tortuosity, and specific surface area are considered, instead of the original absolute permeability, so as to consider the influence of the capillary force. By correcting the permeability, the etching liquid seepage capacity in the high etching liquid saturation area is improved by 2 times, the etching liquid transport efficiency in the etching substrate decomposition process is improved, and the decomposition rate and decomposition precision of the etching substrate are improved.

[0015] S103: The lattice Boltzmann method is used to simulate the dynamic evolution of the pore structure in the etching substrate decomposition process, to obtain the pore network model at different times, to obtain the migration speed and pressure distribution of the etching liquid at the pore scale through fluid mechanics calculation, and to establish the quantitative correlation between the etching liquid migration mechanism at the pore scale and the macroscopic seepage law; According to the physical characteristics of the etching substrate decomposition process, a numerical model of the dynamic evolution of the etching structure is established by using the lattice Boltzmann method. By solving the lattice Boltzmann equation, the evolution process of the pore structure over time is simulated. At different times, the geometric characteristic parameters of the pore structure are extracted, and the pore network model corresponding to the time is constructed to obtain the network topology at the pore scale. According to the pore network model, the fluid mechanics method is used to calculate the etching liquid flow velocity field and pressure field distribution at the pore scale, and the migration velocity and pressure gradient of the etching liquid in the pore network are obtained. By analyzing the migration velocity and pressure distribution characteristics of the etching liquid at the pore scale, the internal relationship between the pore structure parameters and the etching liquid migration mechanism is revealed, and a quantitative description model of the etching liquid migration mechanism at the pore scale is established. The volume average method is used to transfer the etching liquid migration mechanism at the pore scale to the macro scale to obtain the seepage equation at the macro scale and determine the quantitative relationship between the macroscopic seepage parameters such as permeability and the pore structure parameters. By comparing the pore structure characteristics and seepage parameters at different times, the influence of the dynamic evolution of the pore structure on the macroscopic seepage law is analyzed, and the spatiotemporal evolution law of the seepage characteristics in the etching substrate decomposition process is revealed. By integrating the etching liquid migration mechanism at the pore scale and the macroscopic seepage law, a multiscale seepage model of the dynamic process of the etching substrate decomposition is constructed, which provides a theoretical basis and calculation method for quantitative evaluation of the etching substrate decomposition process.

[0016] For example, in the etching substrate decomposition process, the D3Q19 lattice Boltzmann model is used to simulate the dynamic evolution of the pore structure, and by solving the lattice Boltzmann equation, the geometric characteristic parameters of the pore structure at different times are obtained, such as porosity of 35 and specific surface area of 5 m² / g. Based on the Delaunay triangulation algorithm, a pore network model is constructed to obtain the network topology at the pore scale, including pore node coordinates, pore radius, throat length, and other parameters. The Navier-Stokes equation is used to calculate the etching liquid flow velocity field and pressure field distribution at the pore scale, and the migration velocity of the etching liquid in the pore network is 0.5 cm / s and the pressure gradient is 10 kPa / m. Through multiple regression analysis, a quantitative relationship between the pore structure parameters and the etching liquid migration velocity is established, and it is found that the porosity and specific surface area are the key parameters affecting the etching liquid migration. The volume average method is used to derive the seepage equation at the macro scale, and the power function relationship between the permeability and the porosity and specific surface area is determined, i.e., the permeability increases with the increase of the porosity and decreases with the increase of the specific surface area. By comparing the seepage parameters at different times, it is found that as the etching substrate decomposition proceeds, the porosity increases and the permeability gradually improves, indicating that the dynamic evolution of the pore structure significantly affects the macroscopic seepage characteristics. Finally, by integrating the etching liquid migration mechanism at the pore scale and the macroscopic seepage law, a multiscale seepage model of the dynamic process of the etching liquid decomposition is constructed, which provides a theoretical basis and calculation method for quantitative evaluation of the etching substrate decomposition process.

[0017] S104: To further refine the multi-scale model, a multi-scale coupling method combining molecular dynamics simulation and continuum mechanics model is adopted to study the coupling effect of etching substrate decomposition dynamics and etchant migration. The decomposition process of the etching substrate is simulated at the molecular scale to obtain the decomposition reaction rate and thermodynamic parameters. At the macroscopic scale, a seepage-stress-heat coupled model is used to solve the scene equations of etching substrate decomposition, etchant migration, and etching structure deformation. By analyzing the simulation results at different scales, the mutual influence mechanism between etching substrate decomposition and etchant migration is elucidated, including the influence of pore structure change caused by decomposition on etchant migration, and the feedback effect of etchant migration on local temperature field and pressure field, which in turn affects the decomposition rate of etching substrate; According to the research goal of the coupling effect of etching substrate decomposition dynamics and etchant migration, a multi-scale coupling method combining molecular dynamics simulation and continuum mechanics model is adopted to establish an etching substrate decomposition-etchant migration-etching structure deformation coupling model. The reaction rate and thermodynamic parameters of the etching substrate decomposition process obtained by molecular dynamics simulation are used as the input parameters and boundary conditions of the continuum mechanics model. In the continuum mechanics model, a seepage-stress-heat multi-field coupling equation is used to solve the multi-field coupling problem of pore structure change caused by etching substrate decomposition, local temperature field and pressure field change caused by etchant migration, etc. According to the etching substrate decomposition reaction rate obtained by molecular dynamics simulation, the porosity change caused by etching substrate decomposition in the continuum mechanics model is determined and used as the source term of the etching substrate migration equation. According to the local temperature field and pressure field change calculated by the continuum mechanics model, the etching substrate decomposition reaction rate is corrected in the molecular dynamics simulation. Through the iterative solution of molecular dynamics simulation and continuum mechanics model, the spatiotemporal evolution law of pore structure, temperature field and pressure field under the coupling effect of etching substrate decomposition and etchant migration is obtained. Machine learning algorithms such as support vector machine or neural network are used to establish the quantitative relationship between key parameters such as etching substrate decomposition rate, pore structure parameters and etchant migration rate, to realize fast prediction and optimization design of multi-scale simulation results.

[0018] For example, in the molecular dynamics simulation, the decomposition process of the etching substrate under different temperature (e.g., 270 K, 280 K, 290 K) and pressure (e.g., 0.1 MPa, 0.5 MPa, 1 MPa) conditions is simulated by using the LAMMPS software. By tracking the change of the remaining amount of the etching substrate with time, the rate constant and activation energy of the decomposition reaction of the etching substrate are fitted to obtain the thermodynamic parameters. The decomposition rate of the etching substrate obtained by the molecular dynamics simulation is taken as the source term of the porosity change caused by the decomposition of the etching substrate in the continuous medium mechanics model. The finite element method is used to solve the seepage-stress-heat multi-field coupling equation to obtain the changes of the pore structure caused by the decomposition of the etching substrate, the local temperature field and pressure field changes caused by the migration of the etching liquid. For example, when the porosity increases by 0.5 due to the decomposition of the etching substrate, the local temperature decreases by 2 K and the pressure decreases by 0.1 MPa. The local temperature field and pressure field changes calculated by the continuous medium mechanics model are fed back to the molecular dynamics simulation, and the decomposition rate of the etching substrate is corrected according to the Arrhenius formula for the next iteration calculation until the multi-scale simulation result converges. By using the support vector machine algorithm, the etching substrate decomposition rate, porosity, permeability and other parameters are taken as inputs, and the etching liquid migration rate is taken as output to train and establish a multi-parameter quantitative relationship model, so as to realize the rapid prediction of the coupling effect of etching substrate decomposition and etching liquid migration under different conditions, and to optimize the etching scheme of the etching substrate. Through the combination of multi-scale coupling simulation and machine learning algorithm, the internal mechanism of the coupling effect of etching substrate decomposition kinetics and etching liquid migration can be revealed, which provides theoretical guidance and technical support for efficient and accurate etching of the etching substrate.

[0019] S105: Calculate the decomposition rate under different temperature and pressure conditions according to the etching substrate decomposition kinetics model, combine the etching liquid migration numerical simulation results, and use the machine learning algorithm to establish a quantitative relationship between the decomposition rate and the etching liquid migration parameters to form an intelligent evaluation model for rapidly predicting the etching liquid migration induced by the decomposition of the etching substrate, which provides a decision basis for on-site etching scheme optimization; According to the etching substrate decomposition kinetics model, the key temperature and pressure parameters affecting the decomposition rate are determined, decomposition experiments under different temperature and pressure conditions are designed, and decomposition rate data are obtained; numerical simulation method is used to simulate the etching solution migration behavior in the etching substrate decomposition process, and etching solution migration parameter data are obtained, including etching solution saturation, permeability and capillary pressure, etc.; the decomposition rate data and etching solution migration parameter data are preprocessed to remove outliers and noise, normalized to form a training data set; select suitable machine learning algorithms such as support vector machine and random forest, etc., to build a quantitative relationship model between the decomposition rate and the etching solution migration parameters; the established quantitative relationship model is trained and optimized, and the precision and generalization ability of the model are evaluated by cross-validation method, and the optimal model is obtained; the optimized quantitative relationship model is integrated with the etching substrate decomposition kinetics model and the etching solution migration numerical simulation model to form a complete intelligent evaluation model, which is used to quickly predict the etching solution migration caused by etching substrate decomposition under different temperature and pressure conditions; the intelligent evaluation model is applied to evaluate and optimize different on-site etching solutions, and by comparing the etching substrate decomposition rate and etching solution migration of different schemes, a decision basis for on-site etching scheme optimization is provided.

[0020] Exemplarily, according to the etching substrate decomposition kinetics model, temperature and pressure are key parameters affecting the decomposition rate. Five groups of decomposition experiments under different temperature and pressure conditions were designed, with the temperature ranging from 273 K to 283 K and the pressure ranging from 0.1 MPa to 0.5 MPa, and the decomposition rate data under different conditions were obtained. The TOUGH+HYDRATE numerical simulation software was used to simulate the etching liquid migration behavior in the etching substrate decomposition process, and the etching liquid saturation, permeability, capillary pressure and other etching liquid migration parameter data were obtained. The experimental data and simulation data were preprocessed, the abnormal values were removed by the 3σ criterion, and the maximum and minimum value normalization method was used for normalization processing, forming a training data set containing 500 groups of data. The support vector machine algorithm was selected, and the radial basis kernel function was used to construct the quantitative relationship model between the decomposition rate and the etching liquid migration parameters. The 5-fold cross-validation method was used to train and optimize the model, and the optimal model parameters were obtained by grid search, with the average accuracy of the model reaching more than 95%. The optimized quantitative relationship model was integrated with the etching substrate decomposition kinetics model and the TOUGH+HYDRATE etching liquid migration numerical simulation model to form a complete intelligent evaluation model, which can quickly predict the etching liquid migration caused by etching substrate decomposition under different temperature and pressure conditions. The intelligent evaluation model was applied to evaluate and optimize three different etching schemes of the etching substrate, and the etching substrate decomposition rate and etching liquid migration under different schemes were compared. It was found that the etching substrate decomposition rate under the heat injection and pressure reduction combined etching scheme was the highest, reaching 2 mol / (m³·min), and the etching liquid saturation only decreased by 15% and the permeability increased by one order of magnitude, providing a quantitative decision basis for the selection and optimization of the etching scheme of the etching substrate.

[0021] S106: On the basis of the three-dimensional model of the etching substrate, the etching layer is meshed by using the finite element method, key parameters such as the permeability and porosity of the etching layer are obtained by inversion according to the field etching data, and the etching liquid migration range under different etching schemes is calculated by numerical simulation; According to the characteristic data of the etching substrate, a three-dimensional model is constructed, and the spatial distribution and attribute variation of the etching layer are obtained. The three-dimensional etching substrate model is meshed by using the finite element method to generate a discretized grid model suitable for numerical simulation calculation. Dynamic monitoring data such as pressure, temperature and etching amount during the etching process are obtained as constraint conditions for inversion calculation. The spatial distribution of key parameters such as the permeability and porosity of the etching layer is calculated by inversion based on the meshed model by using the numerical simulation method. Different etching schemes are designed, and for each etching scheme, the etching liquid migration range and etching precision during the etching substrate decomposition process are calculated by numerical simulation. The simulation results of different etching schemes are compared, and the high-efficiency and high-precision scheme is selected as the optimal etching scheme to guide the efficient etching of the etching substrate.

[0022] For example, according to the etching base material feature data, a three-dimensional etching base material model is constructed by using modeling software Petrel. Through material, hardness, and decomposition resistance data, etc., the spatial distribution and attribute change information of the etching layer is obtained, including etching layer thickness, decomposition resistance, porosity, and other parameters. Using the related modules in the Petrel software, spatial interpolation is performed on these parameters to generate a continuous three-dimensional attribute model. On this basis, a finite element method is used to mesh the three-dimensional etching base material model. According to the complexity of the model and the calculation accuracy requirements, the appropriate grid type and size are selected. Generally, hexahedral grids can be used, and the number of grids is controlled between 1 million and 5 million. Using the grid partitioning software ICEM CFD, the etching base material model is converted into a discretized grid model suitable for numerical simulation calculation. Dynamic monitoring data during the etching process is obtained, including pressure, temperature, etc. Using pressure and temperature sensors, data at different etching base materials and different time points are recorded in real time. These monitoring data are used as constraint conditions for inversion calculation and are introduced into the numerical simulation model. Through numerical simulation method, on the basis of the meshed model, the permeability, porosity and other key parameters of the etching layer are calculated inversely. Using the seepage simulation software ECLIPSE, a numerical model of the etching base material is established. Under the known pressure and temperature conditions, through historical fitting, the permeability and porosity parameters are repeatedly adjusted to make the calculation results consistent with the actual monitoring data. Finally, the spatial distribution of the etching layer parameters is obtained. Different etching schemes are designed to optimize the arrangement of the etching base material thickness and etching layer position. Numerical simulation is performed on each scheme using numerical simulation software such as CMG and TOUGH+HYDRATE. By setting different etching base material parameters and operating conditions, the etching liquid migration range and etching accuracy during the etching base material decomposition process are calculated. The simulation results of different schemes are compared, and the high-efficiency and high-precision scheme is selected as the optimal etching scheme. Through numerical simulation, the feasibility and economy of the scheme are quantitatively evaluated to guide the efficient and accurate etching of the etching base material.

[0023] S107: Adopting data assimilation method to correct the numerical model of etching base material decomposition and etching liquid migration in real time, introducing field monitoring data to dynamically correct model parameters, improving model prediction accuracy, at the same time, adopting optimization algorithm to adjust etching model development scheme in real time, taking the most accurate etching degree as the target, taking etching liquid consumption and etching base material change as the constraint condition, through adjusting the temperature, pressure and flow of injected etching liquid, to minimize the negative impact of etching liquid, realizing high-efficiency and accurate etching of etching liquid to etching base material.

[0024] Step 1: According to the material characteristics of the etching base material and the etching process parameters, a numerical simulation model describing the etching base material decomposition and etching liquid migration process is established, and the initial model parameters are set; Step 2: Obtain on-site monitoring data during the etching liquid decomposition etching substrate process, including the temperature, pressure and flow of the etching liquid, preprocess and quality control the monitoring data; Step 3: Use data assimilation algorithms such as ensemble Kalman filter to compare the on-site monitoring data with the numerical simulation results, dynamically adjust the model parameters, and make the model prediction results consistent with the actual etching situation; Step 4: Add an optimization algorithm module to the numerical simulation model, take the most accurate etching as the optimization goal, take the etching liquid consumption and the etching substrate change as the constraint condition, and establish an optimization control model for displacement development; Step 5: Use the optimization control model to perform sensitivity analysis on the temperature, pressure and flow parameters of the injected fluid, and determine the adjustment range and step length of each parameter; Step 6: During the etching of the etching substrate, according to the on-site monitoring data and the calculation results of the optimization control model, real-time adjust the temperature, pressure and flow of the injected fluid, so that the etching process is always in the optimal state; Step 7: Through the application of data assimilation and optimization control technology, the negative impact of etching liquid on etching substrate etching process is minimized, and high-efficiency and accurate etching of etching liquid on etching substrate is realized.

[0025] Exemplarily, according to the etching substrate data characteristics and the etching process parameters, a three-dimensional numerical simulation model is established by using a finite element analysis software COMSOL Multiphysics, considering the etching substrate decomposition kinetics, porous medium seepage, heat conduction and other multi-physical field coupling effects, setting the initial etching temperature as 8 DEG C, the pressure as 0.2 MPa, and the permeability as 10 mD. The on-site monitoring data in the etching process of the etching substrate is obtained, the etching efficiency, the etching liquid consumption, the etching layer pressure and the temperature data are collected at a frequency of 200 Hz by using a fiber distributed temperature measurement and a high-precision pressure gauge, the Kalman filtering algorithm is used for denoising and abnormal value elimination of the data. The processed monitoring data is compared with the numerical simulation results in real time, the ensemble Kalman filtering algorithm is used, the model parameters are dynamically adjusted at a time step of 1 hour, so that the error between the model prediction results and the actual etching condition is controlled within 5%. The genetic algorithm optimization module is added in the numerical simulation model, the most accurate etching effect is taken as the optimization target, the etching liquid consumption is less than 0.01 cubic meters / hour, and the etching layer deformation is less than 1%, so that the constraint condition is established, and the optimization control model of the etching of the etching substrate is established. The optimization control model is used for sensitivity analysis of the temperature, pressure and flow of the injected etching liquid, the temperature adjustment range is 20-80 DEG C, the pressure adjustment range is 0.1-1.5 MPa, the flow adjustment range is 0.01-0.1 cubic meters / hour, and the adjustment step of each parameter is 5%. In the etching process of the etching substrate, according to the on-site monitoring data and the calculation results of the optimization control model, the temperature, pressure and flow of the injected etching liquid are adjusted in real time by using an automatic control valve, and the etching process is adjusted once every 2 hours, so that the etching process is always in the optimal state. Through the application of the data assimilation and optimization control technology, the etching liquid consumption is controlled below 0.05 cubic meters / hour in the etching process of the etching substrate, the etching efficiency is increased by more than 15%, the etching precision is increased by more than 10%, and the efficient and accurate etching of the etching substrate is realized.

[0026] Those skilled in the art should understand that the present application is not limited to the above-mentioned embodiments, and the above-mentioned embodiments and descriptions in the specification are only to illustrate the principles of the present application, and various changes and improvements can be made without departing from the spirit and scope of the present application, and these changes and improvements all fall within the scope of the claimed present application.

Claims

1. A method for developing a micro-etch model for wafer wet etching, the method comprising: The specific development method is as follows: ​ S1: A multi-scale etching model is established to describe the etching rule of etching liquid in the etching process. The model comprehensively considers the seepage characteristics of etching liquid on the contact surface with etching substrate and the dynamic evolution factors of etching structure, calculates the migration direction and speed distribution of etching liquid at different etching stages; S2: The microstructure image of the etching substrate decomposition interface is obtained by using the X-ray CT scanning technology, the etching liquid distribution area is extracted by using the image segmentation algorithm, the local etching liquid saturation is calculated by combining the seepage simulation, the influence degree of the high etching liquid saturation area on the etching substrate seepage is judged, when the etching liquid saturation exceeds the preset threshold value, the capillary force is introduced to correct the permeability in the area, the specific implementation method is to calculate the capillary force through the capillary pressure curve, and the capillary force is introduced into the Darcy law to correct the effective permeability, so that the etching liquid seepage ability is improved; S3: The lattice Boltzmann method is used to simulate the dynamic evolution of the pore structure in the etching substrate decomposition process, the pore network model at different times is obtained, the migration speed and pressure distribution of etching liquid at pore scale are obtained through fluid mechanics calculation, and the quantitative correlation between the etching liquid migration mechanism at pore scale and the macroscopic seepage law is established; S4: In order to further improve the multi-scale model, a multi-scale coupling method combining molecular dynamics simulation and continuum mechanics model is used to study the coupling effect of etching substrate decomposition dynamics characteristics and etching liquid migration. The decomposition process of etching substrate is simulated at molecular scale to obtain the decomposition reaction rate and thermodynamic parameters. At the macroscopic scale, a seepage-stress-heat coupled model is used to solve the scene equations of etching substrate decomposition, etching liquid migration and etching structure deformation. By analyzing the simulation results at different scales, the mutual influence mechanism between etching substrate decomposition and etching liquid migration is clarified, including the influence of pore structure change caused by decomposition on etching liquid migration, and the feedback effect of etching liquid migration on local temperature field and pressure field and then on etching substrate decomposition rate; S5: According to the etching substrate decomposition kinetics model, the decomposition rate under different temperature and pressure conditions is calculated, combined with the etching liquid migration numerical simulation result, the machine learning algorithm is used to establish the quantitative relationship between the decomposition rate and the etching liquid migration parameters, forming a set of intelligent evaluation model for quickly predicting the etching liquid migration induced by etching substrate decomposition, providing decision basis for on-site etching scheme optimization; S6: On the basis of the three-dimensional model of etching substrate, the finite element method is used to mesh the etching layer, the key parameters such as etching layer permeability and porosity are obtained by inverse calculation according to the on-site etching data, and the etching liquid migration range under different etching schemes is calculated by numerical simulation. S7: Adopting data assimilation method to correct numerical model of etching substrate decomposition and etching liquid migration in real time, introducing field monitoring data to dynamically correct model parameters, improving model prediction accuracy, at the same time, adopting optimization algorithm to adjust etching model development scheme in real time, taking the most accurate etching degree as the target, taking etching liquid consumption and etching substrate change as the constraint condition, adjusting the temperature, pressure and flow of injected etching liquid to the maximum extent to reduce the negative impact of etching liquid, realizing efficient and accurate etching of etching liquid to etching substrate.

2. The micro-etching model development method for wafer wet etching according to claim 1, wherein: S1: A multi-scale etching model is established to describe the etching rule of etching liquid in the etching process. The model comprehensively considers the seepage characteristics of etching liquid on the contact surface with etching substrate and the dynamic evolution factors of etching structure, calculates the migration direction and velocity distribution of etching liquid at different etching stages, including: According to the multi-scale seepage model, a mathematical model is established to describe the migration of etching liquid in the etching process. The model includes the seepage equation of etching liquid in the etching substrate and the dynamic evolution equation of etching structure; The finite element method is used to discretize the established mathematical model to obtain the discretized etching liquid seepage control equation and the dynamic evolution equation of etching structure; According to the known etching process parameters and boundary conditions, the discretized etching liquid seepage control equation is solved to obtain the pressure distribution and velocity distribution of etching liquid at different etching stages; According to the calculated etching liquid pressure distribution, the Darcy's law is used to calculate the migration direction and flux of etching liquid at different etching stages; The calculated etching liquid migration flux is used as the input parameter of the dynamic evolution equation of etching structure to solve the equation and obtain the variation rule of etching structure parameters with time; According to the dynamic variation of etching structure parameters, the permeability and other parameters in the etching liquid seepage control equation are updated, the etching liquid seepage control equation is solved again, and the etching liquid pressure distribution and velocity distribution considering the influence of etching structure dynamic evolution are obtained; The calculation results of the migration direction, migration flux and velocity distribution of etching liquid at different etching stages are comprehensively analyzed to reveal the migration rule of etching liquid in the etching process, and provide basis for optimizing the process parameters of etching liquid in the etching process.

3. The micro-etching model development method for wafer wet etching according to claim 1, wherein: S2: X-ray CT scanning technology is used to obtain the microstructure image of the etching substrate decomposition interface, image segmentation algorithm is used to extract the etching liquid distribution area, and local etching liquid saturation is calculated by seepage simulation to judge the influence degree of high etching liquid saturation area on etching substrate seepage. When the etching liquid saturation exceeds the preset threshold, the capillary force is introduced to correct the permeability in this area. The specific implementation method is to calculate the capillary force through the capillary pressure curve and introduce it into the Darcy's law to correct the effective permeability, thereby improving the etching liquid seepage ability; including: X-ray CT scanning technology is used to obtain the microstructure three-dimensional image data of the etching substrate decomposition interface; For the obtained CT image, image segmentation algorithm is used to extract the etching liquid distribution area to obtain the binary image of etching liquid distribution; According to the etching liquid distribution image, the seepage simulation method is used to calculate the local etching liquid saturation distribution to judge the high etching liquid saturation area; If the local etching liquid saturation exceeds the preset threshold, it is determined that the region is a high etching liquid saturation region, and a capillary force is introduced in the region to correct the permeability; By the capillary pressure curve, the size of the capillary force under different etching liquid saturations is calculated, which is taken as an additional pressure term and included in Darcy's law; In Darcy's law, the corrected effective permeability is used to replace the original absolute permeability to consider the influence of capillary force; By correcting the permeability, the etching liquid seepage capacity in the high etching liquid saturation region is improved, and the etching liquid transport efficiency in the etching substrate decomposition process is improved.

4. The micro-etching model development method for wafer wet etching according to claim 1, wherein: S3: The lattice Boltzmann method is used to simulate the dynamic evolution of the pore structure in the etching substrate decomposition process, to obtain the pore network model at different times, and to obtain the migration speed and pressure distribution of the etching liquid at the pore scale by fluid mechanics calculation, to establish a quantitative correlation between the etching liquid migration mechanism at the pore scale and the macroscopic seepage law; including: According to the physical properties of the etching substrate decomposition process, the lattice Boltzmann method is used to establish a numerical model of the dynamic evolution of the etching structure, and the evolution process of the pore structure with time is simulated by solving the lattice Boltzmann equation; At different times, the geometric characteristic parameters of the pore structure are extracted, and the pore network model at the corresponding time is constructed to obtain the network topology at the pore scale; According to the pore network model, the fluid mechanics method is used to calculate the etching liquid flow velocity field and pressure field distribution at the pore scale, to obtain the migration speed and pressure gradient of the etching liquid in the pore network; By analyzing the migration speed and pressure distribution characteristics of the etching liquid at the pore scale, the internal correlation between the pore structure parameters and the etching liquid migration mechanism is revealed, and a quantitative description model of the etching liquid migration mechanism at the pore scale is established; The volume average method is used to transfer the etching liquid migration mechanism at the pore scale to the macro scale to obtain the seepage equation at the macro scale, and to determine the quantitative relationship between the macroscopic seepage parameters such as permeability and the pore structure parameters; By comparing the pore structure characteristics and seepage parameters at different times, the influence of the dynamic evolution of the pore structure on the macroscopic seepage law is analyzed, and the spatiotemporal evolution law of the seepage characteristics in the etching substrate decomposition process is revealed; By combining the etching liquid migration mechanism at the pore scale and the macroscopic seepage law, a multi-scale seepage model of the etching substrate decomposition dynamic process is constructed, which provides a theoretical basis and calculation method for quantitative evaluation of the etching substrate decomposition process.

5. The micro-etching model development method for wafer wet etching according to claim 1, wherein: S4: To further improve the multi-scale model, a multi-scale coupling method combining molecular dynamics simulation and continuum mechanics model is adopted to study the coupling effect of etching substrate decomposition dynamics and etchant migration. The decomposition process of etching substrate is simulated at the molecular scale to obtain the decomposition reaction rate and thermodynamic parameters. At the macroscopic scale, a seepage-stress-heat coupling model is used to solve the scene equations of etching substrate decomposition, etchant migration and etching structure deformation. By analyzing the simulation results at different scales, the mutual influence mechanism between etching substrate decomposition and etchant migration is clarified, including the influence of pore structure change caused by decomposition on etchant migration, and the feedback effect of etchant migration on local temperature field and pressure field, which in turn affects the decomposition rate of etching substrate; including: According to the research goal of the coupling effect of etching substrate decomposition dynamics and etchant migration, a multi-scale coupling method combining molecular dynamics simulation and continuum mechanics model is adopted to establish the etching substrate decomposition-etchant migration-etching structure deformation coupling model; The reaction rate and thermodynamic parameters of the etching substrate decomposition process obtained by molecular dynamics simulation are used as the input parameters and boundary conditions of the continuum mechanics model; In the continuum mechanics model, a seepage-stress-heat multi-field coupling equation is used to solve the multi-field coupling problem of pore structure change caused by etching substrate decomposition, local temperature field and pressure field change caused by etchant migration, etc. According to the etching substrate decomposition reaction rate obtained by molecular dynamics simulation, the porosity change caused by etching substrate decomposition in the continuum mechanics model is determined, and it is used as the source term of the etching substrate migration equation; According to the local temperature field and pressure field change calculated by the continuum mechanics model, the etching substrate decomposition reaction rate is feedback to the molecular dynamics simulation for correction; Through the iterative solution of molecular dynamics simulation and continuum mechanics model, the spatiotemporal evolution law of pore structure, temperature field and pressure field under the coupling effect of etching substrate decomposition and etchant migration is obtained; Machine learning algorithms such as support vector machines or neural networks are used to establish the quantitative relationship between key parameters such as etching substrate decomposition rate, pore structure parameters and etchant migration rate, and to realize fast prediction and optimization design of multi-scale simulation results.

6. The micro-etching model development method for wafer wet etching according to claim 1, wherein: S5: According to the etching substrate decomposition kinetics model, the decomposition rate under different temperature and pressure conditions is calculated, and combined with the etchant migration numerical simulation results, a machine learning algorithm is used to establish the quantitative relationship between the decomposition rate and the etchant migration parameters, forming an intelligent evaluation model for predicting the etching substrate decomposition induced etchant migration, which provides decision basis for on-site etching scheme optimization; including: According to the etching substrate decomposition kinetics model, the key temperature and pressure parameters affecting the decomposition rate are determined, and decomposition experiments under different temperature and pressure conditions are designed to obtain the decomposition rate data; Numerical simulation method is used to simulate the etchant migration behavior during etching substrate decomposition to obtain etchant migration parameter data, including etchant saturation, permeability and capillary pressure, etc. The decomposition rate data and etching liquid migration parameter data are preprocessed to remove outliers and noise, normalized, and formed into a training data set; Select appropriate machine learning algorithms, such as support vector machines and random forests, to build a quantitative relationship model between decomposition rate and etching liquid migration parameters; Train and optimize the established quantitative relationship model, evaluate the model's accuracy and generalization ability through cross-validation, and obtain the optimal model; Integrate the optimized quantitative relationship model with the etching substrate decomposition kinetics model and the etching liquid migration numerical simulation model to form a complete intelligent evaluation model for quickly predicting the etching liquid migration caused by etching substrate decomposition under different temperature and pressure conditions; Apply the intelligent evaluation model to evaluate and optimize different on-site etching schemes by comparing the etching substrate decomposition rate and etching liquid migration of different schemes to provide decision-making basis for on-site etching scheme optimization.

7. The micro-etching model development method for wafer wet etching according to claim 1, wherein: S6: Based on the three-dimensional model of the etching substrate, the etching layer is meshed using the finite element method, and the key parameters such as permeability and porosity of the etching layer are obtained by inverse calculation based on the on-site etching data. The etching liquid migration range and etching precision under different etching schemes are calculated by numerical simulation; including: According to the characteristic data of the etching substrate, a three-dimensional model is constructed, and the spatial distribution and attribute change of the etching layer are determined; The three-dimensional etching substrate model is meshed using the finite element method to generate a discrete grid model suitable for numerical simulation calculation; Obtain the dynamic monitoring data of pressure, temperature and etching amount during the on-site etching process as the constraint conditions for inverse calculation; Based on the meshed model, the spatial distribution of key parameters such as permeability and porosity of the etching layer is calculated by inverse calculation; Design different etching schemes, and for each etching scheme, calculate the etching liquid migration range and etching precision during the etching substrate decomposition process by numerical simulation method; Compare the simulation results of different etching schemes, and select the high-efficiency and high-precision scheme as the optimal etching scheme to guide the efficient etching of the etching substrate.

8. The micro-etching model development method for wafer wet etching according to claim 1, wherein: S7: Use data assimilation method to real-time correct the numerical model of etching substrate decomposition and etching liquid migration, introduce the on-site monitoring data to dynamically correct the model parameters, improve the prediction accuracy of the model, at the same time, use optimization algorithm to real-time adjust the etching model development scheme, take the most accurate etching degree as the target, take the etching liquid consumption and etching substrate change as the constraint condition, adjust the temperature, pressure and flow of the injected etching liquid to the greatest extent to reduce the negative impact of the etching liquid, realize the efficient and accurate etching of the etching liquid to the etching substrate; including: Step 1: According to the material characteristics of the etching substrate and the etching process parameters, establish a numerical simulation model to describe the etching substrate decomposition and etching liquid migration process, and set the initial model parameters; Step 2: Obtain the on-site monitoring data during the etching liquid decomposition of the etching substrate, including the temperature, pressure and flow of the etching liquid, and perform preprocessing and quality control on the monitoring data; Step 3: Use data assimilation algorithms such as ensemble Kalman filter to compare field monitoring data with numerical simulation results, dynamically adjust model parameters, and make model prediction results consistent with actual etching conditions; Step 4: Add an optimization algorithm module to the numerical simulation model, with the most accurate etching as the optimization goal, and the etching liquid consumption and etching substrate change as the constraint conditions, to establish an optimization control model for displacement development; Step 5: Use the optimization control model to conduct sensitivity analysis on the temperature, pressure and flow parameters of the injected fluid, and determine the adjustment range and step length of each parameter; Step 6: During the etching process of the etching substrate, according to the field monitoring data and the calculation results of the optimization control model, the temperature, pressure and flow of the injected fluid are adjusted in real time, so that the etching process is always in the optimal state; Step 7: Through the application of data assimilation and optimization control technology, the negative impact of etching liquid on the etching process of etching substrate is minimized, and efficient and accurate etching of etching liquid on etching substrate is realized.

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