A copper etching solution and a formula optimization method thereof based on COMSOL simulation

Abstract

The application discloses a copper etching liquid and a formula optimization method thereof based on COMSOL simulation, and belongs to the field of etching liquid optimization.The method comprises the following steps: obtaining the formula, ratio, bulk concentration, sample parameter and etching performance data of multiple copper etching liquids, analyzing the relationship between the etching rate of copper and the electrochemical corrosion rate and calibrating the reaction rate constant, and adopting the membrane cell method to measure the diffusion coefficient function corresponding to different copper ion concentrations; based on the reaction rate constant and the diffusion coefficient function, the etching morphology and key parameter value of the copper etching liquid formula are predicted by using the COMSOL etching model, and the electrochemical parameters, mass transfer parameters and geometric parameters required by the target formula are extracted; through etching experiment verification, the copper etching liquid components and the optimal proportion satisfying the target etching profile quality parameters are obtained. The application reconfigures the etching liquid, promotes the performance upgrading and optimization of the product, and thus realizes the formula optimization of the copper etching liquid.

Description

Technical Field

[0001] This application relates to the field of etching solution optimization, and more particularly to a copper etching solution and its formulation optimization method based on COMSOL simulation. Background Technology

[0002] Copper etching solutions are widely used in the panel industry and play a significant role in it. In recent years, driven by the huge demand from downstream consumer electronics products such as TVs, monitors, laptops, tablets, and mobile phones, as well as specialized display products such as commercial displays, automotive displays, industrial control displays, and medical displays, the panel industry has grown in scale and requires more precision. Therefore, the demand for copper etching solutions and the technical requirements have become more stringent.

[0003] The development of existing copper etching solution formulations is mainly based on empirical methods: researchers conduct a large number of beaker experiments by adjusting the components and proportions based on previous research, observe the morphology after etching using scanning electron microscopy, measure parameters such as CDloss and Taper, and repeatedly adjust until a formulation that meets the requirements is obtained.

[0004] Therefore, existing technologies rely entirely on beaker experiments and trial-and-error based on experience, which cannot quantitatively correlate the physicochemical parameters of the etching solution with the etching results. They ignore the multi-physics coupling of mass transfer, reaction kinetics and geometric deformation, and lack effective means to predict and control molybdenum residue and undercut in copper / molybdenum bilayer structures. This results in low development efficiency, long cycle and high cost, making it difficult to meet the needs of the panel industry for refinement and rapid iteration.

[0005] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0006] To overcome the above problems, this application aims to propose a copper etching solution and its formulation optimization method based on COMSOL simulation. The purpose is to solve the problem of lack of effective prediction and control methods for molybdenum residue and undercut in copper / molybdenum bilayer structures, which leads to low development efficiency, long cycle, high cost, and difficulty in meeting the needs of the panel industry for refinement and rapid iteration.

[0007] Therefore, the specific technical solution adopted in this application is as follows: A first aspect of the present invention provides a recipe optimization method based on COMSOL simulation, the method comprising: S1. Obtain the formulation, ratio, bulk concentration, sample parameters and etching performance data of multiple copper etching solutions, analyze the relationship between copper etching rate and electrochemical corrosion rate and calibrate the reaction rate constant, and use the membrane cell method to determine the diffusion coefficient function corresponding to different copper ion concentrations. S2. Based on the reaction rate constant and diffusion coefficient function, the etching morphology and key parameter values ​​of the copper etching solution formulation are predicted using the COMSOL etching model, and the electrochemical parameters, mass transfer parameters and geometric parameters required for the target formulation are extracted. The COMSOL etching model includes: A dilute mass transport module is used to simulate the diffusion and convection transport process of etchants in solution, defining the diffusion coefficient, bulk concentration, and convection and diffusion equations as they vary with ion concentration. In addition, a deformable geometry module is used to describe the movement of the interface between the copper layer and the etchant, which couples the reaction rate with the copper material properties through the normal velocity formula and introduces a mesh re-division mechanism to avoid computational divergence. Furthermore, based on the first-order surface reaction kinetic equation, an electrochemical parameter module containing electrochemical corrosion rate, reaction rate constant, and concentration dependence is constructed; S3. Verify and optimize the electrochemical parameters, mass transfer parameters, and geometric parameters of the target formulation through etching experiments to obtain the copper etching solution composition and optimal ratio that meet the target etching profile quality parameters.

[0008] Optionally, the relationship between the etching rate and electrochemical corrosion rate of copper is analyzed and the reaction rate constant is calibrated, including: At a constant temperature, a copper sample is immersed in the copper etching solution to be tested and shaken at a constant speed for a fixed time. The etching rate is obtained by measuring the change in film thickness and taking the average value to obtain the etching rate data of the current formula. Corrosion current tests were performed on copper electrodes with the same formulation to obtain the corresponding electrochemical corrosion rates; The etching rate and corrosion current density of the same formulation were paired and sorted by etching rate from smallest to largest to verify that the two are positively correlated. Several sets of data within the positive correlation region were selected, and the measured corrosion current density and etching rate data were used as the input basis for calibrating the reaction rate constant in the COMSOL etching model.

[0009] Optionally, the diffusion coefficient function corresponding to different copper ion concentrations is determined using the membrane cell method, including: Clean and dry the membrane tank and diaphragm, calibrate the membrane tank constant using a standard KCl system, and verify the membrane tank constant using an acetic acid solution. Several etching solutions with different initial copper ion concentrations were prepared as concentrated solutions, and after injecting an equal volume of deionized water into the dilute solutions, they were respectively loaded into the upper and lower chambers of the membrane pool. After the membrane tank is kept at the target temperature, stirring is started. Samples are taken from the upper and lower chambers of the membrane tank at fixed time intervals, and the copper ion concentration is measured to obtain the concentration in the concentrated chamber and the concentration in the dilute chamber. Based on the membrane pool constant, single-chamber volume, and effective membrane area, the diffusion coefficient corresponding to each initial concentration is calculated, and the diffusion coefficient function as a function of copper ion concentration is obtained. The calculation process of the diffusion coefficient is as follows:

[0010] In the formula, Indicates the diffusion coefficient; Represents the membrane pool constant; Indicates the volume of a single chamber in the membrane tank; This indicates the effective diffusion cross-sectional area of ​​the diaphragm; Indicates the initial copper ion concentration in the concentration chamber; Indicates the initial copper ion concentration in the dilute chamber; Indicates the concentration chamber in time t The concentration of copper ions at that time; Indicates the rarefaction chamber in time t The concentration of copper ions at that time; Indicates diffusion time.

[0011] Optionally, the rare matter transport module includes: Define the concentration variable of the etchant and add dilute substances to transfer the physical field; In the material property node, the diffusion coefficient is set as a function of the copper ion concentration, and the change of the concentration field is controlled by the convection and diffusion equations. In the initial value node, the initial concentration is set to be equal to the bulk concentration, and a constant bulk concentration is applied at the far field boundary as the mass supply boundary for the etchant. A first-order reaction consumes etchant on the surface of the copper layer, forming a concentration gradient from the bulk to the surface, driving diffusion and convection mass transfer; The expressions for the convection and diffusion equations are as follows:

[0012] In the formula, This indicates the rate of change of concentration over time; This indicates the concentration of the etchant in the solution; Indicates time; Indicates the convection velocity of the fluid; Convection velocity indicating concentration; This represents the diffusion coefficient of the etchant in solution; This represents the divergence operator.

[0013] Optionally, the deformable geometry module includes: Add a free deformation node in the deformable geometry module, and select the boundary where the copper layer contacts the etchant as the moving boundary; In the boundary displacement settings of the moving boundary, select the normal displacement mode, and enter the negative surface reaction rate, copper molar mass and copper density in the expression input field to obtain the normal moving velocity. The boundary is driven to move inward over time using the normal movement velocity, while enabling moving mesh smoothing and mesh re-meshing mechanisms, and setting automatic re-meshing when mesh deformation exceeds a threshold.

[0014] Optionally, in the deformation geometry module, by inputting a negative surface reaction rate, copper molar mass, and copper density in the expression input field for boundary displacement settings, the normal migration velocity of the interface between the copper layer and the etching solution is calculated, and its expression is:

[0015] In the formula, This indicates the normal velocity of the interface between the copper layer and the etching solution. Indicates the surface reaction rate; Indicates the molar mass of copper; This indicates the density of solid copper.

[0016] Optionally, the electrochemical parameter module includes: Define the surface reaction rate constant and correlate the surface reaction rate constant with the electrochemical corrosion rate in the electrochemical parameter settings; The surface reaction rate constant is input into the surface reaction node on the copper layer surface boundary in the dilute mass transport module, and a first-order surface reaction kinetic equation is selected to establish a linear relationship between the surface reaction rate and the interface concentration. Based on the first-order kinetic equation, the value of the reaction rate constant is set as a function of concentration or temperature, and the dependence of the reaction rate on the interface concentration is controlled. In the case of electrochemical etching, the equilibrium potential, exchange current density and Tafel coefficient are set, and electrode potential or current density conditions are applied at the electrode boundary.

[0017] Optionally, by inputting the surface reaction rate constant and interface concentration at the surface reaction node on the copper layer surface boundary of the dilute mass transport module in the electrochemical parameter module, a first-order surface reaction kinetic equation is obtained, the expression of which is:

[0018] In the formula, Indicates the surface reaction rate; This represents the forward reaction rate constant; This indicates the local concentration of the etchant at the interface.

[0019] Optionally, obtaining the copper etching solution composition and preferred ratio that meet the target etching profile quality parameters includes: Copper etching solution samples were prepared according to the target formulation parameters, and their electrochemical corrosion rate, diffusion coefficient function and bulk concentration were tested. The copper and molybdenum bilayer sample was immersed in the prepared etching solution and shaken at a constant temperature for a fixed time to complete the etching process. The cross-sectional morphology of the etched sample was observed using scanning electron microscopy, and the key dimensional losses, cone angle, undercut depth, and molybdenum layer residue were measured. The morphological parameters are compared with the quality parameters of the target etched profile; If the preset requirements are met, record the current electrochemical parameters, mass transfer parameters, and geometric parameters. If the conditions are not met, the surface reaction rate constant, diffusion coefficient function, or geometric dimensions in the model are adjusted according to the deviation, and a new formula is re-predicted and prepared. When all morphological parameters meet the target requirements, the composition and preferred ratio of the copper etching solution are determined.

[0020] In a second aspect, the present invention provides a copper etching solution, wherein, as determined by the above-described formulation optimization method, the copper etching solution comprises the following components in parts by weight: 3-8 parts hydrogen peroxide, 1-2 parts phosphoric acid, 6-20 parts citric acid, 3-5 parts succinic acid, 1-2 parts ammonium bifluoride, 3-5 parts 3-diethylaminopropylamine, 4-6 parts isopropanolamine, 4-6 parts 2-amino-2-methyl-1-propanol; the balance being pure water.

[0021] Compared with existing technologies, this application has the following advantages: This application builds a Comsol etching model for copper etching solution, uses the main properties and kinetic parameters of copper etching solution to perform high-precision simulation of the etching process, and re-adjusts the etching solution to promote the performance upgrade and optimization of the product, thereby achieving the optimization of the copper etching solution formula; moreover, the entire R&D process is targeted, avoids a large number of experimental verifications, greatly shortens the R&D cycle, and also reduces the consumption of human, material and financial resources. Attached Figure Description

[0022] The above-mentioned features, characteristics, and advantages of this application, as well as their implementation methods, will become clearer and more understandable in conjunction with the following description of the embodiments, which are illustrated in detail with reference to the accompanying drawings. Schematic diagrams are shown here: Figure 1 This is a flowchart of the formulation optimization method based on COMSOL simulation in this application; Figure 2 This is a graph showing the relationship between the corrosion current and the etching rates of copper and molybdenum in the formulation optimization method of this application. Figure 3 This is a conceptual diagram of the COMSOL etching model for the formulation optimization method in this application; Figure 4 This is a model diagram output from the COMSOL etching model in this application; Figure 5 This is a scanning electron microscope (SEM) schematic diagram of the sample etched by the optimized copper etching solution in this application. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0024] This embodiment provides a COMSOL-based formulation optimization method. By building a COMSOL etching model for the copper etching solution, and utilizing the main properties and kinetic parameters of the copper etching solution to perform high-precision simulation of the etching process, the etching solution can be re-formulated to promote product performance upgrades and optimizations, thereby achieving formulation optimization of the copper etching solution. Figures 1-5 As shown, the method includes: We obtained the formulation, ratio, bulk concentration, sample parameters and etching performance data of multiple copper etching solutions, analyzed the relationship between copper etching rate and electrochemical corrosion rate and calibrated the reaction rate constant, and used the membrane cell method to determine the diffusion coefficient function corresponding to different copper ion concentrations.

[0025] Preferably, the analysis of the relationship between the etching rate and the electrochemical corrosion rate of copper and the calibration of the reaction rate constant include: At a constant temperature, a copper sample is immersed in the copper etching solution to be tested and shaken at a constant speed for a fixed time. The etching rate is obtained by measuring the change in film thickness and taking the average value to obtain the etching rate data of the current formula. Corrosion current tests were performed on copper electrodes with the same formulation to obtain the corresponding electrochemical corrosion rates; The etching rate and corrosion current density of the same formulation were paired and sorted by etching rate from smallest to largest to verify that the two are positively correlated. Several sets of data within the positive correlation region were selected, and the measured corrosion current density and etching rate data were used as the input basis for calibrating the reaction rate constant in the COMSOL etching model.

[0026] Preferably, the determination of the diffusion coefficient function corresponding to different copper ion concentrations using the membrane cell method includes: Clean and dry the membrane tank and diaphragm, calibrate the membrane tank constant using a standard KCl system, and verify the membrane tank constant using an acetic acid solution. Several etching solutions with different initial copper ion concentrations were prepared as concentrated solutions, and after injecting an equal volume of deionized water into the dilute solutions, they were respectively loaded into the upper and lower chambers of the membrane pool. After the membrane tank is kept at the target temperature, stirring is started. Samples are taken from the upper and lower chambers of the membrane tank at fixed time intervals, and the copper ion concentration is measured to obtain the concentration in the concentrated chamber and the concentration in the dilute chamber. Based on the membrane pool constant, single-chamber volume, and effective membrane area, the diffusion coefficient corresponding to each initial concentration is calculated, and the diffusion coefficient function as a function of copper ion concentration is obtained. The calculation process of the diffusion coefficient is as follows:

[0027] In the formula, Indicates the diffusion coefficient; Represents the membrane pool constant; Indicates the volume of a single chamber in the membrane tank; This indicates the effective diffusion cross-sectional area of ​​the diaphragm; Indicates the initial copper ion concentration in the concentration chamber; Indicates the initial copper ion concentration in the dilute chamber; Indicates the concentration chamber in time t The concentration of copper ions at that time; Indicates the rarefaction chamber in time t The concentration of copper ions at that time; Indicates diffusion time.

[0028] It should be explained that the diffusion coefficient is specifically measured using the membrane cell method, as detailed below: (a) Preparation (2 hours); 1. Membrane tank cleaning: hot alkaline solution soaking → tap water rinsing → deionized water ultrasonication (30 min) → drying at 120℃ → cooling to room temperature to ensure no residual solute.

[0029] 2. Diaphragm pretreatment, detailed as follows: (1) Sintered glass diaphragm: Boil in deionized water for 1 hour → sonicate for 30 minutes → dry → weigh (dry weight m1); (2) Wetting: Soak the sample in the solvent for 2 hours to ensure that there are no air bubbles in the pores; take it out and gently aspirate the surface liquid, weigh it (wet weight m2), and calculate the pore volume Vp=(m2−m1) / ρ (ρ is the solvent density). 3. Calibration of the pool constant K (crucial, must be performed every time the diaphragm is replaced), specifically: using a standard KCl system (25℃, D = 1.85 × 10⁻⁵ cm⁻¹). 2 / s), measure the concentration-time data according to the experimental procedure, and substitute it into the formula to calculate K; 4. Solution preparation: Accurately prepare CO (e.g., 0.33 mol / L KCl), keep at a constant temperature of 25℃ for 1 hour, and degas for later use.

[0030] (II) Sample loading and assembly (30 min); 1. The lower chamber (concentration chamber) is filled with liquid. Specific instructions are as follows: (1) The membrane tank is fixed vertically with the lower chamber facing upward, and a magnetic stir bar (PTFE material) is placed inside. (2) Transfer V1 (e.g., 50 mL) of CO solution and slowly inject it along the wall to avoid air bubbles; the liquid level should be about 5 mm from the lower surface of the diaphragm. 2. Diaphragm installation, detailed instructions are as follows: After wetting, lay the diaphragm flat on the lower flange, align it with the sealing groove, and gently press it down (no air bubbles, no leakage); avoid fingerprints contaminating the diaphragm surface. 3. The upper chamber (diluted chamber) is filled with liquid, as detailed below: (1) Fasten the upper chamber and fix the flange (apply force evenly to prevent cracking); place the agitator in; (2) Take V2 (e.g., 50 mL) of deionized water and slowly inject it into the upper chamber, with the liquid level about 5 mm from the upper surface of the diaphragm; ensure that the liquid levels in the two chambers are level (to eliminate static pressure difference); 4. The device is in place, as detailed below: Place the membrane tank in a constant temperature water bath (25℃), with the liquid level submerged in 2 / 3 of the membrane tank; connect the upper and lower chamber magnetic stirrers and adjust the speed to 60 rpm (gentle stirring, without eddies or liquid surface fluctuations).

[0031] (iii) Diffusion experiment (3–5 h); 1. Initial time ( t =0), the specific explanation is as follows: (1) Stir for 10 minutes to ensure uniform concentration; take 1 mL of sample from the upper chamber using a syringe. C m ), take 1 mL of sample from the lower chamber ( C n (Check against the prepared values); (2) Start timing immediately and record initial data.

[0032] 2. Timed sampling and concentration monitoring, detailed as follows: (1) Take a sample every 30 minutes for 3–5 hours (the concentration change should be 10%–30%). (2) Sampling: Take 1 mL from each of the upper and lower chambers (add an equal volume of constant-temperature deionized water to maintain a constant volume); measure the conductivity (KCl system) or refractive index (sucrose system) with a conductivity meter, and convert the concentration. C n , C m ; (3) Record: time t, temperature T, C n and C m Simultaneously observe the stirring status and liquid level.

[0033] 3. Experiment terminated: when C m / C n Stop when ≈0.15; turn off the agitator and water bath, remove the membrane tank, and drain the solution; (iv) Post-processing (30 min); The membrane tank and diaphragm were rinsed three times with deionized water, ultrasonicated for 30 minutes, and then dried for later use. Organize experimental data and verify temperature and time records; The cell constant of the membrane was measured using a KCl solution with a known diffusion coefficient, and the measured cell constant was verified using an acetic acid solution with a known diffusion coefficient. This allowed for the determination of the diffusion coefficients of copper and molybdenum ions in the etching solution. As shown in Tables 1 and 2 below, the diffusion coefficients gradually increased with the increase of copper and molybdenum ion concentrations. The diffusion coefficient of molybdenum ions was greater than that of copper ions.

[0034] Table 1 Relationship between copper ion concentration and diffusion coefficient

[0035] Table 2 Relationship between molybdenum ion concentration and diffusion coefficient

[0036] It should be noted that Cu represents copper ions, Mo represents molybdenum ions; ppm is a unit of mass concentration in parts per million; CL 0 and CR 0 represents the initial copper or molybdenum ion concentrations in the concentrated (lower) and dilute (upper) chambers, respectively; t is the diffusion experiment time (hours); CL f and CR f denoted by , respectively, the final concentrations in the concentrated and dilute chambers at the end of the experiment; D is the diffusion coefficient (square meters per second); T is the experimental temperature (degrees Celsius); β is the membrane cell constant (reciprocal of square centimeters), obtained by standard solution calibration; ΔC is the initial concentration difference, i.e., the initial concentration in the concentrated chamber minus the initial concentration in the dilute chamber.

[0037] S2. Based on the reaction rate constant and diffusion coefficient function, the etching morphology and key parameter values ​​of the copper etching solution formulation are predicted using the COMSOL etching model, and the electrochemical parameters, mass transfer parameters and geometric parameters required for the target formulation are extracted. The COMSOL etching model includes: A dilute mass transport module is used to simulate the diffusion and convection transport process of etchants in solution, defining the diffusion coefficient, bulk concentration, and convection and diffusion equations as they vary with ion concentration. In addition, a deformable geometry module is used to describe the movement of the interface between the copper layer and the etchant, which couples the reaction rate with the copper material properties through the normal velocity formula and introduces a mesh re-division mechanism to avoid computational divergence. Furthermore, based on the first-order surface reaction kinetic equation, an electrochemical parameter module containing electrochemical corrosion rate, reaction rate constant, and concentration dependence is constructed.

[0038] Preferably, the rare substance delivery module includes: Define the concentration variable of the etchant and add dilute substances to transfer the physical field; In the material property node, the diffusion coefficient is set as a function of the copper ion concentration, and the change of the concentration field is controlled by the convection and diffusion equations. In the initial value node, the initial concentration is set to be equal to the bulk concentration, and a constant bulk concentration is applied at the far field boundary as the mass supply boundary for the etchant. A first-order reaction consumes etchant on the surface of the copper layer, forming a concentration gradient from the bulk to the surface, driving diffusion and convection mass transfer; The expression for the convection and diffusion equations is as follows:

[0039] In the formula, This indicates the rate of change of concentration over time; This indicates the concentration of the etchant in the solution; Indicates time; Indicates the convection velocity of the fluid; Convection velocity indicating concentration; This represents the diffusion coefficient of the etchant in solution; This represents the divergence operator.

[0040] Preferably, the deformable geometry module includes: Add a free deformation node in the deformable geometry module, and select the boundary where the copper layer contacts the etchant as the moving boundary; In the boundary displacement settings of the moving boundary, select the normal displacement mode, and enter the negative surface reaction rate, copper molar mass and copper density in the expression input field to obtain the normal moving velocity. The boundary is driven to move inward over time using the normal movement velocity, while enabling moving mesh smoothing and mesh re-meshing mechanisms, and setting automatic re-meshing when mesh deformation exceeds a threshold.

[0041] Preferably, in the deformation geometry module, the normal migration velocity of the interface between the copper layer and the etching solution is calculated by inputting a negative surface reaction rate, copper molar mass, and copper density in the expression input field for the boundary displacement setting. The expression is as follows:

[0042] In the formula, This indicates the normal velocity of the interface between the copper layer and the etching solution. Indicates the surface reaction rate; Indicates the molar mass of copper; This indicates the density of solid copper.

[0043] Preferably, the electrochemical parameter module includes: Define the surface reaction rate constant and correlate the surface reaction rate constant with the electrochemical corrosion rate in the electrochemical parameter settings; The surface reaction rate constant is input into the surface reaction node on the copper layer surface boundary in the dilute mass transport module, and a first-order surface reaction kinetic equation is selected to establish a linear relationship between the surface reaction rate and the interface concentration. Based on the first-order kinetic equation, the value of the reaction rate constant is set as a function of concentration or temperature, and the dependence of the reaction rate on the interface concentration is controlled. In the case of electrochemical etching, the equilibrium potential, exchange current density and Tafel coefficient are set, and electrode potential or current density conditions are applied at the electrode boundary.

[0044] Preferably, in the electrochemical parameter module, the surface reaction rate constant and interface concentration are input into the surface reaction node at the copper layer surface boundary of the dilute mass transport module to obtain the first-order surface reaction kinetic equation, the expression of which is:

[0045] In the formula, Indicates the surface reaction rate; This represents the forward reaction rate constant; This indicates the local concentration of the etchant at the interface.

[0046] It should be noted that before using the COMSOL etching model, the measured parameters should be organized, as shown in Table 3. Table 3 Key Parameters

[0047] Based on the content of Table 3, the specific operations are as follows: Open the COMSOL etching model → Select the model wizard → Select 2D / 3D (2D cross-section is usually sufficient for copper etching trenches, while 3D is used for deep holes or complex structures); Select the research type: Transient study (etching is a process that changes over time, so transient studies must be used); Add a core physics field, as follows: Add the following physics fields and enable multiphysics coupling: Transport of Diluted Species: Simulating the diffusion and convection of etchant; Deformed Geometry: Simulates the changes in copper surface morphology caused by etching; (Optional) Laminar Flow: If the etching solution is flowing (spraying / stirring), add this module to simulate the flow field; static etching can be omitted, only diffusion is used; The multiphysics coupling setting is described as follows: adding the coupling between rare matter transport and deformation geometry in a multiphysics field allows the surface reaction rate to drive geometric deformation, which is the core of the etching morphology change. Construct the initial geometric model (corresponding to the sample's geometric dimensions), enter the geometry module, and draw the initial cross-section for copper etching. Specific instructions are as follows: (1) Photoresist mask: top rectangle, corresponding to mask thickness and line width; (2) Copper layer: The rectangle below the mask, corresponding to the copper layer thickness and the design line width / trench depth; (3) Etching solution area: The area around the copper layer and the mask, which serves as the fluid domain for mass transfer; Generate geometry and construct domains, ensuring that the copper layer and etchant area are two independent domains; And execute in sequence: the dilute mass transport module, which is used to simulate the diffusion and convection transfer process of etchant in solution, and defines the diffusion coefficient, bulk concentration, and convection and diffusion equations as they vary with ion concentration; In addition, a deformable geometry module is used to describe the movement of the interface between the copper layer and the etchant, which couples the reaction rate with the copper material properties through the normal velocity formula and introduces a mesh re-division mechanism to avoid computational divergence. In addition, based on the first-order surface reaction kinetic equation, an electrochemical parameter module is constructed that includes electrochemical corrosion rate, reaction rate constant, and concentration dependence. Key process parameters (CDLoss, Taper angle, Undercut) were extracted and are shown in Table 4. Table 4 Extraction Methods

[0048] S3. Verify and optimize the electrochemical parameters, mass transfer parameters, and geometric parameters of the target formulation through etching experiments to obtain the copper etching solution composition and optimal ratio that meet the target etching profile quality parameters.

[0049] Preferably, the process of obtaining the copper etching solution composition and preferred ratio that meet the target etching profile quality parameters includes: Copper etching solution samples were prepared according to the target formulation parameters, and their electrochemical corrosion rate, diffusion coefficient function and bulk concentration were tested. The copper and molybdenum bilayer sample was immersed in the prepared etching solution and shaken at a constant temperature for a fixed time to complete the etching process. The cross-sectional morphology of the etched sample was observed using scanning electron microscopy, and the key dimensional losses, cone angle, undercut depth, and molybdenum layer residue were measured. The morphological parameters are compared with the quality parameters of the target etched profile; If the preset requirements are met, record the current electrochemical parameters, mass transfer parameters, and geometric parameters. If the conditions are not met, the surface reaction rate constant, diffusion coefficient function, or geometric dimensions in the model are adjusted according to the deviation, and a new formula is re-predicted and prepared. When all morphological parameters meet the target requirements, the composition and preferred ratio of the copper etching solution are determined.

[0050] It should be noted that if the simulation results do not meet the target (e.g., CDLoss is too large, Taper angle exceeds the limit, Undercut occurs), the parameters will be returned for modification. Adjustment Decrease Reduce the lateral etching rate and decrease the CDLoss and Taper angle; Adjustment Increase Improve mass transfer and reduce insufficient etching at the bottom of the trench; Adjust etching time: shorten over-etching time to suppress undercut; Repeat the solution-analysis-debugging process until the simulated morphology and parameters meet the target requirements. The formula corresponding to the parameters at this point is the required predicted formula.

[0051] Specific examples are illustrated below: Run the original results using the measured parameters, and then run a complete transient simulation using the measured electrochemical / diffusion parameters and target etching time to obtain the baseline morphology and key parameters: Has the etching penetrated through? Are there any residues on the bottom? What is the CDLoss? Does it exceed the process specifications? Does the taper angle / undercut meet the requirements? What is the concentration field distribution within the trench? Is the concentration at the bottom too low? The purpose of this step is to determine the current baseline level of the recipe and where the problem lies. Single-factor optimization: First identify the main issues, then optimize them one by one; Instead of changing multiple parameters at the same time, fix other variables first, adjust only one core parameter, and observe the trend.

[0052] Scenario A: CDLoss / Taper angle is too large (side erosion is too severe); What should be prioritized for adjustment; the reaction rate constant. Inhibitor parameters; The operation is as follows: First fix , Etching time remains unchanged, but reduction (For example, run a simulation once for each 20% reduction); Observe: Does CDLoss decrease? Does the sidewall become steeper? Can it still be etched through within the etching time? logic: By directly controlling the surface reaction rate, the rate of lateral erosion on the back sidewall will be suppressed, and the Taper angle and CDLoss will decrease accordingly.

[0053] If lower Later, the side etching improved, but the bottom etching time became longer. This was addressed by fine-tuning the etching time or slightly increasing it. To compensate.

[0054] Scenario B: Poor etching uniformity, insufficient etching at the bottom of the trench (taper angle is too large); What should be adjusted first; diffusion coefficient Bulk concentration ; The operation is as follows: fixed With the etching time remaining constant, the efficiency is improved. (For example, increasing by 30% each time) or increasing (For example, increasing by 10% each time); Observations: Does the bottom etchant concentration increase? Does the difference in etching rates between the top and bottom decrease? Does the Taper angle decrease? logic: and By controlling mass transfer capacity, the etchant replenishment at the bottom of the trench is more sufficient, the difference in etching rate between the top and bottom is reduced, and the sidewalls are more uniform.

[0055] Scene C: Undercut appears (the area under the mask is hollowed out); What should be prioritized for adjustment? Etching time, inhibitor parameters; The operation is as follows: Keeping other parameters constant, shorten the etching time (e.g., reduce the over-etching time) and observe whether the Undercut disappears; If the time cannot be shortened further (otherwise the penetration will be insufficient), the inhibitor parameters can be increased to enhance the sidewall passivation. Logic: Undercut is essentially over-etching with no passivation on the sidewalls. Shortening the time directly reduces additional side-wall etching, while inhibitors suppress sidewall corrosion at the reaction level.

[0056] After single-factor debugging solves major problems, multi-factor combinations are then used to find the parameter points that are optimal for both performance and process windows.

[0057] Design a small number of combination experiments (such as a 3-factor, 3-level orthogonal array) and run different... , , Combinations, recording the characteristics of each combination: Etching time (whether it etched through); CDLoss; Taper angle; Uniformity (top / bottom etch rate ratio); Objective: To find the range of parameters that simultaneously satisfy all criteria, rather than a single optimal value; Find the 2-3 best-performing parameters from the simulation, map them to the actual etching solution formulation, and conduct experimental verification. Comparison of experimental SEM morphology and simulated morphology: If the trend is consistent (e.g.) The decrease in CDLoss (and the corresponding decrease in CDLoss) indicates that the model is reliable and the parameters can be further optimized. If the deviation is large (for example, the simulation has no undercut, but the experiment does), it means that the model is missing key influencing factors (such as mask adhesion, additive effect), and the model needs to be corrected and then re-adjusted.

[0058] In addition, the following criteria were used to determine the current optimal parameters: all core morphological indicators met the standards; The formulation corresponding to the optimal parameters needs to be insensitive to small fluctuations (temperature, concentration deviation, time error): For example, when the etching time fluctuates by ±10% and the concentration by ±5%, the morphology indicators can still remain within the acceptable range. If a parameter value is slightly off and exceeds the limit, it means that the process window is too narrow and unusable in actual production. It needs to be adjusted to a more stable range. The simulation results with optimal parameters must be consistent with the trends and morphological characteristics of the experimental results.

[0059] In addition, it should be explained that CDloss represents the actual critical dimensions of the copper lines / trenches / vias after etching, and the amount of reduction / deviation compared to the design target dimensions.

[0060] In simple terms, it refers to how much thinner the original linewidth became after etching, usually expressed as a difference (nm / µm) or a percentage: CD Loss = Design CD − Actual CD after etching; Tape refers to the angle between the sidewall of the copper line / trench after etching and the vertical direction (wafer surface normal). Undercut means that after copper etching, the copper under the photomask is horizontally etched and hollowed out, forming an inwardly concave, suspended sidewall structure. The angle of this inverted tilt is called the Undercut angle. In addition, the copper etching solution formulation is shown in Table 5: Table 5 Copper Etching Solution Formulation Table

[0061] Based on Table 5, the comparative etching performance is shown in Table 6: Table 6 Comparison of Etching Performance

[0062] Note: The etching conditions of Comparative Examples 1 and 2 were exactly the same as those of Example 3 (32°C, 300 r / min, the sample was a copper / molybdenum double layer). The comparison shows that Example 3 of this application is significantly better than the comparative example in terms of CDloss, Taper angle control, and suppression of Mo residue and undercut, proving that the technical solution has unexpected technical effects.

[0063] This embodiment also provides a copper etching solution. As determined by the above-described formulation optimization method, the copper etching solution contains the following components in parts by weight: 3-8 parts hydrogen peroxide, 1-2 parts phosphoric acid, 6-20 parts citric acid, 3-5 parts succinic acid, 1-2 parts ammonium bifluoride, 3-5 parts 3-diethylaminopropylamine, 4-6 parts isopropanolamine, 4-6 parts 2-amino-2-methyl-1-propanol; the balance is pure water.

[0064] It should be explained that the preparation process of the copper etching solution is as follows: Preparation (2 hours); 1. Membrane tank cleaning: hot alkaline solution soaking → tap water rinsing → deionized water ultrasonication (30 min) → drying at 120℃ → cooling to room temperature to ensure no residual solute; 2. Diaphragm pretreatment: Sintered glass diaphragm: Boil in deionized water for 1 hour → sonicate for 30 minutes → dry → weigh (dry weight m1); Wetting: Soak in the solvent to be tested for 2 hours to ensure that there are no air bubbles in the pores; Remove the surface liquid, weigh it (wet weight m2), and calculate the pore volume V. p =(m2−m1) / ρ(ρ is the solvent density; 3. Calibration of the pool constant K (crucial, must be done every time the diaphragm is replaced).

[0065] Then, in a Class 1000 cleanroom, pure water, hydrogen peroxide, phosphoric acid, citric acid, succinic acid, ammonium bifluoride, 3-diethylaminopropylamine, isopropanolamine, and 2-amino-2-methyl-1-propanol are added in sequence, stirred, filtered, and packaged to obtain the finished product. This is existing technology and will not be explained in detail here.

[0066] It should be noted that the calculation formulas and all parameters involved in the calculations in this application have been dimensionless beforehand. The process of dimensionless processing is well known in the industry and will not be described here.

[0067] Although the present application has disclosed the preferred embodiments above, the embodiments are merely examples for the purpose of illustration and are not intended to limit the present application. Those skilled in the art can make some modifications and refinements without departing from the spirit and scope of the present application. The scope of protection claimed by the present application should be determined by the claims.

Claims

1. A recipe optimization method based on COMSOL simulation, characterized in that, The method includes: We obtained the formulation, ratio, bulk concentration, sample parameters and etching performance data of multiple copper etching solutions, analyzed the relationship between copper etching rate and electrochemical corrosion rate and calibrated the reaction rate constant, and used the membrane cell method to determine the diffusion coefficient function corresponding to different copper ion concentrations. Based on the reaction rate constant and diffusion coefficient function, the etching morphology and key parameter values ​​of the copper etching solution formulation are predicted using the COMSOL etching model, and the electrochemical parameters, mass transfer parameters and geometric parameters required for the target formulation are extracted. The COMSOL etching model includes: A dilute mass transport module is used to simulate the diffusion and convection transport process of etchants in solution, defining the diffusion coefficient, bulk concentration, and convection and diffusion equations as they vary with ion concentration. In addition, a deformable geometry module is used to describe the movement of the interface between the copper layer and the etchant, which couples the reaction rate with the copper material properties through the normal velocity formula and introduces a mesh re-division mechanism to avoid computational divergence. Furthermore, based on the first-order surface reaction kinetic equation, an electrochemical parameter module containing electrochemical corrosion rate, reaction rate constant, and concentration dependence is constructed; The electrochemical parameters, mass transfer parameters, and geometric parameters of the target formulation were verified and optimized through etching experiments, and the copper etching solution composition and optimal ratio that meet the target etching profile quality parameters were obtained.

2. The formulation optimization method according to claim 1, characterized in that, The analysis of the relationship between the etching rate and electrochemical corrosion rate of copper and the calibration of the reaction rate constant include: At a constant temperature, a copper sample is immersed in the copper etching solution to be tested and shaken at a constant speed for a fixed time. The etching rate is obtained by measuring the change in film thickness and taking the average value to obtain the etching rate data of the current formula. Corrosion current tests were performed on copper electrodes with the same formulation to obtain the corresponding electrochemical corrosion rates; The etching rate and corrosion current density of the same formulation were paired and sorted by etching rate from smallest to largest to verify that the two are positively correlated. Several sets of data within the positive correlation region were selected, and the measured corrosion current density and etching rate data were used as the input basis for calibrating the reaction rate constant in the COMSOL etching model.

3. The formulation optimization method according to claim 1, characterized in that, The method of determining the diffusion coefficient function corresponding to different copper ion concentrations using the membrane cell method includes: Clean and dry the membrane tank and diaphragm, calibrate the membrane tank constant using a standard KCl system, and verify the membrane tank constant using an acetic acid solution. Several etching solutions with different initial copper ion concentrations were prepared as concentrated solutions, and after injecting an equal volume of deionized water into the dilute solutions, they were respectively loaded into the upper and lower chambers of the membrane pool. After the membrane tank is kept at the target temperature, stirring is started. Samples are taken from the upper and lower chambers of the membrane tank at fixed time intervals, and the copper ion concentration is measured to obtain the concentration in the concentrated chamber and the concentration in the dilute chamber. Based on the membrane pool constant, single-chamber volume, and effective membrane area, the diffusion coefficient corresponding to each initial concentration is calculated, and the diffusion coefficient function as a function of copper ion concentration is obtained. The calculation process of the diffusion coefficient is as follows: ； In the formula, Indicates the diffusion coefficient; Represents the membrane pool constant; Indicates the volume of a single chamber in the membrane tank; This indicates the effective diffusion cross-sectional area of ​​the diaphragm; Indicates the initial copper ion concentration in the concentration chamber; Indicates the initial copper ion concentration in the dilute chamber; Indicates the concentration chamber in time t The concentration of copper ions at that time; Indicates the rarefaction chamber in time t The concentration of copper ions at that time; Indicates diffusion time.

4. The formulation optimization method according to claim 1, characterized in that, The rare substance delivery module includes: Define the concentration variable of the etchant and add dilute substances to transfer the physical field; In the material property node, the diffusion coefficient is set as a function of the copper ion concentration, and the change of the concentration field is controlled by the convection and diffusion equations. In the initial value node, the initial concentration is set to be equal to the bulk concentration, and a constant bulk concentration is applied at the far field boundary as the mass supply boundary for the etchant. A first-order reaction consumes etchant on the surface of the copper layer, forming a concentration gradient from the bulk to the surface, driving diffusion and convection mass transfer; The expression for the convection and diffusion equations is as follows: ； In the formula, This indicates the rate of change of concentration over time; This indicates the concentration of the etchant in the solution; Indicates time; Indicates the convection velocity of the fluid; Convection velocity indicating concentration; This represents the diffusion coefficient of the etchant in solution; This represents the divergence operator.

5. The formulation optimization method according to claim 4, characterized in that, The deformable geometry module includes: Add a free deformation node in the deformable geometry module, and select the boundary where the copper layer contacts the etchant as the moving boundary; In the boundary displacement settings of the moving boundary, select the normal displacement mode, and enter the negative surface reaction rate, copper molar mass and copper density in the expression input field to obtain the normal moving velocity. The boundary is driven to move inward over time using the normal movement velocity, while enabling moving mesh smoothing and mesh re-meshing mechanisms, and setting automatic re-meshing when mesh deformation exceeds a threshold.

6. The formulation optimization method according to claim 5, characterized in that, In the deformation geometry module, by inputting a negative surface reaction rate, copper molar mass, and copper density in the expression input field for boundary displacement, the normal migration velocity of the interface between the copper layer and the etching solution is calculated, and its expression is: ； In the formula, This indicates the normal velocity of the interface between the copper layer and the etching solution. Indicates the surface reaction rate; Indicates the molar mass of copper; This indicates the density of solid copper.

7. The formulation optimization method according to claim 6, characterized in that, The electrochemical parameter module includes: Define the surface reaction rate constant and correlate the surface reaction rate constant with the electrochemical corrosion rate in the electrochemical parameter settings; The surface reaction rate constant is input into the surface reaction node on the copper layer surface boundary in the dilute mass transport module, and a first-order surface reaction kinetic equation is selected to establish a linear relationship between the surface reaction rate and the interface concentration. Based on the first-order kinetic equation, the value of the reaction rate constant is set as a function of concentration or temperature, and the dependence of the reaction rate on the interface concentration is controlled. In the case of electrochemical etching, the equilibrium potential, exchange current density and Tafel coefficient are set, and electrode potential or current density conditions are applied at the electrode boundary.

8. The formulation optimization method according to claim 7, characterized in that, In the electrochemical parameter module, by inputting the surface reaction rate constant and interface concentration at the surface reaction node on the copper layer surface boundary of the dilute mass transport module, the first-order surface reaction kinetic equation is obtained, and its expression is: ； In the formula, Indicates the surface reaction rate; This represents the forward reaction rate constant; This indicates the local concentration of the etchant at the interface.

9. The formulation optimization method according to claim 1, characterized in that, The copper etching solution composition and preferred ratio for obtaining the target etching profile quality parameters include: Copper etching solution samples were prepared according to the target formulation parameters, and their electrochemical corrosion rate, diffusion coefficient function and bulk concentration were tested. The copper and molybdenum bilayer sample was immersed in the prepared etching solution and shaken at a constant temperature for a fixed time to complete the etching process. The cross-sectional morphology of the etched sample was observed using scanning electron microscopy, and the key dimensional losses, cone angle, undercut depth, and molybdenum layer residue were measured. The morphological parameters are compared with the quality parameters of the target etched profile; If the preset requirements are met, record the current electrochemical parameters, mass transfer parameters, and geometric parameters. If the conditions are not met, the surface reaction rate constant, diffusion coefficient function, or geometric dimensions in the model are adjusted according to the deviation, and a new formula is re-predicted and prepared. When all morphological parameters meet the target requirements, the composition and preferred ratio of the copper etching solution are determined.

10. A copper etching solution, as determined by the formulation optimization method according to any one of claims 1-9, characterized in that, The copper etching solution comprises the following components in parts by weight: 3-8 parts hydrogen peroxide, 1-2 parts phosphoric acid, 6-20 parts citric acid, 3-5 parts succinic acid, 1-2 parts ammonium bifluoride, 3-5 parts 3-diethylaminopropylamine, 4-6 parts isopropanolamine, 4-6 parts 2-amino-2-methyl-1-propanol; the balance is pure water.

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