Method and system for rapidly detecting concentration of copper ions in electroplating solution

Abstract

The invention relates to the technical field of electrochemical analysis, in particular to a method and system for rapidly detecting the concentration of copper ions in electroplating liquid, and the method comprises the following steps: in an electroplating starting stage, eliminating the influence of bath liquid temperature on a copper ion interface supply rate acquired in real time by utilizing a temperature gain coefficient, and establishing a reference model of the rate with respect to current density; and in the subsequent electroplating process, the expansion ratio of the surface area of the electrode is calculated by comparing the real-time double-electric-layer discharge time constant with the reference time constant determined in the starting stage. And determining the effective mass transfer flux of the interface by combining the normalized ion supply rate and the surface area expansion ratio, comparing the effective mass transfer flux with the theoretical demand flux obtained by the reference model, and dynamically adjusting the output step length of the rectifier. The interference of temperature fluctuation and dendritic crystal growth is avoided, so that the comprehensive targets of accurate regulation and control, defect prevention and intelligent diagnosis are achieved, and the intelligent level of electrochemical analysis is remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of electrochemical analysis technology, specifically to a rapid detection method and system for copper ion concentration in electroplating solutions. Background Technology

[0002] In the field of electrochemistry, achieving uniform copper plating in high aspect ratio vias is crucial for improving product reliability. The core challenge lies in conducting appropriate electrochemical analysis to precisely control the rectifier's output current density, thereby improving production efficiency while ensuring plating quality. The ideal control strategy is to bring the current density close to the mass transfer limit, but without exceeding it and causing "burnt-in" defects. "Burt-in" defects are primarily caused by a sharp decrease in copper ion concentration at the electrode interface (i.e., concentration polarization), and the degree of risk is influenced by a complex coupling of thermodynamic factors (such as bath temperature) and interfacial geometric factors (such as the evolution of electrode microstructure).

[0003] Currently, the industrial sector is increasingly employing smart sensors (online and digital sensors composed of temperature, voltage, and other sensors) to replace traditional manual titration or offline analysis in electrochemical analysis, aiming to achieve online monitoring of interfacial mass transfer states (i.e., copper ion concentration). These smart sensors can acquire key electrochemical parameters in real time, such as the electric double-layer discharge time constant and ion replenishment rate. However, existing technologies suffer from a significant drawback: the data acquired by smart sensors lacks deep integration with the rectifier's control commands, failing to establish a control core capable of multi-parameter coupled analysis and intelligent decision-making.

[0004] Specifically, existing rectifier control strategies often fail to adaptively eliminate the interference of temperature on key electrochemical parameters. Existing control logic (such as simple PID control) cannot dynamically decouple this thermodynamic interference, which can easily lead to excessively high dangerous currents being set under temperature fluctuation conditions. For example, when the bath temperature increases due to the Joule effect, the ion diffusion rate will increase, and the results detected by the sensor may contain physical artifacts, leading to misjudgments. At the same time, the control process also struggles to effectively quantify the time-varying effects of microstructure. For example, the growth of dendrites on the electrode surface during electroplating changes the effective specific surface area, causing local current density concentration. Existing methods cannot incorporate the evolution of microstructure as a key variable into the mass transfer capacity calculation, resulting in a slow response to "hidden" mass transfer bottlenecks and a lag in control.

[0005] In summary, the current bottleneck in electroplating process control lies in "how to further achieve intelligent electrochemical analysis and detection, and intelligent decision-making and regulation of the electrochemical process." This bottleneck severely restricts the development of electroplating technology towards higher precision, higher efficiency, and higher quality. Summary of the Invention

[0006] To address the above problems, this invention provides a method and system for rapid detection of copper ion concentration in electroplating solutions.

[0007] The present invention provides a rapid detection method and system for copper ion concentration in electroplating solution, which adopts the following technical solution: One embodiment of the present invention provides a rapid detection method for copper ion concentration in electroplating solution, the method comprising the following steps: Determining the gain coefficient of copper ion diffusion affected by temperature ; During the start-up phase of the electroplating process, the current density output by the rectifier, the collected bath temperature, and the copper ion interface replenishment rate are first utilized... The influence of the bath temperature on the collected copper ion interface replenishment rate is removed, and then a first model of the copper ion interface replenishment rate with respect to the current density is constructed. After the start-up phase of the electroplating process, it is used again. The influence of the bath temperature in the collected copper ion interface replenishment rate is removed to obtain the normalized ion replenishment rate. The surface area expansion ratio is determined based on the real-time collected double-layer discharge time constant and the reference time constant of the dendrite-free flat surface. The reference time constant of the dendrite-free flat surface is determined by the double-layer discharge time constant collected during the start-up phase. The effective mass transfer flux at the interface is determined by the normalized ion replenishment rate and the surface area expansion ratio; the theoretical required flux is obtained by substituting the real-time output current density of the rectifier into the first model constructed in the startup phase; the step size of the rectifier output current density is adjusted by the difference between the effective mass transfer flux at the interface and the theoretical required flux; and electroplating faults are detected.

[0008] Preferably, the gain coefficient for measuring the effect of temperature on copper ion diffusion is... The specific steps include the following: Several bath temperatures were set, and the limiting diffusion current density at each temperature was measured. A linear slope of the limiting diffusion current as a function of temperature was fitted, and this linear slope was used as the gain coefficient. .

[0009] Preferably, the specific steps for constructing the first model of the copper ion interface replenishment rate with respect to current density are as follows: During the start-up phase of the electroplating process, several data points are sampled. Each data point includes the collected current density, bath temperature, and copper ion interface replenishment rate. use The result obtained after removing the influence of the bath temperature in the collected copper ion interface replenishment rate is recorded as the first replenishment rate for each data point. A linear model is constructed, with the current density of each data point as the independent variable of the linear model and the first replenishment rate as the dependent variable of the independent variable of the linear model. Using the current density and the first replenishment rate of all data points, the linear model is fitted by the least squares method, and the fitted linear model is used as the first model.

[0010] Preferably, the specific steps for determining the surface area expansion ratio based on the real-time acquired electric double-layer discharge time constant and the reference time constant of the dendrite-free flat surface are as follows: The electric double-layer discharge time constant was collected during the start-up phase of the electroplating process; the gain coefficient of electrolyte thermal conductivity was utilized. The influence of the bath temperature in the double-layer discharge time constant is removed to obtain the first constant; the average value of the first constant corresponding to all double-layer discharge time constants collected during the start-up phase of the electroplating process is recorded as the reference time constant for dendrite-free flat surface. For any double-layer discharge time constant acquired in real time after the start-up phase of the electroplating process, the gain coefficient of electrolyte thermal conductivity is used. The influence of the bath temperature in the double-layer discharge time constant is removed to obtain the corrected double-layer discharge time constant. The ratio of the corrected double-layer discharge time constant to the reference time constant of the dendrite-free flat surface is denoted as the surface area expansion ratio.

[0011] Preferably, the effective mass transfer flux at the interface is positively correlated with the normalized ion replenishment rate and negatively correlated with the surface area expansion ratio.

[0012] Preferably, the specific steps for adjusting the step size of the rectifier output current density based on the difference between the effective mass transfer flux at the interface and the theoretical required flux, and for detecting electroplating faults, are as follows: The concentration polarization risk potential is determined based on the difference between the effective mass transfer flux at the interface and the theoretical required flux, and the concentration polarization risk potential is positively correlated with the difference. The step size of the rectifier output current density is adjusted by the difference between the preset safety margin target potential energy and the concentration polarization risk potential energy, and the step size is positively correlated with the difference. When the change in concentration polarization risk potential energy is greater than 0 and the step size is less than 0, the moment is marked as an abnormal moment. When several abnormal moments exist consecutively, it is determined that there is a fault in the electroplating process.

[0013] Preferably, the specific steps for removing the influence of the bath temperature on the collected copper ion interface replenishment rate are as follows: The average temperature of the plating bath collected during the start-up phase of the electroplating process is recorded as follows: ; For the copper ion interface replenishment rate collected at any bath temperature, the copper ion interface replenishment rate after removing the aforementioned influence is related to the bath temperature and... The difference was negatively correlated with the copper ion interface replenishment rate, and positively correlated with the [other factors]. It shows a negative correlation.

[0014] Preferably, the specific steps for removing the influence of the bath temperature on the double-layer discharge time constant are as follows: The average temperature of the plating bath collected during the start-up phase of the electroplating process is recorded as follows: ; For the double-layer discharge time constant collected at any bath temperature, the double-layer discharge time constant after removing the aforementioned influence is compared with the bath temperature and... The difference is positively correlated with the electric double layer discharge time constant, and also with... Positive correlation; The acquisition process includes: Several bath temperatures were set, and the conductivity at each bath temperature was measured. The linear slope of the conductivity change with bath temperature was used as... .

[0015] Preferably, the specific methods for acquiring the copper ion interface replenishment rate and the electric double layer discharge time constant are as follows: During the operation of the rectifier, the output current is interrupted at a preset period. For the first time window after the interruption, the potential within the first time window follows the law of ohmic impedance and capacitor discharge. The double-layer discharge time constant is extracted by fitting the potential within the first time window through exponential decay. For the second time window after the interruption, the recovery slope of the potential within the second time window is used as the copper ion interface replenishment rate. The length of the first time window is less than the length of the second time window.

[0016] Another embodiment of the present invention provides a rapid detection system for copper ion concentration in an electroplating solution. The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor runs the computer program, it implements all the steps of the aforementioned rapid detection method for copper ion concentration in an electroplating solution.

[0017] The beneficial effects of the technical solution of the present invention are: This invention transforms the detection target from the static, lagging total copper ion concentration in the solution to the dynamic, effective interfacial mass flux reflecting the real-time ion replenishment capability at the electrode interface, by constructing a first model during the startup phase and calculating the effective interfacial mass flux in real time after startup. This avoids interference from temperature fluctuations and dendrite growth. This method enables rapid, online detection of copper ion interfacial concentration, promptly capturing risks arising from process fluctuations and overcoming the shortcomings of traditional offline titration methods, such as slow response and inability to reflect dynamic interfacial processes.

[0018] This invention adjusts the step size of the rectifier output current density based on the difference between the effective mass transfer flux at the interface and the theoretically required flux. This technical feature allows the rectifier's control to move beyond experience or fixed thresholds, and instead be based on a quantified risk indicator (i.e., mass transfer flux difference) directly related to the current actual state of the interface. When insufficient or excessive effective mass transfer flux at the interface is detected, the current step size can be automatically and quickly increased or decreased, or even the current can be reduced, thus preventing concentration polarization and "burnt-out" defects caused by copper ion depletion at the interface from the source. This closed-loop control significantly improves the process safety margin and enables early fault warning, enhancing the reliability of the entire production system.

[0019] In summary, this invention successfully transforms an advanced "electrochemical state sensing" method into a highly efficient "process control" means by deeply integrating real-time detection, dynamic evaluation, and closed-loop control. It achieves a leap from "static concentration detection" to "dynamic mass transfer capacity assessment," avoiding interference from temperature fluctuations and dendrite growth, thereby achieving the comprehensive goals of precise control, defect prevention, and intelligent diagnosis, significantly improving the level of intelligence in electrochemical analysis during electroplating production. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the steps of a rapid detection method for copper ion concentration in an electroplating solution according to an embodiment of the present invention. Detailed Implementation

[0022] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a rapid detection method and system for copper ion concentration in electroplating solutions proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0023] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0024] The following description, in conjunction with the accompanying drawings, details the specific scheme of a rapid detection method and system for copper ion concentration in electroplating solutions provided by this invention.

[0025] Example 1: Please see Figure 1 The diagram illustrates a flowchart of a rapid detection method for copper ion concentration in an electroplating solution according to an embodiment of the present invention. The method includes the following steps: Step S101: Determine the gain coefficient of copper ion diffusion affected by temperature. Electrolyte thermal conductivity gain coefficient and the inhibition index when effective mass transfer flux is affected by dendrite growth .

[0026] (1) Determination of the thermal gain coefficient of ion diffusion (Abbreviated as gain coefficient): This is used to quantify the effect of temperature increase on the diffusion rate of copper ions.

[0027] As an example, the process includes: Electroplating production was conducted in a laboratory environment using a standard electrolyte identical to the production line formulation. Linear sweep voltammetry was performed on a rotating disk electrode (RDE) apparatus. Several bath temperatures were set (e.g., 20°C, 25°C, 30°C, 35°C), and the limiting diffusion current density at each temperature was measured. Using 25°C as a baseline, the linear slope of the limiting diffusion current as a function of temperature was fitted, which is the... .

[0028] (2) Determine the gain coefficient of electrolyte thermal conductivity : Used to quantify the effect of temperature rise on solution conductivity (and double-layer discharge rate).

[0029] As an example, the process includes: The same temperature-scanning method was used on the standard electrolyte to record the conductivity changes with temperature. The relative rate of change was calculated using linear regression. . This is used in subsequent steps to eliminate cases where the decrease in solution resistance due to increased temperature causes a false reduction in the time constant.

[0030] (3) Determine the dendrite growth retardation index (Abbreviated as the stagnation index): It is an empirical parameter describing the nonlinear decay of effective mass transfer flux with increasing surface roughness.

[0031] As an example, the process includes: A set of samples with different surface roughnesses (obtained by controlling electroplating time) were prepared using a standard Hull cell experiment. The true surface area of ​​each sample was measured using a laser confocal microscope. The ratio of the true surface area to the apparent geometric area of ​​the sample was taken as the surface area ratio, and the limiting diffusion current density was measured simultaneously. The limiting diffusion current was determined by fitting a power-law relationship between the limiting diffusion current and the surface area ratio. .

[0032] Step S102: During the start-up phase of the electroplating process, the current density output by the rectifier, the collected bath temperature, and the copper ion interface replenishment rate are first determined using... The influence of bath temperature on the collected copper ion interface replenishment rate was removed, and then a first model of the copper ion interface replenishment rate with respect to current density was constructed. A reference time constant is used to obtain a dendrite-free, flat surface.

[0033] (1) Due to individual differences in equipment during electroplating production (such as rectifier precision and tank conductivity impedance) and the unsteady fluctuations in tank temperature each time the machine is started, directly using fixed decision-making and control strategies cannot adapt to the dynamically changing electrochemical environment. Therefore, during the start-up phase of the production batch, an ideal mass transfer benchmark adapted to the current state of the tank is established by utilizing the rectifier current ramp-up process. Specifically: During the rectifier startup phase, a soft-start procedure is executed to linearly increase the output current density from zero to the set production target value (e.g., ...). During the climb phase at startup, multiple data samples were taken to obtain... There are _i_ sampling points, where the i-th sampling point contains the current density output by the rectifier. Bath temperature Double-layer discharge time constant (referred to as time constant) and copper ion interface replenishment rate (Abbreviated as replenishment rate) .

[0034] (2) During the current density ramp-up, the Joule heating effect causes the bath temperature to drift. To establish a unified thermodynamic reference plane, The arithmetic mean of the bath temperature at each sampling point is locked as the batch reference temperature for this batch. .Should This will serve as the sole zero point for all subsequent thermodynamic normalization calculations, eliminating comparison errors caused by differences in initial temperatures between batches.

[0035] (3) To obtain the baseline characteristics representing the initial flatness of this batch of electrodes, the influence of temperature fluctuations on the solution conductivity during sampling must be eliminated. (Using coefficients...) Will Each time constant at each sampling point is traced back to the batch reference temperature. Under these conditions, and by calculating the mean, the reference time constant for a dendrite-free, smooth surface is obtained. : Here This represents the standardized double-layer response characteristics of a dendrite-free, flat surface at the reference temperature, and will serve as the denominator for subsequent calculations of the surface area expansion ratio.

[0036] in, This indicates that each time constant is traced back to the batch reference temperature. The time constant under the given conditions, abbreviated as the first constant, represents the time constant after removing the influence of temperature.

[0037] (4) The diffusion rate of copper ions is significantly affected by temperature. In order to construct an ideal model that only reflects the relationship between current drive and concentration supply, it is necessary to eliminate the thermal acceleration component caused by temperature fluctuation.

[0038] Utilization coefficient The replenishment rate at the i-th sampling point Perform temperature normalization to generate the first replenishment rate at the i-th sampling point. : It should be noted that the above temperature correction formula is based on the operating temperature range allowed by the process (e.g., ...). The linear approximation within the range is sufficient to meet the accuracy requirements of industrial control.

[0039] (5) Further, the current density at the i-th sampling point As the independent variable, with Using the least squares method as the dependent variable, linear regression analysis was performed to establish the following first model: based on The ideal mass transfer linear regression coefficients are calculated using the least squares method based on the current density and the first replenishment rate at each sampling point. (Slope) and (Intercept). These two coefficients constitute the ideal kinetic reference for the current batch, characterizing the theoretical relationship between ion replenishment capability and current under ideally flat surfaces and reference temperatures.

[0040] Step S103: After the start-up phase of the electroplating process, utilize again... The influence of the bath temperature in the collected copper ion interface replenishment rate was removed to obtain the normalized ion replenishment rate, and the surface area expansion ratio was determined based on the real-time collected double-layer discharge time constant and the reference time constant of the dendrite-free flat surface.

[0041] (1) After the start-up phase of the electroplating process (that is, after the current density climbs to the set production target value), the current density output by the rectifier is read at time t, with each second as a time point. and bath temperature Collect the double-layer discharge time constant at time t. Copper ion interface replenishment rate .

[0042] (2) As the electroplating process continues, the Joule heating effect will cause the bath temperature to rise. A drift occurs relative to the initial time. Increased temperature also leads to an increase in the ion diffusion coefficient (manifested as...). Increase) and decrease in electrolyte resistance (manifested as) (To reduce) In order to isolate these numerical drifts caused by thermodynamic factors and ensure that the test results only reflect changes in the concentration field and geometric field, the data needs to be uniformly traced back to the batch reference temperature. Plane. Specifically: First, using Calculate the normalized ion feed rate after removing the thermal acceleration effect. : Should The physical meaning is: at the reference temperature Under the given conditions, the equivalent ion diffusion capacity at time t is driven solely by the concentration gradient from the current solution bulk to the interface, where the effects of temperature changes have been removed.

[0043] Then, using After eliminating the influence of temperature variation on conductivity (or electric double-layer discharge time constant), the corrected electric double-layer discharge time constant at time t is obtained. : The physical meaning is: at the reference temperature Under these conditions, after eliminating the influence of temperature changes on the solution resistance, the equivalent double-layer response characteristics at time t are determined solely by the geometric state of the electrode surface.

[0044] (3) After eliminating temperature interference, The changes are mainly attributed to the alteration of the effective specific surface area of ​​the electrode. As micro-dendritic cells germinate and grow, the actual surface area of ​​the electrode expands relative to its initial flat state, leading to an increase in the double-layer capacitance.

[0045] Calculate the surface area expansion ratio at time t : This represents the function to find the maximum value. In this formula, we introduce... The function acts as a physical boundary constraint, making The value is always greater than or equal to 1, which is based on the irreversibility of the electrodeposition process: under normal DC electroplating conditions, the electrode surface will not spontaneously become smoother than its initial state (i.e., the surface area will not decrease). This index... The value directly quantifies the degree of deterioration of the current electrode surface compared to its initial smoothness during production. For example, This means that the effective conductive surface area has increased by 20%, which usually indicates the beginning of micro-roughening. This metric will serve as a key penalty factor in the next stage of calculating the effective mass transfer flux.

[0046] Step S104: Determine the effective mass transfer flux at the interface based on the normalized ion replenishment rate and the surface area expansion ratio.

[0047] Traditional detection methods typically assume that the electrode surface is an ideal plane and directly use... As a characterization of mass transfer capacity. However, on rough surfaces, electric field lines are highly concentrated at microscopic protrusions, and the local ion flux required to maintain deposition there is much higher than in flat areas. This means that with the surface area expansion ratio... As the mass transfer flux increases, the effective mass transfer flux available per unit macroscopic area decreases sharply. This decrease is not a linear relationship, but a power-law relationship influenced by geometry.

[0048] Furthermore, this embodiment utilizes The normalized ion feed rate is nonlinearly dated to calculate the effective mass transfer flux at the interface. : In this formula, the numerator term Represents the macroeconomic supply capacity determined by the concentration of the bulk commodity; denominator term This represents the gain in transmission resistance caused by the deterioration of the microstructure. When When it increases due to dendrite growth, It will decay at an exponential rate. This computational mechanism ensures that the system can penetrate the appearance of "sufficient bulk solution concentration" and keenly detect signs of localized depletion caused by microscopic roughness at the interface.

[0049] It should be noted that, The physical significance lies in describing the amplification effect of increased microscopic specific surface area on the local ion consumption rate under a specific plating solution system. By introducing this exponent, the complex microscopic flow-electric field coupling problem is simplified into a computable algebraic relationship.

[0050] Step S105: Substitute the real-time output current density of the rectifier into the first model constructed in the startup phase to obtain the theoretical required flux, and adjust the step size of the rectifier output current density based on the difference between the effective mass transfer flux at the interface and the theoretical required flux.

[0051] (1) In order to evaluate whether the current effective mass transfer flux meets the production requirements, the rectifier output current density at time t is first used. Substitute into the first model: This represents the output result of the first model at time t.

[0052] This takes into account the standby and extremely low current pre-plating stages, or the intercept caused by regression fitting errors. When it is negative, Zero or even negative values ​​may occur. To prevent the risk of zero denominators or logical errors in subsequent calculations, the system performs non-zero clamping protection on the theoretical required flux. in, Let represent the theoretical flux required at time t. The smallest positive number set for the system (e.g.) This operation ensured It remains positive under all operating conditions, ensuring the stability of numerical calculations.

[0053] (2) Using the effective mass transfer flux at the interface Compared with theoretical demand flux Calculate the mass transfer limit approximation degree at time t. , It represents the difference between the effective mass transfer flux at the interface and the theoretical required flux. It is a dimensionless scalar that quantifies the deficit of the current actual effective flux relative to the flux required to maintain ideal deposition.

[0054] As an example, The calculation formulas include: (3) Calculate the adjustment step size of the rectifier output current density at time t. ,That and It shows a negative correlation.

[0055] when The larger the value (e.g., approaching 1.0), the closer the copper ion concentration at the interface is to zero, and the hydrogen evolution side reaction is about to occur. The smaller the value (even less than 0), the less likely the rectifier will output excessive current at the next moment, reducing the risk of board burnout. The smaller the value (e.g., approaching 0), the more abundant the interface mass transfer capacity, ensuring production safety. The larger the value, the greater the power output is achieved by increasing the current.

[0056] The current density output by the rectifier at the next time step (i.e., the (t+1)th time step) Set as: .

[0057] This concludes the example.

[0058] In summary, traditional methods can only detect the bulk concentration of copper ions, while this embodiment detects the effective interfacial mass transfer flux. This is a dynamic index. In this embodiment, this index is used to indirectly but more deeply describe the change of copper ion concentration during the electroplating process in an online manner. It can not only reflect the state of copper ions in real time and quickly, but more importantly, it can adaptively eliminate the interference of temperature on key electrochemical parameters and dendrite growth, thereby ensuring the accuracy of regulation.

[0059] Example 2: Step S101 of Example 1 includes: using 25°C as a reference, fitting the linear slope of the limiting current as a function of temperature, i.e. As an example, the process includes: Subtract 25°C from each of the set temperatures to obtain several relative temperatures.

[0060] Plotting relative temperature on the x-axis and limiting diffusion current density on the y-axis, a linear regression is performed on all relative temperatures and limiting diffusion current densities. The equation for this regression line is expressed as J_lim = J_ref × (1 + ×ΔT). Where J_lim represents the ordinate, ΔT the abscissa, and J_ref represents the limiting diffusion current density obtained at 25℃. The slope is obtained by performing linear regression. (That is, using the least squares method to obtain the slope of the equation of a straight line).

[0061] This embodiment uses a typical acidic copper sulfate system as an example, and the value is 0.021 / ℃.

[0062] Step S101 of Example 1 includes: recording the change data of conductivity with temperature. The relative rate of change is calculated through linear regression, which is... As an example, the process includes: Subtract 25°C from each of the set temperatures to obtain several relative temperatures.

[0063] Plotting relative temperature on the x-axis and electrical conductivity on the y-axis, a linear regression is performed on all relative temperatures and electrical conductivities. The equation for this regression line is: Q_lim -1 =Q_ref -1 ×(1+ ×ΔT), or expressed as Q_ref=Q_lim×(1+ ×ΔT). Where Q_lim represents the ordinate, ΔT represents the abscissa, and Q_ref represents the conductivity obtained at 25℃. -1 Q_ref -1 This indicates that taking the reciprocals of Q_lim and Q_re is to transform the physical quantity representing conductivity into a physical quantity representing resistance. The slope is obtained through linear regression. (That is, using the least squares method to obtain the slope of the equation of a straight line).

[0064] Step S101 of Example 1 includes: determining the limiting diffusion current and the surface area ratio by fitting a power-law relationship. As an example, the process includes: In this embodiment, there are 5 samples with identical geometric shapes but different surface roughness, including one sample with a flat surface (i.e., the surface roughness is negligible). The ratio of the actual surface area to the apparent geometric area (i.e., the geometric area obtained by length × width of the sample surface) of each sample is denoted as the surface area ratio. The ratio of the limiting diffusion current density (25°C) of each sample to the limiting diffusion current density (25°C) of the sample with a flat surface is denoted as the normalized limiting diffusion current.

[0065] Using the surface area ratio as the x-axis and the normalized limiting diffusion current as the y-axis, a regression model is established based on the surface area ratio and normalized limiting current of all samples: That is, regression fitting ln(P) = - ×ln(R); where R represents the x-axis and P represents the y-axis. The slope is obtained by performing linear regression. In this embodiment, the rate =1.6. Where ln() represents the logarithmic function with the natural constant as the base.

[0066] Example 3: Step S102 of Embodiment 1 includes: during the climb phase of the startup phase, performing multiple data samplings to obtain... 1 sampling point. As an example, the process includes: During this climb, microsecond-level current interruptions are periodically performed to collect data. In this embodiment, the interrupt duration is set to 5 milliseconds, and an interrupt occurs every 1 second; the term "microsecond-level" means that the interrupt process is extremely short, less than 1 microsecond, and can be ignored.

[0067] Set the total number of valid sampling points to (For example ). Regarding the first Secondary interruption event. Perform the following operations: (1) Record the rectifier output current density at the moment of interruption. and bath temperature .

[0068] (2) Locking after power failure to The first time window (equivalent to a high-frequency time window) is defined. The potential decay within this window is primarily determined by the solution's ohmic impedance and the discharge of the electric double layer capacitance. The electric double layer discharge time constant is extracted through single-exponential decay fitting. .

[0069] (3) Locking after power failure to The second time window (equivalent to the low-frequency time window) is used. The potential rise within this window is primarily determined by the diffusion of copper ions from the bulk to the interface. The slope of the potential rise, i.e., the copper ion interface replenishment rate, is extracted using linear regression. .

[0070] As an example, the electric double-layer discharge time constant is extracted by fitting a single exponential decay. The methods include: For a discharge process of an RC circuit (following the laws of ohmic impedance and capacitor discharge), the change of its voltage (V) with time (j) follows a single exponential decay law: After linear transformation, it can be expressed as: Where V(j) represents the potential at the electrode / solution interface measured at time j. The initial potential amplitude of the exponential decay process (i.e., the voltage value at the discharge start point j=0, where j=0 represents the time j corresponding to the first element in the time window), which is also the potential at the moment of interruption; Represents the time constant; This represents the final value of the decay, i.e., the stable potential after the discharge is complete. In this embodiment, this value is the potential at the last time point of the time window.

[0071] In this embodiment, the potential is sampled at 10 equal intervals within a time window to linearly regress the linearly transformed model described above, resulting in... As .

[0072] In the above formula, exp() represents an exponential function with the natural constant as the base.

[0073] As an example, the potential recovery slope, i.e., the copper ion interfacial replenishment rate, is extracted through linear regression. The methods include: Within a time window, potentials are sampled at 10 equal time intervals. A linear regression method is used to fit a linear model of potential versus time, and the slope of this linear model is used as the... .

[0074] Step S103 in Example 1 includes: collecting the double-layer discharge time constant at time t. As an example, the process includes: After the start-up phase of the electroplating process (i.e., after the current density climbs to the set production target value), every second is considered a time point. The double-layer discharge time constant is obtained according to the method described above in this embodiment. The double-layer discharge time constant obtained at time point t is expressed as: .

[0075] Considering that during high-current-density electroplating, the bubbles generated by the intense hydrogen evolution reaction on the electrode surface and the high-speed turbulence of the electrolyte will cause high-frequency random disturbances to the microscopic electric double layer structure, instantaneous measurements are used directly. This can cause significant fluctuations in subsequent surface area calculations. To filter out noise caused by such non-topographical factors, a sliding window filtering mechanism is introduced.

[0076] Specifically, for all double-layer discharge time constants obtained within a preset time period before time t (e.g., within 5 seconds before time t, including time t), all double-layer discharge time constants constitute a sequence. The maximum and minimum values ​​in the sequence are obtained, and these maximum and minimum values ​​are removed from the sequence. The arithmetic mean of the remaining data in the sequence is calculated, and this average value is used as described in Example 1. .

[0077] Specifically, after the start-up phase of the electroplating process, when there are less than 5 seconds before time t, considering that the high-frequency random disturbances mentioned above have a relatively small impact, at this time... .

[0078] Step S105 in Example 1 includes: calculating the mass transfer limit approximation degree at time t. As another example, The calculation methods also include: make: This represents the first mass transfer difference transmitted at time t.

[0079] Furthermore, in order to Standardize to The standard control signal for the interval, and handles possible numerical out-of-bounds errors, let: when When the value approaches 0, it indicates that the interface mass transfer capacity is excessive, and production is safe; when... When the value approaches 1.0, it indicates that the copper ion concentration at the interface is approaching zero, and the hydrogen evolution side reaction is about to occur.

[0080] Step S105 in Example 1 includes: calculating the adjustment step size of the rectifier output current density at time t. ,That and They are negatively correlated. As an example, the process includes: (1) During electrochemical deposition, when the reactant concentration on the electrode surface approaches zero, the concentration polarization overpotential increases exponentially according to the Nernst equation. To match the control response characteristics with this physical characteristic, the logarithmic barrier function is used to approximate the linear mass transfer limit. Mapped to the concentration polarization risk potential at time t : The dimensionless concentration polarization overpotential at the electrode surface was simulated. When it is at a low level (e.g., 0.5), The rate of change is small (approximately 0.69), and the control process remains in a low-sensitivity state, avoiding frequent current adjustments due to minor fluctuations.

[0081] when When approaching the safety limit (e.g., 0.95), The gain increases sharply (reaching 2.99), and the control process automatically obtains extremely high feedback gain. This design ensures that the system operates smoothly when far from the danger zone, while generating a strong correction signal when approaching the burn plate boundary, thereby accurately locking the maximum safe production capacity.

[0082] (2) To maximize production efficiency without causing plate burning, a proportional adjustment algorithm is used to maintain the operating conditions at a preset safety risk level. Preset safety margin target potential energy. (For example =2.3), calculate the potential energy deviation at time t. : in This defines the maximum concentration polarization risk level allowed by the process. Its setting is based on historical yield data and is typically set to correspond to the mass transfer limit approximation. The potential energy value at ≈0.90 (i.e.) =2.3), to ensure that a safety buffer of about 10% is reserved before approaching the limit.

[0083] (3) Furthermore, using a preset proportional gain coefficient Adjustment step size for calculating rectifier output current density : To ensure that the response rate of the control process matches the timescale of the electrochemical reaction and to avoid overshoot oscillations, The value needs to be adjusted through engineering. As a preferred embodiment, the following is set: The value of makes the potential energy deviation When =0.1, the current adjustment step size It is approximately 1% to 2% of the total current range. For example, for a rectifier with a 100A range, It can be set to 12.

[0084] Example 4: This embodiment also includes the following steps: Step S106: Perform fault blocking based on the adjustment step size of the current density.

[0085] In a normal electrochemical system, reducing the current density inevitably leads to a rebound in the interface concentration, thereby reducing the risk potential energy. Utilizing this physical law, this step constructs a diagnostic logic for non-current-controllable faults.

[0086] Continuous monitoring of current adjustment step size With risk potential change The symbolic relationship, Let represent the concentration polarization risk potential energy of the previous time step at time t. When and When the time t is reached, it is marked as an abnormal time. Specifically, after the start-up phase of the electroplating process, there is no time preceding the time t. Set to 0.

[0087] Thus, the above has been passed. The rectifier output control and abnormal moment marking were completed, forming the "operation-response" logic.

[0088] If the three consecutive moments preceding the current moment (including the current moment) are all abnormal moments, it indicates that a current reduction operation is being performed (attempting to alleviate polarization). However, the detected concentration polarization risk potential energy is abnormally and continuously increasing, indicating an electroplating fault. This also suggests that the aforementioned "operation-response" deviation points solely to a non-current-controllable mass transfer failure, which may originate from mechanical faults (such as nozzle blockage or circulation pump failure leading to flow field collapse) or chemical faults (such as additive depletion causing uncontrolled polarization). In this case, further current adjustment will not solve the problem. An emergency stop command will be immediately triggered, cutting off the rectifier output and issuing an audible and visual alarm, prompting the operator to check the equipment status or replace the plating solution. This "operation-response" logic solves the intelligent detection, intelligent decision-making, and control processes that traditional smart sensors cannot achieve.

[0089] Other embodiments also provide a rapid detection system for copper ion concentration in an electroplating solution, the system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when running the computer program, performs all the steps of all the above embodiments.

[0090] The system also includes several sensors, such as a temperature sensor (for measuring the bath temperature) and a voltage sensor (for measuring the electrode potential). All sensors are connected to the processor, and the program executes all the above embodiments by reading the data collected by these sensors. The hardware device consisting of all the sensors and the processor is considered a smart sensor, which detects the copper ion concentration (determined by...). While indirectly describing the process, it further realizes intelligent fault detection and intelligent decision-making and control of the rectifier.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rapid detection method for copper ion concentration in electroplating solution, characterized in that, The method includes the following steps: Determining the gain coefficient of copper ion diffusion affected by temperature ; During the start-up phase of the electroplating process, the current density output by the rectifier, the collected bath temperature, and the copper ion interface replenishment rate are first utilized... The influence of the bath temperature on the collected copper ion interface replenishment rate is removed, and then a first model of the copper ion interface replenishment rate with respect to the current density is constructed. After the start-up phase of the electroplating process, it is used again. The influence of the bath temperature in the collected copper ion interface replenishment rate is removed to obtain the normalized ion replenishment rate. The surface area expansion ratio is determined based on the real-time collected double-layer discharge time constant and the reference time constant of the dendrite-free flat surface. The reference time constant of the dendrite-free flat surface is determined by the double-layer discharge time constant collected during the start-up phase. The effective mass transfer flux at the interface is determined by the normalized ion replenishment rate and the surface area expansion ratio; the theoretical required flux is obtained by substituting the real-time output current density of the rectifier into the first model constructed in the startup phase; the step size of the rectifier output current density is adjusted by the difference between the effective mass transfer flux at the interface and the theoretical required flux; and electroplating faults are detected.

2. The rapid detection method for copper ion concentration in electroplating solution according to claim 1, characterized in that, The gain coefficient for measuring the effect of temperature on copper ion diffusion The specific steps include the following: Several bath temperatures were set, and the limiting diffusion current density at each temperature was measured. A linear slope of the limiting diffusion current as a function of temperature was fitted, and this linear slope was used as the gain coefficient. .

3. The rapid detection method for copper ion concentration in electroplating solution according to claim 1, characterized in that, The specific steps involved in constructing the first model of the copper ion interface replenishment rate with respect to current density are as follows: During the start-up phase of the electroplating process, several data points are sampled. Each data point includes the collected current density, bath temperature, and copper ion interface replenishment rate. use The result obtained after removing the influence of the bath temperature in the collected copper ion interface replenishment rate is recorded as the first replenishment rate for each data point. Construct a linear model, using the current density of each data point as the independent variable of the linear model and the first replenishment rate as the dependent variable of the independent variable of the linear model. Use the current density of all data points and the first replenishment rate to fit the linear model using the least squares method. The fitted linear model is used as the first model.

4. The method for rapid detection of copper ion concentration in electroplating solution according to claim 1, characterized in that, The specific steps for determining the surface area expansion ratio based on the real-time acquired electric double-layer discharge time constant and the reference time constant of the dendrite-free flat surface are as follows: The electric double-layer discharge time constant was collected during the start-up phase of the electroplating process; Utilizing the gain coefficient of electrolyte thermal conductivity The influence of the bath temperature in the double-layer discharge time constant is removed to obtain the first constant; the average value of the first constant corresponding to all double-layer discharge time constants collected during the start-up phase of the electroplating process is recorded as the reference time constant for dendrite-free flat surface. For any double-layer discharge time constant acquired in real time after the start-up phase of the electroplating process, the gain coefficient of electrolyte thermal conductivity is used. The influence of the bath temperature in the double-layer discharge time constant is removed to obtain the corrected double-layer discharge time constant. The ratio of the corrected double-layer discharge time constant to the reference time constant of the dendrite-free flat surface is denoted as the surface area expansion ratio.

5. The method for rapid detection of copper ion concentration in electroplating solution according to claim 1, characterized in that, The effective mass transfer flux at the interface is positively correlated with the normalized ion replenishment rate and negatively correlated with the surface area expansion ratio.

6. The method for rapid detection of copper ion concentration in electroplating solution according to claim 1, characterized in that, The specific steps involved in adjusting the step size of the rectifier output current density based on the difference between the effective mass transfer flux at the interface and the theoretical required flux, and in detecting electroplating faults, are as follows: The concentration polarization risk potential is determined based on the difference between the effective mass transfer flux at the interface and the theoretical required flux, and the concentration polarization risk potential is positively correlated with the difference. The step size of the rectifier output current density is adjusted by the difference between the preset safety margin target potential energy and the concentration polarization risk potential energy, and the step size is positively correlated with the difference. When the change in concentration polarization risk potential energy is greater than 0 and the step size is less than 0, the moment is marked as an abnormal moment. When several abnormal moments exist consecutively, it is determined that there is a fault in the electroplating process.

7. A rapid detection method for copper ion concentration in an electroplating solution according to claim 1 or 3, characterized in that, The specific steps for removing the influence of the bath temperature on the collected copper ion interface replenishment rate are as follows: The average temperature of the plating bath collected during the start-up phase of the electroplating process is recorded as follows: ; For the copper ion interface replenishment rate collected at any bath temperature, the copper ion interface replenishment rate after removing the aforementioned influence is related to the bath temperature and... The difference was negatively correlated with the copper ion interface replenishment rate, and positively correlated with the [other factors]. It shows a negative correlation.

8. The rapid detection method for copper ion concentration in electroplating solution according to claim 4, characterized in that, The specific steps involved in removing the influence of the bath temperature on the double-layer discharge time constant are as follows: The average temperature of the plating bath collected during the start-up phase of the electroplating process is recorded as follows: ; For the double-layer discharge time constant collected at any bath temperature, the double-layer discharge time constant after removing the aforementioned influence is compared with the bath temperature and... The difference is positively correlated with the electric double layer discharge time constant, and also with... Positive correlation; The acquisition process includes: Several bath temperatures were set, and the conductivity at each bath temperature was measured. The linear slope of the conductivity change with bath temperature was used as... .

9. The rapid detection method for copper ion concentration in electroplating solution according to claim 1, characterized in that, The specific methods for acquiring the copper ion interface replenishment rate and the electric double layer discharge time constant are as follows: During the operation of the rectifier, the output current is interrupted at a preset period. For the first time window after the interruption, the potential within the first time window follows the law of ohmic impedance and capacitor discharge. The double-layer discharge time constant is extracted by fitting the potential within the first time window through exponential decay. For the second time window after the interruption, the recovery slope of the potential within the second time window is used as the copper ion interface replenishment rate. The length of the first time window is less than the length of the second time window.

10. A rapid detection system for copper ion concentration in an electroplating solution, the system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor runs the computer program, it implements all the steps of the rapid detection method for copper ion concentration in electroplating solution according to any one of claims 1 to 9.

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