A method, apparatus, and medium for predicting performance of a polishing liquid
Patent Information
- Application Number
- CN202610832637.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-10
- Publication Date
- 2026-09-22
AI Technical Summary
长期以来，抛光液配方研发以实验试错为主，开发周期长、成本高，严重依赖资深研发人员的经验
[0021]由于采用了上述的技术方案，本发明与现有技术相比，具有以下的优点和积极效果：本发明通过将抛光液各组分的几何-拓扑分子描述符与电子结构特征按摩尔数加权聚合，获得维度恒定、组分置换不变且可外推至新组分的配方级特征，解决了传统独热编码无法体现组分摩尔贡献、不能外推的缺陷。本发明融合磨料类型、工艺参数与Preston物理特征，兼顾化学反应本质与经典物理规律，显著提升预测精度。本发明采用多随机种子随机森林深度集成模型，同步输出去除速率点估计与认识不确定性度量，实现预测可信度量化，便于识别低置信样本并人工复核。
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Figure CN122800007A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of polishing slurry prediction technology, and in particular to a method, device and medium for predicting polishing slurry performance. Background Technology
[0002] Chemical mechanical polishing (CMP) is a key process in advanced integrated circuit manufacturing for achieving global planarization of wafer surfaces, and its effectiveness is primarily determined by the formulation of the polishing slurry. For a long time, slurry formulation development has relied heavily on trial and error, resulting in long development cycles, high costs, and a heavy dependence on the experience of senior researchers. In recent years, some studies have incorporated machine learning into slurry performance prediction; however, most existing methods use one-hot encoding of components or concentration vectors as input, failing to reflect the contribution of component molar numbers to the overall properties of the formulation. Furthermore, most neglect molecular electronic structure information closely related to electrochemical reactions (such as the HOMO-LUMO band gap), and lack quantification of prediction reliability, failing to provide engineers with a basis for identifying extrapolated formulations. In addition, prediction models for different polished materials such as silicon oxide, silicon nitride, polycrystalline silicon, and oxide layers are usually implemented as independent projects, lacking a unified framework. Summary of the Invention
[0003] The technical problem to be solved by the present invention is to provide a method, device and medium for predicting the performance of polishing fluid, which can achieve high-precision and quantifiable reliability prediction of the performance of polishing fluid under multiple material channels.
[0004] The technical solution adopted by this invention to solve its technical problem is: to provide a method for predicting the performance of polishing fluid, comprising the following steps:
[0005] Obtain multi-component data of the target polishing fluid formulation, wherein the multi-component data includes the molecular structure identifier and molar number of each component;
[0006] For each component, a geometric-topological molecular descriptor vector and an electronic structure feature vector are extracted from the molecular structure identifier. The geometric-topological molecular descriptor vector and the electronic structure feature vector are then weighted and aggregated according to the number of moles to obtain the formula-level features.
[0007] The formulation-level features are concatenated with the abrasive type, process parameters, and Preston physical features of the target polishing fluid formulation to obtain the formulation-level feature vector;
[0008] The recipe-level feature vector is input into a deep ensemble model consisting of multiple random forest regression base learners with different random seeds to obtain multiple independent prediction values.
[0009] Calculate the mean and standard deviation of multiple independent predictions, and use the mean as a removal rate point estimate and the standard deviation as a measure of the cognitive uncertainty of the prediction.
[0010] The geometry-topology molecular descriptor vector includes at least two of the following: molecular weight, oil-water partition coefficient, topological polar surface area, number of hydrogen bond donors, number of hydrogen bond acceptors, and number of rotatable bonds.
[0011] The electronic structure feature vector is extracted by one or a combination of the following methods: (a) single-point energy calculation based on semi-empirical quantization; (b) single-point energy calculation based on density functional theory; (c) latent representation inference from a pre-trained molecular neural network; (d) lookup from a pre-calculated feature library of formulation components, and if no match is found, fall back to one of (a) to (c) and write back to the cache.
[0012] The electronic structure eigenvectors include the HOMO-LUMO bandgap.
[0013] The electronic structure eigenvectors also include one or more of the highest occupied molecular orbital energy level, the lowest unoccupied molecular orbital energy level, and the molecular dipole moment.
[0014] The hyperparameters of the random forest regression base learner satisfy the following: the number of decision trees is no less than 100, the maximum depth is no less than 10, the maximum feature ratio is between 0.5 and 1.0, and bootstrap sampling is enabled; the random seeds of the random forest regression base learner are... structure, For the first A random seed for a random forest regression base learner. It is an integer constant.
[0015] A non-negative constraint is applied when calculating the mean of multiple independent predicted values.
[0016] The method for predicting the performance of the polishing slurry includes:
[0017] Calculate the ratio of the cognitive uncertainty measure to the removal rate point estimate, and add a low confidence label when the ratio exceeds a preset threshold.
[0018] The technical solution adopted by the present invention to solve its technical problem is: to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-mentioned polishing fluid performance prediction method.
[0019] The technical solution adopted by the present invention to solve its technical problem is: to provide a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-mentioned polishing fluid performance prediction method.
[0020] Beneficial effects
[0021] By employing the above-mentioned technical solutions, this invention has the following advantages and positive effects compared with existing technologies: This invention obtains formulation-level features with constant dimensions, invariant component substitution, and extrapolation to new components by weighting and aggregating the geometric-topological molecular descriptors and electronic structure features of each component of the polishing slurry using molar number weights. This solves the shortcomings of traditional one-hot encoding, which cannot reflect the molar contribution of components and cannot extrapolate. This invention integrates abrasive type, process parameters, and Preston physical characteristics, taking into account both the nature of chemical reactions and classical physical laws, significantly improving prediction accuracy. This invention uses a multi-random seed random forest deep ensemble model, simultaneously outputting removal rate point estimates and cognitive uncertainty measures, realizing the quantification of prediction confidence, facilitating the identification of low-confidence samples and manual verification. Attached Figure Description
[0022] Figure 1 This is a flowchart of the polishing fluid performance prediction method according to the first embodiment of the present invention. Detailed Implementation
[0023] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.
[0024] The first embodiment of this invention relates to a method for predicting the performance of polishing slurries. This method can uniformly encode multi-component formulations at both the molecular descriptor and electronic structure levels, and simultaneously output the predicted mean and cognitive uncertainty, achieving high-precision and quantifiable reliability prediction of polishing slurry performance under multi-material pathways. Figure 1 As shown, the specific steps include:
[0025] Step 1: Obtain multi-component data of the target polishing slurry formulation. This multi-component data includes the molecular structure identifier and molar quantity of each component. The multi-component data obtained in this step may also include abrasive type, process type, pH, conductivity, polishing pressure, etc.
[0026] Step 2: Extract the geometry-topology molecular descriptor vector and electronic structure feature vector for the molecular structure identifier of each component, and perform weighted aggregation of the geometry-topology molecular descriptor vector and electronic structure feature vector according to the number of moles to obtain the formula-level features.
[0027] The geometry-topology molecular descriptor vector in this step includes at least two of the following: molecular weight, oil-water partition coefficient, topological polar surface area, number of hydrogen bond donors, number of hydrogen bond acceptors, and number of rotatable bonds. The electronic structure eigenvector includes at least the HOMO-LUMO band gap, and may also include one or more of the following: highest occupied molecular orbital energy level, lowest unoccupied molecular orbital energy level, and molecular dipole moment.
[0028] When extracting electronic structure feature vectors, any one or a combination of the following methods can be used:
[0029] (a) Single-point energy calculation based on semi-empirical quantization method PM6 or PM7; (b) Single-point energy calculation based on density functional theory (DFT), which uses functional and basis set combinations including but not limited to B3LYP / 6-31G; (d) Latent representation inference from pre-trained molecular neural network; (d) Lookup table from pre-calculated feature library of formulation components, and if not found, fall back to one of (a) to (c) and write back to cache.
[0030] In this embodiment, before weighting and aggregating the geometry-topology molecular descriptor vector and the electronic structure feature vector according to the number of moles, the electronic structure feature vector can also be Z-score normalized.
[0031] Step 3: Concatenate the formula-level features and the abrasive type and process parameters of the target polishing fluid formula with the Preston physical features to obtain a formula-level feature vector. The Preston physical features are represented as follows: , among which, among which, For polishing pressure, This is the dilution ratio.
[0032] Step 4: Input the recipe-level feature vector into a deep ensemble model composed of multiple random forest regression base learners with different random seeds to obtain multiple independent prediction values.
[0033] The hyperparameters of the random forest regression base learner used in this embodiment satisfy the following conditions: the number of decision trees is not less than 100, the maximum depth is not less than 10, the maximum feature ratio is between 0.5 and 1.0, and bootstrap sampling is enabled. The number of random forest regression base learners is 3 to 20, where the... The random seeds for a random forest regression base learner can be set according to... structure, For the first A random seed for a random forest regression base learner. It is an integer constant.
[0034] Step 5: Calculate the mean and standard deviation of multiple independent predictions, using the mean as the removal rate point estimate and the standard deviation as a measure of the uncertainty in prediction. In this step, a non-negativity constraint is applied when calculating the mean of the multiple independent predictions to ensure that the removal rate point estimate is a non-negative physical quantity. After this step, the ratio of the uncertainty in prediction to the removal rate point estimate can be calculated. When the ratio exceeds a preset threshold, a low-confidence flag can be added, prompting manual review or additional experiments.
[0035] It is worth mentioning that the method of this embodiment can simultaneously support at least two independent material pathways: the first pathway is for predicting the removal rate of silicon oxide and / or silicon nitride; the second pathway is for predicting the removal rate of polysilicon and / or oxide layer; the two pathways share the above steps.
[0036] The present invention will be further illustrated by a specific embodiment below.
[0037] Data Acquisition and Preprocessing: This embodiment receives multi-component input of the polishing slurry formulation, including the SMILES string of each component, the corresponding mole number (or normalized mole fraction / mass percentage), abrasive type, CVD type, pH, conductivity, polishing pressure, dilution ratio, and other process parameters.
[0038] Geometric-topological descriptor extraction: For each non-empty SMILES, the cheminformatics toolkit RDKit is used to extract at least the geometric-topological molecular descriptors including MolWt, LogP, TPSA, HBD, HBA, and RotatableBonds.
[0039] HOMO-LUMO electronic structure feature extraction: For each non-empty smiles, a 3D structure is first generated and pre-optimized by the force field. Then, a semi-empirical quantization method PM6 (keyword example: "PM6 PRECISE EF SHIFT=80 LARGE", implemented in MOPAC) is used to calculate the single-point energy, outputting E. HOMO E LUMO Molecular dipole moment; Calculation of HOMO-LUMO band gap ΔE HL = E LUMO -E HOMO The above four quantities are standardized by Z-score and used as electronic structure feature vectors.
[0040] Mohr weighted aggregation: concatenating the geometric-topological descriptor and electronic structure features of each component to obtain the component-level feature φ(s) i ), massage number n i Weighted summation yields the formula-level molecular-electronic structure characteristics f mol = Σ ni · φ(s i ).
[0041] Preston physical characteristics splicing: combining formulation-level molecular-electronic structure characteristics with process scalars such as abrasive / CVD category, unique heating, pH, conductivity, and heating time, along with Preston physical characteristics. By concatenating the components, we obtain the formula-level feature vector x.
[0042] Deep Ensemble Inference: Train K=5 independent random forest regressors as base learners. Each base learner has built-in normalization preprocessing, and its hyperparameters include the number of decision trees n_estimators=400, maximum depth max_depth=20, maximum feature ratio max_features=0.8, and bootstrap sampling ratio max_samples=0.9. The random seed of the k-th base learner is constructed according to seedk =17·k + 1 (k = 0, 1, …, K−1).
[0043] Output and downstream applications: The mean of the predictions of the K base learners is taken as the final point estimate, and a non-negative constraint is applied to the mean to ensure that the removal rate is a non-negative physical quantity; the standard deviation of the K predictions is taken as the proxy quantity for recognizing uncertainty; when the ratio of uncertainty to mean exceeds a preset threshold, a low confidence mark is added to the output to prompt manual review or additional experiments.
[0044] Deployed on a general-purpose computing server or cloud platform, it provides a batch prediction interface based on HTTP or MCP protocol. After each training, it automatically records model cards to the model governance database. The model cards contain information such as model ID, number of training samples, feature dimension, R² of training set and K-fold cross-validation, RMSE / MAE, average uncertainty, feature data hash value and code repository commit number.
[0045] In this embodiment, a specific test condition is used, specifically:
[0046] On the Python 3.12 + scikit-learn platform, 800 polishing fluid formulation samples were used from an internal database. Five-fold cross-validation was employed, with a fixed random seed of 42. The training process involved parallel training of five random forest base learners, each using a different random seed (17·k + 1, k = 0…4). Each base learner had 400 decision trees, a maximum depth of 20, a maximum feature ratio of 0.8, and a bootstrap sampling ratio of 0.9. StandardScaler normalization preprocessing was used. Five independent Deep Ensemble models were trained for each of the four objectives: sio_rr, sin_rr, poly_rr, and ox_rr. Evaluation metrics included mean absolute error (MAE) and coefficient of determination (R²).
[0047] In this embodiment, for each component SMILES, 6-dimensional geometry-topology descriptors (MolWt, LogP, TPSA, HBD, HBA, RotBonds) are extracted using RDKit, while 4-dimensional electronic structure features (E) are calculated using MOPAC + PM6. HOMO E LUMO ΔE HL The dipole moment is normalized by Z-score; the two are concatenated to obtain a 10-dimensional component-level feature, which is then aggregated into a formulation-level molecular-electronic structure feature by weighting the number of moles of each component; this feature is concatenated with the unique thermal and Preston physical features of the abrasive / CVD category to obtain a formulation-level feature vector; and five random forest base learners are used to form a Deep Ensemble for ensemble inference, outputting the prediction mean and uncertainty.
[0048] To demonstrate the effectiveness of the present invention, several comparative examples are also provided in this embodiment, as follows:
[0049] The difference between Comparative Example 1 and this embodiment is that only the one-heat code of each component name is used as the input feature, the regression model adopts ridge regression, molar weighted aggregation is not performed, HOMO-LUMO electronic structure features are not introduced, and Deep Ensemble is not used. The rest is completely the same as this embodiment.
[0050] The difference between Comparative Example 2 and this embodiment is that only the one-heat code of each component name is used as the input feature, the regression model adopts the XGBoost single model, without molar weighted aggregation, without introducing HOMO-LUMO electronic structure features, and without using Deep Ensemble. The rest is completely the same as this embodiment.
[0051] The difference between Comparative Example 3 and this embodiment is that: RDKit geometry-topology descriptors are used and aggregated with mole number weights as input features, the regression model adopts the XGBoost single model, HOMO-LUMO electronic structure features are not introduced, and Deep Ensemble is not used, while the rest is completely the same as this embodiment.
[0052] The difference between Comparative Example 4 and this embodiment is that: the RDKit geometry-topology descriptor and HOMO-LUMO electronic structure features are concatenated and then weighted by mole number as input features. The regression model adopts the XGBoost single model and does not use Deep Ensemble integration and uncertainty output. The rest is completely the same as this embodiment.
[0053] The prediction error is calculated using the mean absolute error (MAE) and the coefficient of determination (R²). 2 The model's predictive performance is evaluated using the Coefficient of Determination. The specific formula is:
[0054] Mean Absolute Error (MAE): ;
[0055] in, For the true value, is the predicted value, and n is the number of samples.
[0056] Coefficient of determination (R) 2 ):
[0057]
[0058] in, This is the average of the true values.
[0059] The prediction errors obtained in this embodiment and comparative examples 1-4 were detected as follows: The embodiment and each comparative example were trained and predicted using 5-fold cross-validation under the same n=800 dataset and model parameters. The true and predicted values of each sample were recorded. Then, the MAE and R-values of the SiO pathway (represented by sio_rr) and the Poly pathway (represented by poly_rr) were calculated respectively according to the above formulas. 2 All calculations were performed on a unified evaluation platform to ensure consistency and fairness in the comparison. Prediction error results are shown in Table 1. A smaller MAE indicates higher accuracy and better performance of the prediction model; R... 2 The closer the value is to 1, the stronger the model's fitting ability.
[0060] Table 1
[0061]
[0062] It is easy to see that this invention obtains formulation-level features with constant dimensionality, invariant component substitution, and extrapolation to new components by weighting and aggregating the geometric-topological molecular descriptors and electronic structure features of each component of the polishing slurry according to molar numbers. This solves the shortcomings of traditional one-hot encoding, which cannot reflect the molar contribution of components and cannot be extrapolated. This invention integrates abrasive type, process parameters, and Preston physical characteristics, taking into account both the nature of chemical reactions and classical physical laws, significantly improving prediction accuracy. This invention uses a multi-random seed random forest deep ensemble model to simultaneously output the removal rate point estimate and the cognitive uncertainty measure, realizing the quantification of prediction confidence, facilitating the identification of low-confidence samples and manual verification.
[0063] A second embodiment of the present invention relates to an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the polishing slurry performance prediction method of the first embodiment.
[0064] The third embodiment of the present invention relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the polishing slurry performance prediction method of the first embodiment.
[0065] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage and optical storage) containing computer-usable program code.
[0066] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0067] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction methods implemented in a process. Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0068] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0069] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for predicting the performance of a polishing slurry, characterized in that, Includes the following steps: Obtain multi-component data of the target polishing fluid formulation, wherein the multi-component data includes the molecular structure identifier and molar number of each component; For each component, a geometric-topological molecular descriptor vector and an electronic structure feature vector are extracted from the molecular structure identifier. The geometric-topological molecular descriptor vector and the electronic structure feature vector are then weighted and aggregated according to the number of moles to obtain the formula-level features. The formulation-level features are concatenated with the abrasive type, process parameters, and Preston physical features of the target polishing fluid formulation to obtain the formulation-level feature vector; The recipe-level feature vector is input into a deep ensemble model consisting of multiple random forest regression base learners with different random seeds to obtain multiple independent prediction values. Calculate the mean and standard deviation of multiple independent predictions, and use the mean as a removal rate point estimate and the standard deviation as a measure of the cognitive uncertainty of the prediction.
2. The method for predicting the performance of polishing slurry according to claim 1, characterized in that, The geometry-topology molecular descriptor vector includes at least two of the following: molecular weight, oil-water partition coefficient, topological polar surface area, number of hydrogen bond donors, number of hydrogen bond acceptors, and number of rotatable bonds.
3. The method for predicting the performance of polishing slurry according to claim 1, characterized in that, The electronic structure feature vector is extracted by one or a combination of the following methods: (a) single-point energy calculation based on semi-empirical quantization; (b) single-point energy calculation based on density functional theory; (c) latent representation inference from a pre-trained molecular neural network; (d) lookup from a pre-calculated feature library of formulation components, and if no match is found, fall back to one of (a) to (c) and write back to the cache.
4. The method for predicting the performance of polishing slurry according to claim 1, characterized in that, The electronic structure eigenvectors include the HOMO-LUMO bandgap.
5. The method for predicting the performance of polishing slurry according to claim 4, characterized in that, The electronic structure eigenvector also includes one or more of the highest occupied molecular orbital energy level, the lowest unoccupied molecular orbital energy level, and the molecular dipole moment.
6. The method for predicting the performance of polishing slurry according to claim 1, characterized in that, The hyperparameters of the random forest regression base learner satisfy the following: the number of decision trees is no less than 100, the maximum depth is no less than 10, the maximum feature ratio is between 0.5 and 1.0, and bootstrap sampling is enabled; the random seeds of the random forest regression base learner are... structure, For the first A random seed for a random forest regression base learner. It is an integer constant.
7. The method for predicting the performance of polishing slurry according to claim 1, characterized in that, A non-negative constraint is applied when calculating the mean of multiple independent predicted values.
8. The method for predicting the performance of polishing slurry according to claim 1, characterized in that, Also includes: Calculate the ratio of the cognitive uncertainty measure to the removal rate point estimate, and add a low confidence label when the ratio exceeds a preset threshold.
9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the polishing fluid performance prediction method as described in any one of claims 1-8.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the polishing fluid performance prediction method as described in any one of claims 1-8.