High-precision tin-based soldering lug component optimization method and system for microelectronic interconnection based on machine learning

Abstract

The invention discloses a high-precision tin-based soldering lug component optimization method and system for microelectronic interconnection based on machine learning, and belongs to the technical field of material design and artificial intelligence. According to the method, a multi-dimensional feature database of alloy components and performance indexes is constructed; machine learning ensemble learning is adopted to train a performance prediction model, and SHAP interpretability analysis is introduced to quantify the contribution degree of each alloy element to the performance; on the basis, a multi-objective optimization model is established, and optimal Sn-Ag-Cu-X multi-component alloy components are intelligently recommended by taking oxidation resistance, wettability, cost and the like as constraints. According to the method, through a closed-loop optimization framework of calculation design, experimental verification and model iteration, rapid, accurate and low-cost design of tin-based soldering lug components is achieved, the research and development period is remarkably shortened, and the bottleneck problem of a traditional trial and error method in multi-element alloy system optimization is solved.

Description

Technical Field

[0001] This invention relates to the fields of materials design and artificial intelligence, specifically to a method and system for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning. Background Technology

[0002] Tin-based solder is a key basic material for microelectronic interconnect packaging, and its properties (such as oxidation resistance, wettability, and mechanical reliability) directly determine the lifespan and reliability of electronic devices. As electronic devices develop towards miniaturization and high density, extremely stringent requirements are placed on the comprehensive performance of tin-based solder.

[0003] Currently, the development of high-performance tin-based solder sheets mainly relies on a "thermodynamic calculation-experimental trial and error" model. Although thermodynamic software such as Thermo-Calc can assist in phase diagram calculations and initial composition screening, the synergistic mechanism of trace elements (such as Ga, Ce, Ni, etc.) in Sn-Ag-Cu-X multi-component systems is complex and exhibits strong nonlinear effects, making it difficult to accurately quantify their influence using traditional methods. This results in long development cycles and high costs for new alloys, and makes it difficult to achieve synergistic optimization of multiple objectives such as oxidation resistance and wettability.

[0004] Machine learning technology offers a novel solution to these challenges. By learning the complex mapping relationship between composition, process, and performance from historical experimental and simulated data, machine learning models can quickly predict the performance of new compositions and guide optimization directions. However, effectively applying machine learning to tin-based solder design still faces challenges: first, it requires building a high-quality, high-dimensional feature database; second, the model's predictions need to be interpretable to guide metallurgists in understanding the mechanisms of element interaction; and third, it requires close integration of prediction with multi-objective optimization to directly output engineering-applicable composition schemes.

[0005] Therefore, developing an intelligent design method that integrates data-driven modeling, interpretability analysis, and multi-objective optimization is of great significance for breaking through the research and development bottleneck of high-performance tin-based solder pads. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method and system for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning.

[0007] To achieve the above technology, the following are included: A machine learning-based method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnects: S1. Data Acquisition and Feature Engineering; Historical data on tin-based solder alloys were collected to construct a multi-dimensional feature database containing alloy composition, process characteristics, and performance indicators. The alloy composition includes: Sn, Ag, Cu and trace elements (Ga, Ce, Ni, Cr and Bi); Performance indicators include: antioxidant properties, wettability, oxidative weight gain, and spread area.

[0008] S2, Machine Learning Model Construction and Training; Based on traditional standardization methods, traditional loss functions, and SHAP importance results for each alloying element, an improved multi-scale weighted standardization method, an improved alloy-specific loss function, and an improved SHAP weight calculation method are constructed and input into a machine learning algorithm for prediction. Machine learning algorithms can include gradient boosting decision trees, random forests, or support vector machines, taking alloy composition and process characteristics as input and predicted performance indicators as output. The expression for the improved multi-scale weighted normalization method is as follows: In the formula, Indicates the first The final value (Z score) after standardization of the feature, the _th The standardized values ​​of the content of alloying elements (such as Ag, Cu, Ga, etc.) are used to eliminate dimensions while retaining the characteristic importance weights; Representing the The weight coefficients of each feature are calculated using the following formula: , Indicates the types of alloying elements, the first The contribution weight of each alloying element to the properties (oxidation weight gain / spreading area) (obtained by normalization of SHAP values) reflects the core role of elements in metallurgy; Indicates the first The median of the features, the th The median content of alloying elements is more resistant to extreme values ​​(such as high Ce and Cr content in a few formulations) than the mean, and is more in line with actual formulation design. Representing the The range of each feature ( ), No. The range of values ​​for the content of a certain alloying element reflects the upper and lower limits of the addition of that element in the existing formula (e.g., the content of Bi element ranges from 0 to 5 wt%, with a range of 5). Indicates the first The mean of the nth feature, the nth The average content of a characteristic alloying element across all samples in the dataset reflects the overall addition level of that element; Indicates the first The standard deviation of the feature, the The degree of dispersion in the content of a certain alloying element reflects the range of fluctuation of that element in different formulations; Indicates the first The original values ​​of each feature; The expression for the improved alloy-specific loss function is as follows: In the formula, The weighting coefficient, which emphasizes the overall numerical deviation, is set to 0.6 in this invention. The weighting coefficient, which emphasizes relative error (to avoid the influence of dimensions), is set to 0.3 in this invention; The weighting coefficient, which emphasizes process feasibility constraints, is set to 0.1 in this invention. Indicates the first The true value of each feature; Indicates the first Predicted values ​​for each sample; This represents a penalty term for out-of-bounds composition, constraining the predicted alloy composition to conform to the feasible range of industrial processes, and avoiding formulations that have no practical processing significance. The expression is as follows: In the formula, Representing the The importance of the SHAP feature of a type of element, i.e. the penalty weight: the core element (such as Ag with a high SHAP value) is penalized more severely when it goes out of bounds, which is in line with the laws of metallurgy. Indicates the first The industrially feasible upper and lower limits of an element, and the range in which the element can be added in industrial production (e.g., the upper limit of Ce: 2wt%, exceeding which it cannot be smelted). The index function is a determination function, which is 0 when the element content is within the feasible range and 1 when the element content exceeds the feasible range. The improved SHAP weight calculation expression is as follows: In the formula, Indicates the first The dynamic SHAP value of each feature; This represents the nonlinear sensitivity coefficient, ranging from 0.1 to 0.3, which controls the correction magnitude of the nonlinear term to the SHAP value (the stronger the nonlinearity of the alloy system, the higher the sensitivity coefficient). (The larger the value) The model output represents the first... The second-order partial derivatives of each feature, quantizing the elements. The nonlinear effect on performance (such as the abrupt change in the growth rate of spreading area after the Ag content increases to a certain threshold) is expressed as: ,in, Indicates the disturbance term; Indicates the first The coefficient of variation of each feature, element The relative dispersion of the content (the larger the coefficient of variation, the more significant the impact of element content fluctuations on performance). The key calculation method for SHAP is: In the formula, Represents the total number of samples. An index representing the total number of samples; Indicates the first The feature in the first Dynamic SHAP values ​​on each sample.

[0009] S3. Model interpretability analysis and feature selection; The SHAP analysis method is used to interpret the trained prediction model, quantify the contribution of each input feature to the output performance index, and identify alloying elements and their optimal content ranges.

[0010] S4. Multi-objective component optimization; With the target performance as the optimization direction, and combining the obtained alloying elements and their optimal content range, a multi-objective optimization model is established. An optimization algorithm is used to search for the Pareto optimal solution set in the composition space and output the recommended alloy composition. The optimization algorithm aims to maximize antioxidant performance and wettability while minimizing raw material costs; the optimization algorithm used is either a genetic algorithm or a particle swarm optimization algorithm. First, based on the traditional optimization objective function, an optimization instruction is defined; The optimized instruction expression is: In the formula, The weighting coefficients representing oxidative weight gain are obtained by normalizing the SHAP values ​​and reflect the priority of oxidative weight gain in multi-objective optimization (e.g., if antioxidant capacity is more important, the weighting coefficients are higher). The performance sensitivity index (1.5) represents the oxidative weight gain and controls the penalty for deviation of oxidative weight gain from the target value. That is, when the index is greater than 1, the larger the deviation, the heavier the penalty (antioxidant performance is a hard constraint). The weighting coefficient representing the spread area is complementary to the weighting coefficient of oxidation weight gain (the sum is 1), reflecting the optimization priority of the spread area; The performance sensitivity index (1.2) represents the spread area, which controls the penalty for deviations of the spread area from the target value (the index is slightly lower, allowing for a certain deviation). This represents a cost regularization term, which constrains the formulation cost and prevents the excessive addition of high-cost elements (such as Ag); Representing the The cost coefficient of an element reflects its market cost (e.g., Ag's cost). =10), Cu =1), the higher the coefficient, the higher the cost). Weighting factor for oxidative weight gain The expression is as follows: In the formula, Indicates the global importance of SHAP in terms of antioxidant properties; Indicates the global importance of the spread area; Weighting coefficient of spread area The expression is as follows: ; Cost regularization term The expression is as follows: In the formula, Indicates the weighting coefficient of the cost item; Indicates the first The content of each element; Indicates the first Cost coefficient of each element; and They represent the first The upper and lower limits of the feasible process for each element; Based on optimization instructions, to achieve synergistic prediction of alloy oxidation resistance and wettability, a core reasoning formula is constructed that integrates the nonlinear contributions of elements, dynamic weights, and interaction effects. This formula quantifies the comprehensive contribution of the alloy formulation to the target performance. The comprehensive score of the alloy target performance is a weighted fusion of the oxidation resistance component, wettability component, and element synergistic effect term, as shown in the following expression: In the formula, This indicates the overall score of the alloy's target performance; Indicates the first Dynamic weights of each characteristic element against oxidation; Indicates the first The content of each characteristic element; Indicates the first The performance index of each characteristic element against oxidation; Indicates the first Dynamic weights of each feature element on wettability; Indicates the first The performance index of each characteristic element on wettability; Represents the synergistic effect term of elements; , and These represent the first weighting coefficient, the second weighting coefficient, and the third weighting coefficient, respectively. No. Dynamic weights of each characteristic element against oxidation The calculation method is as follows: In the formula, Indicates the first Traditional SHAP values ​​for the resistance of a characteristic element to oxidation; This indicates a nonlinear sensitivity parameter for antioxidant properties; This indicates the antioxidant properties prediction for elemental characteristic elements. The second derivative; No. Dynamic weights of each feature element for wettability The expression is as follows: In the formula, No. Traditional SHAP values ​​for the wettability of a feature element; This represents a nonlinear sensitivity parameter for wettability; This indicates the wettability prediction for elemental characteristic elements. The second derivative; No. Performance index of each characteristic element against oxidation The expression is as follows: In the formula, Indicates the antioxidant capacity adjustment parameter; Indicates the first Global SHAP importance of individual characteristic elements against oxidation; In the formula, Indicates the wettability adjustment parameter; Indicates the first Global SHAP importance of wettability of each feature element; Elemental Synergistic Effect Term The expression is as follows: In the formula, Representing characteristic elements and elements The synergy coefficient between them; The indicator function is a determination function that determines the interaction importance of element pairs (i, j) when it exceeds a threshold. The value is 1 if it is true, and 0 otherwise; where, Only element pairs with significant SHAP interaction importance (such as Ag-Cu, Ce-Ni) are retained. The synergy coefficient is determined by experimentally verified elemental interaction rules (e.g., Ag-Cu eutectic synergy). Cr-Bi antagonism ; The method of using optimization algorithms to search for the Pareto optimal solution set in the composition space is as follows: taking the comprehensive score of the alloy target performance as input, global optimization algorithms such as genetic algorithm and particle swarm algorithm are used to search, and the Pareto optimal solution set is output, which is a set of candidate alloy compositions that achieve the best balance between oxidation resistance, wettability and cost.

[0011] S5. Experimental verification and model iteration; The optimal alloy composition recommended by S4 was experimentally prepared and its performance was tested. The obtained experimental data was fed back into the database to retrain and optimize the performance prediction model, forming a closed-loop iterative optimization system.

[0012] A tin-based solder pad composition optimization system, comprising: 1. Data Management Module: Used to execute the steps in S1, and to store, clean, and manage the multi-dimensional feature database.

[0013] 2. Model Training and Prediction Module: This module executes the steps of S2 and provides interfaces for various machine learning algorithms for model training, evaluation, and performance prediction.

[0014] 3. Interpretability Analysis Module: Used to perform the steps of S3, integrates improved SHAP analysis tools, and visualizes the importance of features and the interpretation of individual predictions.

[0015] 4. Multi-objective optimization module: Used to perform the steps of S4. It has a built-in optimization algorithm based on innovative formulas and automatically searches for and recommends the optimal components according to the user-defined objectives and constraints.

[0016] 5. User Interface: Used to perform S5 steps, providing a graphical interface to facilitate user input of parameters, setting of optimization goals, and display of component-performance relationships, SHAP analysis results, and Pareto frontiers in chart form.

[0017] Beneficial effects of the present invention The present invention improves prediction accuracy through formula innovation: by using an improved alloy-specific loss function and a multi-scale normalization method, the model prediction accuracy is 15-20% higher than that of traditional methods, and the R² value reaches over 0.92.

[0018] This invention significantly improves optimization efficiency: the innovative multi-objective optimization function, by introducing cost regularization and performance sensitivity index, increases the optimization convergence speed by 30% and avoids getting trapped in local optima.

[0019] The physical significance of this invention is clearer: the dynamic SHAP weight update mechanism can better capture the nonlinear synergistic effect among trace elements, providing more accurate theoretical guidance for the study of metallurgical mechanisms.

[0020] This invention enhances engineering practicality: by using a component out-of-bounds penalty term and cost regularization, it ensures that the recommended components meet both performance requirements and actual production processes and economic constraints.

[0021] The core innovation of this invention lies in the deep integration of metallurgical physics mechanisms with machine learning algorithms. Through a series of improved formulas, it achieves a leap from "data-driven" to "physical information-driven" approaches, providing a completely new technical path for the design of multi-element alloy systems. These improved formulas not only enhance the technical performance of the model, but more importantly, they establish a bridge between machine learning and materials science, giving the algorithm output clear physical meaning and engineering guidance value. Attached Figure Description

[0022] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is a system structure diagram of the present invention; Figure 3 This is a graph showing the oxidative weight gain prediction results of the machine learning model in an embodiment of the present invention; Figure 4 This is a graph showing the predicted area of ​​the machine learning model in an embodiment of the present invention. Figure 5 This is a scatter plot showing the correlation between oxidation and weight gain in embodiments of the present invention. Figure 6 This is a scatter plot showing the correlation between the spread area and the actual area in an embodiment of the present invention. Figure 7 This is a bar chart ranking the importance of characteristic oxidation weight gain obtained by SHAP analysis in this invention; Figure 8 This is a bar chart showing the importance ranking of feature spread areas obtained using SHAP analysis in this invention. Figure 9 This is an interface diagram of the system of the present invention; Figure 10 This is a graph showing the prediction results of the system of the present invention. Detailed Implementation

[0023] The present invention will be further described in detail below with reference to specific embodiments.

[0024] like Figure 1 and Figure 2 As shown, a method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnects based on machine learning includes the following steps: S1. Data Acquisition and Feature Engineering; Historical data on tin-based solder alloys were collected to construct a multi-dimensional feature database containing alloy composition, process characteristics, and performance indicators. Historical data on tin-based solder alloys were obtained by collecting tin-based solder data from historical experiments, literature, and thermodynamic simulations. The alloy composition includes: Sn, Ag, Cu and trace elements (Ga, Ce, Ni, Cr and Bi); Performance indicators include: antioxidant properties and wettability; The collected data undergoes outlier processing, extreme value removal, standardization, and dimensional difference elimination.

[0025] S2, Machine Learning Model Construction and Training; Based on traditional standardization methods, traditional loss functions, and SHAP importance results for each alloying element, an improved multi-scale weighted standardization method, an improved alloy-specific loss function, and an improved SHAP weight calculation method are constructed and input into a machine learning algorithm for prediction. Machine learning algorithms can include gradient boosting decision trees, random forests, or support vector machines, taking alloy composition and process characteristics as input and predicted performance indicators as output. Five-fold cross-validation is used for prediction, and the results are as follows: Figure 3 and Figure 4 As shown; The expression for the traditional standardization method is as follows: In the formula, This represents the standardized value; Indicates original features; This represents the mean; Indicates standard deviation; The traditional loss function is expressed as follows: In the formula, Indicates mean square error; Indicates the number of samples. An index representing the number of samples; Indicates the first The true value of each sample; Indicates the first Predicted values ​​for each sample; The expression for the improved multi-scale weighted normalization method is as follows: In the formula, Indicates the first The final value (Z score) after standardization of the feature, the _th The standardized values ​​of the content of alloying elements (such as Ag, Cu, Ga, etc.) are used to eliminate dimensions while retaining the characteristic importance weights; Representing the The weight coefficients of each feature are calculated using the following formula: , Indicates the types of alloying elements, the first The contribution weight of each alloying element to the properties (oxidation weight gain / spreading area) (obtained by normalization of SHAP values) reflects the core role of elements in metallurgy; Indicates the first The median of the features, the th The median content of alloying elements is more resistant to extreme values ​​(such as high Ce and Cr content in a few formulations) than the mean, and is more in line with actual formulation design. Representing the The range of each feature ( ), No. The range of values ​​for the content of a certain alloying element reflects the upper and lower limits of the addition of that element in the existing formula (e.g., the content of Bi element ranges from 0 to 5 wt%, with a range of 5). Indicates the first The mean of the nth feature, the nth The average content of a characteristic alloying element across all samples in the dataset reflects the overall addition level of that element; Indicates the first The standard deviation of the feature, the The degree of dispersion in the content of a certain alloying element reflects the range of fluctuation of that element in different formulations; Indicates the first The original values ​​of each feature; The expression for the improved alloy-specific loss function is as follows: In the formula, The weighting coefficient, which emphasizes the overall numerical deviation, is set to 0.6 in this invention. The weighting coefficient, which emphasizes relative error (to avoid the influence of dimensions), is set to 0.3 in this invention; The weighting coefficient, which emphasizes process feasibility constraints, is set to 0.1 in this invention. Indicates the first The true value of each feature; Indicates the first Predicted values ​​for each sample; This represents a penalty term for out-of-bounds composition, constraining the predicted alloy composition to conform to the feasible range of industrial processes, and avoiding formulations that have no practical processing significance. The expression is as follows: In the formula, Representing the The importance of the SHAP feature of a type of element, i.e. the penalty weight: the core element (such as Ag with a high SHAP value) is penalized more severely when it goes out of bounds, which is in line with the laws of metallurgy. Indicates the first The industrially feasible upper and lower limits of an element, and the range in which the element can be added in industrial production (e.g., the upper limit of Ce: 2wt%, exceeding which it cannot be smelted). The index function is a determination function, which is 0 when the element content is within the feasible range and 1 when the element content exceeds the feasible range. The traditional method for calculating SHAP weights is as follows: In the formula, Indicates the first The SHAP value of each feature; A set representing all features; Represents a subset of features; Indicates the use of subsets The model output value when predicting features in the model; Indicates the use of subsets And add features The model output value when making predictions; The improved SHAP weight calculation expression is as follows: In the formula, Indicates the first The dynamic SHAP value of each feature; This represents the nonlinear sensitivity coefficient, ranging from 0.1 to 0.3, which controls the correction magnitude of the nonlinear term to the SHAP value (the stronger the nonlinearity of the alloy system, the higher the sensitivity coefficient). (The larger the value) The model output represents the first... The second-order partial derivatives of each feature, quantizing the elements. The nonlinear effect on performance (such as the abrupt change in the growth rate of spreading area after the Ag content increases to a certain threshold) is expressed as: ,in, Indicates the disturbance term; Indicates the first The coefficient of variation of each feature, element The relative dispersion of the content (the larger the coefficient of variation, the more significant the impact of element content fluctuations on performance). The key calculation method for SHAP is: In the formula, Represents the total number of samples. An index representing the total number of samples; Indicates the first The feature in the first Dynamic SHAP values ​​on each sample.

[0026] S3. Model interpretability analysis and feature selection; The SHAP analysis method was used to interpret the trained prediction model, quantify the contribution of each input feature to the output performance index, and identify alloying elements and their optimal content ranges. The results are as follows: Figure 5 , Figure 6 , Figure 7 and Figure 8 As shown.

[0027] S4. Multi-objective component optimization; With the target performance as the optimization direction, and combining the obtained alloying elements and their optimal content range, a multi-objective optimization model is established. An optimization algorithm is used to search for the Pareto optimal solution set in the composition space and output the recommended alloy composition. The optimization algorithm aims to maximize antioxidant performance and wettability while minimizing raw material costs; the optimization algorithm used is either a genetic algorithm or a particle swarm optimization algorithm. First, based on the traditional optimization objective function, an optimization instruction is defined; The traditional optimization function is expressed as: in, Indicates an optimization instruction; This represents the antioxidant prediction function; Indicates the target value for antioxidant properties; This represents the wettability prediction function; Indicates the target value for wettability; The optimized instruction expression is: In the formula, The weighting coefficients representing oxidative weight gain are obtained by normalizing the SHAP values ​​and reflect the priority of oxidative weight gain in multi-objective optimization (e.g., if antioxidant capacity is more important, the weighting coefficients are higher). The performance sensitivity index (1.5) represents the oxidative weight gain and controls the penalty for deviation of oxidative weight gain from the target value. That is, when the index is greater than 1, the larger the deviation, the heavier the penalty (antioxidant performance is a hard constraint). The weighting coefficient representing the spread area is complementary to the weighting coefficient of oxidation weight gain (the sum is 1), reflecting the optimization priority of the spread area; The performance sensitivity index (1.2) represents the spread area, which controls the penalty for deviations of the spread area from the target value (the index is slightly lower, allowing for a certain deviation). This represents a cost regularization term, which constrains the formulation cost and prevents the excessive addition of high-cost elements (such as Ag); Representing the The cost coefficient of an element reflects its market cost (e.g., Ag's cost). =10), Cu =1), the higher the coefficient, the higher the cost). Weighting factor for oxidative weight gain The expression is as follows: In the formula, Indicates the global importance of SHAP in terms of antioxidant properties; Indicates the global importance of the spread area; Weighting coefficient of spread area The expression is as follows: ; Cost regularization term The expression is as follows: In the formula, Indicates the weighting coefficient of the cost item; Indicates the first The content of each element; Indicates the first Cost coefficient of each element; and They represent the first The upper and lower limits of the feasible process for each element; Based on optimization instructions, to achieve synergistic prediction of alloy oxidation resistance and wettability, a core reasoning formula is constructed that integrates the nonlinear contributions of elements, dynamic weights, and interaction effects. This formula quantifies the comprehensive contribution of the alloy formulation to the target performance. The comprehensive score of the alloy target performance is a weighted fusion of the oxidation resistance component, wettability component, and element synergistic effect term, as shown in the following expression: In the formula, This indicates the overall score of the alloy's target performance; Indicates the first Dynamic weights of each characteristic element against oxidation; Indicates the first The content of each characteristic element; Indicates the first The performance index of each characteristic element against oxidation; Indicates the first Dynamic weights of each feature element on wettability; Indicates the first The performance index of each characteristic element on wettability; Represents the synergistic effect term of elements; , and These represent the first weighting coefficient, the second weighting coefficient, and the third weighting coefficient, respectively. No. Dynamic weights of each characteristic element against oxidation The calculation method is as follows: In the formula, Indicates the first Traditional SHAP values ​​for the resistance of a characteristic element to oxidation; This indicates a nonlinear sensitivity parameter for antioxidant properties; This indicates the antioxidant properties prediction for elemental characteristic elements. The second derivative; No. Dynamic weights of each feature element for wettability The expression is as follows: In the formula, No. Traditional SHAP values ​​for the wettability of a feature element; This represents a nonlinear sensitivity parameter for wettability; This indicates the wettability prediction for elemental characteristic elements. The second derivative; No. Performance index of each characteristic element against oxidation The expression is as follows: In the formula, Indicates the antioxidant capacity adjustment parameter; Indicates the first Global SHAP importance of individual characteristic elements against oxidation; In the formula, Indicates the wettability adjustment parameter; Indicates the first Global SHAP importance of wettability of each feature element; Elemental Synergistic Effect Term The expression is as follows: In the formula, Representing characteristic elements and elements The synergy coefficient between them; The indicator function is a determination function that determines the interaction importance of element pairs (i, j) when it exceeds a threshold. The value is 1 if it is true, and 0 otherwise; where, Only element pairs with significant SHAP interaction importance (such as Ag-Cu, Ce-Ni) are retained. The synergy coefficient is determined by experimentally verified elemental interaction rules (e.g., Ag-Cu eutectic synergy). Cr-Bi antagonism ; The method of using optimization algorithms to search for the Pareto optimal solution set in the composition space is as follows: taking the comprehensive score of the alloy target performance as input, global optimization algorithms such as genetic algorithm and particle swarm algorithm are used to search, and the Pareto optimal solution set is output, which is a set of candidate alloy compositions that achieve the best balance between oxidation resistance, wettability and cost.

[0028] S5. Experimental verification and model iteration; The optimal alloy composition recommended by S4 was experimentally prepared and its performance was tested. The obtained experimental data was fed back into the database to retrain and optimize the performance prediction model, forming a closed-loop iterative optimization system.

[0029] like Figure 9 and Figure 10 As shown, a tin-based solder pad composition optimization system includes: 1. Data Management Module: Used to execute the steps in S1, and to store, clean, and manage the multi-dimensional feature database.

[0030] 2. Model Training and Prediction Module: This module executes the steps of S2 and provides interfaces for various machine learning algorithms for model training, evaluation, and performance prediction.

[0031] 3. Interpretability Analysis Module: Used to perform the steps of S3, integrates improved SHAP analysis tools, and visualizes the importance of features and the interpretation of individual predictions.

[0032] 4. Multi-objective optimization module: Used to perform the steps of S4. It has a built-in optimization algorithm based on innovative formulas and automatically searches for and recommends the optimal components according to the user-defined objectives and constraints.

[0033] 5. User Interface: Used to perform S5 steps, providing a graphical interface to facilitate user input of parameters, setting of optimization goals, and display of component-performance relationships, SHAP analysis results and Pareto frontiers in chart form; 5.1 Interface Architecture and Functional Modules; The user interface of this invention adopts a modular design and is built based on the MATLAB App Designer framework. It mainly includes the following core functional modules: 5.1.1 System Information Display Module; Title display area: Uses a dark blue background with white text to highlight "Intelligent Optimization System for Sn-Ag-Cu-X Alloy Welding Sheet Composition"; Performance range indicator: Real-time display of the performance reference range of model training data (oxidative weight gain: 0.065-0.14 mg / cm² / h, spreading area: 42-65 mm²). Status monitoring panel: Dynamically displays system running status, model loading progress, and optimization calculation progress. 5.1.2 Multi-mode optimization selection module; It offers seven preset optimization modes, and enables one-click operation via color-coded function buttons: Custom target performance optimization - Allows users to freely set specific target values ​​for oxidation weight gain and spread area. Low-oxidation weight gain optimization - Preset target: oxidative weight gain <0.075 mg / cm² / h, spreading area >48 mm²; High Spread Area Optimization - Preset Target: Spread area > 56 mm², oxidative weight gain < 0.09 mg / cm² / h; Balanced performance optimization - Preset targets: oxidative weight gain <0.082 mg / cm² / h, spreading area >52 mm²; Extreme performance optimization - Offers two extreme performance optimization options: extremely low oxidation weight gain and extremely high spread area; Performance Range Exploration - Automated testing of the feasibility of various typical performance targets; System Exit - Safely close the application; 5.2 Target Input and Constraint Management; 5.2.1 Target performance input mechanism; Numeric input control: Uses the MATLAB uieditfield component, supports numeric input accurate to 6 decimal places; Input range validation: Real-time detection of whether user input values ​​are within the effective range of the model (oxidation weight gain: 0.06-0.15, spreading area: 40-70). Intelligent suggestion system: When the input exceeds the suggested range, a warning dialog box pops up to prompt the user for confirmation; 5.2.2 Constraint Integration; Composition constraints: Based on training data statistics, there are built-in concentration range constraints for 8 alloying elements. Ag (wt%): 0.5-4.0 Cu (wt%): 0.3-1.2 Ga (wt%): 0.0-0.1 Ce (wt%): 0.0-0.08 Ni (wt%): 0.0-0.1 Cr (wt%): 0.0-0.06 Bi (wt%): 0.0-2.5 In (wt%): 0.0-3.0 Performance constraints: Each optimization mode has built-in different performance constraints to ensure the practical feasibility of the recommended components; 5.3 Optimize the algorithm and interaction logic; 5.3.1 Multi-starting point optimization strategy; The system employs a multi-initial-point optimization algorithm, pre-setting 5 sets of empirical initial guesses: Intermediate value combination: [2.5, 0.6, 0.05, 0.03, 0.04, 0.02, 0.5, 0.1] Low oxidation tendency combination: [3.0, 0.5, 0.03, 0.02, 0.03, 0.01, 0.3, 0.0] High spreadability combination: [2.0, 0.8, 0.07, 0.04, 0.05, 0.03, 1.0, 0.5] High-Yin Combination: [3.5, 0.4, 0.02, 0.05, 0.02, 0.01, 0.2, 0.2] Low silver, high bismuth-indium combination: [1.5, 1.0, 0.08, 0.01, 0.06, 0.04, 1.5, 1.0] 5.3.2 Intelligent process optimization; Objective function construction: The sum of squared relative errors is used as the optimization objective function to avoid the influence of units; L-BFGS-B optimization: The scipy.optimize.minimize algorithm is called to perform constraint optimization; Multi-round trial mechanism: Each optimization task undergoes a maximum of 5 rounds of trials to ensure that the globally optimal solution is found; Results filtering: Feasible solutions are automatically filtered based on an error threshold (<0.5); 5.4 Result visualization and performance evaluation; 5.4.1. Structured results display; The optimization results are displayed in a hierarchical structure: text ================================================== Optimization results ================================================== Target performance: Oxidative weight gain: 0.070 mg / cm² / h Coverage area: 45.0 mm² Predictive performance: Oxidative weight gain: 0.0767 mg / cm² / h (error: 0.0067) Coverage area: 45.68 mm² (error: 0.68) Recommended alloy composition: Ag (wt%): 3.5000 Cu (wt%): 0.4000 Ga (wt%): 0.0200 Ce (wt%): 0.0500 Ni (wt%): 0.0200 Cr (wt%): 0.0100 Bi (wt%): 0.2000 In (wt%): 0.2000 5.4.2 Intelligent Performance Evaluation System; Automatically assess performance level based on prediction results: Antioxidant performance evaluation: Excellent: Oxidative weight gain <0.075 mg / cm³ 2 / h ; Good: Oxidative weight gain 0.075-0.082 mg / cm³ 2 / h ; Generally: Oxidative weight gain >0.082 mg / cm³ 2 / h ; Spreading performance evaluation: Excellent: Spread area > 56 mm 2 ; Good: Spread area 52-56 mm 2 ; General: Spreading area <52 mm 2 ; 5.4.3 Optimization process visualization; Real-time progress display: Dynamically displays the optimization calculation progress in the status bar; Trial count statistics: Shows the number of attempts required to find the optimal solution; Error analysis: Accurately displays the absolute and relative errors between the predicted and target values; 5.5 Advanced interactive features; 5.5.1 Dynamic Interface Response; Conditional display: The input panel in the custom optimization mode is dynamically shown / hidden based on user selection; Real-time feedback: All user actions provide instant visual feedback and status updates; Error recovery: A robust exception handling mechanism ensures system stability under various abnormal conditions; 5.5.2 Multi-scenario adaptability; Preset Modes: Provides professional preset parameters for common application scenarios; Custom mode: Fully customizable input functionality to meet specific needs; Exploration mode: Quickly assess the feasibility of achieving different performance targets; 5.5.3 User experience optimization; Intuitive operation: Adopting logical processes and interface layouts that conform to user cognition; Professional display: Using the Consolas monospace font ensures data alignment and readability; Color coding: Different functional modules and performance levels are distinguished by color.

[0034] To verify this invention, predictions were made for Sn-Ag-Cu-Ce-Ga alloys with high oxidation resistance. Target performance: 30% improvement in antioxidant performance at 260℃ high temperature, and wettability of not less than 50mm²; The alloy composition (wt%) obtained through optimization using the MATLAB model is shown in Table 1: Table 1: Prediction Results of High Oxidation Resistance Sn-Ag-Cu-Ce-Ga Alloys Performance prediction results: Oxidative weight gain: 0.067 mg / cm² / h (Excellent); Coverage area: 51.3 mm² (Good); Note: By adding appropriate amounts of Ga and Ce, and optimizing the Ag content, the oxidation resistance of the solder pad at high temperatures is significantly improved, making it suitable for microelectronic packaging with high reliability requirements.

[0035] To verify the present invention, predictions were made for Sn-Ag-Cu-Bi-In alloys with ultra-high wettability. Target performance: Spreading area ≥ 58 mm², while controlling oxidative weight gain ≤ 0.09 mg / cm² / h The alloy composition (wt%) obtained by optimization using the MATLAB model is shown in Table 2. Table 2: Prediction results of ultra-high wettability Sn-Ag-Cu-Bi-In alloy Performance prediction results: Oxidative weight gain: 0.086 mg / cm² / h (good); Coverage area: 59.2 mm² (Excellent); Note: The addition of Bi and In effectively lowers the melting point and improves wettability, while the moderate Ag content balances the cost, making it suitable for scenarios with extremely high requirements for weld spreadability.

[0036] To verify this invention, a prediction was made for the optimal Sn-Ag-Cu-Ni-Ce-Ga alloy. Target performance: Achieving the optimal balance between antioxidant properties (≤0.075), wettability (≥53), and cost. The alloy composition (wt%) obtained through optimization using the MATLAB model is shown in Table 3. Table 3: Prediction Results of the Overall Optimal Sn-Ag-Cu-Ni-Ce-Ga Alloy Performance prediction results: Oxidative weight gain: 0.073 mg / cm² / h (Excellent); Coverage area: 54.1 mm² (Good); Note: This ingredient, through the synergistic effect of multiple trace elements, exhibits balanced performance across various indicators, making it suitable for general-purpose high-precision solder pads and offering the best overall cost-effectiveness.

[0037] To verify the present invention, predictions were made for Sn-Ag-Cu-Ce-Ni-Cr alloys used in extreme environments; Target performance: Oxidation resistance ≤0.070 under extreme high temperature and high humidity conditions, with a 50% improvement in long-term reliability. The alloy composition (wt%) obtained by optimization using the MATLAB model is shown in Table 4. Table 4: Prediction Results of Sn-Ag-Cu-Ce-Ni-Cr Alloy for Extreme Environments Performance prediction results: Oxidative weight gain: 0.069 mg / cm² / h (Excellent) Coverage area: 50.8 mm² (Good) Note: The addition of Ce, Ni, and Cr multi-component composites forms stable intermetallic compounds and a dense oxide layer, which significantly improves the long-term service reliability of the solder pads under extreme environments.

[0038] It should be noted that the above are merely preferred embodiments of this application and do not limit the scope of patent protection of this application. Any equivalent structural or procedural changes made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of this application.

Claims

1. A method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnects based on machine learning, characterized in that, Includes the following steps: S1. Data Acquisition and Feature Engineering: Collect historical data on tin-based solder alloys and construct a multi-dimensional feature database containing alloy composition, process characteristics, and performance indicators; S2. Machine Learning Model Construction and Training: Based on traditional standardization methods, traditional loss functions, and the SHAP importance results of each alloying element, an improved multi-scale weighted standardization method, an improved alloy-specific loss function, and an improved SHAP weight calculation method are constructed and input into the machine learning algorithm for prediction. S3. Model interpretability analysis and feature selection: Using the SHAP analysis method, the trained prediction model is interpreted, the contribution of each input feature to the output performance index is quantified, and alloying elements and their optimal content ranges are identified. S4. Multi-objective composition optimization: Taking the target performance as the optimization direction, and combining the obtained alloying elements and their optimal content range, a multi-objective optimization model is established. An optimization algorithm is used to search for the Pareto optimal solution set in the composition space and output the recommended alloy composition. S5. Experimental Verification and Model Iteration: The alloy composition recommended in S4 is experimentally prepared and its performance is tested. The obtained experimental data is fed back into the database to retrain and optimize the performance prediction model, forming a closed-loop iterative optimization system.

2. The method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning according to claim 1, characterized in that: The alloy composition includes Sn, Ag, Cu and trace elements; the performance indicators include oxidation resistance and wettability.

3. The method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning according to claim 1, characterized in that: The machine learning algorithm takes alloy composition and process characteristics as input and predicts performance indicators as output.

4. The method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning according to claim 1, characterized in that: The expression for the improved multi-scale weighted normalization method is as follows: In the formula, Indicates the first The final value after standardization of each feature; Representing the The weight coefficients of each feature are calculated as follows: , Indicates the types of alloying elements; Indicates the first The median of the features; Representing the The range of each characteristic; Indicates the first The mean of each feature; Indicates the first Standard deviation of each feature; Indicates the first The original values ​​of each feature.

5. The method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning according to claim 1, characterized in that: The expression for the improved alloy-specific loss function is as follows: In the formula, This represents the weighting coefficient that emphasizes the overall numerical deviation, and is set to 0.

6. This represents the weighting coefficient that emphasizes relative error, and is set to 0.

3. This represents the weighting coefficient that emphasizes process feasibility constraints, and is set to 0.

1. Indicates the first The true value of each feature; Indicates the first Predicted values ​​for each sample; This represents a penalty term for out-of-bounds composition, constraining the predicted alloy composition to conform to the feasible range of industrial processes, and avoiding formulations that have no practical processing significance. The expression is as follows: In the formula, Representing the Importance of SHAP features of elements; Indicates the first The upper and lower limits of industrial feasibility for each element.

6. The method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning according to claim 1, characterized in that: The improved SHAP weight calculation expression is as follows: In the formula, Indicates the first The dynamic SHAP value of each feature; This represents the nonlinear sensitivity coefficient, with a value ranging from 0.1 to 0.

3. The model output represents the first... The second-order partial derivatives of each feature; Indicates the first The coefficient of variation of each feature.

7. The method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning according to claim 1, characterized in that: In the multi-objective component optimization, the optimization algorithm aims to maximize antioxidant performance and wettability while minimizing raw material costs. First, based on the traditional optimization objective function, an optimization instruction is defined, expressed as follows: In the formula, Weighting coefficients representing oxidative weight gain; The performance sensitivity index for oxidative weight gain is set to 1.5, which controls the penalty for oxidative weight gain deviating from the target value. The weighting coefficient representing the spread area is complementary to the weighting coefficient for oxidation weight gain; The performance sensitivity index representing the spread area is set to 1.2, which controls the penalty for the spread area deviating from the target value. This represents a cost regularization term, which constrains formulation costs and prevents the excessive addition of high-cost elements; Representing the The cost coefficient of an element reflects its market cost. Secondly, a comprehensive score for the target performance of the alloy is constructed based on the optimization instructions, expressed as follows: In the formula, This indicates the overall score of the alloy's target performance; Indicates the first Dynamic weights of each characteristic element against oxidation; Indicates the first The content of each characteristic element; Indicates the first The performance index of each characteristic element against oxidation; Indicates the first Dynamic weights of each feature element on wettability; Indicates the first The performance index of each characteristic element on wettability; Represents the synergistic effect term of elements; , and These represent the first weighting coefficient, the second weighting coefficient, and the third weighting coefficient, respectively. Finally, the method of using an optimization algorithm to search for the Pareto optimal solution set in the composition space is as follows: taking the comprehensive score of the alloy target performance as input, the optimization algorithm is used to search and output the Pareto optimal solution set, which is a set of candidate alloy compositions that achieve the best balance between oxidation resistance, wettability and cost.

8. The method for optimizing the composition of high-precision tin-based solder pads for microelectronic interconnection based on machine learning according to claim 7, characterized in that: The weighting coefficient of the oxidative weight gain The expression is as follows: In the formula, Indicates the global importance of SAP in terms of antioxidant properties; Indicates the global importance of the spread area; The weighting coefficient of the spread area The expression is as follows: ； The cost regularization term The expression is as follows: In the formula, Indicates the weighting coefficient of the cost item; Indicates the first The content of each element; Indicates the first Cost coefficient of each element; and They represent the first The upper and lower limits of the feasible process for each element; The first Dynamic weights of each characteristic element against oxidation The calculation method is as follows: In the formula, Indicates the first Traditional SHAP values ​​for the resistance of a characteristic element to oxidation; This indicates a nonlinear sensitivity parameter for antioxidant properties; This indicates the antioxidant properties prediction for elemental characteristic elements. The second derivative; The first Dynamic weights of each feature element for wettability The expression is as follows: In the formula, No. Traditional SHAP values ​​for the wettability of a feature element; This represents a nonlinear sensitivity parameter for wettability; This indicates the wettability prediction for elemental characteristic elements. The second derivative; The first Performance index of each characteristic element against oxidation The expression is as follows: In the formula, Indicates the antioxidant capacity adjustment parameter; Indicates the first Global SHAP importance of individual characteristic elements against oxidation; In the formula, Indicates the wettability adjustment parameter; Indicates the first Global SHAP importance of wettability of each feature element; The elemental synergistic effect term The expression is as follows: In the formula, Representing characteristic elements and elements The synergy coefficient between them; The indicator function is a determination function that determines the interaction importance of element pairs (i, j) when it exceeds a threshold. The value is 1 if it is true, and 0 otherwise; where, Only element pairs with significant SHAP interaction importance are retained.

9. A machine learning-based high-precision tin-based solder pad composition optimization system for microelectronic interconnects, used to implement the machine learning-based high-precision tin-based solder pad composition optimization method for microelectronic interconnects as described in any one of claims 1 to 8, characterized in that, include: Data Management Module: Used to execute the steps of S1 to store, clean, and manage the multi-dimensional feature database; Model Training and Prediction Module: Used to perform the steps of S2 to provide interfaces for various machine learning algorithms for model training, evaluation, and performance prediction; Interpretability Analysis Module: Used to perform the steps of S3, and visualizes the importance of features and the interpretation of individual predictions by integrating improved SHAP analysis tools; Multi-objective optimization module: used to perform the steps of S4, with built-in optimization algorithm based on innovative formula, automatically searching and recommending the optimal component according to the user-defined objectives and constraints; User interface: Used to perform S5 steps, providing a graphical interface to facilitate user input of parameters, setting of optimization goals, and display of component-performance relationships, SHAP analysis results and Pareto frontiers in chart form.

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