A multi-fidelity process index prediction and process parameter multi-objective optimization method

Abstract

This invention discloses a method for predicting multi-fidelity process indicators and optimizing process parameters across multiple objectives, belonging to the field of semiconductor manufacturing technology. The method includes: obtaining a multi-fidelity dataset comprising high-fidelity and low-fidelity data using high-fidelity and low-fidelity simulation models; constructing an adaptive weight fusion multi-fidelity prediction model using a cascaded architecture of low-fidelity data pre-training and high-fidelity data fine-tuning; using the multi-fidelity prediction model as the interactive environment, constructing a spatiotemporally decoupled dual-domain embedded critic network based on reinforcement learning to achieve multi-objective optimization of process parameters; embedding the critic network into the internal feature flow of the multi-fidelity prediction model, dynamically adjusting the feature fusion weights based on spatiotemporal dual-domain bias to form a bidirectional iterative closed loop of prediction and optimization, and selecting the optimal combination of process parameters. This method reduces the dependence on high-cost, high-precision data, achieves deep matching between multi-objective value assessment and process physical processes, and integrates prediction and optimization into a closed-loop collaborative process.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor manufacturing technology, specifically relating to a method for predicting multi-fidelity process indicators and optimizing process parameters with multiple objectives. Background Technology

[0002] In the semiconductor manufacturing field, many production processes involve strong multi-physics coupling, dynamic temporal evolution, and the need to control the spatial distribution uniformity of finished products. Typical examples include semiconductor wafer cleaning, thin film deposition, dry etching, precision electroplating, and fluid thermal treatment. These processes rely on multi-field coupling to complete material processing, and the relationship between process input parameters and processing output indicators exhibits a highly complex nonlinear mapping relationship. There are two core control objectives in the production process: one is to improve process efficiency, and the other is to reduce the spatial non-uniformity of the surface / internal indicators of the processed object. These two are usually conflicting and difficult to optimize simultaneously. Taking the wafer cleaning process as an example, it integrates multi-physics coupling of chemical reaction kinetics, fluid transport, and heat conduction. It relies on the microscopic reaction between chemical solutions and the wafer surface to remove impurity films. The industry uses etching rate to represent processing efficiency and etching non-uniformity to represent spatial distribution quality. Process parameters include chemical solution temperature, concentration, flow rate, and wafer rotation speed. Traditional high-precision cleaning simulation calculations are costly and have slow iteration speeds. Parameter tuning is highly dependent on manual intervention, making it difficult to simultaneously maximize etching rate and minimize non-uniformity. This is a typical microcosm of the optimization challenges of complex industrial processes.

[0003] The current industry-standard process development and production line control models generally face multiple challenges: on the one hand, the complex multi-physics coupling mechanism in the production process makes it difficult to accurately predict process indicators; on the other hand, the setting of process parameters still relies heavily on human experience in production, making it difficult to achieve accurate parameter matching; in addition, high-precision simulation is commonly used for process indicator prediction, but its computational cost is high and the cycle is long, making it difficult to support large-scale process evaluation.

[0004] To address these challenges, existing research on modeling and parameter optimization for complex industrial processes mainly falls into two major technical approaches: one is data-driven process modeling. This approach relies on high-precision simulation tools such as TCAD, finite element method, and CFD, or on data collected from physical experiments, to construct machine learning, artificial neural networks, and ensemble learning surrogate models to replace full-scale high-precision simulations, reducing the time required for single-indicator prediction. Some studies also improve model prediction accuracy by optimizing sampling strategies and refining network structures to predict process output indicators such as device electrical characteristics, processing speed, and dimensional morphology. The other approach is intelligent algorithm-based process parameter optimization. This approach combines intelligent algorithms such as genetic algorithms, particle swarm optimization, Bayesian optimization, and traditional reinforcement learning to optimize parameters; it constructs surrogate models as environmental feedback to search for Pareto optimal solutions within the parameter space.

[0005] While the two general technical solutions mentioned above can achieve basic modeling and parameter optimization, they still have the following limitations when applied to industrial scenarios such as wafer cleaning, which involve complex mechanisms, highly coupled parameters, and extremely high requirements for result stability: First, it relies heavily on high-precision simulation / experimental data, resulting in low data utilization efficiency.

[0006] Most existing modeling solutions only use a single precision dataset to train the model. High-fidelity, high-precision data acquisition is costly and the sample size is limited. The inherent laws and complementary value of low-fidelity, low-cost simulation data have not been fully explored. When there are insufficient high-precision samples, the model's prediction accuracy and generalization ability drop significantly, and its adaptability to all working conditions is poor.

[0007] Second, the multi-objective optimization is poorly adapted to the physical properties of the process and relies heavily on manual labor.

[0008] Traditional multi-objective optimization uses fixed-weight linear weighting to handle conflicting objectives, which cannot adapt to the dynamic changes in the objective trade-offs under different operating conditions and is prone to getting trapped in local optima. Furthermore, traditional reinforcement learning often uses a commentator network structure with scalar rewards, which cannot distinguish the essential differences between the temporal evolution characteristics and spatial distribution characteristics of the process. The value assessment is divorced from the physical mechanism of the process, the optimization direction is unstable, and manual intervention is still required to adjust the weights.

[0009] Third, the prediction model and optimization algorithm are coupled in a one-way serial manner, without bidirectional closed-loop collaborative capability.

[0010] Existing technologies generally adopt a serial architecture of "one-way output of the surrogate model to the optimization algorithm". The deviation and error information generated during the optimization iteration process cannot be used to update the optimization prediction model in reverse. The prediction accuracy and optimization effect cannot be improved synchronously and collaboratively. The model is difficult to adapt to the dynamic changes in the production line. The overall solution lacks universality and adaptability for engineering implementation.

[0011] In summary, existing process prediction and parameter optimization technologies suffer from multiple drawbacks, including strong reliance on high-precision data, low matching degree between multi-objective optimization and process physical characteristics, and one-way coupling between prediction and optimization without closed-loop collaboration. These shortcomings make it difficult to meet the actual production needs of high precision, high efficiency, and dynamic adaptation. Summary of the Invention

[0012] To address the aforementioned problems in the existing technology, this invention provides a method for predicting multi-fidelity process indicators and optimizing process parameters based on multiple objectives. The technical problem to be solved by this invention is achieved through the following technical solution: In a first aspect, this invention proposes a method for predicting multi-fidelity process indicators and optimizing process parameters based on multiple objectives, including: S1. Using a pre-built high-fidelity simulation model and a low-fidelity simulation model, perform a mixed sampling operation on the target process to obtain a multi-fidelity dataset including high-fidelity data and low-fidelity data. S2. Using a multi-fidelity dataset as input, an adaptive weight fusion multi-fidelity prediction model is built using a cascaded architecture of low-fidelity data pre-training and high-fidelity data fine-tuning. The multi-fidelity prediction model includes a low-fidelity baseline network, a high-fidelity fine-tuning network, and a feature attention fusion module. The low-fidelity baseline network and the high-fidelity fine-tuning network are used to extract features from the low-fidelity data and the high-fidelity data, respectively, to obtain low-fidelity basic temporal features and high-fidelity corrected spatial features. The feature attention fusion module is used to fuse the low-fidelity basic temporal features and the high-fidelity corrected spatial features based on adaptive weights to output the prediction results of process indicators. S3. Using a multi-fidelity prediction model as the interactive environment, a spatiotemporally decoupled dual-domain embedded critic network is constructed based on reinforcement learning to form a multi-objective optimization model for process parameters. The optimization model is then used to perform multi-objective optimization of process parameters to obtain the Pareto optimal solution set. S4. The critic network is embedded into the internal feature flow of the multi-fidelity prediction model. The weight of the feature attention fusion module is dynamically updated based on the spatiotemporal dual-domain bias output by the critic network, forming a two-way iterative closed loop of process index prediction and multi-objective optimization of process parameters. At the same time, the optimal combination of process parameters is obtained by screening from the Pareto optimal solution set based on the spatiotemporal dual-domain bias.

[0013] The beneficial effects of this invention are: This invention provides a method for multi-fidelity process index prediction and multi-objective optimization of process parameters. First, a mixed sampling operation is performed on the target process using both high-fidelity and low-fidelity simulation models to construct a multi-fidelity dataset including both low-fidelity and high-fidelity data. Then, an adaptive weight fusion multi-fidelity prediction model is built using a cascaded architecture of low-fidelity data pre-training and high-fidelity data fine-tuning. Next, using the multi-fidelity prediction model as the interaction environment, a spatiotemporally decoupled dual-domain embedded critic network is constructed based on reinforcement learning, forming a multi-objective optimization model for process parameters. This optimization model is then used to perform multi-objective optimization of process parameters, obtaining the Pareto optimal solution set. Finally, the critic network is embedded into the internal feature flow of the multi-fidelity prediction model. The weights of the feature attention fusion module are dynamically updated based on the spatiotemporal dual-domain bias output by the critic network, forming a bidirectional iterative closed loop for process index prediction and multi-objective optimization of process parameters. Simultaneously, the optimal combination of process parameters is selected from the Pareto optimal solution set based on the spatiotemporal dual-domain bias. This method employs an adaptive weighted fusion multi-fidelity prediction model, achieving a dual improvement in prediction accuracy and computational efficiency, significantly reducing data dependence and application costs. Furthermore, it proposes a spatiotemporally decoupled dual-domain embedded critic network structure, enabling deep matching of multi-objective value assessment with process physical processes, thus eliminating the reliance on human experience inherent in traditional fixed-weight strategies. Simultaneously, it effectively avoids the problems of unstable optimization direction and weak physical meaning caused by traditional scalar reward fitting. In addition, this method embeds the critic network into the feature flow within the prediction model, forming a two-way closed loop of improved prediction accuracy and optimized strategy, achieving integrated and synergistic improvement in prediction and optimization, and meeting the practical production needs for high precision, high efficiency, and dynamic adaptation.

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a method for predicting multi-fidelity process indicators and optimizing process parameters based on multiple objectives, provided in an embodiment of the present invention. Figure 2 A flowchart illustrating another method for predicting multi-fidelity process indicators and optimizing process parameters based on multiple objectives provided in this embodiment of the invention. Figure 3 This is an architecture diagram of the adaptive weight fusion multi-fidelity prediction model provided in an embodiment of the present invention; Figure 4 This is an architecture diagram of the multi-objective optimization model for process parameters provided in an embodiment of the present invention. Detailed Implementation

[0016] 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 embodiments described below are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] The first aspect of this invention provides a method for predicting multi-fidelity process indicators and optimizing process parameters based on multiple objectives. (See also: [link to related document]) Figure 1 Figure 2 , Figure 1 This is a flowchart illustrating a method for predicting multi-fidelity process indicators and optimizing process parameters based on multiple objectives, provided in an embodiment of the present invention. Figure 2 This is a flowchart illustrating another method for predicting multi-fidelity process indicators and optimizing process parameters based on an embodiment of the present invention. The method includes: S1. Using a pre-built high-fidelity simulation model and a low-fidelity simulation model, perform a mixed sampling operation on the target process to obtain a multi-fidelity dataset that includes both low-fidelity and high-fidelity data.

[0018] Optionally, in this embodiment, S1 can be implemented according to the following sub-steps S11-S14.

[0019] S11. Determine the key parameters of the target process, their value ranges, and sampling intervals, and design multiple sets of typical working condition sampling sets for the high-fidelity simulation model and the low-fidelity simulation model respectively within the predefined parameter space. S12. Based on the value range and sampling interval of key parameters and the sampling set of multiple typical working conditions, a hybrid sampling strategy combining boundary constraints and internal space filling is adopted to collect original working condition samples using high-fidelity simulation models and low-fidelity simulation models respectively. S13. The output of each point of the process object in the original working condition sample is collected by using a multi-layer concentric circle nine-point sampling method, and the spatial non-uniformity index characterizing the processing quality is calculated based on the mean and standard deviation of the nine-point output. S14. Bind the spatial non-uniformity index to the corresponding original working condition sample, and summarize all samples to form a multi-fidelity dataset including low-fidelity data and high-fidelity data.

[0020] Optionally, in this embodiment, the target process is an industrial processing process that simultaneously meets the requirements of temporal evolution characteristics and spatial uniformity control, such as semiconductor wafer cleaning, thin film deposition, dry etching, precision electroplating, and fluid thermal treatment.

[0021] The following section uses semiconductor wafer cleaning process as an example to provide a detailed introduction to the construction of multi-fidelity datasets.

[0022] Specifically, for the wafer cleaning process, a high-fidelity simulation model with multi-physics coupling and a simplified low-fidelity simulation model were constructed. Based on the high-fidelity and low-fidelity simulation models, a hybrid sampling strategy based on boundary constraints and internal space filling was used to complete data acquisition.

[0023] First, four process parameters that have the most significant impact on the cleaning effect are selected as simulation input variables: solution temperature, solution concentration, solution flow rate, and wafer rotation speed. The value range and sampling interval of each parameter are determined. Within the defined parameter space, multiple sampling sets of typical working conditions are designed for high-fidelity and low-fidelity simulation models respectively.

[0024] Then, data acquisition was completed using a hybrid sampling strategy based on boundary constraints and internal space filling. The specific sampling strategy was as follows: typical working conditions were selected in the boundary region of the parameter space, including the minimum and maximum values ​​of each parameter and their extreme coupling combinations, in order to capture the nonlinear response characteristics and potential instability behavior of the cleaning process under extreme conditions. This part of the sample can enhance the model's ability to fit the process boundary conditions. On this basis, multiple sets of representative working condition points were selected in the parameter space according to preset parameter intervals, so that key parameters such as solution temperature, solution concentration, solution flow rate and wafer rotation speed could be fully varied and combined within their value ranges, ensuring that the sample fully covers the main effects of the parameters and their coupling relationships.

[0025] Because the flow field during the cleaning process exhibits a significant radial distribution, a nine-point sampling scheme was used to collect etching rate information during the simulation process to comprehensively evaluate the cleaning effect. The sampling points were arranged in a three-layer concentric circle pattern. After obtaining the nine etching rates, the etching non-uniformity was calculated using the following formula: Assuming the etching rates at the nine points are respectively , , ,…, The average etching rate for: ; in, This represents the number of sampling points, which is 9 in this case.

[0026] Standard deviation of etching rate for: ; Standard deviation non-uniformity for: ; The standard deviation non-uniformity calculated above is used as an index of etching non-uniformity to characterize the spatial non-uniformity of processing quality.

[0027] It should be noted that, based on the sample size matching principle of multi-fidelity modeling, the computation cost of a single set of high-fidelity data is about 12-15 times that of low-fidelity data. Therefore, this embodiment adopts a sample size matching of 1:6 to maximize the coverage of the basic process rules by low-fidelity data while controlling the total computation cost.

[0028] This resulted in a multi-fidelity dataset that includes both low-fidelity and high-fidelity data.

[0029] S2. Using a multi-fidelity dataset as input, an adaptive weight fusion multi-fidelity prediction model is built using a cascaded architecture of low-fidelity data pre-training and high-fidelity data fine-tuning.

[0030] Optionally, in this embodiment, S2 can be implemented according to the following sub-steps S21-S23.

[0031] S21: Train a low-fidelity benchmark network using all low-fidelity data in the multi-fidelity dataset to output low-fidelity basic temporal features; the low-fidelity benchmark network includes MLP layers and Bi-LSTM layers.

[0032] Specifically, the low-fidelity baseline network, serving as the basic framework of the model, requires pre-training on a large amount of low-fidelity data to fully learn the fundamental nonlinear mapping and temporal evolution of process parameters to process indicators, providing a general feature foundation for subsequent high-fidelity fine-tuning. The network adopts a hybrid architecture of MLP parameter encoding and Bi-LSTM temporal encoding, adapting to both the coupling characteristics of static process parameters and the dynamic temporal characteristics of the etching process.

[0033] S22: Train a high-fidelity fine-tuning network using a small amount of high-fidelity data to output high-fidelity corrected spatial features.

[0034] In this embodiment, the high-fidelity fine-tuning network is a lightweight branch network, trained with only a small amount of high-fidelity data. It learns the systematic errors and differences between high-fidelity and low-fidelity data through its core, avoiding overfitting caused by full fine-tuning of the backbone network. This embodiment employs a fully connected neural network, and its lightweight design is suitable for high-fidelity scenarios with small sample sizes.

[0035] S23: By adaptively allocating weights through the feature attention fusion module to fuse low-fidelity basic temporal features and high-fidelity corrected spatial features, network training is completed, resulting in a reasonable multi-fidelity prediction model.

[0036] In this embodiment, the feature attention fusion module, as the core of the multi-fidelity prediction model, is mainly used to achieve adaptive weight fusion of high-fidelity and low-fidelity features. It dynamically adjusts the fusion weights according to the input conditions, weakening the systematic errors of low-fidelity data and enhancing the accuracy advantages of high-fidelity data. The fusion weights can be adaptively adjusted according to the bias signal output by the reinforcement learning commentator.

[0037] Through the above steps, the construction of a multi-fidelity prediction model with adaptive weight fusion was achieved. Please refer to [link / reference]. Figure 3 , Figure 3 This is an architecture diagram of the adaptive weight fusion multi-fidelity prediction model provided in this embodiment of the invention. The multi-fidelity prediction model includes a low-fidelity baseline network, a high-fidelity fine-tuning network, and a feature attention fusion module. The low-fidelity baseline network and the high-fidelity fine-tuning network are used to extract features from the low-fidelity data and the high-fidelity data, respectively, to obtain low-fidelity basic temporal features and high-fidelity corrected spatial features. The feature attention fusion module is used to fuse the low-fidelity basic temporal features and the high-fidelity corrected spatial features based on adaptive weights, and output the prediction results of process indicators.

[0038] The multi-fidelity prediction model constructed in this embodiment breaks through the inherent idea of ​​simple data collaborative modeling in traditional multi-fidelity models. It adopts a cascaded architecture of low-fidelity data pre-training and high-fidelity data fine-tuning. First, it learns the basic nonlinear mapping law of the process through a large amount of low-cost low-fidelity data, and then uses a small amount of high-cost high-fidelity data to perform targeted correction of features. At the same time, a feature attention fusion module is introduced to adaptively quantify the contribution weight of high-fidelity and low-fidelity features and actively weaken the systematic error of low-fidelity data. The overall data flow of the model is as follows: Input process parameters X and time series t to a low-fidelity baseline network to output low-fidelity basic time series features; input process parameters X and time series t to a high-fidelity fine-tuning network to output high-fidelity corrected spatial features; input both low-fidelity basic time series features and high-fidelity corrected spatial features to a feature attention fusion module, and output fused features by adaptively adjusting weights; input the fused features to the final output head to obtain high-fidelity accurate process index prediction results.

[0039] It is understandable that, such as Figure 2 and Figure 3 As shown, before constructing a multi-fidelity prediction model using a multi-fidelity dataset, the model further includes standardization preprocessing of the low-fidelity and high-fidelity data in the multi-fidelity dataset, including outlier removal and feature normalization, to eliminate the interference of different dimensional parameters on model training.

[0040] After preprocessing, the dataset needs to be divided into a training set and a test set. The training set is used to train the multi-fidelity prediction model, and the test set is used to verify the prediction accuracy of the multi-fidelity prediction model. If the prediction accuracy meets the requirements, that is, the model prediction accuracy meets the standard, the model training is completed and a reasonable multi-fidelity prediction model is obtained. Otherwise, the model parameters need to be adjusted and training continues.

[0041] This embodiment employs an adaptive weighted fusion multi-fidelity prediction model to replace traditional high-precision physical simulation. It first learns the fundamental nonlinear mapping and temporal evolution of the process using a large amount of low-cost, low-fidelity data. Then, it uses a small amount of high-cost, high-fidelity data to perform targeted corrections on the features, significantly reducing the model's dependence on high-fidelity data. Simultaneously, a feature attention fusion module is designed, which can adaptively learn the initial fusion weights based on offline feature reconstruction errors. Furthermore, it can combine the bias signals output by the dual-domain reviewers in reinforcement learning to dynamically quantify the contribution weights of high- and low-fidelity features, actively mitigating the systematic errors of low-fidelity data. This achieves high-precision, full-condition prediction of process indicators using only a small amount of high-fidelity data, significantly reducing computational costs and dependence on high-cost, high-precision data.

[0042] S3. Using a multi-fidelity prediction model as the interactive environment, a spatiotemporally decoupled dual-domain embedded critic network is constructed based on reinforcement learning to form a multi-objective optimization model for process parameters. The optimization model is then used to perform multi-objective optimization of process parameters to obtain the Pareto optimal solution set.

[0043] Specifically, this embodiment uses an improved reinforcement learning mechanism to realize a multi-objective optimization model for process parameters. At the same time, the prediction model and the reinforcement learning optimization module form a closed-loop optimization structure. That is, the reinforcement learning algorithm calls the multi-fidelity prediction model as environmental feedback during the optimization process, thereby avoiding a large number of high-cost simulation calculations and improving the efficiency of process parameter search.

[0044] Please see Figure 4 , Figure 4 The architecture diagram of the multi-objective optimization model for process parameters provided in the embodiments of the present invention includes a three-layer architecture: an environment interaction layer, an agent layer, and a training control layer. The environment interaction layer includes an Actor policy network, a multi-fidelity prediction model, a reward calculation module, and a state update module. The Actor policy network takes the state as input and outputs process parameters and actions to the multi-fidelity prediction model to obtain process indicators. The reward calculation module calculates the reward based on the process indicators and inputs the reward into the state update module to update the state. At the same time, the state, actions, rewards, and the updated state are combined into the interaction experience. The agent layer includes an experience replay pool, a time-accumulated domain critic network, a spatially distributed domain critic network, and an Actor network update module. The interaction experience output by the environment interaction layer is stored in the experience replay pool. Experience is sampled from the experience replay pool and input into the time-accumulated domain critic network and the spatially distributed domain critic network, respectively, and outputs temporal bias and spatial bias. The Actor network update module updates the Actor policy network synchronously according to the temporal bias and spatial bias. The training control layer completes the multi-objective optimization of process parameters by controlling multiple rounds of iterative loops, and finally generates and outputs the Pareto optimal solution set.

[0045] Furthermore, in this embodiment, multi-objective optimization of process parameters is achieved by constructing a Markov decision process, specifically including: A. The optimization objectives are to maximize process efficiency and minimize spatial non-uniformity; B. Define the state space as the action of the agent to output process parameters, including process parameters, real-time process indicators, and time series matrix of indicator time series changes; C. When normalizing the motion space to [-1,1] and mapping the normalized motion to the actual process parameters, the single adjustment range shall not exceed 10% of the parameter range; D. Based on a multi-objective decoupling strategy, set independent decoupling reward functions for different optimization objectives.

[0046] Optionally, as one implementation method, the independent decoupled reward function can be constructed as follows: The efficiency index is normalized based on the global maximum and minimum values ​​of the process output, and an efficiency bonus with a value range of [0,1] is generated. By applying a negative mapping to the spatial non-uniformity values, a uniform reward that fits the reinforcement learning reward maximization paradigm is generated.

[0047] The following section will continue to use the cleaning process as an example to illustrate the multi-objective optimization process of process parameters.

[0048] First, the optimization objectives of the cleaning process are set as "maximizing the etching rate" and "minimizing the etching non-uniformity". At the same time, the value constraints of each key process parameter are defined, and the process parameter optimization problem is transformed into a Markov decision process (MDP).

[0049] Then, the interaction environment of the reinforcement learning agent is based on the multi-fidelity prediction model built in S2, which is used to simulate the mapping relationship between process parameters and process indicators.

[0050] Next, the state vector is defined as a state matrix with continuous time sequence dimension, which includes the four key process parameters at the current time, the predicted etching rate and etching non-uniformity at the current time, and the changes in indicators from the previous time to the current time, thus fully depicting the dynamic evolution of the process.

[0051] Subsequently, a normalized continuous action space model is adopted, and the action vector output by the agent has a value range of [-1,1]. It is transformed into the incremental adjustment value of the corresponding process parameter within the constraint range through linear mapping. The single adjustment amplitude does not exceed 10% of the parameter value range to avoid the parameter iteration exceeding the process safety boundary.

[0052] Finally, set the reward function.

[0053] To address the inherent conflict between maximizing etching rate and minimizing etching non-uniformity in cleaning process optimization, directly employing the traditional linear weighted summation method can easily lead to mutual masking of objectives with different physical dimensions during training, resulting in unstable gradient update directions. Therefore, this invention adopts a multi-objective decoupling strategy at the reward function design level, constructing independent reward feedback channels for each of the two optimization objectives.

[0054] 1. Design of the etching rate reward function.

[0055] Since the optimization objective of the etching rate is to maximize it, in order to eliminate the differences in physical dimensions and accelerate the convergence of the neural network, the absolute rate of the environmental output is first normalized using the theoretical extremum of the process window. The etching rate reward function is defined as follows: ; in, This represents the normalized, standardized efficiency reward function value. The function's range is [0,1], and it aims to guide the agent in searching for parameter regions that can improve the etching rate. The subscript R indicates the reward term corresponding to the process efficiency (here, the etching rate of the wafer cleaning process). express The state of the Markov decision process at any given moment. express The process parameters output by the Actor at any given time are the actions. A unified symbol representing normalized rewards. This represents the original process efficiency index obtained from the current iteration. In this case, it refers to the etching rate in the wafer cleaning scenario, and is output by the multi-fidelity prediction model. This represents the theoretical maximum value of the process efficiency within the process window. This represents the theoretical minimum of the process efficiency within the process window.

[0056] 2. Design of reward function for etching non-uniformity.

[0057] Since the optimization objective for etching non-uniformity is to minimize it (i.e., the smaller the value, the higher the wafer surface quality), a negative mapping mechanism is used to construct the reward to align with the standard reinforcement learning paradigm of "maximizing cumulative expected reward." The etching non-uniformity reward function is defined as follows: ; in, Represents the normalized spatial uniformity reward value, subscript It represents an index of spatial inhomogeneity. This represents the non-uniformity scalar after the original normalization. This represents the non-uniformity index at the current moment. This represents the theoretical maximum value of etching uniformity within the process window. This represents the theoretical minimum value of etching uniformity within the process window.

[0058] This function transforms minimizing the non-uniformity value into maximizing the negative reward for non-uniformity by introducing a negative sign. When process parameters cause a deterioration in uniformity, the output value of this negative reward function will be smaller, thus penalizing the agent.

[0059] Furthermore, in traditional reinforcement learning methods, critic networks are typically used to fit scalar cumulative reward functions based on the Bellman equation. These methods struggle to characterize the fundamental differences between the temporal evolution and spatial distribution characteristics of wafer cleaning processes, leading to weak physical meaning and unstable optimization directions in multi-objective optimization. To address this, this invention reconstructs the functional form of traditional critic networks, proposing a spatiotemporally decoupled dual-domain embedded critic network structure. This structure no longer uses scalar cumulative reward as the learning objective; instead, it transforms the value assessment process into a physical feature bias modeling problem based on the physical process of the wafer cleaning process, establishing independent value assessment mechanisms in both the temporal and spatial domains.

[0060] Please continue reading Figure 4 The spatiotemporally decoupled dual-domain embedded critic network in this embodiment includes a time-accumulation domain critic network (T-Critic) and a spatial distribution domain critic network (S-Critic). The time-accumulation domain critic network reuses the low-fidelity basic timing features output by the low-fidelity baseline network, compares the actual process timing trajectory with the ideal efficiency trajectory, and outputs the timing deviation. The spatial distribution domain critic network reuses the high-fidelity corrected spatial features output by the high-fidelity fine-tuning network, compares the discrete difference between the output at each sampling point and the mean, and outputs the spatial deviation.

[0061] Specifically, for the time-accumulation domain critic network, it is mainly used for value assessment of the etching rate optimization objective. Its core function is to evaluate the deviation of the etching rate from the ideal trajectory over time under the current process parameters. The specific implementation is as follows: Network input: process parameter sequence X and time series information; Feature source: Directly reuse the temporal coding features of the low-fidelity baseline network in the multi-fidelity prediction model; Network output: Estimated value of etching rate timing trajectory deviation ; Loss function of time-cumulative domain critic network Defined as: ; in, The number of sampling points on the wafer surface. To predict the etching rate output by the model, This represents the ideal etching rate trajectory.

[0062] For the spatially distributed domain critic network, its main purpose is to evaluate the value of etching non-uniformity optimization objectives. Its core function is to assess the dispersion and non-uniformity risk of the spatial distribution of etching rates on the wafer surface under current process parameters. The specific implementation is as follows: Network input: Current process parameter X; Feature source: Spatial features of high-fidelity fine-tuning branches in multi-fidelity models; Network output: Spatial distribution bias estimate ; Loss function of spatially distributed critic network Defined as: ; in, The number of sampling points on the wafer surface. For the first Etching rate at each sampling point The average etching rate is given.

[0063] Furthermore, this embodiment also reconstructs the value representation of the critic network, but still retains the policy optimization mechanism in reinforcement learning.

[0064] Specifically, in terms of the comments from critics , As an evaluation signal for policy optimization, the Actor network updates itself with the objective of minimizing the overall bias, and its loss function... for: ; In the formula, Indicates the time-domain bias loss weight. This represents the spatial domain bias loss weight, which operates during the Actor network training phase and is a weighting coefficient for the optimization objective. This represents the temporal bias in the output of the commentator network in the time-cumulative domain. This represents the spatial bias of the commentator network output in the spatial distribution domain.

[0065] This invention redefines the traditional value function based on the physical essence of the process, retains the efficient search capability of reinforcement learning in a continuous decision space, and achieves a deep matching between value assessment and the physical process of cleaning.

[0066] This embodiment constructs a multi-objective optimization framework based on improved reinforcement learning, which reconstructs the traditional scalar reward-based value function and transforms it into a structured evaluation mechanism based on process physical characteristic deviations. Simultaneously, it proposes a spatiotemporally decoupled dual-domain embedded critic network structure. Through two independent branches—a time-cumulative domain critic and a spatially distributed domain critic—it characterizes the dynamic evolution deviation of etching rate in the time domain and the distribution deviation of etching uniformity in the spatial domain, respectively. This achieves deep matching between multi-objective value evaluation and process physical processes, eliminating the reliance on human experience in traditional fixed-weight strategies. Furthermore, it effectively avoids the problems of unstable optimization direction and weak physical meaning caused by traditional scalar reward fitting.

[0067] S4. The critic network is embedded into the internal feature flow of the multi-fidelity prediction model. The weight of the feature attention fusion module is dynamically updated based on the spatiotemporal dual-domain bias output by the critic network, forming a two-way iterative closed loop of process index prediction and multi-objective optimization of process parameters. At the same time, the optimal combination of process parameters is obtained by screening from the Pareto optimal solution set based on the spatiotemporal dual-domain bias.

[0068] Unlike the traditional agent model, which provides environmental feedback for reinforcement learning in a one-way coupling manner, this invention proposes a bidirectional enhanced embedded collaborative mechanism that embeds the critic network into the feature flow inside the prediction model, so that reinforcement learning and the prediction model form a unified integrated structure.

[0069] On the one hand, by utilizing the spatiotemporal dual-domain bias output by the critic network, the feature fusion weights in the multi-fidelity prediction model are calculated in real time to achieve dynamic updates of feature fusion. The calculation formula is as follows: ; In the formula, The fusion weights represent the low-fidelity features. The fusion weights represent the high-fidelity features.

[0070] This mechanism allows for the dynamic adjustment of the contribution ratio of high-fidelity and low-fidelity features based on real-time deviations during process optimization, thereby further improving the full-condition prediction accuracy of the multi-fidelity model.

[0071] On the other hand, based on the aforementioned adaptive weight adjustment mechanism, a two-way closed-loop optimization link of prediction and optimization is formed. The entire process of two-way collaborative iteration can be described as follows: The multi-fidelity prediction model, which uses adaptive weight fusion, outputs process indicators and internal features to a dual-domain critic network. As the prediction accuracy of the model improves, the critic network performs value assessments based on accurate process data and temporal and spatial features, resulting in a reduction in the output temporal and spatial bias values. The two types of bias estimates output by the critic are used as adjustment criteria to update the fusion weights of low-fidelity temporal features and high-fidelity spatial features in the feature attention fusion module of the prediction model in real time. The optimized feature fusion ratio can further improve the prediction accuracy of subsequent inference and training of the prediction model, forming an internal loop of self-iterative improvement for the prediction model.

[0072] Meanwhile, the temporal bias and spatial bias output by the time accumulation domain critic and the spatial distribution domain critic are error signals with clear process physical meaning. These signals are synchronously sent to the Actor network update module to guide the Actor policy network to iteratively update the strategy of outputting process parameters, continuously optimize the reinforcement learning strategy, and simultaneously improve the multi-objective optimization capability of process parameters.

[0073] The entire process forms a two-way coupled closed loop. Improved prediction model accuracy reduces critic bias. Bias information, on the one hand, optimizes the feature fusion weights of the prediction model and continuously improves prediction accuracy. On the other hand, it serves as a physical error signal to drive the reinforcement learning agent to continuously optimize parameter adjustment strategies. The two modules of prediction modeling and process parameter optimization provide each other with optimization basis and iterate and upgrade synchronously.

[0074] The aforementioned closed-loop link enables bidirectional synergistic enhancement of the prediction model and the reinforcement learning optimization strategy, breaking the limitation of unidirectional coupling in existing technologies.

[0075] After training with a multi-objective reinforcement learning algorithm, the agent generates a set of non-dominated solutions in the target space, namely the Pareto front. Although each solution on the Pareto front is mathematically optimal, in actual processes, engineers cannot execute multiple sets of parameters simultaneously. Therefore, a method based on minimizing the combined bias in both the spatiotemporal domains is ultimately required for the final decision.

[0076] Optionally, as one implementation method, the optimal combination of process parameters is obtained by screening from the Pareto optimal solution set based on spatiotemporal dual-domain bias, including: For each solution in the Pareto optimal solution set, a customizable spatiotemporal dimension decision preference weight is set, and a comprehensive evaluation index is calculated by combining the spatiotemporal dual-domain bias corresponding to each solution. The Pareto solution with the smallest comprehensive evaluation index is selected as the optimal combination of process parameters.

[0077] Specifically, for the first Pareto front solution set... For each solution, the corresponding time-cumulative domain bias estimate is calculated using the trained spatiotemporally decoupled dual-domain embedded critic network. Deviation estimate from spatial distribution domain A comprehensive evaluation index is constructed based on the two-domain deviation, and the calculation formula is as follows: ; in, Denotes the first solution in the Pareto front solution set. The comprehensive evaluation index corresponding to each solution and For decision preference weights, satisfying It can be flexibly adjusted according to the priority requirements of etching rate and etching uniformity in the actual process scenario.

[0078] This comprehensive evaluation index The overall deviation level of the corresponding process parameter solutions in the time and space domains was quantified. The smaller the value, the better the solution performs in both the temporal evolution of etching rate and the spatial distribution of etching uniformity.

[0079] Based on the above method, a comprehensive evaluation index is selected from the Pareto solution set. The smallest solution is the final decision solution, i.e. the optimal process formulation.

[0080] Thus, multi-fidelity process index prediction and multi-objective optimization of process parameters have been achieved.

[0081] This embodiment constructs an embedded bidirectional enhanced multi-fidelity and reinforcement learning collaborative mechanism, embedding the critic network into the feature flow within the prediction model to form a bidirectional closed loop of prediction accuracy improvement and optimization strategy optimization, breaking through the limitation of the unidirectional serial coupling of traditional surrogate models combined with optimization algorithms. Simultaneously, an error-driven adaptive adjustment mechanism for feature weights is designed, utilizing the deviation signal output by the critic network to dynamically optimize the feature fusion weights of the multi-fidelity model, achieving a bidirectional synergistic improvement in prediction model accuracy and reinforcement learning optimization effect. Furthermore, the full-condition data during the optimization process can back-optimize the generalization ability of the prediction model, enabling the model to quickly adapt to the dynamic changes of actual production line conditions without repeated modeling and training, significantly improving the engineering feasibility and practical application value of the technical solution.

[0082] In summary, this invention provides a multi-fidelity process index prediction and multi-objective optimization method for process parameters. On the one hand, it employs an adaptive weight fusion multi-fidelity prediction model, achieving a dual improvement in prediction accuracy and computational efficiency, significantly reducing data dependence and application costs. On the other hand, it proposes a spatiotemporally decoupled dual-domain embedded critic network structure, enabling deep matching of multi-objective value assessment and process physical processes, thus eliminating the reliance on human experience in traditional fixed-weight strategies. Simultaneously, it effectively avoids the problems of unstable optimization direction and weak physical meaning caused by traditional scalar reward fitting. Furthermore, this method embeds the critic network into the feature flow within the prediction model, forming a two-way closed loop of improved prediction accuracy and optimized strategy, achieving integrated and synergistic improvement of prediction and optimization, and meeting the practical production needs of high precision, high efficiency, and dynamic adaptation.

[0083] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting multi-fidelity process indicators and optimizing process parameters based on multiple objectives, characterized in that, include: S1. Using a pre-built high-fidelity simulation model and a low-fidelity simulation model, perform a mixed sampling operation on the target process to obtain a multi-fidelity dataset including high-fidelity data and low-fidelity data. S2. Using the multi-fidelity dataset as input, an adaptive weight fusion multi-fidelity prediction model is built using a cascaded architecture of low-fidelity data pre-training and high-fidelity data fine-tuning. The multi-fidelity prediction model includes a low-fidelity baseline network, a high-fidelity fine-tuning network, and a feature attention fusion module. The low-fidelity baseline network and the high-fidelity fine-tuning network are used to extract features from the low-fidelity data and the high-fidelity data, respectively, to obtain low-fidelity basic temporal features and high-fidelity corrected spatial features. The feature attention fusion module is used to fuse the low-fidelity basic temporal features and the high-fidelity corrected spatial features based on adaptive weights to output the process index prediction results. S3. Using the multi-fidelity prediction model as the interactive environment, construct a spatiotemporally decoupled dual-domain embedded critic network based on reinforcement learning to form a multi-objective optimization model for process parameters, and use the optimization model to perform multi-objective optimization of process parameters to obtain the Pareto optimal solution set. S4. Embed the critic network into the internal feature flow of the multi-fidelity prediction model, and dynamically update the weight of the feature attention fusion module based on the spatiotemporal dual-domain bias output by the critic network, forming a bidirectional iterative closed loop of process index prediction and multi-objective optimization of process parameters; at the same time, the optimal combination of process parameters is obtained by screening from the Pareto optimal solution set based on the spatiotemporal dual-domain bias.

2. The method for predicting multi-fidelity process indicators and optimizing process parameters with multiple objectives according to claim 1, characterized in that, S1 includes: Determine the key parameters of the target process, their value ranges, and sampling intervals, and design multiple sets of typical operating conditions for the high-fidelity simulation model and the low-fidelity simulation model within the predefined parameter space; Based on the value range and sampling interval of the key parameters and the sampling set of the multiple typical working conditions, a hybrid sampling strategy combining boundary constraints and internal space filling is adopted to collect original working condition samples using the high-fidelity simulation model and the low-fidelity simulation model respectively. The output of each point of the process object in the original working condition sample is collected by a multi-layer concentric circle nine-point sampling method, and the spatial non-uniformity index characterizing the processing quality is calculated based on the mean and standard deviation of the obtained nine-point output. The spatial non-uniformity index is bound to the corresponding original working condition sample, and all samples are aggregated to form a multi-fidelity dataset including low-fidelity data and high-fidelity data.

3. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 1, characterized in that, In S2, using the aforementioned multi-fidelity dataset as input, a multi-fidelity prediction model is built using a cascaded architecture of low-fidelity data pre-training and high-fidelity data fine-tuning, including: The low-fidelity benchmark network is trained using all the low-fidelity data in the multi-fidelity dataset to output low-fidelity basic temporal features; wherein, the low-fidelity benchmark network includes MLP layers and Bi-LSTM layers. A high-fidelity fine-tuning network is trained using a small amount of the high-fidelity data to output high-fidelity corrected spatial features; wherein the high-fidelity fine-tuning network employs a fully connected neural network. By adaptively allocating weights through the feature attention fusion module to fuse the low-fidelity basic temporal features and the high-fidelity modified spatial features, network training is completed, resulting in a reasonable multi-fidelity prediction model.

4. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 1, characterized in that, In S3, the multi-objective optimization model for process parameters includes a three-layer architecture: an environment interaction layer, an agent layer, and a training and control layer. The environment interaction layer includes an Actor policy network, a multi-fidelity prediction model, a reward calculation module, and a state update module. The Actor policy network takes the state as input and outputs process parameter actions to the multi-fidelity prediction model to obtain process indicators. The reward calculation module calculates rewards based on the process indicators and inputs the rewards into the state update module to update the state. At the same time, the state, actions, rewards, and updated state are combined into interactive experience. The agent layer includes an experience replay pool, a time-accumulated domain critic network, a spatially distributed domain critic network, and an Actor network update module; the interactive experience output by the environment interaction layer is stored in the experience replay pool. Experience samples are sampled from the experience replay pool and input into the time-accumulation domain critic network and the spatial distribution domain critic network, respectively, and output temporal bias and spatial bias, respectively; the Actor network update module updates the Actor policy network synchronously according to the temporal bias and spatial bias; The training control layer completes multi-objective optimization of process parameters by controlling multiple rounds of iterative loops, and finally generates and outputs the Pareto optimal solution set.

5. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 4, characterized in that, In S3, the multi-objective optimization of process parameters is achieved by constructing a Markov decision process, specifically including: The optimization objectives are to maximize process efficiency and minimize spatial non-uniformity. The state space is defined as the action of the agent to output process parameters, including process parameters, real-time process indicators, and time-series matrices of the time-series changes of the indicators; When the motion space is normalized to [-1,1] and the normalized motion is mapped to the actual process parameters, the single adjustment range shall not exceed 10% of the parameter range; Based on a multi-objective decoupling strategy, independent decoupling reward functions are set for different optimization objectives.

6. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 5, characterized in that, The independent decoupled reward function is constructed as follows: The efficiency index is normalized based on the global maximum and minimum values ​​of the process output, and an efficiency bonus with a value range of [0,1] is generated. By applying a negative mapping to the spatial non-uniformity values, a uniform reward that fits the reinforcement learning reward maximization paradigm is generated.

7. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 4, characterized in that, The time-cumulative domain critic network reuses the low-fidelity basic timing features output by the low-fidelity benchmark network, compares the actual process timing trajectory with the ideal efficiency trajectory, and outputs the timing deviation. The spatial distribution domain critic network, by reusing the high-fidelity corrected spatial features output by the high-fidelity fine-tuning network, compares the discrete difference between the output of each sampling point and the mean, and outputs the spatial deviation.

8. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 4, characterized in that, In S4, the weights of the feature attention fusion module are dynamically updated based on the dual-domain bias output by the critic network, including: Using the spatiotemporal dual-domain bias output by the critic network, the feature fusion weights in the multi-fidelity prediction model are calculated in real time to achieve dynamic updates of feature fusion. The calculation formula is as follows: ； In the formula, The fusion weights represent the low-fidelity features. This represents the temporal bias in the output of the commentator network in the time-cumulative domain. The fusion weights represent the high-fidelity features. This represents the spatial bias of the commentator network output in the spatial distribution domain.

9. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 1, characterized in that, In S4, the optimal combination of process parameters is obtained by filtering from the Pareto optimal solution set based on the spatiotemporal dual-domain bias, including: For each solution in the Pareto optimal solution set, a customizable spatiotemporal dimension decision preference weight is set, and a comprehensive evaluation index is calculated by combining the spatiotemporal dual-domain bias corresponding to each solution. The Pareto solution with the smallest comprehensive evaluation index is selected as the optimal combination of process parameters.

10. The method for predicting multi-fidelity process indicators and optimizing process parameters according to claim 1, characterized in that, The target process is an industrial processing technology that simultaneously meets the requirements of temporal evolution characteristics and spatial uniformity control, including semiconductor wafer cleaning, thin film deposition, dry etching, precision electroplating, and fluid thermal treatment.

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