Numerical simulation method for optimizing optimal current distribution scheme of partitioned anodes

Abstract

The invention discloses a numerical simulation method for optimizing an optimal current distribution scheme of a partition anode, and the method comprises the following steps: S1, building a corresponding geometric model according to a wafer and an electroplating equipment entity; s2, adapting corresponding calculation formulas and boundary conditions on the geometric model based on an electroplating principle; s3, constructing an optimization objective function and setting a corresponding optimization variable; and S4, subdivision and calculation of a model grid are carried out. According to the method, the geometric model is established, the optimization objective function is established based on the interface total current density and the local current density, and the wafer surface bump height uniformity optimization is converted into current distribution uniformity optimization, so that the optimal current distribution scheme is calculated through numerical simulation, the bump height uniformity can be ensured to be optimal, and the wafer surface bump height uniformity optimization is realized. The time cost and the material cost are effectively saved, in addition, limitation of wafer surface pattern changes is avoided, and practicability and robustness are achieved.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor processing, and specifically relates to a numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes. Background Technology

[0002] A wafer is a silicon wafer used to fabricate silicon semiconductor circuits; its raw material is silicon. High-purity polycrystalline silicon is dissolved, doped with silicon crystal seed crystals, and then slowly pulled out to form a cylindrical single-crystal silicon wafer. After grinding, polishing, and slicing, the silicon crystal ingot forms a silicon wafer. Further, a conductive metal layer is electroplated onto the wafer, and the conductive metal layer is processed to create conductive circuitry.

[0003] Currently, the anode is an indispensable material in wafer electroplating processes. The most common anodes are soluble anodes made of copper or phosphorus. However, these anodes often develop surface unevenness defects after prolonged use. Therefore, insoluble anodes have emerged. Furthermore, to improve the uniformity of bump height on the wafer surface, a single anode can be partitioned, meaning the current magnitude of each partition can be independently set. Thus, compared to a single soluble anode, the basic purpose of partitioned anodes is to redistribute the total current applied to the surface of the soluble anode to achieve optimal current distribution.

[0004] However, to maintain uniform bump height on the wafer surface, the total current applied to the partitioned anode surface should be consistent with the total current applied to the soluble anode surface. Mathematically, there are infinitely many solutions under this constraint. Conventional methods require manual planning of DOE experiments, i.e., calculating and adjusting variables to obtain multiple sets of wafer samples for comparison to find the sample with the best uniformity of bump height on the wafer surface; or numerical simulation can be used, first constructing a geometric model of the electroplating equipment and the wafer; then adapting the corresponding calculation formulas and boundary conditions based on the model; finally, meshing the model, changing the current applied to the partitioned anode surface and calculating, and comparing the results to find the optimal uniformity of bump height.

[0005] However, in the actual process design, the existing technology requires manual and continuous changes to the current applied to the anode surface of the partition, and repeated calculations for comparison. The workload is enormous, resulting in very high time and material costs. Furthermore, the inconsistency of the wafer surface pattern will cause corresponding changes in the current distribution scheme, further increasing the complexity of the experiment. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a novel numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes includes the following steps: S1. Based on the actual wafers and electroplating equipment, establish the corresponding geometric models; S2. Based on the principle of electroplating, the corresponding calculation formulas and boundary conditions are adapted to the geometric model; S3. Construct the objective function and set the corresponding optimization variables. Based on step S2, the local current density of each die on the wafer is obtained, and the local current density of each die on the wafer is integrated and averaged to obtain the mean local current density. Then, based on the total interface current density of each die on the wafer and the mean local current density, an optimization objective function is established to reflect the uniformity of the current distribution on the wafer surface. Based on the optimization objective function, the current ratio of each partition on the anode is set as the optimization variable to adjust the total interface current density of each die on the wafer. S4. Perform model mesh generation and calculation. The constructed geometric model is meshed using the finite element method and iteratively calculated and solved. During the solution process, the data processing software automatically calculates, compares and iteratively optimizes the variable values ​​until the uniformity of the wafer surface current distribution reflected by the optimization objective function in step S3 is optimal. At this point, the calculation ends and the result is output to obtain the optimal current distribution scheme.

[0008] According to a specific embodiment and preferred aspect of the present invention, in step S3, the output result of the established optimization objective function is a dimensionless value, and when the dimensionless value is the smallest, the uniformity of the current distribution on the wafer surface is optimal.

[0009] Preferably, the established optimization objective function is: Where q is a dimensionless value; i tot denoted as the total interface current density; bond1 is the average local current density; N is an even value.

[0010] Preferably, N=2. This ensures the output value is positive and the value is squared to increase precision for easier comparison.

[0011] According to another specific embodiment and preferred aspect of the present invention, the number of anode zones is m, and in step S3, the current distribution coefficients of each anode zone are set sequentially as A1, A2...A... mThe current magnitude in each anode region is the product of the total anode current and the corresponding current distribution coefficient. The data processing software uses the current distribution coefficients of each anode region as optimization variables. Compared to directly using the current magnitude as the optimization variable, this application effectively reduces the dimensionality of variables and computational complexity by using current distribution coefficients. When the total current I... sum When fixed, taking the constraint that the sum of the current distribution coefficients is 1 as an example, the original m independent current variables can be transformed into m-1 free variables (the mth variable can be obtained by subtracting the remaining m-1 coefficients from 1), reducing the search space of the optimization algorithm and improving the iteration efficiency. At the same time, this method significantly enhances the model's versatility and scalability. No matter how the total current changes, the distribution coefficients only depend on the number of anode partitions and the characteristics of the wafer surface, avoiding the need to reset variables due to adjustments in the total current. Moreover, when the number of anode partitions increases or decreases, only the number of coefficients needs to be adjusted to quickly adapt to the new scenario. In addition, from a physical perspective, the distribution coefficients intuitively reflect the current proportion of each partition, making it easier for process engineers to understand and control. The results of coefficient optimization can directly guide the parameter settings of production equipment, which is more in line with engineering application requirements than the original current values, effectively reducing the cost of technology conversion and operational difficulty.

[0012] Preferably, the constraint condition for the sum of the current distribution coefficients in each region of the anode is set as an inequality constraint, and the upper and lower limits of the sum of the current distribution coefficients are limited. Here, due to the influence of factors such as solution conductivity, electrode polarization effect, and temperature change, the electroplating efficiency is not a constant value, and the current will generate non-negligible losses or gains during the transmission and deposition process. Therefore, this application, based on inequality constraints, introduces relaxation variables and penalty function mechanisms to integrate inequality constraints into the objective function optimization process, ensuring that the solution results accurately match the complex actual production scenario and achieve the optimal solution for bump height uniformity, effectively improving the fit between numerical simulation and actual production, and enhancing the practicality and robustness of the model.

[0013] Specifically, 0.99 ≤ A1 + A2 + ... + A m ≤1.01.

[0014] Preferably, the upper limit of the current distribution coefficient for each zone of the anode is set to 1, and the lower limit is set to 0.

[0015] According to another specific embodiment and preferred aspect of the present invention, in step S4, based on the finite element method, the multi-physics coupling problem such as electric field distribution, metal ion migration, and deposition rate in the electroplating process is solved. At the same time, intelligent optimization algorithms such as genetic algorithm and particle swarm optimization algorithm are invoked to iteratively optimize the current distribution coefficient of each region of the anode with the goal of minimizing the output value of the objective function.

[0016] Furthermore, in step S1, the dimensions and shape of the wafer are measured; the pattern on the wafer surface is measured; the number, layout, and size of the anode partitions are measured; the structure of the cathode wafer fixture is measured; and the shape and size of the electroplating tank cavity are measured. Based on the measured data, a corresponding three-dimensional model is constructed at a 1:1 scale. This accurately reflects the physical structure of the wafer electroplating system, laying a solid foundation for subsequent formula adaptation, boundary condition setting, and numerical simulation calculations based on the electroplating principle.

[0017] Due to the implementation of the above technical solutions, the present invention has the following advantages compared with the prior art: Existing technologies require manual adjustment of the current applied to the partitioned anode surface and repeated calculations for comparison, resulting in a massive workload and high time and material costs. Furthermore, inconsistencies in wafer surface patterns lead to changes in the current distribution scheme, further increasing the complexity of the experiment. This application addresses these shortcomings by providing a comprehensive numerical simulation method for optimizing the partitioned anode current distribution scheme. This method first establishes a corresponding geometric model based on the actual wafer and electroplating equipment. Second, based on electroplating principles, appropriate calculation formulas and boundary conditions are adapted to the geometric model. Finally, based on electroplating principles, it is known that the height of the bumps formed by electroplating on the wafer surface is positively correlated with the local current density on its surface. Based on the relationship, this application constructs an optimization objective function and sets corresponding optimization variables. It obtains the local current density of each die on the wafer and performs an integral average of the local current density of each die to obtain the mean local current density. Then, based on the total interface current density and the mean local current density of each die on the wafer, an optimization objective function is established to reflect the uniformity of the current distribution on the wafer surface. Based on the optimization objective function, the current ratio of each partition on the anode is set as an optimization variable to adjust the total interface current density of each die on the wafer. Finally, the model mesh is divided and calculated. The variable values ​​are calculated, compared, and iteratively optimized using data processing software until the uniformity of the current distribution on the wafer surface reflected by the optimization objective function is optimal, at which point the optimal current allocation scheme is obtained. Therefore, compared with the prior art, the present invention establishes a geometric model and establishes an optimization objective function based on the total current density and local current density of the interface, transforming the optimization of the uniformity of the bump height on the wafer surface into the optimization of the uniformity of the current distribution. Thus, the optimal current distribution scheme can be calculated through numerical simulation, which can ensure the optimal uniformity of the bump height, effectively saving time and material costs. In addition, it is not limited by the changes in the wafer surface pattern, and has practicality and robustness. Attached Figure Description

[0018] Figure 1 This is a flowchart of the numerical simulation method used in this embodiment to optimize the optimal current distribution scheme for partitioned anodes; Figure 2 This is a cloud map showing the height distribution of bumps on the wafer surface obtained in this embodiment; Figure 3 The height distribution cloud map of the wafer surface bumps obtained for this comparative example; Detailed Implementation

[0019] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0020] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc., indicating the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0021] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0022] In this application, unless otherwise expressly specified and limited, the terms "installation," "connection," "joining," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0023] In this application, unless otherwise expressly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "on top of," and "over" the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0024] It should be noted that when an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intervening element. When an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0025] Examples, such as Figure 1 As shown, the numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes in this embodiment includes the following steps: S1, establishing a corresponding geometric model based on the actual wafer and electroplating equipment; S2, adapting the corresponding calculation formula and boundary conditions to the geometric model based on the electroplating principle; S3, constructing the optimization objective function and setting the corresponding optimization variables; S4, performing model meshing and calculation.

[0026] Specifically, this embodiment takes a 12-inch notch wafer, a die with a wafer surface pattern of 4mm×4mm, and a six-zone insoluble anode as an example. The structure of the six-zone insoluble anode can be referred to the anode involved in another Chinese patent of the applicant with publication number CN116988127A, which will not be elaborated here.

[0027] The data processing software used in this embodiment is Comsol Multiphysics 6.1 Version.

[0028] In step S1, starting from the actual wafer electroplating scenario, the dimensions and shape of the wafer are accurately measured; the pattern on the wafer surface; the number, layout, and size of the anode partitions; the structure of the cathode wafer fixture; and the shape and size of the electroplating tank cavity. Based on the measured data, a corresponding CAD geometric model is constructed at a 1:1 scale. This accurately reflects the physical structure of the wafer electroplating system, laying a solid foundation for subsequent formula adaptation, boundary condition setting, and numerical simulation calculations based on electroplating principles.

[0029] Meanwhile, during the modeling process, different parts such as wafers, anodes, internal components, and electrolyte areas can be modeled and assembled separately to ensure the accurate relative positions of each component. The model is simplified as necessary to remove minor structures that have little impact on the electroplating process (such as screw holes and chamfers) to reduce the complexity of subsequent numerical calculations and improve computational efficiency while ensuring model accuracy. In addition, to facilitate the setting of boundary conditions and mesh generation, the surfaces of the model need to be named and grouped appropriately.

[0030] In step S2, based on the electroplating principle: the copper anode undergoes an oxidation reaction to generate Cu. 2+ The metal reaches the wafer surface through diffusion, convection, and electromigration, where it undergoes a reduction reaction to form copper metal. If the anode is insoluble, then Cu... 2+ Derived from electroplating solutions, the formulas involved mainly include: (1); (2); Equation (1) is the Nernst-Planck equation (NP equation) to describe the directional movement of charged ions, with terms from left to right representing diffusion, electromigration, and convection, respectively; Equation (2) is the Butler-Volume equation (BV equation) to describe the electrochemical reactions occurring on the wafer surface, also known as the electrode kinetic equation. loc The local current density is represented by , and i0 represents the reaction exchange current density. Both are related in real time to the current density of the reduction reaction occurring on the wafer surface. Due to the reduction reaction and the grounding of the wafer edge, the values ​​are negative. It is important to note that the local current density is defined for each die, therefore each die has a corresponding local current density. Additionally, there is a variable for the current transfer from the liquid phase (electroplating solution) to the solid phase (wafer), called the total interfacial current density, denoted as i. tot Similarly, this value is also negative, and this variable can be understood as the total current density of the current coming from the anode to the cathode surface.

[0031] In step S3, the local current density of each die on the wafer is obtained based on step S2, and the local current density of each die on the wafer is integrated and averaged to obtain the mean local current density. Then, an optimization objective function is established based on the total interface current density of each die on the wafer and the mean local current density to reflect the uniformity of the current distribution on the wafer surface. Based on the optimization objective function, the current ratio of each partition on the anode is set as the optimization variable to adjust the total interface current density of each die on the wafer.

[0032] For ease of implementation, the output of the established optimization objective function is a dimensionless value, and the uniformity of the current distribution on the wafer surface is optimal when the dimensionless value is minimized. Therefore, the optimization objective function established in this embodiment is: (3); In equation (3), q is a dimensionless numerical value; i tot denoted as the total interface current density; bond1 is the average local current density; N is an even value, and in this embodiment, N is preferably 2.

[0033] To further facilitate implementation, the current distribution coefficients for each anode zone are set as A1, A2...A6, respectively. The current magnitude of each anode zone is the product of the total anode current and the corresponding current distribution coefficient. The data processing software uses the current distribution coefficients of each anode zone as optimization variables. Compared to directly using current magnitude as the optimization variable, this application effectively reduces the dimensionality of variables and computational complexity by using current allocation coefficients. When the total current is fixed, taking the constraint that the sum of A1, A2...A6 is 1 as an example, the original 6 independent current variables can be transformed into 5 free variables (the 6th variable can be obtained by subtracting the other 5 coefficients from 1), reducing the search space of the optimization algorithm and improving iteration efficiency. At the same time, this method significantly enhances the model's versatility and scalability. Regardless of how the total current changes, the allocation coefficients only depend on the number of anode partitions and the wafer surface characteristics, avoiding the need to reset variables due to adjustments in the total current. Furthermore, when the number of anode partitions increases or decreases, only the number of coefficients needs to be adjusted to quickly adapt to new scenarios. In addition, from a physical perspective, the allocation coefficients intuitively reflect the current proportion of each partition, making it easier for process engineers to understand and control. The optimization results of the coefficients can directly guide the setting of production equipment parameters, which is more in line with engineering application needs than the original current values, effectively reducing technology conversion costs and operational difficulties.

[0034] Meanwhile, the constraint condition for the sum of the current distribution coefficients in each region of the anode is set as an inequality constraint, and the upper and lower limits of the sum of the current distribution coefficients are limited. Here, due to the influence of factors such as solution conductivity, electrode polarization effect, and temperature change, the electroplating efficiency is not a constant value, and the current will generate non-negligible losses or gains during the transmission and deposition process. Therefore, this application, based on inequality constraints, introduces relaxation variables and penalty function mechanisms to integrate inequality constraints into the objective function optimization process, ensuring that the solution results accurately match the complex actual production scenario and achieve the optimal solution for bump height uniformity, effectively improving the fit between numerical simulation and actual production, and enhancing the practicality and robustness of the model.

[0035] In some specific implementations, 0.99≤A1+A2+……+A6≤1.01; and the upper limit of the current distribution coefficient for each anode zone is set to 1 and the lower limit to 0.

[0036] In step S4, the variable values ​​are calculated, compared and iteratively optimized using data processing software until the uniformity of the wafer surface current distribution reflected by the objective function in step S3 is optimal, at which point the optimal current distribution scheme is obtained.

[0037] Specifically, after setting the above-mentioned objective function and constraints, the constructed geometric model is meshed. Hybrid mesh technology is used to locally refine key areas such as the wafer surface and anode partitions to ensure that details in areas with drastic changes in current density can be captured. For areas with relatively uniform flow fields, such as the electrolyte, a coarser mesh is used to reduce the computational load while ensuring computational accuracy. Based on the finite element method, the multi-physics coupling problems such as electric field distribution, metal ion migration, and deposition rate in the electroplating process are solved. At the same time, intelligent optimization algorithms such as genetic algorithms and particle swarm optimization algorithms are invoked to iteratively optimize the current distribution coefficients of each anode region with the goal of minimizing the output value of the objective function.

[0038] This case uses the SNOPT optimization algorithm. In each iteration, the algorithm calculates the uniformity of current distribution based on the current coefficient combination and feeds the result back to the optimization module to adjust the parameters until the objective function converges and a coefficient allocation scheme that satisfies the constraints and has the best uniformity of current distribution is obtained.

[0039] Therefore, based on the current distribution scheme of each anode region determined by the above numerical simulation method, simulation was performed using the simulation tool Comsol Multiphysics. The resulting wafer surface bump height distribution cloud map is shown below. Figure 2 As shown in the figure, the uniformity data of the bump height on the wafer surface are shown in Table 1.

[0040] Table 1 In contrast to the embodiments, the difference in this comparative example lies in that the current distribution coefficient in this comparative example is determined by the area ratio of each region of the anode, and is a fixed value. The ratio coefficient determined in this way is calculated using conventional methods, and the simulation is performed using the simulation tool Comsol Multiphysics based on the calculation results. The obtained wafer surface bump height distribution cloud map is shown below. Figure 3 As shown in the figure, the uniformity data of the bump height on the wafer surface are shown in Table 2.

[0041] Table 2 As can be seen from the data comparison, the uniformity of the wafer surface bump height calculated by the optimized algorithm in the embodiment is significantly improved.

[0042] In summary, by adopting this numerical simulation method, firstly, a corresponding geometric model is established based on the actual wafer and electroplating equipment; secondly, based on the electroplating principle, corresponding calculation formulas and boundary conditions are adapted to the geometric model; then, based on the electroplating principle, it is known that the height of the bumps formed by electroplating on the wafer surface is directly proportional to the local current density on its surface. Therefore, this application constructs an optimization objective function and sets corresponding optimization variables. By obtaining the local current density of each die on the wafer and integrating and averaging the local current density of each die on the wafer to obtain the average local current density; then, based on the total interface current density and the average local current density of each die on the wafer, an optimization objective function is established to reflect the uniformity of the current distribution on the wafer surface; based on the optimization objective function, the current ratio of each partition on the anode is set as an optimization variable to adjust the total interface current density of each die on the wafer; finally, the model mesh is divided and calculated, and the variable values ​​are calculated, compared, and iteratively optimized using data processing software until the uniformity of the current distribution on the wafer surface reflected by the optimization objective function is optimal, at which point the optimal current allocation scheme is obtained. Therefore, compared with existing technologies, this invention establishes a geometric model and sets an optimization objective function based on the total interface current density and local current density. This transforms the optimization of wafer surface bump height uniformity into the optimization of current distribution uniformity. The optimal current allocation scheme is then calculated through numerical simulation, ensuring optimal bump height uniformity and effectively saving time and material costs. Furthermore, it is not limited by changes in wafer surface patterns, possessing practicality and robustness. The current allocation coefficient effectively reduces the dimensionality of variables and computational complexity, decreases the search space of the optimization algorithm, improves iteration efficiency, and significantly enhances the model's versatility and scalability. Regardless of changes in the total current, the allocation coefficient depends only on the number of anode partitions and the characteristics of the wafer surface. This approach avoids the need to reset variables due to adjustments in the total current. Furthermore, when the number of anode zones increases or decreases, only the number of coefficients needs to be adjusted to quickly adapt to new scenarios. From a physical perspective, the allocation coefficients intuitively reflect the current proportion of each zone, facilitating understanding and control by process engineers. The optimized coefficient results can directly guide the setting of production equipment parameters, better meeting engineering application needs compared to the original current values, effectively reducing technology transfer costs and operational difficulties. Based on inequality constraints, by introducing relaxation variables and penalty function mechanisms, the inequality constraints are integrated into the objective function optimization process, ensuring that the solution accurately matches complex actual production scenarios while achieving the optimal solution for bump height uniformity, effectively improving the fit between numerical simulation and actual production.

[0043] The present invention has been described in detail above, with the aim of enabling those skilled in the art to understand and implement the invention. However, this description should not be construed as limiting the scope of protection of the invention. All equivalent changes or modifications made in accordance with the spirit and essence of the invention should be included within the scope of protection of the invention.

Claims

1. A numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes, comprising the following steps: S1. Based on the actual wafers and electroplating equipment, establish the corresponding geometric models; S2. Based on the principle of electroplating, the corresponding calculation formulas and boundary conditions are adapted to the geometric model. Its features are, The numerical simulation method further includes the following steps: S3. Construct the objective function and set the corresponding optimization variables. Based on step S2, the local current density of each die on the wafer is obtained, and the local current density of each die on the wafer is integrated and averaged to obtain the mean local current density. Based on the total interface current density of each die on the wafer and the mean local current density, an optimization objective function is established to reflect the uniformity of the current distribution on the wafer surface. Based on the optimization objective function, the current ratio of each partition on the anode is set as the optimization variable to adjust the total interface current density of each die on the wafer. S4. Perform model mesh generation and calculation. The constructed geometric model is meshed using the finite element method and iteratively calculated and solved. During the solution process, the data processing software automatically calculates, compares and iteratively optimizes the variable values ​​until the uniformity of the wafer surface current distribution reflected by the optimization objective function in step S3 is optimal. At this point, the calculation ends and the result is output to obtain the optimal current distribution scheme.

2. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 1, characterized in that, In step S3, the output of the established optimization objective function is a dimensionless value, and the uniformity of the current distribution on the wafer surface is optimal when the dimensionless value is minimized.

3. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 2, characterized in that, The established optimization objective function is: ； Where q is the dimensionless numerical value; i tot The total current density at the interface is denoted as ; bond1 is the average local current density; and N is an even value.

4. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 3, characterized in that, N=2。 5. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 1, characterized in that, The number of zones in the anode is m. In step S3, the current distribution coefficients for each zone of the anode are set to A1, A2...A... m The current magnitude in each anode region is the product of the total anode current and the corresponding current distribution coefficient. The data processing software uses the current distribution coefficient of each anode region as the optimization variable.

6. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 5, characterized in that, The constraint condition for the sum of the current distribution coefficients of each anode region is set as an inequality constraint, and the upper and lower limits of the sum of the current distribution coefficients are limited.

7. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 6, characterized in that, 0.99 ≤ A1 + A2 + ... + A m ≤1.01。 8. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 5, characterized in that, The upper limit of the current distribution coefficient for each zone of the anode is set to 1, and the lower limit is set to 0.

9. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to any one of claims 5-8, characterized in that, In step S4, based on the finite element method, the multi-physics coupling problem of electric field distribution, metal ion migration, and deposition rate in the electroplating process is solved. At the same time, intelligent optimization algorithms such as genetic algorithm and particle swarm optimization algorithm are called to iteratively optimize the current distribution coefficient of each region of the anode with the goal of minimizing the output value of the objective function.

10. The numerical simulation method for optimizing the optimal current distribution scheme of partitioned anodes according to claim 1, characterized in that, In step S1, the dimensions and shape of the wafer are measured; the pattern on the wafer surface is measured; the number, layout and size of the anode partitions are measured; the structure of the cathode wafer fixture is measured; the shape and size of the electroplating tank cavity is measured; and a corresponding three-dimensional model is constructed according to the measurement data at a 1:1 scale.

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