Construction method for predicting double-sided local coating film thickness based on machine learning simulation model

Abstract

The invention relates to a construction method for predicting the film thickness of a double-sided local coating based on a machine learning simulation model, and belongs to the technical field of electroplating. According to the method, the LR logistic regression model is perfected and constructed through the machine learning simulation model, and the LR logistic regression model is trained by utilizing the constructed logistic regression model, so that the optimal electronic electroplating production conditions of semiconductor devices with different structures can be quickly determined, and the optimal plating piece double-sided local electronic electroplating control mode is further obtained; according to the method, the accuracy of predicting the thickness of the double-sided local coating of the semiconductor device can be realized, the error with the thickness of the coating of an actual electroplating product can be greatly reduced, further improvement of an electronic electroplating module can be realized, the uniformity of the thickness of the double-sided local coating of the semiconductor device can be improved, and the requirement of high quality of the semiconductor device can be met.

Description

Technical Field

[0001] The invention relates to a construction method for predicting the thickness of a double-sided local coating based on a machine learning simulation model, and belongs to the technical field of electroplating. Background Art

[0002] Metal coating deposition is a unique characterization technology that is sensitive to the local electrochemical-physical environment structure of metal ions in the electronic electroplating process. It has a wide range of applications in the fields of physics, electrochemistry, and electronic electroplating high-end manufacturing. In the electroplating system, metal ions are subjected to different constant currents in the electrochemical-physical environment, and different coating thicknesses are deposited on the product plating area.

[0003] However, the mechanism of metal coating deposition depends on the type of electroplating system in the electrochemical-physical environment. The thickness of the deposited coating in the immersion electroplating system requires a longer electroplating time under the same constant current; while in the jet electroplating system, the factors affecting the metal coating deposition are more numerous and complex; therefore, the actual measured coating thickness is significantly different from the predicted result due to the interference of various influencing factors, which makes it difficult to accurately predict and confirm the film thickness in electroplating production.

[0004] At present, the industry has used cross-sectional testing methods based on scanning electron microscopes (SEM), or dual beam focused ion beams (Dual Beam FIB), which can use ion beams to cut samples while using electron beams to observe the sample cross section to directly measure the coating thickness, thereby achieving accurate confirmation of the coating thickness. However, the equipment required for accurate coating thickness testing is expensive and the analysis cost is very high, making it difficult to be widely used in the daily accurate prediction of coating film thickness management in various electroplating systems. Therefore, exploring and creating an accurate, fast, and easy-to-promote method for calculating coating thickness has become a very important topic.

[0005] In the prior art, there is only a multi-layer feedback metal coating control method such as CN115747750A, which can find out the important process parameters in the coating process through an algorithm model, and extract these process parameters to optimize the target film thickness, thereby finding the optimal process parameters. However, this plasma vacuum technology metal coating method neither provides the theoretical basis for predicting and controlling multi-layer metal coating from the perspective of metal coating theory, nor describes the actual operation mode of establishing the model, especially the important core content of how the multi-layer metal coating theory and the established model are organically combined. Summary of the invention

[0006] In order to solve the above problems, the present invention provides a method for constructing a prediction method of the double-sided local coating thickness based on a machine learning simulation model. By importing the coating thickness experimental data generated by the electronic plating module during the electroplating process under different electronic plating conditions, the machine learning simulation model is improved by predicting the double-sided local coating thickness system and an LR logistic regression model is constructed. According to the results of continuous training of the LR logistic regression model, a coating thickness prediction data condition group is obtained, which specifically includes the following steps: S1: constructing a database based on electronic plating conditions and constructing an initial machine learning simulation model linked to the database; setting the database in a memory; S2: extract at least two sets of electronic plating conditions from the database, and predict the double-sided local plating film thickness through the prediction calculation module in the double-sided local plating film thickness prediction system; use the electronic plating module to perform actual plating operation on the semiconductor device according to the extracted electronic plating conditions, and import the obtained plating film thickness experimental data into the plating film thickness threshold judgment module; S3: Predict the thickness of the local coating on both sides d 预测值 Comparison with target threshold: When predicting the local coating thickness on both sides d 预测值 When formula D is satisfied, the LR logistic regression model is entered; and the predicted coating thickness that does not meet the target threshold is d 预测值 Cannot enter the training module, and the electronic plating conditions extracted from the database in S2 are based on the measured coating thickness value d 实测值 Make corrections and calculate the corrected electronic plating conditions, then return to S2 to re-measure the coating thickness. d 实测值 , and re-determine and correct the predicted double-sided local coating thickness after electronic plating d Whether the predicted value meets the threshold range until the local coating thickness on both sides is predicted d 预测值 When formula D is satisfied, the LR logistic regression model is entered; The predicted double-sided local coating thickness is calculated using all the predicted double-sided local coating thicknesses that satisfy formula D. d 预测值 To build the LR logistic regression model; The formula D associated with the target threshold is: d 实测值 (100%-5%)≤ d 预测值 ≤ d 实测值 (100%+5%) (Formula D) S4: Predict the thickness of the local coating on both sides d 预测值 And the measured value of electronic plating module d 实测值 Importing a training module in an LR logistic regression operation system, and performing system training through the LR logistic regression operation system, wherein the LR logistic regression operation system includes a training module, a stability generation module, and a coating film thickness calculation module; S5: The model morphology is judged according to the coating film thickness result obtained by S4 and compared with the target threshold. If the target threshold is reached, the electronic electroplating conditions are determined to be optimized, and the optimized electronic electroplating conditions are applied to the production commissioning of the electronic electroplating device; if the target value is not reached, the set of training electronic electroplating conditions is discarded and returned to S4 for retraining.

[0007] The initial machine learning simulation model includes: a processor, a memory, an electronic electroplating module, a prediction calculation module and a coating film thickness threshold judgment module connected to the electronic electroplating module, a set partitioning module, and a training module, a stability generation module, a coating thickness calculation module, and a model morphology judgment module connected in sequence.

[0008] Furthermore, in the process of constructing the initial machine learning simulation model linked to the database in S1-S2, COMSOL Multiphysics finite element simulation software is used in the prediction calculation module and the electronic electroplating module, and formula C-2 is used as the calculation basis to simulate the local double-sided electronic electroplating process of the semiconductor device according to the prediction conditions calculated by formula C-2; the formula C-2 is: d = CI t n k / S p in, A (Ampere / dm 2 ) = I / S A = ρ d / t C η k d = A hh = t C h k / p (Formula C-2) In formula C-2, d is the thickness of the electroplating layer; C is the electrochemical equivalent; I is the current intensity; t is the electroplating time; or k is the cathode current efficiency; S is the surface area of ​​the plating area; r is the metal density of the electroplating layer;A is the current density.

[0009] In the above-mentioned S3, the corrected electronic plating conditions are predicted and calculated by formula C-2.

[0010] Furthermore, the prediction conditions include current density and electroplating time.

[0011] Furthermore, in S3, satisfying the target threshold means predicting the thickness of the local coating on both sides. d 预测值 It is between the minimum threshold and the maximum threshold, the minimum threshold is -5% of the coating specification value, and the maximum threshold is +5% of the coating specification value.

[0012] Furthermore, the LR logistic regression model is composed of sensitive condition parameter modeling, and the sensitive condition parameters include the type of electroplating solution; the temperature of the electroplating solution; the specific gravity of the electroplating solution; the diameter of the pipeline for transporting the electroplating solution; the type of electroplating power supply; the current intensity; the electroplating time; the cathode current efficiency; the surface area of ​​the plating area; the metal density of the electroplating layer; the current density; and the flow rate of the electroplating solution.

[0013] In the present invention, when the COMSOL Multiphysics finite element simulation software is used in the electronic electroplating module in the construction process of the model for predicting the double-sided local coating film thickness, the influencing factors of the machine learning simulation model for predicting the double-sided local coating film thickness are composed of sensitive parameters and sudden feeling parameters, and the sudden feeling parameters include the plating tank size in the electronic electroplating module, the pump power for conveying the electroplating solution, the electroplating power supply power, the electroplating mold size, and the type and size of the electrolytic anode.

[0014] Furthermore, in S4, further training of the initial LR logistic regression model uses a logistic regression algorithm to construct an equation group operation, and constructing the logistic regression model specifically includes the following steps: Set continuous random variable X The logistic distribution means X It has the following distribution and density functions:

[0015] (Equation 1)

[0016] (Equation 2) In equation 1 and equation 2, m is a positional parameter, c is the shape parameter; When the position parameter m Approaches zero, c = 1, we get the common Sigmoid curve:

[0017] (Equation 3) The binomial logistic regression model is introduced, which is a classification model composed of conditional probability P ( Y | X ) represents the form of parameterized logistic distribution; in this case, the random variable X Take it as a real number, random variable Y The value is 1 or 0, and the model parameters are estimated through supervised learning methods; Further defined, the binomial logistic regression model is the following conditional probability distribution:

[0018] (Equation 4)

[0019] (Equation 5) In equation 4 and equation 5, x ∈R n is the input, y∈{0,1}, w ∈R n Yes and b ∈R is a parameter, w is called the weight vector, b is called bias, w·x yes w and b The inner product of The weight vector and input vector are expanded and still recorded as w , x , that is:

[0020]

[0021] Then, the logistic regression model is expressed as:

[0022] (Equation 6)

[0023] (Equation 7) Next, set the probability of a time odds, which refers to the ratio of the probability of the event occurring to the probability of the event not occurring. If the probability of the event occurring is p , then the probability of the event is:

[0024] The function expression of the logarithmic probability of the event log odds or log (log odds) = logit is:

[0025] For logistic regression, the above formula P ( Y = 1 | x )and P ( Y = 0 | x ) can be obtained:

[0026] (Equation 8) According to Equation 8, in the logistic regression model, the output is Y = 1 is the input x A linear function of, or expressed as, the output Y = 1 is given by the input x The model represented by the linear function of constitutes the preliminary logistic regression model; Consider the input x Linear function for classification w · x , its value range w · x ∈R, and x ∈R n+1 , w ∈R n+1 ; Define the linear function by logistic regression w · x Converted into probability, it can be expressed as:

[0027] (Equation 9) When the value of the linear function z = w · x → + ∞, then P ( Y = 1 | x ) → 1; when the value of the linear function z = w · x → -∞, then P ( Y = 1 | x ) → 0; the resulting graph is the logistic regression model.

[0028] The training module in S4 uses the predicted coating thickness parameter calculation that meets the threshold, specifically including the following steps: In S3, for a given training set data T = {( x 1, y 1), ( x 2, y 2)···,( x N , y N )},in,

[0029] y i ∈{0,1}, the maximum likelihood estimation method is used to predict the model parameters, thus obtaining the iterative logistic regression model.

[0030] The likelihood function is expressed as:

[0031] The log-likelihood function is expressed as:

[0032] (Equation 10) Calculate Equation 10 L ( w ) maximum value, thus obtaining w The predicted value of w The predicted value represents the coating thickness.

[0033] For Equation 10, we use the gradient descent method and the Newton-like method, setting w The maximum likelihood estimate of is w ∧ , then the learned logistic regression model is:

[0034] (Equation 11)

[0035] (Equation 12) However, the binomial logistic regression model is only introduced for binary classification problems; when used for multi-classification problems, a multinomial logistic regression model needs to be introduced. The specific steps are: Setting discrete random variables Y The value set of is {1, 2, ···, K}, that is, the category label is K The multinomial logistic regression model obtained by analogy is:

[0036] (Equation 13)

[0037] (Equation 14) Both binomial logistic regression and multinomial logistic regression are widely used classification algorithms. Their principles are based on statistics and probability theory. They model the probability of the first combination of input features, and then use a logistic function to map the linear combination to a probability value between 0 and 1, thereby indicating the probability of belonging to a sample and belonging to a certain category.

[0038] The machine learning (ML) method proposed in the present invention focuses on using data and algorithms to enable it to imitate the way humans learn and gradually improve accuracy. The machine learning method is becoming a new tool in many fields of chemistry and physics, learning the relationship between variables based on a large amount of data. The structure of the electronic electroplating device of the local electrochemical-physical environment of metal ions in the electroplating system and the thickness of the coating are a pair of variables with strong correlation. In order to use the machine learning method for prediction and classification, it is necessary to characterize the structure of the electronic electroplating device of the local electrochemical-physical environment of metal ions, and the machine learning algorithm formed according to some possibly labeled or unlabeled input data is applied to the prediction or classification algorithm, and the generated error function expansion is used for comparing known samples with the simulation algorithm to evaluate the accuracy of the method; the algorithm fits the data points in the training set and adjusts the weights to reduce the difference between the known experimental samples and the algorithm evaluation results. For the machine learning algorithm, repeat the iterative "evaluation and optimization" process, update and improve the weights autonomously, and construct a machine learning algorithm that is accurately applied to prediction or classification; the machine learning method has been widely used in the fields of physics and chemistry.

[0039] Beneficial effects of the present invention: The present invention improves and constructs an LR logistic regression model through a machine learning simulation model, and uses the constructed logistic regression model to train the LR logistic regression model, so that the optimal electronic electroplating production conditions for semiconductor devices of various structures can be quickly established, and then the optimal double-sided local electronic electroplating control method for plated parts can be obtained. It can not only achieve the accuracy of predicting the local coating thickness on both sides of semiconductor devices, and greatly reduce the error with the actual coating thickness of electroplated products, but also achieve further improvement of the electronic electroplating mold, and promote the improvement of the uniformity of the local coating thickness on both sides of semiconductor devices, so as to meet the high quality requirements of semiconductor devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the structure of a semiconductor device to be electroplated in one embodiment of the present invention.

[0041] Figure 2 It is a schematic diagram of test points in testing the coating thickness of a semiconductor device to be electroplated in one embodiment of the present invention.

[0042] Figure 3 The figure is a flow chart of the overall method of the present invention.

[0043] Figure 4 The present invention is based on Example 1 and Example 3, which is a trend diagram of the coating film thickness variation with different current densities, derived from the model derived by deep analysis of the coating film thickness calculation module of the machine learning simulation model.

[0044] Figure 5 The present invention provides a trend diagram of the coating film thickness variation with different current densities, which is derived from the model derived by deep analysis of the coating film thickness calculation module of the machine learning simulation model in Examples 4 to 6 of the present invention.

[0045] Figure 6 It is a scatter plot of the double-sided local gold-plated film thickness between the coating film thickness and the electroplating time of the present invention.

[0046] Figure 7 It is a scattered point diagram of double-sided local gold-plated film thickness and electroplating time after optimization and improvement of the coating film thickness of the present invention.

[0047] In the figure, 100, substrate; 200, semiconductor device; 20, electroplating area; 300, machine learning simulation model; 301, double-sided local coating thickness prediction system; 302, LR logistic regression operation system; 310, prediction calculation module; 320, electronic electroplating module; 330, coating thickness threshold judgment module; 340, training module; 350, stability generation module; 360, coating thickness calculation module; 370, model morphology judgment module. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] In the present invention, unless otherwise clearly specified and limited, the terms "connected", "connected", and "fixed" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0050] The predicted conditions studied in the present invention include current density and electroplating time.

[0051] In the present invention, when the COMSOL Multiphysics finite element simulation software is used in the electronic electroplating module in the construction process of the model for predicting the double-sided local coating film thickness, the influencing factors of the machine learning simulation model for predicting the double-sided local coating film thickness are composed of sensitive parameters and sudden feeling parameters, and the sudden feeling parameters include the plating tank size in the electronic electroplating module, the pump power for conveying the electroplating solution, the electroplating power supply power, the electroplating mold size, and the type and size of the electrolytic anode.

[0052] The present invention provides a method for constructing a prediction method for the thickness of a double-sided local coating based on a machine learning simulation model. By importing the experimental data of the coating thickness generated by an electronic plating module during the electroplating process under different electronic plating conditions, the machine learning simulation model is improved through a system for predicting the thickness of a double-sided local coating and an LR logistic regression model is constructed. According to the result of continuous training of the LR logistic regression model, a coating thickness prediction data condition group is obtained. The method specifically includes the following steps: S1: construct a database based on electronic electroplating conditions, and construct an initial machine learning simulation model linked to the database; set the database in a memory; the initial machine learning simulation model includes: a processor, a memory, an electronic electroplating module, a prediction calculation module and a coating thickness threshold determination module connected to the electronic electroplating module, a set partitioning module, and a training module, a stability generation module, a coating thickness calculation module, and a model morphology determination module connected in sequence S2: extract at least two sets of electronic plating conditions from the database, and predict the double-sided local plating film thickness through the prediction calculation module in the double-sided local plating film thickness prediction system; use the electronic plating module to perform actual plating operation on the semiconductor device according to the extracted electronic plating conditions, and import the obtained plating film thickness experimental data into the plating film thickness threshold judgment module; In S1-S2, in the process of constructing the initial machine learning simulation model linked to the database, COMSOL Multiphysics finite element simulation software is used in the prediction calculation module and the electronic electroplating module, and formula C-2 is used as the calculation basis to simulate the local double-sided electronic electroplating process of the semiconductor device according to the prediction conditions calculated by formula C-2; the formula C-2 is: d = CI t n k / S p in, A (Ampere / dm 2 ) = I / S A = ρ d / t C η k d = A hh = t C h k / p (Formula C-2) In formula C-2, d is the thickness of the electroplating layer; C is the electrochemical equivalent; I is the current intensity; t is the electroplating time; or k is the cathode current efficiency; S is the surface area of ​​the plating area; r is the metal density of the electroplating layer; A is the current density; S3: Predict the thickness of the local coating on both sides d 预测值 Compared with the target threshold, meeting the target threshold means predicting the local coating thickness on both sides. d 预测值 Between the minimum threshold and the maximum threshold, the minimum threshold is the coating specification value -5%, and the maximum threshold is the coating specification value +5%: when predicting the local coating thickness on both sides d 预测值 When formula D is satisfied, the LR logistic regression model is entered; and the predicted coating thickness that does not meet the target threshold is d 预测值 Cannot enter the training module, and the electronic plating conditions extracted from the database in S2 are based on the measured coating thickness value d 实测值 Make corrections, calculate the corrected electronic plating conditions through formula C-2, return to S2 and re-measure the coating thickness d 实测值 , and re-determine and correct the predicted double-sided local coating thickness after electronic plating d Whether the predicted value meets the threshold range until the local coating thickness on both sides is predicted d 预测值 When formula D is satisfied, the LR logistic regression model is entered; The predicted double-sided local coating thickness is calculated using all the predicted double-sided local coating thicknesses that satisfy formula D. d 预测值 To build the LR logistic regression model; The formula D associated with the target threshold is: d 实测值 (100%-5%)≤ d 预测值 ≤ d 实测值 (100%+5%) (Formula D) S4: Predict the thickness of the local coating on both sides d 预测值 And the measured value of electronic plating module d 实测值 The training module in the LR logistic regression operation system is imported, and the system training is performed through the LR logistic regression operation system, wherein the LR logistic regression operation system includes a training module, a stability generation module and a coating film thickness operation module; the LR logistic regression model is composed of sensitive condition parameter modeling, and the sensitive condition parameters include the type of electroplating solution; the temperature of the electroplating solution; the specific gravity of the electroplating solution; the diameter of the pipeline for conveying the electroplating solution; the type of electroplating power supply; the current intensity; the electroplating time; the cathode current efficiency; the surface area of ​​the plating area; the metal density of the electroplating layer; the current density; and the flow rate of the electroplating solution; The further training of the initial LR logistic regression model uses a logistic regression algorithm to construct an equation group operation. The construction of the logistic regression model specifically includes the following steps: Set continuous random variable X The logistic distribution means X It has the following distribution and density functions:

[0053] (Equation 1)

[0054] (Equation 2) In equation 1 and equation 2, m is a positional parameter, c is the shape parameter; When the position parameter m Approaches zero, c = 1, we get the common Sigmoid curve:

[0055] (Equation 3) The binomial logistic regression model is introduced, which is a classification model composed of conditional probability P ( Y | X ) represents the form of parameterized logistic distribution; in this case, the random variable X Take it as a real number, random variable Y The value is 1 or 0, and the model parameters are estimated through supervised learning methods; Further defined, the binomial logistic regression model is the following conditional probability distribution:

[0056] (Equation 4)

[0057] (Equation 5) In equation 4 and equation 5, x ∈R n is the input, y∈{0,1}, w ∈R n Yes and b ∈R is a parameter, w is called the weight vector, b is called bias, w·x yes w and b The inner product of The weight vector and input vector are expanded and still recorded as w , x , that is:

[0058]

[0059] Then, the logistic regression model is expressed as:

[0060] (Equation 6)

[0061] (Equation 7) Next, set the probability of a time odds, which refers to the ratio of the probability of the event occurring to the probability of the event not occurring. If the probability of the event occurring is p , then the probability of the event is:

[0062] The function expression of the logarithmic probability of the event log odds or log (log odds) = logit is:

[0063] For logistic regression, the above formula P ( Y = 1 | x )and P ( Y = 0 | x ) can be obtained:

[0064] (Equation 8) According to Equation 8, in the logistic regression model, the output is Y = 1 is the inputx A linear function of, or expressed as, the output Y = 1 is given by the input x The model represented by the linear function of constitutes the preliminary logistic regression model; Consider the input x Linear function for classification w · x , its value range w · x ∈R, and x ∈R n+1 , w ∈R n+1 ; Define the linear function by logistic regression w · x Converted into probability, it can be expressed as:

[0065] (Equation 9) When the value of the linear function z = w · x → + ∞, then P ( Y = 1 | x ) → 1; when the value of the linear function z = w · x → -∞, then P ( Y = 1 | x ) → 0; the resulting graph is the logistic regression model.

[0066] The training module in S4 uses the predicted coating thickness parameter calculation that meets the threshold, specifically including the following steps: In S3, for a given training set data T = {( x 1, y 1), ( x 2, y 2)···,( x N , y N )},in,

[0067] y i ∈{0,1}, the maximum likelihood estimation method is used to predict the model parameters, thus obtaining the iterative logistic regression model.

[0068] The likelihood function is expressed as:

[0069] The log-likelihood function is expressed as:

[0070] (Equation 10) Calculate Equation 10 L ( w ) maximum value, thus obtaining w The predicted value of w The predicted value represents the coating thickness.

[0071] For Equation 10, we use the gradient descent method and the Newton-like method, setting w The maximum likelihood estimate of is w ∧ , then the learned logistic regression model is:

[0072] (Equation 11)

[0073] (Equation 12) However, the binomial logistic regression model is only introduced for binary classification problems; when used for multi-classification problems, a multinomial logistic regression model needs to be introduced. The specific steps are: Setting discrete random variables Y The value set of is {1, 2, ···, K}, that is, the category label is K The multinomial logistic regression model obtained by analogy is:

[0074] (Equation 13)

[0075] (Equation 14) Both binomial logistic regression and multinomial logistic regression are widely used classification algorithms. Their principles are based on statistics and probability theory. They model the probability of the first combination of input features, and then use a logistic function to map the linear combination to a probability value between 0 and 1, thereby indicating the probability of belonging to a sample and belonging to a certain category. S5: The model morphology is judged according to the coating film thickness result obtained by S4 and compared with the target threshold. If the target threshold is reached, the electronic electroplating conditions are determined to be optimized, and the optimized electronic electroplating conditions are applied to the production commissioning of the electronic electroplating device; if the target value is not reached, the set of training electronic electroplating conditions is discarded and returned to S4 for retraining.

[0076] Using the above method, according to formula B, various parameters as shown in Table 1 are introduced. In order to obtain a gold-plated film thickness of ≥300nm, Example 1 is set. In Example 1, the gold-plated solution can use a current density range as low as 7A / dm 2 , since the double-sided local electroplating area of ​​the semiconductor device is 5481mm 2 =0.5481dm 2 Therefore, the current parameter for gold plating is 7A / dm 2 ×0.5481dm 2 =3.84A.

[0077] Further, according to the method described in Example 1, Example 2 is set, and Example 2 selects a higher current density of 15A / dm 2 , the required gold plating current parameter is 8.22A.

[0078] The electroplating time is calculated from formula B to obtain formula C. or k It is the cathode current efficiency of gold plating. According to the electroplating manual, the theoretical cathode current efficiency of potassium cyanide gold plating solution is 33%. However, it is well known that due to the many and complex factors that affect the cathode current efficiency of gold plating solution, the actual cathode current efficiency is <33%. t = S ρ d / CI η k (Formula C) The specific parameters and conditions of Example 1 and Example 2 are shown in Table 1: Table 1

[0079] First, according to the various conditions in Table 1, the electronic plating module 320 is assembled, and according to the current density and plating time of Example 1 and Example 2 shown in Table 2, the corresponding predicted coating film thickness is calculated according to Formula C. d 预测值 It indicates that when it is necessary to predict the coating thickness of 309nm≥300nm, the electroplating time of Example 1 and Example 2 is as shown in Table 2.

[0080] Table 2

[0081] Further, according to the current density and predicted electroplating time conditions of the embodiments 1 and 2, the electronic electroplating module 320 is used to Figure 1 The semiconductor device 200 is subjected to gold plating, and the semiconductor device 200 has a total of 58 independent electroplating areas 20, and the electroplating area of ​​each area is the same. The actual semiconductor device 200 obtained by electroplating is used to actually test the coating film thickness.

[0082] Furthermore, the plating thickness test method of the semiconductor device 200 after electroplating is based on Figure 2 The five test points marked are the central black points of the electroplating area 20. The semiconductor device 200 is electroplated using an electronic electroplating device module in a jetting manner to obtain the actual coating film thickness. d 实测值 The results are shown in Table 3.

[0083] Table 3

[0084] It can be seen from Table 3 that the actual coating film thickness test values ​​of Example 1 and Example 2, 280.8nm and 276.4nm, are lower than the minimum threshold of 285nm, and therefore do not meet the coating film thickness threshold determination module 330 restriction of Formula D, and the obtained data cannot be included in the simulation model database.

[0085] Set the measured coating thickness d 实测值 The specified film thickness of semiconductor devices is ≥300nm, and the predicted value of coating film thickness d 预测值 The following conditions must be met: Figure 3 The following restrictions are imposed on the coating thickness threshold determination module 330 in the machine learning simulation model shown: 300nm (100%-5%) ≤ d 预测值 ≤300nm (100%+5%) 285nm≤ d 预测值 ≤315nm The general formula can be summarized as: d 实测值 (100%-5%)≤ d 预测值 ≤ d 实测值 (100%+5%) (Formula D) That is, only the predicted coating thickness value between the minimum threshold of 285 nm and the maximum threshold of 315 nm described in Formula D can be input into the database for constructing the coating thickness threshold determination module 330 .

[0086] It can be seen from Table 3 that the actual coating film thickness test values ​​of Example 1 and Example 2, 280.8nm and 276.4nm, are lower than the minimum threshold of 285nm, and therefore do not meet the coating film thickness threshold determination module 330 restriction of Formula D, and the obtained data cannot be included in the simulation model database.

[0087] Further, from Formula C and the electroplating conditions in Table 1, it can be seen that during the electroplating process, the cathode current efficiency of the electroplating solution is or k It is a concentrated reflection of all influencing factors of the electronic electroplating device module system. Therefore, under the condition that the electroplating time remains unchanged, the actual current efficiency of Example 1 is 30% less than the current efficiency used in the prediction, and the actual current efficiency of Example 2 is 30% less than the current efficiency used in the prediction.

[0088] Furthermore, from the actual electroplating results of Example 1 and Example 2, it can be seen that the cathode current efficiency cannot be exactly the same due to the different current densities used. Therefore, the error between the predicted coating thickness and the measured coating thickness needs to be increased by increasing the electroplating time to achieve the predicted coating thickness that satisfies the formula D. d 预测值 restriction requirements.

[0089] The error between the predicted coating thickness and the measured coating thickness in Example 1 = 300nm - 280.8nm = 19.2nm; Furthermore, the film thickness difference of 19.2 nm is calculated again using formula C, and the required electroplating time is 3.1 sec, that is, the corrected electroplating time of Example 1 is: 35+3.1 sec=38.1 sec; Similarly, the error of Example 2 = 300nm-276.4nm=21.6nm; the required electroplating time is 1.9sec, that is, the corrected electroplating time of Example 2 is: 21+1.9sec=22.9sec; Furthermore, the corrected electroplating time is shown in Table 4.

[0090] Table 4

[0091] According to the same conditions and processing methods of the first embodiment 1 and embodiment 2, the second measured film thickness data of embodiment 1 and embodiment 2 are shown in Table 5.

[0092] Table 5

[0093] It can be seen from Table 5 that through the adjustment of the electroplating time, for the predicted coating film thickness of 300nm, the actual coating film thickness values ​​of 301.2 and 302.2nm in Example 1 and Example 2 are within the range of the minimum threshold of 285nm and the maximum threshold of 315nm described in Formula D. Therefore, the electroplating conditions of the modified Example 1 and Example 2 meet the coating thickness calculation module 360 ​​for constructing a double-sided local predicted coating film thickness for machine learning, and the actual experimental data is imported into the memory for storage.

[0094] Furthermore, in order to screen the preferred range of coating film thickness variation with current density, Example 3 is set. Example 3 needs to adopt the same 38.1sec predicted coating film thickness as Example 1, and needs to adopt the same electroplating method as Example 1 to conduct the electroplating experiment. The experimental conditions of Example 3 are shown in Table 6.

[0095] Table 6

[0096] Furthermore, according to the experimental conditions in Table 6, the semiconductor device 200 prepared by electroplating in Example 3 is tested by the same coating thickness testing method as in Example 1, and the coating thickness data obtained is shown in Table 7.

[0097] Table 7

[0098] It can be seen from Table 6 that the predicted coating thickness of Example 3 is 570nm. According to Formula D, its minimum threshold is 541.5nm and its maximum threshold is 598.5nm; further, the actual film thickness experimental average value calculated from Table 7 is 567.6nm, so the error between the predicted value and the test value is only 570-567.6=2.4nm, which has excellent accuracy; at the same time, the actual film thickness experimental average value of Example 3 is 567.6nm, which is close to the center between the minimum threshold of 541.5nm and the maximum threshold of 598.5nm, and the result satisfies the coating thickness calculation module 360 ​​for constructing a double-sided local prediction of coating thickness for machine learning, and imports the actual experimental data into the memory for storage.

[0099] Furthermore, all the electroplating parameters of Example 1 and Example 3, and the corresponding coating film thickness data, are subjected to deep original acid analysis by the training module 340, the stability generation module 350, and the coating thickness calculation module 360 ​​of the machine learning simulation model, and then to accuracy verification by the model morphology discrimination module 370. If the accuracy verification requirements are met, it is Yes, and all the data are imported into the memory 380 for backup and storage; if the accuracy verification requirements are not met, it is No, and the training module 340 is returned to the next cycle for processing until the accuracy verification requirements are met.

[0100] In short, the experimental data of Example 1 and Example 3 are all obtained through deep analysis and data calculation of the machine learning simulation model, and the better simulation experimental results are obtained by organically integrating the experimental data and the simulated quantitative data; Taking the electroplating time as 38.1 sec as a benchmark, the simulation quantification experimental results of deriving the simulation data, namely, the process of the scatter point trend of the local gold plating film thickness distribution on both sides, will be described in detail below.

[0101] First, under the condition that the electroplating time remains unchanged, formula C is transformed into: I / S = ρ d / t C η k I / S = A (Ampere / dm 2 ) A = ρ d / t C η k d = A hh = t C h k / p (Formula C-2) In formula C-2, specific gravity, plating time and C are known constants, and the plating efficiency or k are variables with known ranges, so all constants are expressed as h Expressed as, we get the simplified formula C-2, that is, the current density A (Ampere / dm 2 ) and coating thickness d mutual relationship.

[0102] The experimental data of Example 1 and Example 3 are analyzed in depth by the coating thickness calculation module of the machine learning simulation model to derive the simulation quantitative experimental results of the fusion of simulation data and experimental data. The specific parameters are shown in Table 8. The derived model is as follows Figure 4 shown.

[0103] Table 8

[0104] The invention is constructed as Figure 4 The applied machine learning simulation model shown is used to perform in-depth analytical calculations on the coating thickness of the machine learning simulation model under the electronic electroplating gold plating conditions set in Example 1 and Example 3, and obtain simulated quantitative experimental results, that is, the scatter point trend morphology of the coating thickness distribution that effectively plates the metal to the local double-sided surfaces of the semiconductor device.

[0105] from Figure 4It can be seen that the distribution scatter plot of the coating thickness of the double-sided local coating thickness electronic electroplating module based on the machine learning simulation model is a parabola that gradually rises with the increase of current density; when the current density is 5-50A / dm 2 The coating thickness in the range shows a rapid upward trend, exceeding 50A / dm 2 Then it rises slowly, 60A / dm 2 After that, it began to show a downward trend. This change reflects the cathode current efficiency in formula C-2. or k As the current density A increases, its efficiency decreases accordingly; that is, the current density is relatively low <5A / dm 2 The cathode current efficiency or k 底 Approaching current density 5~50A / dm 2 Regional or k 中 Average value, 51~70A / dm 2 Regional or k 高 The average is lower than or k 中 Average value; therefore, the current density is 5~50A / dm 2 Regional or k 中 The average value is the electronic plating condition in the best area in terms of efficiency in forming the coating film thickness.

[0106] from Figure 4 It can be further known that the current density of Example 1 is 7A / dm 2 and 15A / dm in Example 3 2 The measured values ​​are consistent with the simulated quantization experimental results derived from the deep analysis and calculation of the machine learning simulation model, which proves that the machine learning simulation model constructed by the present invention has good accuracy.

[0107] In summary, Figure 4 It can be seen that the simulation quantitative experimental results obtained by the in-depth analysis of the coating thickness calculation module of the machine learning simulation model are comparable to the 7A / dm 2 ~15A / dm 2 The actual test results of the electronic plating modules in the range have shown good accuracy.

[0108] Furthermore, in order to optimize and improve the matching performance in a wider current density area, the 20A / dm2 、50A / dm 2 and 70A / dm 2 Current density conditions, actual electroplating tests of Implementation 4 to Implementation 6 were carried out using an electronic electroplating module, and the specific conditions are shown in Table 9.

[0109] Table 9

[0110] Furthermore, according to the electronic electroplating conditions shown in Table 9, the electroplating test was carried out through the electronic electroplating module, and the actual test film thickness data obtained are shown in Table 10.

[0111] Table 10

[0112] From the actual test coating data of Examples 4 to 6 in Table 10, Figure 5 In the figure, ー is used to represent the coating thickness value ● predicted by the machine learning simulation model of the present invention, and the comparison results are shown in Table 11.

[0113] like Figure 5 As shown in the figure, the distribution scatter plot of the coating thickness of the double-sided local coating thickness electronic electroplating module based on the machine learning simulation model is a parabola that gradually rises with the increase of current density; when the current density is 5-50A / dm 2 The coating thickness in the range shows a rapid upward trend, exceeding 50A / dm 2 Then it rises slowly, 60A / dm 2 It then began to show a downward trend. Figure 4 The overall trend is similar.

[0114] Further, by Figure 5 It can be seen that Examples 4 to 6 extract the current density 20A / dm in the machine learning simulation model database 2 , 50A / dm 2 and 70A / dm 2 conditions, and Figure 4 The current density of the extracted examples 1 and 3 is 7A / dm 2 15A / dm 2 and 70A / dm 2 Compared with the conditions of the current density, the range of current density selection is wider. Therefore, the coating thickness calculation module of the machine learning simulation model is used to obtain the coating thickness change trend with the current density. Figure 5 It is closer to the measured value obtained by the electronic electroplating module; that is, the more measured data, the more the obtained coating thickness changes with the current density after being imported into the machine learning simulation model processing system of the present invention. Figure 5 The more accurate.

[0115] See Table 11: Table 11

[0116] According to the standard discrimination module of the machine learning simulation model of the present invention, the predicted value must satisfy the range of formula D; d 实测值 (100%-5%)≤ d 预测值 ≤ d 实测值 (100%+5%) (Formula D) From Table 11, we can see that at current densities of 20, 50 and 70 A / dm 2 Under the conditions of , the predicted double-sided local coating film thickness value based on the machine learning simulation model not only meets the standard judgment range of formula D, but the errors between the predicted value and the measured value are only 1.8, -2.8 and 4nm, respectively, which fully demonstrates the prediction accuracy of the machine learning simulation model constructed by the present invention.

[0117] Optimization of coating thickness and electroplating time by building a machine learning simulation model: In the simulation model for predicting the local double-sided coating thickness constructed by the aforementioned coating film thickness and current density, although the optimization results of the coating film thickness and current density of the machine learning simulation model were obtained under the premise of fixed electroplating time, that is, the constructed model of the relationship between the two already has good accuracy; however, due to the actual electroplating data of only 38.1 seconds, the dependency between the coating film thickness and the electroplating time in the database of the machine learning simulation model needs to be further optimized to improve and obtain a simulation model with more accurate prediction of the local double-sided coating thickness.

[0118] The formula C is rearranged as follows to obtain the electroplating time: t With current density A Formula C-3: t = S ρ d / CI η k I / S = A (Ampere / dm 2 ) t = ρ d / CA η k S / I = 1 / A t = d H / AH = ρ / C η k (Formula C-3) In formula C-3, the specific gravity of the electroplating solution, the electroplating time, and C are known constants. or kare variables with known ranges, so all constants are expressed as h、H Expressed as, the simplified formula C-3 is obtained, that is, the plating time t , coating thickness d and current density A (Ampere / dm 2 ) between them; H is a variable constant as shown in the formula.

[0119] Formula C-3 is used to construct an optimization method for a film thickness calculation module of a machine learning simulation model of the present invention in which the coating thickness varies with the electroplating time.

[0120] First, the actual electroplating time in the database of the predicted double-sided local coating thickness based on the machine learning simulation model of the present invention is 38.1 sec. Figure 4 The following steps, as mentioned above, the measured coating thickness corresponding to the electroplating time of 38.1 sec meets the requirements of the coating thickness threshold determination module 330, and further passes through the simulated depth analysis operation of the training module 340, the stability generation module 350, and the coating thickness calculation module 360, and is selected and selected by the model morphology determination module 370, and the data that meets the model construction is stored in the memory 380; and so on, the simulation calculation results of the double-sided local coating thickness predicted by the model are shown in Tables 12 and 13. Figure 6 shown.

[0121] Table 12

[0122] Depend on Figure 6 From the scatter plot of double-sided local gold-plated film thickness versus electroplating time shown, it can be seen that the simulation calculation results of the double-sided local coating film thickness predicted by the machine learning simulation model show an arc-shaped upward trend, forming a model morphology with good distribution.

[0123] In order to further optimize and improve the simulation results and make them closer to the actual measured value of the gold-plated film thickness, the plating time conditions of 20sec, 50sec and 70sec are preferably used based on the prediction of the machine learning simulation model, and the actual plating tests of Examples 7 to 9 are carried out through the electronic plating module 320. The specific plating conditions are shown in Table 13.

[0124] Table 13

[0125] Furthermore, the electroplating test was carried out by the electronic electroplating module, and the actual test film thickness data obtained are shown in Table 14 and Figure 7 shown.

[0126] Table 14

[0127] The simulation calculation results of the double-sided local coating film thickness predicted by the model shown in Table 12, that is, the comparison results between the predicted coating film thickness values ​​for electroplating time of 20 sec, 50 sec and 70 sec and the actual tested coating values ​​of Examples 7 to 9, are shown in Table 15.

[0128] Table 15

[0129] Note: According to the standard discrimination module of the machine learning simulation model of the present invention, the predicted value must meet the range of formula D; d 实测值 (100%-5%)≤ d 预测值 ≤ d 实测值 (100%+5%) (Formula D) It can be seen from Table 15 that in Examples 7 to 9, under the selected electroplating times of 20 sec, 50 sec and 70 sec, the simulation calculation results of the double-sided local coating film thickness obtained based on the model prediction are all lower than the experimental test coating values, which are -15.4nm, -47.2nm and -27.2nm respectively; each of the predicted values ​​is within the minimum threshold and maximum threshold range calculated by Formula D, and can be used to predict the double-sided local coating film thickness.

[0130] Furthermore, the electroplating conditions and measured values ​​of coating film thickness obtained in Examples 6 to 9 are all imported into the machine learning simulation model, and through the simulated deep analysis operation of the training module 340, the stability generation module 350, and the coating thickness calculation module 360, and after screening by the model morphology discrimination module 370, the data that meets the requirements for building the model is stored in the memory 380; the model that fails to meet the model morphology returns to the training module 340 and repeats the above steps again, and so on, so as to make the model morphology more perfect and achieve better prediction accuracy of the machine learning simulation model.

[0131] Furthermore, by Figure 7 The simulation results of the predicted double-sided local coating thickness with plating time of 10 sec and 60 sec are selected, and the current density is the same as 30 A / dm 2 , the electroplating test is carried out by the electronic electroplating module 320, and then the electroplating conditions and the corresponding coating film thickness are adjusted according to Figure 3 The process is simulated and operated to realize the method for constructing the predicted double-sided local coating film thickness based on the machine learning simulation model of the present invention.

[0132] In general, according to the above-mentioned embodiments 1-9, the present invention can continuously optimize and improve the predicted coating film thickness data extracted from the machine learning simulation model database by importing the coating film thickness experimental data generated by the electronic plating module during the electroplating process under different electronic plating conditions. The more coating film thickness experimental data actually tested by the electronic plating module, the closer the predicted coating film thickness data obtained after model training and improvement fed back to the simulation model is to the actual measured value; the optimal electronic plating production conditions for various semiconductor devices with different structures can be quickly established, the electronic plating conditions can be accurately managed, the electroplating production efficiency can be improved, the amount of precious metals used can be greatly reduced, and the uniformity of the coating film thickness and the high performance quality can be effectively improved.

[0133] In summary, the method for constructing a predicted double-sided local coating film thickness based on a machine learning simulation model of the present invention extracts the electronic plating conditions associated with the predicted coating film thickness in the model database through the double-sided local coating film thickness prediction system and the LR logistic regression operation system, and uses the electronic plating conditions for the electronic plating module to obtain the actual coating film thickness value, and further imports the actual coating film thickness value into the machine learning simulation model. The prediction coating film thickness system and the logistic regression operation system of the simulation model perform training simulation processing on the threshold relationship between the predicted coating film thickness and the actual coating film thickness, thereby realizing the method for constructing a predicted double-sided local coating film thickness based on a machine learning simulation model.

[0134] First, the current density and coating film thickness of the machine learning simulation model are optimized by extracting the electronic plating conditions corresponding to the predicted film thickness. Under the condition that the plating time remains unchanged, the current density is used as the only variable, and the coating film thickness data is actually tested using the electronic plating module. The measured film thickness data are processed by the predicted double-sided local coating film thickness system and the LR logistic regression operation system to realize the optimization model of current density and coating film thickness. It can be seen from the actual operation results that the more coating film thickness data tested under the actual current density conditions, the more accurate the optimization model of current density and coating film thickness of the simulation model is.

[0135] Secondly, the optimization of the electroplating time and the coating film thickness of the machine learning simulation model is carried out by extracting the electronic electroplating conditions corresponding to the predicted film thickness. Under the condition of constant current density, the electroplating time is used as the only variable. The electronic electroplating module is also used to actually test the coating film thickness data. The measured film thickness data is processed by the predicted double-sided local coating film thickness system and the LR logistic regression operation system. The predicted coating film thickness realizes the optimization model of the electroplating time and the coating film thickness under the condition of satisfying the threshold range. It can also be seen that the more electroplating time data tested by the electronic electroplating module, the more the measured coating film thickness data obtained are fed back and applied to the training model operation processing, and the more accurate the optimization model of the current time and coating film thickness of the obtained simulation model is.

[0136] Furthermore, the induction parameters related to the electronic electroplating module of the machine learning simulation model, for example, the electroplating mold size, the type and size of the electrolytic anode, can also be optimized through the method for constructing a method for predicting the double-sided local coating film thickness based on the machine learning simulation model of the present invention, so as to obtain an optimization model of the electroplating mold size, the type and size of the electrolytic anode and the coating film thickness, thereby improving and perfecting the electroplating mold size, the type and size of the electrolytic anode, and achieving the purpose of obtaining better coating film thickness distribution performance and high performance quality.

[0137] In summary, the method for constructing a prediction method for double-sided local coating film thickness based on a machine learning simulation model of the present invention can quickly establish the optimal electronic electroplating production conditions for various semiconductor devices with different structures through the comprehensive calculation and processing of the double-sided local coating film thickness prediction system and the LR logistic regression calculation system, and then obtain the optimal double-sided local electronic electroplating control method for the plated parts. It can not only achieve the accuracy of predicting the double-sided local coating film thickness of semiconductor devices, greatly reduce the error with the actual coating film thickness of electroplated products, but also achieve further improvement of the electronic electroplating mold, promote the improvement of the uniformity of the double-sided local coating film thickness of semiconductor devices, and meet the high quality requirements of semiconductor devices.

[0138] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Anyone familiar with this technology can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be based on the definition of the claims.

Claims

1. A method for predicting the thickness of double-sided local coatings based on a machine learning simulation model, characterized in that: By importing the experimental data of coating thickness generated by the electronic plating module in the electroplating process under different electronic plating conditions, the machine learning simulation model is improved by predicting the double-sided local coating thickness system and building an LR logistic regression model. According to the results of continuous training of the LR logistic regression model, the coating thickness prediction data condition group is obtained, which specifically includes the following steps: S1: constructing a database based on electronic plating conditions and constructing an initial machine learning simulation model linked to the database; setting the database in a memory; S2: extract at least two sets of electronic plating conditions from the database, and predict the double-sided local plating film thickness through the prediction calculation module in the double-sided local plating film thickness prediction system; use the electronic plating module to perform actual plating operation on the semiconductor device according to the extracted electronic plating conditions, and import the obtained plating film thickness experimental data into the plating film thickness threshold judgment module; S3: Predict the thickness of the local coating on both sides d 预测值 Comparison with target threshold: When predicting the local coating thickness on both sides d 预测值 When formula D is satisfied, the LR logistic regression model is entered; The predicted coating thickness that does not meet the target threshold d 预测值 Cannot enter the training module, and the electronic plating conditions extracted from the database in S2 are based on the measured coating thickness value d 实测值 Make corrections and calculate the corrected electronic plating conditions, then return to S2 to re-measure the coating thickness. d 实测值 , and re-determine and correct the predicted double-sided local coating thickness after electronic plating d Whether the predicted value meets the threshold range until the local coating thickness on both sides is predicted d 预测值 When formula D is satisfied, the LR logistic regression model is entered; The predicted double-sided local coating thickness is calculated using all the predicted double-sided local coating thicknesses that satisfy formula D. d 预测值 To build the LR logistic regression model; The formula D associated with the target threshold is: d 实测值 （100%-5%）≤ d 预测值 ≤ d 实测值 （100%+5%） S4: Predict the thickness of the local coating on both sides d 预测值 And the measured value of electronic plating module d 实测值 Importing a training module in an LR logistic regression operation system, and performing system training through the LR logistic regression operation system, wherein the LR logistic regression operation system includes a training module, a stability generation module, and a coating film thickness calculation module; S5: according to the coating film thickness result obtained by S4, the model morphology is judged and compared with the target threshold value. If the target threshold value is reached, it is judged that the electronic electroplating condition is optimized, and the optimized electronic electroplating condition is applied to the production commissioning of the electronic electroplating device; If the target value is not reached, the set of training electronic plating conditions is discarded and the training is returned to S4 for retraining.

2. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 1, characterized in that: The initial machine learning simulation model includes: a processor, a memory, an electronic electroplating module, a prediction calculation module and a coating film thickness threshold judgment module connected to the electronic electroplating module, a set partitioning module, and a training module, a stability generation module, a coating thickness calculation module, and a model morphology judgment module connected in sequence.

3. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 2, characterized in that: In S1-S2, in the process of constructing the initial machine learning simulation model linked to the database, COMSOL Multiphysics finite element simulation software is used in the prediction calculation module and the electronic electroplating module, and formula C-2 is used as the calculation basis to simulate the local double-sided electronic electroplating process of the semiconductor device according to the prediction conditions calculated by formula C-2; the formula C-2 is: d = CI t η k / S ρ in, A (Ampere / dm 2 ) = I / S A = ρ d / t C η k d = A hh = t C η k / ρ In formula C-2, d is the thickness of the electroplating layer; C is the electrochemical equivalent; I is the current intensity; t is the electroplating time; η k is the cathode current efficiency; S is the surface area of ​​the plating area; ρ is the metal density of the electroplating layer; A is the current density; In the above-mentioned S3, the corrected electronic plating conditions are predicted and calculated by formula C-2.

4. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 3, characterized in that: The prediction conditions include current density and electroplating time.

5. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 4, characterized in that: In S3, satisfying the target threshold means predicting the local coating thickness on both sides. d 预测值 It is between the minimum threshold value and the maximum threshold value, the minimum threshold value is -5% of the coating specification value, and the maximum threshold value is +5% of the coating specification value.

6. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 5, characterized in that: The LR logistic regression model is composed of sensitive condition parameter modeling, and the sensitive condition parameters include the type of electroplating solution; the temperature of the electroplating solution; the specific gravity of the electroplating solution; Diameter of the pipeline for conveying electroplating solution; Type of electroplating power supply; Current intensity; Electroplating time; Cathode current efficiency; surface area of ​​plating area; metal density of electroplating layer; current density; electroplating solution flow rate.

7. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 6, characterized in that: When COMSOL Multiphysics finite element simulation software is used in the electronic electroplating module, the influencing factors of the machine learning simulation model for predicting the thickness of the double-sided local coating are composed of sensitive parameters and sudden feeling parameters. The sudden feeling parameters include the size of the plating tank in the electronic electroplating module, the pump power for delivering the electroplating solution, the power of the electroplating power supply, the size of the electroplating mold, and the type and size of the electrolytic anode.

8. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 1, characterized in that: In S4, further training of the initial LR logistic regression model uses a logistic regression algorithm to construct an equation group operation, and constructing a logistic regression model specifically includes the following steps: Set continuous random variable X The logistic distribution means X It has the following distribution and density functions: Equation 1: Equation 2: In equation 1 and equation 2, μ is a positional parameter, γ is the shape parameter; When the position parameter μ Approaches zero, γ = 1, we get the common Sigmoid curve: Equation 3: The binomial logistic regression model is introduced, which is a classification model composed of conditional probability P ( Y | X ) represents the form of parameterized logistic distribution; in this case, the random variable X Take it as a real number, random variable Y The value is 1 or 0, and the model parameters are estimated through supervised learning methods; Further defined, the binomial logistic regression model is the following conditional probability distribution: Equation 4: Equation 5: In equation 4 and equation 5, x ∈R n is the input, y∈{0,1}, w ∈R n Yes and b ∈R is a parameter, w is called the weight vector, b is called bias, w x yes w and b The inner product of The weight vector and input vector are expanded and still recorded as w , x , that is: Then, the logistic regression model is expressed as: Equation 6: Equation 7: Next, set the probability of a time odds, which refers to the ratio of the probability of the event occurring to the probability of the event not occurring. If the probability of the event occurring is p , then the probability of the event is: The log odds of the event, log odds or log (log odds) = logit, is expressed as: For logistic regression, the above formula P ( Y = 1 | x )and P ( Y = 0 | x ) can be obtained: Equation 8: According to Equation 8, in the logistic regression model, the output is Y = 1 is the input x A linear function of, or expressed as, the output Y = 1 is given by the input x The model represented by the linear function of constitutes the preliminary logistic regression model; Consider the input x Linear function for classification w · x , its value range w · x ∈R, and x ∈R n+1 , w ∈R n+1 ; The linear function is defined by logistic regression w · x Converted into probability, it is expressed as: Equation 9: When the value of the linear function z = w · x → + ∞, then P ( Y = 1 | x ) → 1; when the value of the linear function z = w · x →- ∞, then P ( Y = 1 | x ) → 0; the resulting graph is the logistic regression model.

9. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 7, characterized in that: The training module in S4 uses the predicted coating thickness parameter calculation that meets the threshold, specifically including the following steps: In S3, for a given training set data T = {( x 1, y 1), ( x 2, y 2)···,( x N , y N )},in, y i ∈{0,1}, the maximum likelihood estimation method is used to predict the model parameters, thus obtaining the iterative logistic regression model. The likelihood function is expressed as: The log-likelihood function is expressed as Equation 10: Calculate Equation 10 L ( w ) maximum value, thus obtaining w The predicted value of w The predicted value represents the coating thickness; for equation 10, the gradient descent method and the Newton-like method are used, setting w The maximum likelihood estimate of is w ∧ , then the learned logistic regression model is: Equation 11: Equation 12: 。 10. The method for predicting the thickness of double-sided local coatings based on a machine learning simulation model according to claim 8, characterized in that: The binomial logistic regression model is only introduced when it is used for binary classification problems; when it is used for multi-classification problems, a multinomial logistic regression model needs to be introduced. The specific steps are as follows: Setting discrete random variables Y The value set of is {1, 2, ···, K }, that is, the category label is K The multinomial logistic regression model obtained by analogy is: Equation 13: Equation 14: Both binomial logistic regression and multinomial logistic regression are widely used classification algorithms. Their principles are based on statistics and probability theory. They model the probability of the first combination of input features, and then use a logistic function to map the linear combination to a probability value between 0 and 1, thereby indicating the probability of belonging to a sample and belonging to a certain category.

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