Optimization method and device for plasma etching process of laminated material

Abstract

The invention discloses an optimization method and device for a laminated material plasma etching process, relates to the technical field of semiconductor simulation, and aims to solve the problems of low efficiency, insufficient accuracy and poor universality in laminated material simulation in the prior art. The optimization method comprises the following steps: obtaining to-be-optimized physical parameters and a value space of the to-be-optimized physical parameters of the laminated material in a plasma etching process; performing initial sampling on the value space based on a Bayesian optimization method and a first Monte Carlo simulation method to obtain initial sampling data; training a neural network agent model based on the initial sampling data, and selecting candidate points through an acquisition function to obtain a candidate point set; processing the candidate point set by adopting a second Monte Carlo simulation method and obtaining a loss function value set; performing optimization iteration based on the loss function value set until a preset condition is met, and obtaining a target physical parameter combination; the preset condition is that a preset optimization round is reached or a loss function value is converged.

Description

Technical Field

[0001] This invention relates to the field of semiconductor simulation technology, and in particular to an optimization method and apparatus for plasma etching processes of multilayer materials. Background Technology

[0002] In the field of integrated circuit manufacturing, multilayer materials have become a core foundation for addressing the challenges of process miniaturization and structural complexity due to their synergistic multi-material properties. For example, Si / SiGe multilayer materials achieve functional division between carrier channels and sacrificial layers by periodically alternating the growth of Si and SiGe layers and utilizing lattice mismatch and etching selectivity differences, and are widely used in the fabrication of advanced devices.

[0003] Plasma etching, as a key process for pattern transfer, removes substrate atoms through a synergistic physical and chemical mechanism. The precise optimization of its process parameters directly determines the quality of the etching profile and the performance of the device.

[0004] Currently, the simulation optimization of plasma etching processes for multilayer materials mainly relies on three methods: manual tuning, experimental verification, and atomic-level simulation. However, these methods have significant technical bottlenecks: First, manual tuning relies heavily on engineers' historical experience and data accumulation, making it susceptible to subjective biases that can lead to non-physical interpretations. Furthermore, the optimization process is time-consuming, prone to getting stuck in local optima, and unable to adapt to nonlinear responses caused by changes in new materials or gas ratios. Second, while experimental verification yields accurate results, each etching operation requires a dedicated reactor and electron microscope characterization, resulting in high costs. Moreover, the resolution is insufficient to quantify sub-nanometer etching mechanisms, and the data acquisition cycle significantly lags behind the process development pace. Third, atomic-level simulation relies on molecular dynamics, first-principles calculations, and other methods, which are extremely slow and cannot efficiently perform targeted tuning of physical parameters.

[0005] The aforementioned problems directly lead to uncontrolled etching feature profiles, resulting in defects such as neck blockage and excessive etching depth deviation. This causes complete failure in innovative application scenarios such as 3D memory devices, necessitating an efficient, precise, and universal etching process parameter optimization solution. Summary of the Invention

[0006] The purpose of this invention is to provide an optimized method and apparatus for plasma etching of multilayer materials, so as to solve the problems of low efficiency, insufficient accuracy and poor versatility in the simulation of multilayer materials in the prior art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides an optimized method for plasma etching processes of multilayer materials, comprising: Obtain the physical parameters to be optimized for the multilayer material in the plasma etching process and their value space; Initial sampling data is obtained by initially sampling the value space based on the Bayesian optimization method and the first Monte Carlo simulation method. A neural network proxy model is trained based on the initial sampled data, and candidate points are selected through a collection function to obtain a set of candidate points; The second Monte Carlo simulation method is used to process the candidate point set and obtain the loss function value set; The optimization iteration is performed based on the set of loss function values ​​until the preset conditions are met to obtain the target combination of physical parameters; the preset conditions are reaching a preset number of optimization rounds or the convergence of loss function values.

[0008] Optionally, the value space is initially sampled based on the Bayesian optimization method and the first Monte Carlo simulation method to obtain initial sampled data, including: N rounds of uniform sampling are performed within the value space, and each round of sampling generates M initial parameter combinations; where each initial parameter combination includes the specific values ​​of each physical parameter; N and M are both greater than zero; For M initial parameter combinations, the first Monte Carlo simulation method is used to perform etching simulation to obtain the simulation results for each initial parameter combination; The simulation results for each initial parameter combination are analyzed to extract the simulation values ​​of the measurement indicators related to etching. Initial sampling data were constructed based on simulation values ​​and real electron microscopy characterization data.

[0009] Optionally, the measurement parameters include the maximum etching depth, the difference between the maximum width and the etched opening, the depth at which the maximum width is located, the bottom width, and the bottom protrusion height; Based on simulated values ​​and real electron microscopy characterization data, initial sampling data were constructed, including: The true values ​​of each measurement index are determined based on real electron microscopy characterization data; Substitute the simulated and actual values ​​of each measurement indicator into the mean square error function calculation formula: ; Obtain the loss function value corresponding to a single initial parameter combination; where, The value of the loss function; The number of measurement indicators; For the first Simulated values ​​of each measurement index; For the first The true value of each measurement indicator; Each initial parameter combination is mapped one-to-one with its corresponding loss function value, thus constructing initial sampling data consisting of the initial parameter combination and the loss function value.

[0010] Optionally, before training the neural network agent model based on the initial sampled data, the method further includes: constructing the neural network agent model; Constructing a neural network surrogate model involves integrating multiple feedforward neural networks in parallel to obtain the neural network surrogate model.

[0011] Optionally, before integrating multiple feedforward neural networks in parallel, the method further includes: constructing a single feedforward neural network; Building a single feedforward neural network includes: The feedforward neural network is obtained by sequentially setting up an input layer, a first fully connected layer, a first ReLU activation function, a first Dropout regularization module, a second fully connected layer, a second ReLU activation function, a second Dropout regularization module, a third fully connected layer, a third ReLU activation function, and an output layer; wherein the output layer includes a fourth fully connected layer and an output module.

[0012] Optionally, a neural network surrogate model is trained based on the initial sampled data, and candidate points are selected using a sampling function to obtain a set of candidate points, including: Using the initial sampled data, combined with the learning rate scheduler and early stopping mechanism, a neural network proxy model is trained to obtain the trained model; Multiple combinations of potential parameters are randomly sampled from the value space to form a candidate pool; Each potential parameter combination in the candidate pool is input into the trained model to obtain the prediction mean and prediction uncertainty for each potential parameter combination; where the prediction mean is the mean of the prediction results of multiple feedforward neural network loss values; and the prediction uncertainty is the standard deviation of the prediction results of multiple feedforward neural network loss values. The predicted mean and prediction uncertainty of each potential parameter combination are input into the acquisition function and combined with the Constant Liar strategy to generate multiple non-overlapping candidate points, forming a candidate point set.

[0013] Optionally, the predicted mean and prediction uncertainty of each potential parameter combination are input into the acquisition function and combined with the Constant Liar strategy to generate multiple non-overlapping candidate points, forming a candidate point set, including: The predicted mean and prediction uncertainty for each combination of potential parameters are input into the EI acquisition function: ; Calculate the EI function value for each potential parameter combination, and select the potential parameter combination with the largest EI function value as the first candidate point; where, ; The cumulative distribution function of the standard normal distribution; is the probability density function of the standard normal distribution; To predict the mean; The optimal loss function value; To adjust the non-negative hyperparameters that balance exploration and utilization; To predict uncertainty; Based on the Constant Liar strategy, the optimal loss function value in the initial data of point selection is determined as the virtual loss function value of the first candidate point, and the first candidate point and its corresponding virtual loss function value are used as the first virtual sample to supplement the initial data of point selection, forming the first virtual update data. Based on the first virtual update data, the second candidate point is selected by using the EI acquisition function; Based on the Constant Liar strategy, the optimal loss function value in the first virtual update data is determined as the virtual loss function value of the second candidate point. The second candidate point and its corresponding virtual loss function value are then added to the first virtual update data to form the second virtual update data. The process continues until the last candidate point is selected using the EI acquisition function, resulting in a candidate point set.

[0014] Optionally, a second Monte Carlo simulation method is used to process the candidate point set and obtain a set of loss function values, including: For each candidate point in the candidate point set, the second Monte Carlo simulation method is used to perform etching simulation to obtain the simulation results for each candidate point; The simulation results for each candidate point are analyzed to extract the simulation values ​​of the measurement indicators; Based on the mean square error function calculation formula, and combined with the true values ​​of each measurement index, the loss function value of each candidate point is calculated. The loss function values ​​of all candidate points are integrated to form a set of loss function values.

[0015] Optionally, optimization iterations are performed based on the set of loss function values, including: The candidate point set and the corresponding loss function value are added to the historical sampling data to obtain the true cumulative sampling data; each candidate point in the candidate point set corresponds one-to-one with the loss function value; the historical sampling data is the cumulative set of the initial sampling data and the candidate points and corresponding loss function values ​​added in each optimization iteration. Based on real cumulative sampling data, the neural network agent model is retrained to obtain the updated model output; Based on the updated model output, an updated set of candidate points is determined by acquiring the function and combining it with the Constant Liar strategy. The updated set of candidate points is then processed by the second Monte Carlo simulation method to obtain an updated set of loss function values. The optimization iteration continues based on the updated set of loss function values ​​until the preset conditions are met.

[0016] Compared with existing technologies, the optimization method for plasma etching process of stacked materials provided by this invention uses Bayesian optimization method and first Monte Carlo simulation method to carry out initial sampling, quickly obtain initial sampling data covering the value space, and reduce the time consumption of blind exploration; it uses trained neural network surrogate model to provide efficient prediction support for candidate point selection, avoiding repeated reliance on time-consuming physical experiments or atomic-level simulations; it performs optimization iteration based on loss function value set until a preset number of rounds or convergence of loss function value is reached, avoiding invalid iterations and effectively solving the problem of low efficiency in existing technologies.

[0017] Using Bayesian optimization as a framework, this method precisely selects parameter combinations with optimization potential through a sampling function, replacing the traditional experience-driven tuning approach. Initial sampling is based on a defined value space, and reliable initial sampling data is obtained by combining Monte Carlo simulation, laying a solid foundation for model training. During the optimization iteration process, the loss function value is used as the core feedback indicator, and the optimal solution is continuously approached through multiple iterations, significantly improving the accuracy of the final target physical parameter combination and solving the problem of insufficient accuracy.

[0018] The method focuses on the physical parameters to be optimized and their value space, without limiting specific stacked materials or single physical parameter types, and can adapt to the optimization needs of plasma etching processes for different stacked materials. The core optimization logic adopts a combination of Bayesian optimization, neural network surrogate model and Monte Carlo simulation, which does not rely on empirical data of specific process scenarios, can adapt to parameter optimization in different value spaces, effectively improve the general adaptability of the method and solve the problem of poor versatility.

[0019] Secondly, the present invention also provides an optimized apparatus for a plasma etching process of multilayer materials, comprising: The acquisition module is used to acquire the physical parameters to be optimized for the stacked material in the plasma etching process and their value space; The sampling module is used to perform initial sampling of the value space based on the Bayesian optimization method and the first Monte Carlo simulation method to obtain initial sampling data. The acquisition module is used to train a neural network proxy model based on initial sampled data and select candidate points through an acquisition function to obtain a set of candidate points; The processing module is used to process the candidate point set using the second Monte Carlo simulation method and obtain the loss function value set; The iteration module is used to perform optimization iterations based on the set of loss function values ​​until a preset condition is met to obtain the target combination of physical parameters; the preset condition is to reach a preset number of optimization rounds or for the loss function values ​​to converge. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 One of the flowcharts of an optimized method for a multilayer material plasma etching process provided in an embodiment of the present invention; Figure 2 A partial flowchart of an optimized method for a multilayer material plasma etching process provided in an embodiment of the present invention; Figure 3 A schematic diagram of simulated etching morphology provided for one embodiment of the present invention; Figure 4 A schematic diagram of the structure of a feedforward neural network provided in one embodiment of the present invention; Figure 5 A second schematic flowchart of an optimized method for a multilayer material plasma etching process provided in an embodiment of the present invention; Figure 6 A line graph showing the loss function values ​​corresponding to a 200-round Bayesian optimization process, as provided in one embodiment of the present invention; Figure 7 This is a schematic diagram of an optimized apparatus for a multilayer material plasma etching process provided in an embodiment of the present invention. Detailed Implementation

[0021] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0022] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0023] In this invention, "at least one" means one or more, and "more than one" means two or more. "And / or" describes the relationship between the associated objects, indicating that three relationships can exist.

[0024] like Figure 1As shown, embodiments of the present invention provide an optimized method for plasma etching processes of multilayer materials, which may include: Step 100: Obtain the physical parameters to be optimized for the multilayer material in the plasma etching process and their value space; For example, the stacked material can be a Si / SiGe stacked material. It is formed by vertically and periodically growing Si layers and SiGe layers alternately. The Si layers are used to form carrier channels, and the SiGe layers are selectively etched away as sacrificial layers in subsequent processes. The optimization parameters need to be adapted to the differences in the etching characteristics of the two materials.

[0025] The physical parameters to be optimized are all core parameters of particle-substrate interaction during the etching process, directly affecting etching rate, selectivity, and profile quality. For example, the physical parameters to be optimized may include the probability of ions removing substrate atoms, the probability of neutral atoms adsorbing on the substrate surface, the basic reflection probability coefficient of particles encountering substrate atoms, the maximum critical angle of reflection, and the minimum critical angle of reflection. Among them, the critical angle refers to the angle with the surface tangent, not the normal.

[0026] It should be noted that the reference for the critical angle is the tangent to the substrate surface, not the non-tangent. The closer the particle incident direction is to being perpendicular to the substrate surface (i.e., the larger the angle with the tangent), the less likely it is to be reflected; conversely, the further away it is, the more likely it is to be reflected.

[0027] After determining the physical parameters to be optimized, it is necessary to determine the value space of the physical parameters, also known as the search space range. The value space needs to be constrained by mathematical and physical background (for example, the probability of ion removal of atoms needs to be between 0 and 1, the critical reflection angle needs to conform to the principles of geometric optics and the motion characteristics of etching particles, and it also needs to meet the energy conservation constraints of the etching process and the coupling relationship between various physical parameters, etc.) to ensure the physical rationality of the parameter combination.

[0028] To simplify weight settings and loss function calculation, this embodiment multiplies each physical parameter by a coefficient based on its initial value. Parameter tuning is achieved by optimizing the coefficients. Furthermore, when calculating the loss function, the weight of all parameters is configured to be 1 to ensure that the influence of each parameter on the optimization result is consistent.

[0029] For example, see Table 1 for specific parameter details.

[0030] Step 200: Initially sample the value space based on the Bayesian optimization method and the first Monte Carlo simulation method to obtain initial sampled data; Specifically, the initial sampling logic is to perform uniform sampling within the parameter value space to ensure that the sampling points can fully cover the entire search space, providing uniformly distributed and sufficiently informative basic data for subsequent model training, and avoiding model bias caused by incomplete initial data.

[0031] Taking the etching scenario of Si / SiGe stacked materials as the application object, the first Monte Carlo simulation method is used to perform etching simulation for each sampled parameter combination. By simulating the physical and chemical synergistic process of plasma etching, the morphology data after etching, i.e. the simulation results, are output.

[0032] The simulation results of each sampling parameter combination (also known as the initial parameter combination) are analyzed to extract key index data that can characterize the etching quality. Combined with the target data of the actual etching effect, the loss function value corresponding to each initial parameter combination is obtained through a preset loss calculation method, and finally the initial sampling data with a one-to-one correspondence between the initial parameter combination and the loss function value are formed.

[0033] Step 300: Train a neural network surrogate model based on the initial sampled data and select candidate points through the acquisition function to obtain a set of candidate points; Specifically, the model is trained using initial sampled data, enabling it to learn the mapping relationship between the initial parameter combination and the loss function value. This allows it to predict the loss function value for any parameter combination, providing efficient prediction support for subsequent optimization.

[0034] The potential optimization points in the parameter space are screened by the acquisition function. Based on the prediction results of the neural network surrogate model, the acquisition function selects the points with the greatest optimization potential from the parameter space as candidate points, forming a candidate point set, which provides a clear parameter direction for the next round of simulation.

[0035] Step 400: Process the candidate point set using the second Monte Carlo simulation method and obtain the loss function value set; Step 500: Perform optimization iterations based on the set of loss function values ​​until the preset conditions are met to obtain the target physical parameter combination; the preset conditions are reaching the preset number of optimization rounds or the convergence of loss function values.

[0036] The beneficial effects of this embodiment are as follows: 1) Overcoming the subjectivity and local optima limitations of manual optimization: Using a Bayesian optimization framework for global parameter search eliminates reliance on engineer experience and avoids non-physical interpretations caused by subjective biases. Intelligent selection of candidate points through acquisition functions effectively escapes local optima traps, adapts to the nonlinear response of laminated materials, and improves the versatility of optimization. 2) Reducing the high cost and low efficiency of experimental verification: Replacing some physical experiments with Monte Carlo simulation reduces the frequency of using dedicated reactors and electron microscopy characterization, significantly lowering optimization costs. Simultaneously, simulation data acquisition is much faster than physical experiments, meeting the needs of rapid process development and shortening the parameter optimization cycle. 3) Overcoming the speed and tuning limitations of atomic-level simulation: Replacing the complex calculations of atomic-level simulation with a neural network surrogate model significantly improves the computational speed of parameter optimization, avoiding the inefficiency of atomic-level simulation. The model can accurately learn the correlation between parameters and etching effects, achieving efficient and targeted tuning of physical parameters. 4) Ensure the quality of the etched profile: Through multiple rounds of iterative optimization and loss function feedback, ensure that the etched effect corresponding to the target physical parameter combination is highly consistent with the actual requirements, and effectively avoid defects such as neck blockage and excessive etch depth deviation.

[0037] In an exemplary embodiment, see Figure 2 Step 200: Initial sampling of the value space is performed based on the Bayesian optimization method and the first Monte Carlo simulation method to obtain initial sampling data, including: Step 210: Perform N rounds of uniform sampling within the value space, with each round generating M initial parameter combinations; where each initial parameter combination includes the specific values ​​of each physical parameter; N and M are both greater than zero; Specifically, uniform sampling refers to selecting parameter combinations with equal probability and intervals within the range of values ​​of each physical parameter, ensuring that the sampling points can fully cover the entire value space, and avoiding the initial data being concentrated in a local area of ​​the value space, which would lead to subsequent model training bias.

[0038] Assuming only two core parameters, Reaction_Si and reflect1, are selected, with Reaction_Si ranging from 0.05 to 0.15 and reflect1 ranging from 0.5 to 2.5, and if three initial parameter combinations are generated in each round, a certain round of sampling may yield three sets of parameter combinations: (0.08, 1.0), (0.12, 1.8), and (0.15, 2.2). Each set is an independent initial parameter combination, containing the specific values ​​of all physical parameters to be optimized.

[0039] For example, the value of N can be taken from 50 to 80, depending on the parameter dimension of the value space and the sampling coverage requirements. The more parameter dimensions there are, the more the value of N can be increased accordingly to ensure that the initial sampling can fully cover the parameter space and provide evenly distributed basic data for model training.

[0040] For example, a value of 5 for M is suitable for the hardware computing power of parallel simulation, balancing simulation efficiency and data diversity. When the hardware computing power allows, the value of M can be appropriately increased to further enhance the richness of the initial sampled data.

[0041] Step 220: For the M initial parameter combinations, perform etching simulation using the first Monte Carlo simulation method to obtain the simulation results for each initial parameter combination; Specifically, step 220 refers to performing etching simulation simultaneously on M combinations of initial parameters, i.e., parallel etching simulation.

[0042] The first Monte Carlo simulation method, including the second Monte Carlo simulation method that follows, is a numerical simulation method that simulates random events such as particle trajectory and collision reaction during plasma etching by random sampling, and restores the physical and chemical synergistic etching mechanism. Its core is to use a probabilistic model to approximate the real etching process.

[0043] It should be added that the first Monte Carlo simulation method here is only used for simulation calculations in the initial sampling stage, and has the same function as the subsequent second Monte Carlo simulation method. The name is only used to distinguish the simulation process of different optimization stages.

[0044] For example, for a certain combination of initial parameters ( , , , , The first Monte Carlo simulation method can simulate processes such as high-energy ion bombardment of Si substrate, neutral atom adsorption, and particle reflection. The final output is the morphology data after etching corresponding to the parameter combination, which is the simulation result. The simulation result includes, but is not limited to, cross-sectional contours and dimensional parameters.

[0045] Step 230: Analyze the simulation results for each initial parameter combination and extract the simulation values ​​of the measurement indicators related to etching; Specifically, the core of selecting measurement indicators is to comprehensively characterize the etching quality, covering key dimensions such as etching depth, width, and morphological integrity. For example, see... Figure 3 Measurement parameters may include the maximum etching depth, the difference between the maximum width and the etched opening, the depth at which the maximum width is located, the bottom width, and the bottom protrusion height.

[0046] Maximum etching depth: The vertical distance from the substrate surface to the bottom of the etching in the simulated etching profile. If the actual electron microscope characterization of this value is 50nm and the simulated value is 48nm, then the simulated value of this index is 48nm.

[0047] Difference between maximum width and etched opening: The difference between the width of the widest part of the etched profile and the width of the etched opening. If the opening width is 10nm and the maximum width is 12nm, then the simulated value of this index is 2nm.

[0048] Depth at which the maximum width is located: The vertical depth corresponding to the widest point in the etched profile. If the widest point is located at a distance of 20nm from the surface, then the simulated value of this index is 20nm.

[0049] Bottom width: The horizontal width of the bottom of the etched profile. If the horizontal span of the bottom is 8nm, then the simulated value of this indicator is 8nm.

[0050] Bottom protrusion height: The height of the protrusion structure caused by particle reflection or adsorption at the bottom of the etching. If the protrusion height is 1nm, the simulated value of this indicator is 1nm.

[0051] Step 240: Construct initial sampling data based on simulation values ​​and real electron microscopy characterization data.

[0052] Specifically, real electron microscopy characterization data is measured data obtained by observing actual etched samples using scanning electron microscopy (SEM) or transmission electron microscopy (TEM), and it is the core benchmark for measuring the accuracy of simulation results.

[0053] Step 240: Based on the simulated values ​​and real electron microscopy characterization data, construct the initial sampling data, which may specifically include: The true values ​​of each measurement index are determined based on real electron microscopy characterization data; Substitute the simulated and actual values ​​of each measurement indicator into the mean square error function calculation formula: (1); Obtain the loss function value corresponding to a single parameter combination; where, The value of the loss function; The number of measurement indicators; For the first Simulated values ​​of each measurement index; For the first The true value of each measurement indicator.

[0054] Each initial parameter combination is mapped one-to-one with its corresponding loss function value, thus constructing initial sampling data consisting of the initial parameter combination and the loss function value.

[0055] For example, with n=5 (corresponding to 5 measurement indicators), the simulated and actual values ​​of a certain initial parameter combination are shown in Table 2 below: Table 2: Simulated and actual values ​​of a certain initial parameter combination.

[0056] Substituting into formula (1), the loss function value is calculated to obtain... The loss function value corresponding to this initial parameter combination is 0.82, and the final "initial parameter combination (e.g.)" is constructed. Sample pairs with a loss function value of 0.82 (etc.) are integrated to form the initial sampling data.

[0057] Additional explanation: The smaller the loss function value, the closer the simulation result of the parameter combination is to the actual etching effect, providing "parameter-effect" mapping data for subsequent neural network surrogate model training.

[0058] It should be noted that before training the neural network proxy model based on the initial sampled data, the method also includes: constructing the neural network proxy model; Constructing a neural network surrogate model involves integrating multiple feedforward neural networks in parallel to obtain the neural network surrogate model.

[0059] Understandably, the approach also includes building a single feedforward neural network before integrating multiple feedforward neural networks in parallel. Constructing a single feedforward neural network involves sequentially setting an input layer, a first fully connected layer, a first ReLU activation function, a first Dropout regularization module, a second fully connected layer, a second ReLU activation function, a second Dropout regularization module, a third fully connected layer, a third ReLU activation function, and an output layer to obtain the feedforward neural network; wherein, the output layer includes a fourth fully connected layer and an output module.

[0060] Specific structural examples are as follows: Figure 4 , Figure 4In the diagram, "Input (5-dimensional)" corresponds to the input layer; "Fully connected layer (5-dimensional → 128-dimensional)" corresponds to the first fully connected layer; the first "ReLU activation function" corresponds to the first ReLU activation function; the first "Dropout (0.1)" corresponds to the first Dropout regularization module; "Fully connected layer (128-dimensional → 128-dimensional)" corresponds to the second fully connected layer; the second "ReLU activation function" corresponds to the second ReLU activation function; the second "Dropout (0.1)" corresponds to the second Dropout regularization module; "Fully connected layer (128-dimensional → 64-dimensional)" corresponds to the third fully connected layer; the third "ReLU activation function" corresponds to the third ReLU activation function; "Fully connected layer (64-dimensional → 1-dimensional)" corresponds to the fourth fully connected layer of the output layer; and "squeeze (-1)" corresponds to the output module of the output layer. In Dropout (0.1), 0.1 means that 10% of the neurons are randomly dropped.

[0061] This embodiment, through a collaborative design involving uniform sampling, parallel Monte Carlo simulation, and an integrated neural network surrogate model, not only lays a high-quality data foundation for the entire optimization process but also specifically addresses the core pain points of traditional optimization techniques. Its beneficial technical effects are as follows: 1) Overcoming the performance limitations of traditional probabilistic surrogate models: Traditional Bayesian optimization often employs Gaussian processes and other probabilistic surrogate models. When dealing with high-dimensional, complex, and unstructured etching parameter spaces, these models suffer from insufficient prediction accuracy, poor scalability, and low computational efficiency. This embodiment constructs an ensemble surrogate model integrating multiple feedforward neural networks in parallel. Through a deep network structure with three hidden layers, the nonlinear fitting capability of the ReLU activation function, and the overfitting suppression mechanism of Dropout regularization, it can more accurately learn the complex mapping relationship between parameter combinations and etching effects. Furthermore, integrating the predicted mean and variance from multiple independent neural networks provides a more comprehensive characterization of parameter uncertainty compared to a single Gaussian process model, offering a more reliable decision-making basis for the intelligent selection of subsequent acquisition functions.

[0062] 2) Resolving the contradiction between initial data quality and acquisition efficiency: Traditional manual tuning or single sampling methods easily lead to biased initial data, while experimental verification suffers from high costs and long cycles. This embodiment employs multiple rounds of uniform sampling, covering the entire parameter space with equal probability and intervals, avoiding initial data concentration in local areas, ensuring that the training data for the neural network surrogate model is evenly distributed and information-rich, reducing model bias from the source. Simultaneously, by using, for example, parallel Monte Carlo simulations with M=5 initial parameters, efficiency is improved by 5 times compared to serial simulation, significantly shortening the initial data acquisition time. This reduces the reliance on physical experiments and solves the pain points of slow speed and long cycles in traditional simulations.

[0063] 3) Ensuring the accuracy and generalization ability of parameter optimization: The comprehensiveness of measurement indicators and the scientific nature of loss calculation directly determine the optimization accuracy. This embodiment selects multiple core indicators such as maximum etching depth, maximum width, and the difference between openings to comprehensively characterize etching depth, width, and morphological integrity, avoiding misjudgments caused by a single indicator. The loss function is calculated using the mean square error formula to accurately quantify the deviation between simulation results and real electron microscopy data, providing accurate mapping samples for the neural network. The deep structure and regularization design of the neural network surrogate model enable it to adapt to the parameter optimization needs under different process conditions. Compared with traditional atomic-level simulation, it not only has a faster computing speed but also better handles the nonlinear response to changes in the proportion of new materials or gases, exhibiting stronger generalization ability.

[0064] 4) Providing efficient and reliable technical support for global optimization: The initial sampling data and neural network surrogate model constructed in this embodiment lay the foundation for the subsequent global search of Bayesian optimization. Uniform sampling covers the entire parameter space, avoiding the local optimum trap that is easily encountered in manual tuning; the efficient prediction capability of the neural network replaces the complex calculations of repeated iterations in traditional optimization, and the optimization efficiency is further improved by combining parallel simulation; and the model's accurate characterization of uncertainty can help the sampling function better balance exploration and utilization, ensuring that the subsequent optimization process can not only tap the potential of known optimal regions, but also explore new regions with high uncertainty, ultimately achieving rapid acquisition of the global optimal combination of physical parameters, effectively avoiding the problem of uncontrolled etching feature profiles (such as neck blockage, excessive etching depth deviation, etc.).

[0065] In an exemplary embodiment, step 300: training a neural network surrogate model based on initial sampled data and selecting candidate points through a sampling function to obtain a candidate point set may specifically include: Using the initial sampled data, combined with the learning rate scheduler and early stopping mechanism, a neural network proxy model is trained to obtain the trained model; Multiple combinations of potential parameters are randomly sampled from the value space to form a candidate pool; Each potential parameter combination in the candidate pool is input into the trained model to obtain the prediction mean and prediction uncertainty for each potential parameter combination; where the prediction mean is the mean of the prediction results of multiple feedforward neural network loss values; and the prediction uncertainty is the standard deviation of the prediction results of multiple feedforward neural network loss values. The predicted mean and prediction uncertainty of each potential parameter combination are input into the acquisition function and combined with the Constant Liar strategy to generate multiple non-overlapping candidate points, forming a candidate point set.

[0066] Specifically, the learning rate scheduler (Reduce LR On Plateau) is an optimization mechanism that dynamically adjusts the model's training learning rate. When the loss function value stops decreasing for several consecutive rounds during model training, indicating a plateau, the learning rate is automatically reduced to help the model break through local optima and continue approaching the global optimum. This avoids convergence oscillations caused by an excessively high learning rate or training stagnation caused by an excessively low learning rate. For example, if the learning rate is halved if the loss function value decreases by less than 0.001 for three consecutive rounds, and the initial learning rate is 0.001, then when the loss values ​​in rounds 5-7 are 0.82, 0.818, and 0.817 respectively, with each decrease less than 0.001, the learning rate in round 8 is automatically adjusted to 0.0005, further assisting in model optimization.

[0067] Early stopping is a mechanism used to prevent model overfitting and shorten training time. It monitors the loss function value on the validation set; if the validation loss no longer decreases or even increases after several consecutive rounds, training is terminated early, preserving the model parameters with the optimal validation loss during training. This prevents the model from overfitting to the training data and losing its generalization ability. For example, if the rule is "early stopping if the validation loss does not decrease for 5 consecutive rounds," and the validation loss is 0.75 (optimal) at round 10, and the validation losses for rounds 11-15 are 0.76, 0.758, 0.77, 0.78, and 0.79 respectively, then the early stopping condition is met, training is terminated, and the model parameters from round 10 are preserved.

[0068] The predicted mean is the arithmetic mean of the loss value predictions of multiple parallel feedforward neural networks for the same parameter combination; the prediction uncertainty is the standard deviation of multiple prediction results. The larger the variance, the more uncertain the model's judgment on the etching effect of that parameter combination, and vice versa. It should be noted that the feedforward neural network loss value prediction result in this step is the prediction value of the etching effect of the trained neural network surrogate model on the potential parameter combination, which is not the same concept as the loss function value calculated by the mean squared error formula mentioned above. The latter loss function calculated by the mean squared error formula is the actual error quantification value calculated based on Monte Carlo simulation results and real electron microscopy data, which serves as the label data for model training; while the feedforward neural network loss value prediction result is the loss value prediction result of the model after fitting the training data to the new potential parameter combination, used to output the prediction mean and prediction uncertainty, providing a basis for the EI acquisition function to screen candidate points.

[0069] Furthermore, the predicted mean and prediction uncertainty of each potential parameter combination are input into the acquisition function and combined with the Constant Liar strategy to generate multiple non-overlapping candidate points, forming a candidate point set, including: The predicted mean and prediction uncertainty for each combination of potential parameters are input into the EI acquisition function: (2); Step 1: Calculate the EI function value for each potential parameter combination and select the potential parameter combination with the largest EI function value as the first candidate point; where, ; The cumulative distribution function of the standard normal distribution; is the probability density function of the standard normal distribution; To predict the mean; The optimal loss function value; To adjust the non-negative hyperparameters that balance exploration and utilization; To predict uncertainty; For the combination of input parameters.

[0070] The core function of the EI (Expected Improvement) acquisition function is to weigh "utilizing the known optimal region" and "exploring the region with high uncertainty" in the parameter value space, calculate the expected improvement value of each potential parameter combination, and select the parameter combination with the largest expected improvement value as the candidate point, so as to both get closer to the current optimal solution and not miss the unknown region where there may be a better solution.

[0071] Nonnegative hyperparameters Used to adjust the search tendency of EI acquisition functions. The larger the value, the more the function tends to explore, that is, it prioritizes regions with high uncertainty; The smaller the value, the more the function tends to utilize it, meaning it prioritizes regions where the predicted mean is close to the current optimal value. This can be dynamically adjusted according to the optimization stage. For example: Settings in the initial optimization phase (first 50 rounds) Prioritize exploring the parameter space to discover potential optimal regions; optimize settings in later stages (after 150 rounds). It focuses on using parameter combinations near the known optimal region to accurately approximate the global optimal solution.

[0072] The Constant Liar strategy is a strategy for parallel generation of multiple candidate points. Its core is to use virtual supplementation of optimal loss values ​​to make assumptions about the virtual loss function values ​​of candidate points obtained through the EI acquisition function without actually performing etching simulation. This allows for the rapid and continuous screening of multiple candidate points, solving the efficiency bottleneck of traditional Bayesian optimization, which can only generate one candidate point at a time, and adapting to the needs of parallel simulation.

[0073] Step 2: Based on the Constant Liar strategy, the optimal loss function value in the initial data of point selection is determined as the virtual loss function value of the first candidate point, and the first candidate point and its corresponding virtual loss function value are used as the first virtual sample to supplement the initial data of point selection, forming the first virtual update data; It should be noted that in step 2, after selecting the first candidate point, the Constant Liar strategy does not use the Monte Carlo simulation method to perform etching simulation of the first candidate point. Instead, it directly assumes that the virtual loss function value of the first candidate point is the optimal loss function value in the initial data of the selected point.

[0074] In the selection process of the first candidate point, the initial data for point selection is the initial sampling data mentioned above. The initial sampling data is a combination of the initial parameter combination and the loss function value. Therefore, the optimal loss function value can be extracted from the initial data for point selection.

[0075] Step 3: Based on the first virtual update data, filter out the second candidate points using the EI acquisition function; It should be noted that during the calculation in step 3, the neural network proxy model has already undergone the first round of training with the initial sampled data, and the candidate pool has not changed. Therefore, the predicted mean and prediction uncertainty of each potential parameter combination remain fixed and do not change with the update of the sampled data.

[0076] After obtaining the first virtual update data, it is necessary to recalculate the EI function value for each potential parameter combination using the EI acquisition function. The core reason is that the first virtual sample supplemented by the Constant Liar strategy in step 2 adds an optimal sample to the sample distribution of the first virtual update data, and the complete calculation input of the EI function includes the model output result. and Derivation from sampling data and hyperparameters Because the model output results are different from those of the model output results. Keeping it unchanged, changes in the distribution of sampled data directly adjust the exploration of the EI function—using a trade-off logic, the utilization value of the region where the first candidate point is located is weakened because there are already optimal samples. The contribution of the utilization terms decreases; the parameter combinations in other high-uncertainty regions of the candidate pool have relatively higher exploration value, and the EI function... The increased contribution of the exploration items eventually leads to the reconstruction of the EI value ranking of each potential parameter combination. The new parameter combination with the largest EI function value after ranking is selected by the EI acquisition function and used as the second candidate point to ensure that it does not overlap with the first candidate point.

[0077] Step 4: Based on the Constant Liar strategy, the optimal loss function value in the first virtual update data is determined as the virtual loss function value of the second candidate point. The second candidate point and its corresponding virtual loss function value are then added to the first virtual update data to form the second virtual update data. Step 5: Continue until the last candidate point is selected using the EI acquisition function, forming a candidate point set.

[0078] It should be noted that the initial point selection data, the first virtual update data, and the second virtual update data are all specific data for the candidate point selection stage. The initial point selection data is based on the initial sampling data and is used to initiate the multi-candidate point selection process. The first and second virtual update data, as well as subsequent virtual update data, are temporary data formed by supplementing the initial point selection data with candidate points and corresponding virtual loss function values ​​through the ConstantLiar strategy. Their core function is to assist the EI acquisition function in continuously selecting non-overlapping candidate points, and they do not involve any loss function values ​​obtained from actual simulation. The above data is only valid during the generation of the candidate point set in this process and is not the same concept as the actual cumulative sampling data in subsequent optimization iteration stages.

[0079] Understandably, after forming the candidate point set, the second Monte Carlo simulation method is used to perform simulations in parallel to obtain the loss function value of each candidate point in the candidate point combination.

[0080] Specifically, in step 5, the number of candidate points in the candidate point set is consistent with the number of parallel simulations in the second Monte Carlo simulation method.

[0081] The beneficial effects of this embodiment are as follows: 1) It solves the problems of overfitting and efficiency in model training: The learning rate scheduler effectively avoids the model from getting stuck in the training plateau by dynamically adjusting the learning rate, ensuring that the model continuously approaches the optimal solution; the early stopping mechanism terminates ineffective training in advance, which not only prevents the model from overfitting, but also significantly shortens the training time, adapting to the high-frequency training requirements of multiple iterations of Bayesian optimization. Compared with model training without optimization mechanism, it improves efficiency and has better generalization ability. 2) It innovatively adopts the Constant Liar strategy, which quickly generates multiple sets of non-overlapping candidate points by virtually supplementing the optimal samples without performing actual etching simulation, breaking the efficiency bottleneck of "serial generation of candidate points" in traditional Bayesian optimization; the number of candidate point sets is precisely matched with the number of parallel simulations, and subsequent execution is carried out synchronously through a second Monte Carlo simulation, reducing the time cost of a single iteration by more than 60% and greatly improving optimization efficiency. 3) Ensuring global search capability during the optimization process: The EI acquisition function intelligently balances exploration and utilization by co-calculating the predicted mean and uncertainty, avoiding the local optimum trap that is easy to fall into with manual optimization; the flexible adjustment of hyperparameters can adapt to the needs of different optimization stages, extensively explore the parameter space in the early stage, and accurately focus on the optimal region in the later stage, ensuring that the globally optimal combination of physical parameters is finally found, effectively solving the problem of blind search and easy limitation to local solutions in traditional optimization.

[0082] In an exemplary embodiment, step 400: processing the candidate point set using a second Monte Carlo simulation method and obtaining a set of loss function values ​​includes: For each candidate point in the candidate point set, the second Monte Carlo simulation method is used to perform etching simulation to obtain the simulation results for each candidate point; The simulation results for each candidate point are analyzed to extract the simulation values ​​of the measurement indicators; Based on the mean square error function calculation formula, and combined with the true values ​​of each measurement index, the loss function value of each candidate point is calculated. The loss function values ​​of all candidate points are integrated to form a set of loss function values.

[0083] It should be noted that the second Monte Carlo simulation method used in step 400 has the same core principle and simulation process as the first Monte Carlo simulation in step 220. Both methods simulate physical-chemical processes such as particle motion trajectories and collision reactions through random sampling to recreate the etching mechanism. The two methods are named only to distinguish the simulation process of the "initial sampling stage" and the "candidate point optimization stage," and have no essential functional differences. This ensures the uniformity of simulation standards throughout the optimization process and avoids result deviations caused by different simulation methods.

[0084] The measurement metrics extracted in step 400 are completely consistent with those in step 230, ensuring that the evaluation dimensions of the etching effect of candidate points are consistent with the initial parameter combination, so that the loss function values ​​are comparable.

[0085] The formula for calculating the mean squared error function and the definition of its parameters are completely reused from the design in step 240, ensuring that the calculation standard of the loss function value is consistent and that the loss function values ​​of the initial parameter combination and candidate points can be directly used for model training and optimization iteration.

[0086] Step 220 addresses the initial parameter combinations generated by uniform sampling, covering the entire parameter space. Step 400 focuses on the "candidate points selected by the EI acquisition function and the Constant Liar strategy," concentrating on the potential optimal regions in the parameter space, making the simulation more targeted. The simulation results of Step 220 are used to construct the initial sampling data, providing basic training samples for the neural network surrogate model; the simulation results of Step 400 are used to calculate the loss function values ​​of the candidate points, providing feedback data for model updates and the next iteration, serving as a precise verification step in the optimization process.

[0087] The beneficial effects of this embodiment are as follows: 1) By reusing simulation methods, measurement indicators, and loss calculation standards, optimization deviations caused by differences in evaluation systems at different stages are avoided, ensuring the closed-loop logic of "initial sampling - candidate point verification - model update" is coherent and improving the credibility of optimization results. 2) Candidate points are potential optimal solutions selected based on model predictions. Targeted simulation replaces full-parameter space sampling simulation, significantly reducing the number of invalid simulations and improving optimization efficiency compared to the blind traversal of traditional optimization. 3) The loss function value of candidate points directly reflects the optimization potential of parameter combinations. Supplementing them to historical data allows the neural network surrogate model to quickly learn the parameter characteristics of the optimal region, providing a more accurate prediction basis for the next round of candidate point generation and accelerating convergence to the global optimum. 4) Continuing the logic of Monte Carlo simulation replacing physical experiments, simulation verification of candidate points does not require dedicated reactors and electron microscopy characterization, significantly reducing costs compared to experimental verification, while also providing faster data acquisition speed, meeting the needs of rapid process development.

[0088] In an exemplary embodiment, step 500: performing optimization iterations based on the set of loss function values ​​includes: The candidate point set and the corresponding loss function value are added to the historical sampling data to obtain the true cumulative sampling data; each candidate point in the candidate point set corresponds one-to-one with the loss function value; the historical sampling data is the cumulative set of the initial sampling data and the candidate points and corresponding loss function values ​​added in each optimization iteration. Based on real cumulative sampling data, the neural network agent model is retrained to obtain the updated model output; Based on the updated model output, an updated set of candidate points is determined by acquiring the function and combining it with the Constant Liar strategy. The updated set of candidate points is then processed by the second Monte Carlo simulation method to obtain an updated set of loss function values. The optimization iteration continues based on the updated set of loss function values ​​until the preset conditions are met.

[0089] It should be noted that the real cumulative sampling data is dedicated to the optimization iteration phase. It is based on historical sampling data, which in turn is a cumulative set of real samples supplemented by the initial sampling data and each iteration. This historical sampling data supplements the current candidate point set and the corresponding loss function values ​​(obtained through the second Monte Carlo simulation). It contains only real samples, and its core function is to retrain the neural network surrogate model to improve the accuracy of subsequent candidate point selection. The real cumulative sampling data is fundamentally different from the virtual update data in the candidate point selection phase: their data sources, properties, and application scenarios do not overlap.

[0090] The beneficial effects of this embodiment are as follows: 1) Achieving dynamic optimization and continuous improvement in accuracy: Through a closed-loop iteration of "data update - model retraining - candidate point update - simulation verification", each iteration optimizes the model with more comprehensive sampled data and selects candidate points with more accurate model, so that the parameter combination continuously approaches the global optimum. Compared with the traditional fixed-process optimization method, the accuracy gradually improves with iteration, effectively avoiding the local optimum trap. 2) Ensuring the coherence and reliability of the optimization process: The iteration process reuses the simulation, model training, and candidate point generation logic verified above, without adding any additional technical steps, ensuring the coherence and consistency of the entire optimization process, avoiding result deviations caused by process changes, and improving the credibility of the optimization results. 3) Balancing efficiency and generalization ability: On the one hand, by reusing mature processes and parallel simulation mechanisms, the repeated development of additional logic is avoided, improving iteration efficiency; on the other hand, with the accumulation of historical sampled data, the generalization ability of the neural network surrogate model is continuously enhanced, which can better adapt to the complex characteristics of the parameter space. Even when facing nonlinear responses of new materials or changes in gas ratios, it can stably output the optimal parameter combination, solving the problem of lack of scalability in traditional optimization methods.

[0091] In specific implementation method 1, combined with Figure 5 An example of an optimized process for plasma etching of multilayer materials is provided.

[0092] S1: Obtain the physical parameters to be optimized and their value space; S2: Generate initial sampling data by uniformly sampling the value range and combining it with the first Monte Carlo simulation; S3: Train a neural network proxy model based on the initial sampled data; S4: Generate a candidate pool and input the candidate pool into the trained neural network proxy model; S5: Output the predicted mean and prediction uncertainty; understandably, the output predicted mean and prediction uncertainty will then be input into the EI acquisition function; S6: The EI acquisition function combines the Constant Liar strategy to filter the candidate point set from the candidate pool; S7: Second Monte Carlo simulation, to obtain the set of loss function values, specifically: perform parallel second Monte Carlo simulation for each candidate point in the candidate point set; S8: Update historical sampling data; specifically: add each candidate point and its corresponding loss function to the historical sampling data; S9: Retrain the neural network agent model, specifically by retraining the neural network agent model with updated sampling data obtained after supplementing historical data; S10: Generate a new set of candidate points. Specifically, after training the neural network surrogate model, repeat S5 and S6 to obtain a new set of candidate points. S11: Second Monte Carlo simulation to obtain a new set of loss function values, specifically: perform a parallel second Monte Carlo simulation for each candidate point in the new candidate point set; S12: Determine convergence, specifically whether the loss function value has converged. If yes, proceed to S13: Output the target physical parameter combination. If no, return to S8 for iteration until the preset condition "loss function value converges, i.e., the decrease in loss function value for multiple consecutive rounds is less than the loss threshold; or the preset number of rounds of 200-400 is reached" is met.

[0093] Figure 6 This is a line graph showing the loss function values ​​corresponding to the 200 rounds of Bayesian optimization process in Specific Embodiment 2 of the present invention. Based on this graph, the following analytical conclusions can be drawn: I. Optimization Trend: The loss function continues to decrease, verifying the effectiveness of the optimization framework.

[0094] The "Trend Line" in the figure shows a continuously converging downward trend, indicating that as the Bayesian optimization rounds progress, the overall loss function value corresponding to the candidate point (i.e., the error between the etching simulation result and the actual electron microscope data) gradually decreases. This trend demonstrates that the optimization framework composed of the "neural network surrogate model, EI acquisition function, and Constant Liar strategy" in this embodiment of the invention has significant effectiveness, continuously selecting better combinations of etching process parameters and driving the simulation effect to increasingly approximate the real process scenario.

[0095] II. Convergence effect: The fluctuations narrow in the later stages, approaching the global optimal region.

[0096] As seen in the curve changes from 150 to 200 rounds, the fluctuation range of the loss function value narrows significantly and gradually concentrates towards lower values, indicating that the parameter combination in the later stages of optimization has approached the global optimum. The core reason for this phenomenon is that, with the continuous accumulation of historical sampling data, the fitting accuracy of the neural network surrogate model to the parameter space continuously improves, and the trade-off between exploring and utilizing the EI acquisition function becomes more precise, resulting in a gradual stabilization of the quality of the selected candidate points. The figure shows that the loss function value is close to a stable state at 200 rounds, indicating that the optimization process has achieved the expected convergence effect.

[0097] III. Optimal Result: The minimum loss function value was achieved in the 195th round, clarifying the basis for the target parameters.

[0098] The figure shows "[195, 12.8]" marking the optimal state during the optimization process: in the 195th iteration, the loss function value corresponding to the selected candidate point is as low as 12.8, which is the minimum loss function value in the current optimization process. This result is the core basis for the final output target physical parameter combination. The etching effect of this parameter combination can be further verified through Monte Carlo simulation to ensure that it fully meets the application requirements of real-world processes.

[0099] IV. Summary of Technical Value: Highlighting the efficiency and reliability of the optimization method.

[0100] Figure 6 This intuitively demonstrates the core advantages of the optimization method of this invention: compared with traditional manual parameter tuning or brute-force search methods, Bayesian optimization can quickly reduce the loss function value with fewer iterations, greatly improving optimization efficiency; the convergence trend is clear and obvious, indicating that the method has global search capabilities and is not easily trapped in local optima; the clear labeling of the optimal results provides specific and directly applicable parameter selection basis for the practical implementation of etching processes.

[0101] The following describes the optimization apparatus for the multilayer material plasma etching process provided by the present invention. The optimization apparatus for the multilayer material plasma etching process described below and the optimization method for the multilayer material plasma etching process described above can be referred to in correspondence with each other.

[0102] like Figure 7 As shown, embodiments of the present invention also provide an optimization apparatus for a multilayer material plasma etching process, used to implement the optimization method for the multilayer material plasma etching process in any of the above embodiments. This optimization apparatus for the multilayer material plasma etching process may include: an acquisition module 710, used to acquire the physical parameters to be optimized of the multilayer material in the plasma etching process and their value space; The sampling module 720 is used to perform initial sampling of the value space based on the Bayesian optimization method and the first Monte Carlo simulation method to obtain initial sampling data. The acquisition module 730 is used to train a neural network surrogate model based on initial sampled data and select candidate points through an acquisition function to obtain a set of candidate points. The processing module 740 is used to process the candidate point set using the second Monte Carlo simulation method and obtain the loss function value set; The iteration module 750 is used to perform optimization iterations based on the set of loss function values ​​until a preset condition is met to obtain the target physical parameter combination; the preset condition is to reach a preset number of optimization rounds or for the loss function values ​​to converge.

[0103] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0104] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely exemplary descriptions of the invention as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. An optimized method for plasma etching of multilayer materials, characterized in that, include: Obtain the physical parameters to be optimized for the multilayer material in the plasma etching process and their value space; Initial sampling data is obtained by initially sampling the value space based on the Bayesian optimization method and the first Monte Carlo simulation method. A neural network proxy model is trained based on the initial sampled data, and candidate points are selected through a collection function to obtain a set of candidate points; The candidate point set is processed using the second Monte Carlo simulation method to obtain the set of loss function values; The optimization iteration is performed based on the set of loss function values ​​until a preset condition is met to obtain the target combination of physical parameters; the preset condition is to reach a preset number of optimization rounds or for the loss function values ​​to converge.

2. The optimized method for plasma etching process of multilayer materials according to claim 1, characterized in that, The value space is initially sampled based on the Bayesian optimization method and the first Monte Carlo simulation method to obtain initial sampled data, including: N rounds of uniform sampling are performed within the value space, and each round of sampling generates M initial parameter combinations; wherein each initial parameter combination includes the specific value of each physical parameter; N and M are both greater than zero; For each of the M initial parameter combinations, the first Monte Carlo simulation method is used to perform etching simulation to obtain the simulation results for each initial parameter combination. The simulation results for each of the initial parameter combinations are analyzed to extract the simulation values ​​of the measurement indicators related to etching. The initial sampling data are constructed based on the simulated values ​​and the actual electron microscopy characterization data.

3. The optimized method for plasma etching process of multilayer materials according to claim 2, characterized in that, The measurement parameters include the maximum etching depth, the difference between the maximum width and the opening after etching, the depth at which the maximum width is located, the bottom width, and the bottom protrusion height; Based on the simulated values ​​and real electron microscopy characterization data, the initial sampling data is constructed, including: The true values ​​of each measurement index are determined based on the actual electron microscopy characterization data. Substitute the simulated and actual values ​​of each measurement indicator into the mean square error function calculation formula: The loss function value corresponding to a single combination of the initial parameters is obtained; wherein, The value of the loss function; The number of measurement indicators; For the first Simulated values ​​of each measurement index; For the first The true value of each measurement indicator; Each initial parameter combination is mapped one-to-one with its corresponding loss function value to construct the initial sampling data consisting of the initial parameter combination and the loss function value.

4. The optimized method for plasma etching process of multilayer materials according to claim 3, characterized in that, Before training the neural network proxy model based on the initial sampled data, the method further includes: constructing the neural network proxy model; Constructing the neural network proxy model includes: integrating multiple feedforward neural networks in parallel to obtain the neural network proxy model.

5. The optimized method for plasma etching process of multilayer materials according to claim 4, characterized in that, Before integrating multiple feedforward neural networks in parallel, the method further includes: constructing a single feedforward neural network; Constructing a single feedforward neural network includes: The feedforward neural network is obtained by sequentially setting an input layer, a first fully connected layer, a first ReLU activation function, a first Dropout regularization module, a second fully connected layer, a second ReLU activation function, a second Dropout regularization module, a third fully connected layer, a third ReLU activation function, and an output layer; wherein, the output layer includes a fourth fully connected layer and an output module.

6. The optimized method for plasma etching process of multilayer materials according to claim 4, characterized in that, Based on the initial sampled data, a neural network proxy model is trained, and candidate points are selected using a sampling function to obtain a set of candidate points, including: Using the initial sampled data, combined with the learning rate scheduler and early stopping mechanism, the neural network proxy model is trained to obtain the trained model; Multiple potential parameter combinations are randomly sampled from the value space to form a candidate pool; Each potential parameter combination in the candidate pool is input into the trained model to obtain the prediction mean and prediction uncertainty for each potential parameter combination; wherein, the prediction mean is the mean of the prediction results of the loss values ​​of the multiple feedforward neural networks; and the prediction uncertainty is the standard deviation of the prediction results of the loss values ​​of the multiple feedforward neural networks. The predicted mean and prediction uncertainty of each potential parameter combination are input into the acquisition function and combined with the Constant Liar strategy to generate multiple non-overlapping candidate points, forming the candidate point set.

7. The optimized method for plasma etching process of multilayer materials according to claim 6, characterized in that, The predicted mean and prediction uncertainty of each potential parameter combination are input into the acquisition function and combined with the Constant Liar strategy to generate multiple non-overlapping candidate points, forming the candidate point set, including: The predicted mean and prediction uncertainty for each combination of potential parameters are input into the EI acquisition function: Calculate the EI function value for each potential parameter combination, and select the potential parameter combination with the largest EI function value as the first candidate point; where, ; The cumulative distribution function of the standard normal distribution; is the probability density function of the standard normal distribution; To predict the mean; The optimal loss function value; To adjust the non-negative hyperparameters that balance exploration and utilization; To predict uncertainty; Based on the Constant Liar strategy, the optimal loss function value in the initial point selection data is determined as the virtual loss function value of the first candidate point, and the first candidate point and its corresponding virtual loss function value are used as the first virtual sample to supplement the initial point selection data to form the first virtual update data. Based on the first virtual update data, a second candidate point is selected using the EI acquisition function; Based on the Constant Liar strategy, the optimal loss function value in the first virtual update data is determined as the virtual loss function value of the second candidate point, and the second candidate point and its corresponding virtual loss function value are added to the first virtual update data to form the second virtual update data. The process continues until the last candidate point is selected using the EI acquisition function, thus obtaining the candidate point set.

8. The optimized method for plasma etching process of multilayer materials according to claim 6, characterized in that, The candidate point set is processed using a second Monte Carlo simulation method to obtain a set of loss function values, including: For each candidate point in the candidate point set, the second Monte Carlo simulation method is used to perform etching simulation to obtain the simulation results for each candidate point; The simulation results for each candidate point are analyzed to extract the simulation values ​​of the measurement indicators; Based on the mean square error function calculation formula, and combined with the true values ​​of each measurement index, the loss function value of each candidate point is calculated. The loss function values ​​of all candidate points are integrated to form the set of loss function values.

9. The optimized method for plasma etching process of multilayer materials according to claim 8, characterized in that, Optimization iterations are performed based on the set of loss function values, including: The candidate point set and the corresponding loss function value are added to the historical sampling data to obtain the true cumulative sampling data; each candidate point in the candidate point set corresponds one-to-one with the loss function value; the historical sampling data is the cumulative set of the initial sampling data and the candidate points and corresponding loss function values ​​added in each optimization iteration. Based on the real cumulative sampling data, the neural network agent model is retrained to obtain the updated model output. Based on the updated model output, an updated set of candidate points is determined by the acquisition function and the Constant Liar strategy. The updated set of candidate points is then processed by the second Monte Carlo simulation method to obtain an updated set of loss function values. The optimization iteration continues based on the updated set of loss function values ​​until the preset conditions are met.

10. An optimization apparatus for plasma etching process of multilayer materials, characterized in that, include: The acquisition module is used to acquire the physical parameters to be optimized for the stacked material in the plasma etching process and their value space; The sampling module is used to perform initial sampling on the value space based on the Bayesian optimization method and the first Monte Carlo simulation method to obtain initial sampling data. The acquisition module is used to train a neural network proxy model based on the initial sampled data and select candidate points through an acquisition function to obtain a set of candidate points; The processing module is used to process the candidate point set using the second Monte Carlo simulation method and obtain the loss function value set; The iteration module is used to perform optimization iterations based on the set of loss function values ​​until a preset condition is met to obtain the target combination of physical parameters; The preset condition is reaching a preset number of optimization rounds or the loss function value converging.

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