Method for predicting thickness of cyanide-free electro-coppering coating

Abstract

The invention belongs to the technical field of surface treatment, and discloses a method for predicting the thickness of a cyanide-free electro-coppering coating, which comprises the following steps: step 1, preparing a cyanide-free electro-coppering solution; 2, cyanide-free copper electroplating test parameters are designed, and a test is conducted; 3, the thickness of a cyanide-free copper electroplating coating is obtained according to a cyanide-free copper electroplating test; step 4, establishing a cyanide-free electroplating copper plating layer thickness model; and step 5, performing parameter optimization on the cyanide-free electro-coppering layer thickness model so as to predict the cyanide-free electro-coppering layer thickness according to the parameter-optimized cyanide-free electro-coppering layer thickness model.

Description

Technical Field

[0001] This invention belongs to the field of surface treatment technology, and in particular relates to a method for predicting the thickness of cyanide-free electroplated copper coatings. Background Technology

[0002] Patent KR102317993B1 describes a device and method for predicting coating thickness. This patent describes a device for predicting coating thickness during the coating process. It mainly includes a coating device unit, a unit for detecting and outputting coating solution characteristic information, a main control unit, and a receiving unit. The device uses input information and a neural network algorithm to predict the coating thickness. This patent requires equipment and sensors to predict coating thickness, resulting in a complex structure and high cost.

[0003] Patent CN119089319A describes a method for predicting the thickness of hot-dip galvanized coatings based on a random forest algorithm. This patent utilizes historical data from the hot-dip galvanizing process of producing hot-dip galvanized steel coils to eliminate the time lag of thickness gauges, establishing a random forest network model for coating thickness prediction and training it. This patent improves upon the time lag problem in zinc layer thickness control of galvanized sheets, optimizes process parameter adjustment and thickness target control, but requires relatively accurate prediction of the hot-dip galvanized layer thickness through equipment, sensors, and algorithms. The prediction model in this patent is applicable to hot-dip galvanizing but not to electroplating.

[0004] Patent CN106868440B describes a method for predicting and adjusting the thickness of a continuous hot-dip galvanized steel coating. This patent employs regression analysis to test the coating thickness prediction model, calculates the predicted coating thickness in real time, and determines the air knife adjustment amount based on the hot-dip galvanizing process data and the current target coating thickness. This patent achieves dynamic prediction of coating thickness, ensuring that the coating thickness quickly reaches the target thickness. The prediction model of this patent is applicable to hot-dip galvanizing but not to electroplating. Summary of the Invention

[0005] The technical problem solved by this invention is to address the relationship between current density, plating time, copper ion concentration, and coating thickness in cyanide-free electroplated copper in practical production applications. A predictive method based on modified Faraday's law and multiple regression analysis is proposed to predict the coating thickness of cyanide-free electroplated copper.

[0006] The technical solution of the present invention: a method for predicting the thickness of cyanide-free electroplated copper coating, the method comprising: Step 1: Prepare a cyanide-free copper plating solution; Step 2: Design the experimental parameters for cyanide-free copper electroplating and conduct the experiment; Step 3: Obtain the thickness of the cyanide-free copper plating layer based on the cyanide-free copper plating test; Step 4: Establish a model for the thickness of cyanide-free electroplated copper coating; Step 5: Optimize the parameters of the cyanide-free electroplated copper coating thickness model, and then predict the thickness of the cyanide-free electroplated copper coating based on the optimized cyanide-free electroplated copper coating thickness model.

[0007] Furthermore, step 1 specifically involves: A cyanide-free copper plating solution was prepared, comprising 12-16 g / L basic copper carbonate, 30-60 g / L potassium carbonate, 100-135 mL / L hydroxyethylidene diphosphonic acid, and 0.2-0.8 g / L polyethylene glycol 6000. The solution was prepared at a temperature of 50-65℃ and a current density of 0.8-1.5 A / dm³. 2 The anode is a pure copper plate.

[0008] Furthermore, step 2 specifically involves: The ranges for design current density J, basic copper carbonate concentration C, test temperature T, and test time t are specified. Using the single-variable method, the non-variable parameters are taken as the optimal values ​​within a given range, while the variable parameters are increased from the minimum to the maximum value, thus obtaining a series of data on coating thickness and coating weight.

[0009] Furthermore, step 3 specifically involves: The thickness of the cyanide-free electroplated copper coating was measured using an eddy current thickness gauge. After removing outliers, the average value h was taken. The coating weight was the weight of the sample after electroplating minus the weight of the sample before electroplating.

[0010] Furthermore, step 4 specifically involves: Step 41, establish the equation for current efficiency η: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12) Step 42, obtain h under ideal conditions th Coating thickness formula: Where M is the molar mass of the metal, F is the Faraday constant, and ρ is the density of copper; Step 43: Determine the cyanide-free electroplated copper coating thickness model after using the current efficiency η correction. .

[0011] Furthermore, step 4 also includes: The temperature term is corrected using a temperature correction factor of 1. α(T−T 0 ) , T 0 = 50℃ α =0.008℃ −1 .

[0012] Furthermore, step 4 also includes: The concentration term is corrected using a concentration correction factor of 1. βln(C / C 0 ) , C 0 = 8g / L β =0.08.

[0013] Furthermore, step 4 also includes: The current density term is corrected by a current density correction factor of 1. cJ 2 , c =0.258 A −1 dm 2 .

[0014] Furthermore, the final model for the thickness of cyanide-free electroplated copper coating is as follows: .

[0015] The advantages of this invention are: (1) Through precise model establishment, the coating thickness can be accurately predicted. Compared with the traditional Faraday law which does not consider the temperature-concentration dependence of current efficiency, the prediction deviation is less than 10%.

[0016] (2) Applicable to cyanide-free copper plating process. The relationship between the thickness of cyanide-free copper plating layer and current density and plating time at commonly used temperatures is given.

[0017] (3) Wide range of applications: Existing models are only applicable to fixed parameter ranges and cannot cover a wide range of process conditions. The model established in this invention has a wide range of applications (e.g., J=0.5~1.5 A / dm², t=10~120 min). Detailed Implementation This invention adopts a method of collecting experimental data, establishing a high-precision prediction model based on modified Faraday's law and multiple regression analysis, and supporting a three-level verification system, and then verifying the model to achieve accurate prediction of the thickness of cyanide-free electroplated copper coating in actual production.

[0018] The specific steps are as follows: prepare cyanide-free copper plating solution → design cyanide-free copper plating experiment → collect cyanide-free copper plating thickness data → establish a theoretical framework model for cyanide-free copper plating thickness → optimize the parameters of the theoretical framework model for cyanide-free copper plating thickness → verify the theoretical framework model for cyanide-free copper plating thickness.

[0019] Step 1: Prepare cyanide-free copper plating solution A cyanide-free copper plating solution was prepared, specifically containing 12-16 g / L basic copper carbonate, 30-60 g / L potassium carbonate, 100-135 mL / L hydroxyethylidene diphosphonic acid, and 0.2-0.8 g / L polyethylene glycol 6000. The solution was prepared at a temperature of 50-65℃ and a current density of 0.8-1.5 A / dm³.2 The anode is a pure copper plate (Cu content ≥ 99.9%).

[0020] Step 2: Experimental Design for Cyanide-Free Copper Plating Design parameter range:

[0021] Fixed conditions: 45 g / L potassium carbonate, pH=9.5, stirring speed 350 rpm, anode is pure copper plate (Cu content ≥99.9%).

[0022] A single-variable method was employed, with the non-variable parameter taking its optimal value within a given range, and the variable parameter increasing from its minimum to its maximum value to measure the thickness at 10, 30, 50, 70, 90, and 120 minutes. For example, the basic copper carbonate concentration C was set to 12 g / L, the temperature to 55℃, and the current density increased from 0.8 to 1.5, with thickness and coating weight measured at 10, 30, 50, 70, 90, and 120 minutes respectively. This yielded a series of coating thickness and weight data.

[0023] Step 3: Collect coating thickness and coating weight. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. The sample size was 150×100×1mm. 25 points were measured for each sample. After removing outliers in the coating thickness, the average value h was taken. The coating weight was the weight of the sample after electroplating minus the weight of the sample before electroplating.

[0024] Current efficiency is calculated using a combination of weighing and coulometric measurement, using the following formula:

[0025] In the formula: J Current density (A / dm²) t Time (min) M = 63.55 g / mol F: Faraday constant (96485 C / mol) Based on the actual measured weight of each test piece, the current efficiency... or In the range of 0.80 to 0.95, the current efficiency is established by the equation based on the current density, copper ion concentration and time as η = 0.958 + 0.0006(T-55) - 0.005(J-1.0) - 0.025(J-1.0)² + 0.0015(C-12).

[0026] Step 4: Constructing a Theoretical Framework for Practical Theory Basic Model: The fundamental principle of electroplating thickness prediction is Faraday's law of electrolysis, which states that the amount of electricity passing through the electrode is proportional to the mass of the substance deposited (or dissolved) on the electrode.

[0027] Mass calculation formula:

[0028] in: m: Mass of precipitated metal (g) M: Molar mass of the metal (g / mol), copper is 63.55 g / mol. Q: Total energy (coulombs C), (Current × Time) n: The number of electrons in the electrode reaction. Copper ions reduce Cu²⁺ + 2e⁻ → Cu, therefore n = 2. F: Faraday constant (96485 C / mol) Convert to thickness: Thickness h is mass m divided by density ρ and area A.

[0029]

[0030] Due to current density Substituting (A / dm²) into the above formula, we obtain the thickness formula under ideal conditions:

[0031] In Faraday's law In the middle, h th This is an ideal model that assumes 100% current efficiency, meaning all electrical charge is used for copper deposition. However, in reality, the electroplating process involves side reactions, such as hydrogen evolution (2H⁺ + 2e⁻ → H₂↑), resulting in some current being wasted and the actual amount of metal deposited being less than the theoretical value. Therefore, it is necessary to introduce current efficiency η (η < 1) to correct for this.

[0032] Introducing the current efficiency η, its expression is obtained by fitting experimental data: η = 0.958 + 0.0006(T-55) - 0.005(J-1.0) - 0.025(J-1.0)² + 0.0015(C-12).

[0033] Nonlinear correction: Temperature term: According to the Arrhenius equation, the reaction rate constant has an exponential relationship with temperature, k∝exp(-Ea / RT). This quantitatively describes the effect of temperature on ion migration rate, diffusion rate, and reaction activation energy. As temperature increases, the deposition rate accelerates. Within a relatively small temperature range, it can be linearly approximated, and linearized as follows: α(T−T 0) ; Concentration term: Based on diffusion kinetics theory, the deposition rate on the electrode surface is limited by the ion diffusion rate, while the diffusion flux is proportional to the concentration gradient. This quantitatively describes the effect of the main salt concentration on the deposition rate. Higher concentrations result in greater diffusion driving force and faster deposition rates. The logarithmic form is a commonly used mathematical method for handling this nonlinear relationship; therefore, a logarithmic relationship is employed. βln(C / C 0 ) ; The quadratic term of current density: At high current densities, concentration polarization occurs—the concentration of reacting ions on the electrode surface decreases sharply, becoming the rate-controlling step and leading to a nonlinear decrease in deposition efficiency. This requires compensating for the concentration polarization effect at high current densities to prevent model predictions from deviating too much from measured values ​​in the high current region. J² The term is used to compensate for this higher-order nonlinear effect. It compensates for the concentration polarization effect in the high-current range ( cJ 2 ).

[0034] A high-precision prediction model based on modified Faraday's law and multiple regression analysis, along with a three-level validation system, is established as the basic mathematical model:

[0035] In the formula: h Coating thickness (μm) J Current density (A / dm²) t Time (min) ρ: Density of copper (g / cm³) 3 ) η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12).

[0036] T 0 = 50℃ C 0 = 8g / L α =0.008℃ −1 , β =0.08, c =0.258 A −1 dm 2 F =96485 C / mol r =8.96 g / cm 3 Step 5: Validate the model Extreme condition verification: Case 1: The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±2℃, and the current density is set at 1.0 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The test piece material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 10 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0037] J =1.0A / dm², t =10min, T =55℃, C =12g / L Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12).

[0038]

[0039] predict h =2.924μm, measured 3.232μm, error 9.5%; Case 2: The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±2℃, and the current density is set at 1.0 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The test piece material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 30 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0040] Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12).

[0041]

[0042] J=1.0A / dm², t =30min, T =55℃, C =12g / L predict h =8.774μm, measured 9.18μm, error 4.4%.

[0043] Example 1: Medium-speed electroplating process The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±2℃, and the current density is set at 1.0 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The sample material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 50 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0044] That is, setting parameters: J =1.0A / dm², t =50min, T =55℃, C =12g / L Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12)

[0045] h=14.623 Measured result: 14.136 μm, error 3.4%.

[0046] Example 2: The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±1℃, and the current density is set at 1.0 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The test piece material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 60 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0047] That is, setting parameters: J =1.0A / dm², t =70min, T =55℃, C =12g / L Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12).

[0048]

[0049] Predicted thickness: 20.478 μm Measured value: 19.416 μm, error 5.5%.

[0050] Example 3: Thick Coating Process The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±2℃, and the current density is set at 1.0 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The sample material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 90 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0051] J =1.0A / dm², t =90min, T =55℃, C =12g / L Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12)

[0052] predict h =26.318μm, measured 24.572μm, error 7.1%; Example 4: High Current Density The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±2℃, and the current density is set at 1.5 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The test piece material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 120 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0053] Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12)

[0054] J =1.5A / dm², t =30min, T =55℃, C =12g / L predict h =9.444μm, measured 9.51μm, error 0.7%.

[0055] Example 5: The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±2℃, and the current density is set at 1.5 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The sample material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 90 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0056] parameter: J =1.5A / dm², t =90min, T =55℃, C =12g / L Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12)

[0057] Predicted value: 28.332 μm Measured value: 27.848 μm, error 1.7%.

[0058] Example 6: The cyanide-free copper plating solution specifically contains 12 g / L basic copper carbonate, 45 g / L potassium carbonate, 100~135 mL / L hydroxyethylidene diphosphonic acid, and 0.2~0.8 g / L polyethylene glycol 6000. The temperature is 55±2℃, and the current density is set at 1.5 A / dm³. 2 The pH was 9.5, the stirring speed was 350 rpm, and the anode was a pure copper plate (Cu content ≥ 99.9%). The sample material was 45# steel, with dimensions of 150×100×1mm. The electroplating time was 50 min. The thickness of the cyanide-free electroplated copper coating was measured using a Mini Test 4100 eddy current thickness gauge. 25 points were measured for each sample, and the average value was taken after removing outliers.

[0059] parameter: J =1.5A / dm², t =50min, T =55℃, C =12g / L Model calculation: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12)

[0060] Predicted value: 15.74 μm Measured value: 15.726 μm, error 0.09%.

[0061] This invention's technical solution, through precise model establishment, accurately predicts coating thickness, achieving a prediction deviation of less than 10% compared to traditional Faraday's law, which does not consider the temperature-concentration dependence of current efficiency. It is applicable to cyanide-free copper electroplating processes. The relationship between coating thickness, current density, and electroplating time at commonly used temperatures for cyanide-free copper electroplating is presented. It has a wide applicability range: existing models only apply to fixed parameter ranges and cannot cover a wide range of process conditions. The model established in this invention has a wide applicability range (e.g., J = 0.5~1.5 A / dm², t = 10~120 min).

Claims

1. A method for predicting the thickness of cyanide-free electroplated copper coatings, characterized in that, The method includes: Step 1: Prepare a cyanide-free copper plating solution; Step 2: Design the experimental parameters for cyanide-free copper electroplating and conduct the experiment; Step 3: Obtain the thickness of the cyanide-free copper plating layer based on the cyanide-free copper plating test; Step 4: Establish a model for the thickness of cyanide-free electroplated copper coating; Step 5: Optimize the parameters of the cyanide-free electroplated copper coating thickness model, and then predict the thickness of the cyanide-free electroplated copper coating based on the optimized cyanide-free electroplated copper coating thickness model.

2. The method for predicting the thickness of cyanide-free electroplated copper coating according to claim 1, characterized in that, Step 1 is as follows: A cyanide-free copper plating solution was prepared, comprising 12-16 g / L basic copper carbonate, 30-60 g / L potassium carbonate, 100-135 mL / L hydroxyethylidene diphosphonic acid, and 0.2-0.8 g / L polyethylene glycol 6000. The solution was prepared at a temperature of 50-65℃ and a current density of 0.8-1.5 A / dm³. 2 The anode is a pure copper plate.

3. The method for predicting the thickness of cyanide-free electroplated copper coating according to claim 2, characterized in that, Step 2 is as follows: The ranges for design current density J, basic copper carbonate concentration C, test temperature T, and test time t are specified. Using the single-variable method, the non-variable parameters are taken as the optimal values ​​within a given range, while the variable parameters are increased from the minimum to the maximum value, thus obtaining a series of data on coating thickness and coating weight.

4. The method for predicting the thickness of cyanide-free electroplated copper coating according to claim 3, characterized in that, Step 3 specifically involves: The thickness of the cyanide-free electroplated copper coating was measured using an eddy current thickness gauge. After removing outliers, the average value h was taken. The coating weight was the weight of the sample after electroplating minus the weight of the sample before electroplating.

5. The method for predicting the thickness of cyanide-free electroplated copper coating according to claim 4, characterized in that, Step 4 is as follows: Step 41, establish the equation for current efficiency η: η=0.958+0.0006(T-55)-0.005(J-1.0)-0.025(J-1.0)²+0.0015(C-12) Step 42, obtain h under ideal conditions th Coating thickness formula: Where M is the molar mass of the metal, F is the Faraday constant, and ρ is the density of copper; Step 43: Determine the cyanide-free electroplated copper coating thickness model after using the current efficiency η correction. .

6. The method for predicting the thickness of a cyanide-free electroplated copper layer according to claim 5, characterized in that, Step 4 also includes: The temperature term is corrected using a temperature correction factor of 1. α(T−T 0 ) , T 0 = 50℃ α =0.008℃ −1 .

7. The method for predicting the thickness of a cyanide-free electroplated copper layer according to claim 6, characterized in that, Step 4 also includes: The concentration term is corrected using a concentration correction factor of 1. βln(C / C 0 ) , C 0 = 8g / L β =0.

08.

8. The method for predicting the thickness of a cyanide-free electroplated copper layer according to claim 7, characterized in that, Step 4 also includes: The current density term is corrected by a current density correction factor of 1. γJ 2 , γ =0.258 A −1 dm 2 .

9. The method for predicting the thickness of a cyanide-free electroplated copper layer according to claim 8, characterized in that, The final model for the thickness of cyanide-free electroplated copper is as follows: 。

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