Pulse current closed-loop control method for TGV electroplating cavity self-healing

Abstract

The invention relates to the technical field of advanced packaging of semiconductors, in particular to a pulse current closed-loop control method for TGV electroplating cavity self-healing, which comprises the following steps of: in an electroplating hole filling process, collecting a multi-frequency impedance spectrum and a cathode potential fluctuation signal in parallel through a dual-electrode sensor array, and calculating a TGV electroplating cavity self-healing parameter by combining micro-pressure and conductivity data of an electroplating solution; and constructing an in-hole fluid-electric field coupling state matrix. Based on the matrix, on one hand, the dynamic probability of cavity formation is calculated through a pre-training algorithm, and on the other hand, the deposition front three-dimensional morphology is reconstructed, and the thickness gradient and edge steepness indexes are extracted. The parameters are used as constraints, pulse current waveform parameters are optimized in a rolling mode, the rotating speed and the flow direction of a plating solution stirring device are synchronously and dynamically adjusted, and cooperative control over electrical parameters and a flow field is achieved. And after each electroplating period is finished, updating the morphology data and re-estimating the risk to form a closed loop. According to the method, active prevention and self-healing of cavity defects are realized through multi-source information fusion and electricity-current collaborative optimization.

Description

Technical Field

[0001] This invention relates to the field of advanced semiconductor packaging technology, and in particular to a pulse current closed-loop control method for self-healing voids in TGV electroplating. Background Technology

[0002] In the TGV electroplating via filling process, the formation of voids is a key factor restricting interconnect reliability and yield. Existing technologies mainly rely on a single type of monitoring signal, such as the average cathode potential or AC impedance at a fixed frequency, to indirectly assess the filling status within the voids. Process control often employs preset pulse current parameters and fixed plating solution stirring modes, relying on experience for open-loop or simple single-variable feedback adjustment.

[0003] The shortcomings of these existing technologies lie in the fact that a single signal cannot fully characterize the complex dynamic coupling relationship between metal ion mass transfer within the pore, electrodeposition interface reactions, and fluid microflow. This results in insensitivity to early signs of cavity nucleation and expansion, leading to delayed and vague risk warnings. Static or isolated control strategies cannot respond in real time to the rapid evolution of the microstructure at the deposition front, and the lack of dynamic coordination between current parameters and the fluid environment makes it difficult to effectively intervene in the early stages of cavity formation.

[0004] A method is needed to acquire and fuse multi-dimensional information reflecting the coupling state of multiple physical fields within the pores in real time, enabling dynamic and accurate quantification of void risk. Furthermore, based on this real-time quantified risk and precise morphological characteristics, a coordinated and adaptive closed-loop control of electrical pulse excitation and physical flow field agitation is required to actively suppress void formation and growth during electroplating. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and propose a pulse current closed-loop control method for self-healing voids in TGV electroplating.

[0006] To achieve the above objectives, the present invention employs the following technical solution: a pulse current closed-loop control method for self-healing of voids in TGV electroplating, comprising:

[0007] During the TGV electroplating process, a dual-electrode sensor array immersed in the plating solution is used to collect multi-frequency impedance spectrum signals and cathode potential fluctuation signals in parallel.

[0008] Frequency domain features were extracted from the acquired multi-frequency impedance spectrum signals to obtain impedance feature vectors that reflect the transport characteristics of metal ions within the pores.

[0009] The cathode potential fluctuation signal was recorded synchronously, and combined with the micro-pressure sensing data of the electroplating solution and the conductivity change data, a fluid-electric field coupling state matrix in the hole was constructed.

[0010] The impedance feature vector is input into a pre-trained void risk estimation algorithm to calculate the dynamic probability value of void formation in the current electroplating cycle.

[0011] Based on the fluid-electric field coupling state matrix inside the pore, the three-dimensional morphology of the metal deposition front inside the pore is reconstructed, and the deposition thickness distribution gradient and edge steepness index are extracted.

[0012] Using the dynamic probability value, deposition thickness distribution gradient, and edge steepness index as constraints, the pulse current waveform parameters are continuously optimized.

[0013] The duty cycle, peak current density, and reverse pulse duration of the pulse current are dynamically adjusted based on the optimization results.

[0014] The rotation speed and flow direction of the plating solution stirring device are adjusted synchronously so that the flow field distribution inside the hole and the optimized pulse current waveform work together.

[0015] After each electroplating cycle, the morphology data of the metal growth front is updated, and the probability of void risk is reassessed to form a closed-loop control loop.

[0016] As a further aspect of the present invention, the step of extracting frequency domain features from the acquired multi-frequency impedance spectrum signal to obtain an impedance feature vector reflecting the metal ion transport characteristics within the pore includes:

[0017] A fast Fourier transform is performed on the multi-frequency impedance spectrum signal within a millisecond time window to obtain the impedance amplitude-frequency characteristic curve and the phase-frequency characteristic curve.

[0018] The impedance modulus at characteristic frequency points is extracted from the impedance amplitude-frequency characteristic curve, including the impedance value of the low-frequency diffusion control region, the impedance value of the mid-frequency charge transfer region, and the high-frequency solution resistance value.

[0019] Extract the maximum phase angle and its corresponding frequency from the phase frequency response curve, and calculate the phase peak width and symmetry coefficient;

[0020] The impedance modulus, maximum phase angle, phase peak width, and symmetry coefficient are combined into a multidimensional feature sequence.

[0021] Principal component analysis is used to reduce the dimensionality of the multidimensional feature sequence, retaining the feature components whose contribution rate exceeds the threshold, and generating impedance feature vectors.

[0022] As a further aspect of the present invention, the construction of the fluid-electric field coupling state matrix within the pore includes:

[0023] Dynamic pressure distribution data at different depths within the borehole are obtained using a micro-pressure sensor, and the rate of change of pressure gradient over time is calculated.

[0024] The spatial distribution of conductivity in the plating solution is monitored by a conductivity sensor, and the local electric field intensity distribution is calculated by combining the pulse current density.

[0025] The cathode potential fluctuation signal is decomposed into DC and AC components, and the amplitude modulation characteristics of the AC component are extracted.

[0026] By integrating the pressure gradient change rate, local electric field intensity distribution and amplitude modulation characteristics, a state matrix is ​​constructed with rows corresponding to time points and columns corresponding to spatial sampling points.

[0027] Singular value decomposition is performed on the state matrix to extract the dominant modes that reflect the fluid-electric field coupling strength.

[0028] As a further aspect of the present invention, the step of inputting the impedance feature vector into a pre-trained void risk estimation algorithm to calculate the dynamic probability value of void formation within the current electroplating cycle includes:

[0029] A hole risk classifier is constructed using the gradient boosting decision tree algorithm, with the number of input layer nodes matching the dimension of the impedance feature vector.

[0030] The impedance eigenvectors are spatiotemporally aligned with the synchronously acquired deposition rate data to form a labeled training sample set.

[0031] By iteratively improving the weighted combination of weak classifiers, a nonlinear mapping relationship between impedance characteristics and void defects is established.

[0032] In the current electroplating cycle, the real-time impedance feature vector is input into the trained classifier, and the output is the probability value of hole occurrence based on the joint distribution of multi-dimensional features.

[0033] A time decay factor is introduced to perform a moving average filter on the probability values, generating a smooth dynamic probability curve;

[0034] The training process of the hole risk estimation algorithm includes:

[0035] Collect multi-frequency impedance spectrum signals and corresponding post-electroplating hole morphology detection results from historical electroplating processes. The morphology detection results are used to indicate whether void defects exist.

[0036] Frequency domain features are extracted from historical multi-frequency impedance spectrum signals to generate historical impedance feature vectors.

[0037] The historical impedance feature vectors are combined with the corresponding void defect labeling information to form a labeled training sample set;

[0038] The gradient boosting decision tree algorithm is used to train the training sample set. By iteratively boosting the weighted combination of weak classifiers, a nonlinear mapping relationship between impedance features and void defects is established.

[0039] The performance of the trained classifier was evaluated using the 10-fold cross-validation method, and the maximum depth of the decision tree and the learning rate hyperparameter were adjusted based on the validation results.

[0040] Save the classifiers whose performance meets the preset accuracy threshold as pre-trained hole risk estimation algorithms.

[0041] As a further aspect of the present invention, the reconstructed three-dimensional morphology of the metal deposition front within the hole includes:

[0042] Based on the cathode potential distribution, the contour lines of current density inside the borehole are deduced, and a transfer function between current density and deposition rate is established.

[0043] The theoretical deposition thickness distribution is calculated by integrating the pulse electroplating time.

[0044] Deposition deviations caused by edge effects are corrected by using phase characteristics in the impedance eigenvector;

[0045] The depositional front interface is evolved using the level set method, and an interface update term based on fluid shear force is introduced.

[0046] The output is a set of topographic data containing three-dimensional coordinates, deposition thickness, and interface curvature.

[0047] As a further aspect of the present invention, the extraction of deposition thickness distribution gradient and edge steepness indices includes:

[0048] Perform spatial difference operations on the three-dimensional topography data to calculate the thickness change rate vector of each grid point;

[0049] The modulus distribution of the thickness change rate vector is statistically analyzed, and the maximum modulus value is taken as the gradient of the deposition thickness distribution.

[0050] The rate of curvature change is calculated along the tangent of the deposition interface, and the average value of the curvature extreme points is extracted as the edge steepness.

[0051] The thickness distribution gradient and edge steepness are normalized and combined to form a deposition uniformity index.

[0052] As a further aspect of the present invention, the rolling optimized pulse current waveform parameters include:

[0053] A discrete state-space model is established with pulse duty cycle, peak current density, and reverse pulse duration as control variables;

[0054] The primary objective is to minimize the dynamic probability value, while the sediment thickness distribution gradient and edge steepness indices serve as constraints.

[0055] Solve the quadratic programming problem in the finite time domain at each sampling time to obtain the optimal sequence of control variables;

[0056] Only the optimal control value at the current moment is implemented, and the optimization calculation is re-performed at the next sampling moment;

[0057] A relaxation factor is introduced to handle constraint conflicts and ensure the feasibility of the optimization problem.

[0058] As a further aspect of the present invention, the step of dynamically adjusting the duty cycle of the pulse current, the peak current density, and the reverse pulse duration based on the optimization results includes:

[0059] Adjust the switching timing of the pulse power supply according to the duty cycle command output by the optimization algorithm;

[0060] Adjust the output amplitude of the constant current source according to the peak current density setting;

[0061] Configure the duration of the anodic dissolution phase based on the reverse pulse duration parameter;

[0062] Establish a cross-coupling compensation table for the three parameters to eliminate mutual interference between parameters;

[0063] The parameter combination is converted into an actual electrical signal output through a digital-to-analog converter.

[0064] As a further aspect of the present invention, the synchronous adjustment of the rotation speed and flow direction of the plating solution stirring device includes:

[0065] The fundamental frequency of the stirring impeller is set based on the dominant mode frequency of the fluid-electric field coupling state matrix inside the hole;

[0066] The stirring intensity is adjusted according to the gradient of the deposition thickness distribution, and the local flow velocity is increased in areas with large gradients.

[0067] Computational fluid dynamics simulation was used to optimize the flow pattern, so that the plating solution formed a spiral upward flow field inside the hole;

[0068] The speed of the stirring motor is adjusted in real time by a frequency converter to match the periodic changes of the pulse current;

[0069] Monitor the flow field stability index and switch to turbulence suppression mode when the index exceeds the threshold.

[0070] As a further aspect of the present invention, the updating of the morphology data of the metal growth front and the reassessment of the void risk probability include:

[0071] After each electroplating cycle, new multi-frequency impedance spectrum signals and cathode potential signals are collected.

[0072] The new signal is input into the updated deposition front reconstruction algorithm to generate corrected morphology data;

[0073] By comparing the differences in morphological data from adjacent periods, the advance rate of the depositional front is calculated.

[0074] The propulsion rate is compared with the theoretical value to calibrate the model parameters of the reconstruction algorithm;

[0075] The cavity risk estimation algorithm is retrained using the corrected topographic data to complete the self-learning process of the closed-loop control system.

[0076] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0077] By using a dual-electrode sensor array immersed in the plating bath to acquire multi-frequency impedance spectroscopy and cathode potential fluctuation signals in parallel, and simultaneously fusing micro-pressure and conductivity data, a fluid-electric field coupling state matrix within the pores is constructed. This technology enables comprehensive and synchronous perception of the electrochemical interface reaction kinetics, mass transfer process, and hydrodynamic state within the pores during electroplating. Unlike conventional single-signal monitoring, this multi-source data fusion can capture subtle signs of restricted metal ion transport or uneven deposition earlier and more sensitively, transforming the risk of void formation from a qualitative judgment into a dynamically calculable probability value. The three-dimensional morphology of the metal deposition front reconstructed based on this coupling matrix has a much higher accuracy than predictions based on a single physical model, and can accurately extract key micro-morphological indicators such as deposition thickness distribution gradient and edge steepness.

[0078] Using dynamically calculated void risk probability, real-time extracted deposition thickness distribution gradient, and edge steepness indices as multidimensional constraints, the waveform parameters such as pulse current duty cycle, peak current density, and reverse pulse duration are continuously optimized, while simultaneously adjusting the rotation speed and flow direction of the plating solution agitator. This transforms electrical pulse excitation and physical flow field agitation from two independent or sequential control links into a real-time, coordinated control system. Each optimization adjustment of the current waveform is accompanied by a targeted adaptation of the flow field distribution, ensuring that the optimized mass transfer conditions can immediately support new electrodeposition modes. This coordinated continuous optimization can directly act on the microscopic contours of the deposition front, effectively smoothing the deposition layer, reducing the thickness gradient, mitigating abnormal growth at the edges, and disrupting conditions for void formation. Attached Figure Description

[0079] Figure 1 The flowchart shows the pulse current closed-loop control method for self-healing voids in TGV electroplating according to the present invention.

[0080] Figure 2 This is a flowchart for frequency domain feature extraction of multi-frequency impedance spectrum signals;

[0081] Figure 3 A flowchart for reconstructing the three-dimensional morphology of the metal deposition front within the pore;

[0082] Figure 4 A state monitoring curve for the TGV electroplating hole-filling process before optimization;

[0083] Figure 5 A diagram illustrating the real-time performance of the TGV electroplating pulse current closed-loop control. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0085] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0086] See Figure 1 During the TGV electroplating process for filling voids, a dual-electrode sensor array immersed in the plating solution is used to collect multi-frequency impedance spectral signals and cathode potential fluctuation signals in parallel. Frequency domain features are extracted from the collected multi-frequency impedance spectral signals to obtain an impedance feature vector reflecting the metal ion transport characteristics within the void. Simultaneously, the cathode potential fluctuation signal is recorded. Combined with micro-pressure sensing data and conductivity change data of the plating solution, a fluid-electric field coupling state matrix within the void is constructed. This impedance feature vector is input into a pre-trained void risk estimation algorithm to calculate the dynamic probability value of void formation within the current plating cycle. Based on the fluid-electric field coupling state matrix within the void... The three-dimensional morphology of the metal deposition front in the hole is reconstructed, and the deposition thickness distribution gradient and edge steepness index are extracted. Using the dynamic probability value, deposition thickness distribution gradient and edge steepness index as constraints, the pulse current waveform parameters are continuously optimized. Based on the optimization results, the duty cycle, peak current density and reverse pulse duration of the pulse current are dynamically adjusted, and the rotation speed and flow direction of the plating solution stirring device are simultaneously adjusted so that the flow field distribution in the hole and the optimized pulse current waveform work together. After each electroplating cycle, the morphology data of the metal growth front is updated, and the probability of void risk is reassessed to form a closed-loop control loop.

[0087] See Figure 2In one embodiment of the present invention, during the TGV electroplating filling process, a dual-electrode sensor array is immersed in the plating solution to collect multi-frequency impedance spectroscopy signals and cathode potential fluctuation signals in parallel. In some embodiments, the sampling time window of the dual-electrode sensor array is set to one millisecond to cover the transient characteristics of the electroplating dynamic process. It can be understood that the frequency scanning range of the multi-frequency impedance spectroscopy signal extends from 0.1 Hz to 10,000 Hz, which can simultaneously capture the impedance response related to diffusion, charge transfer, and solution resistance. A fast Fourier transform is performed on the multi-frequency impedance spectroscopy signal within each millisecond time window to obtain the impedance amplitude-frequency characteristic curve and the phase-frequency characteristic curve. From the impedance amplitude-frequency characteristic... The impedance modulus at characteristic frequency points was extracted from the curve, including the impedance values ​​of the low-frequency diffusion control region, the mid-frequency charge transfer region, and the high-frequency solution resistance. Data comparison showed that when the transport of metal ions within the hole was obstructed, the impedance value of the low-frequency diffusion control region increased significantly compared to when the transport was smooth. The high-frequency solution resistance, however, exhibited periodic changes due to fluctuations in the ion concentration of the plating solution. The maximum phase angle and its corresponding frequency were extracted from the phase-frequency characteristic curve. The phase peak width and symmetry coefficient were calculated. The phase peak width was determined by the difference between the frequency points where the phase angle decreased to half of the maximum phase angle. The symmetry coefficient was used to quantify the degree of deviation in the shape of the phase peak, and its calculation formula is expressed as follows:

[0088]

[0089] in: Represents the symmetry coefficient. This represents the difference between the frequency corresponding to the maximum phase angle and the frequency at the half-power point to the left of the phase peak. This represents the difference between the half-power point frequency to the right of the phase peak and the frequency corresponding to the maximum phase angle. In practice, the impedance modulus, maximum phase angle, phase peak width, and symmetry coefficient are combined into a multi-dimensional feature sequence. Principal component analysis is performed on the multi-dimensional feature sequence to reduce its dimensionality. Feature components with a contribution rate exceeding a preset threshold are retained to generate an impedance feature vector. Optionally, the preset threshold is set to 85% to reduce the data dimensionality while retaining the main information.

[0090] In some embodiments, dynamic pressure distribution data at different depths within the hole are acquired using a micro-pressure sensor, and the rate of change of the pressure gradient over time is calculated. This rate of change is obtained through a first-order difference operation on the pressure distribution data at adjacent time points. The spatial distribution of the plating solution's conductivity is monitored using a conductivity sensor, and the local electric field intensity distribution is calculated by combining the pulse current density. The local electric field intensity distribution is calculated from the conductivity data and the instantaneous current density using Ohm's law. The cathode potential fluctuation signal is decomposed into DC and AC components, and the amplitude modulation characteristics of the AC component are extracted. These characteristics are obtained by demodulating the envelope amplitude change of the AC component. Finally, the rate of change of the pressure gradient and the local electric field intensity distribution are fused. Based on amplitude modulation characteristics, a state matrix is ​​constructed with rows corresponding to time points and columns corresponding to spatial sampling points. Singular value decomposition (SVD) is performed on the state matrix to extract the dominant modes reflecting the fluid-electric field coupling strength. The dominant mode corresponds to the left singular vector corresponding to the maximum singular value in the SVD. Data comparison shows that when the flow field inside the orifice is stable and the deposition is uniform, the energy of the dominant mode is concentrated in a narrow frequency band. When the flow field is turbulent or the deposition is abnormal, the energy distribution of the dominant mode exhibits a broadband characteristic. It can be understood that the frequency domain characteristics of the dominant mode are used to indirectly evaluate the stability of the transmission conditions inside the orifice. Optionally, the first three dominant modes in the SVD are retained for subsequent analysis to capture the main coupling modes.

[0091] In one embodiment of the present invention, a cavity risk classifier is constructed using a gradient boosting decision tree algorithm. The number of input layer nodes of the cavity risk classifier is consistent with the dimension of the impedance feature vector. In some embodiments, the impedance feature vector is generated by principal component analysis after dimensionality reduction, with a dimension of twenty. Therefore, the number of input layer nodes of the cavity risk classifier is set to twenty. The impedance feature vector is spatiotemporally aligned with the synchronously acquired deposition rate data to form a labeled training sample set. The spatiotemporal alignment operation ensures that each impedance feature vector sample point is associated with the deposition rate value at the same time and spatial location. It can be understood that the labels in the labeled training sample set originate from the morphology detection results of the hole after electroplating. The morphology detection results are used to indicate whether there are cavities. The labels are marked in binary form, with one for the presence of cavities and zero for the absence of cavities.

[0092] In some embodiments, the training process of the void risk estimation algorithm specifically includes collecting multi-frequency impedance spectrum signals acquired during historical electroplating processes and corresponding post-plating hole morphology detection results; extracting frequency domain features from the historical multi-frequency impedance spectrum signals to generate historical impedance feature vectors; combining the historical impedance feature vectors with corresponding void defect labeling information to form a labeled training sample set; training the labeled training sample set using a gradient boosting decision tree algorithm; establishing a nonlinear mapping relationship between impedance features and void defects by iteratively boosting the weighted combination of weak classifiers; generating a decision tree as a weak classifier in each iteration to correct the prediction residual of the previous decision tree; and finally, generating the classification result by weighted voting of all weak classifiers, with the weighted voting formula expressed as:

[0093]

[0094] in: This indicates that the gradient boosting decision tree algorithm applies the input feature vector. The final predicted output, This represents the total number of weak classifiers. Indicates the first A weak classifier The weighting coefficients, The input historical impedance feature vector is used. The performance of the trained hollow risk classifier is evaluated using the ten-fold cross-validation method. The maximum depth of the decision tree and the learning rate hyperparameters are adjusted according to the validation results. Data comparison shows that when the maximum depth of the decision tree is set to ten and the learning rate is set to 0.05, the classification accuracy of the hollow risk classifier on the validation set is significantly improved compared to the case where the maximum depth is five or the learning rate is 0.1. Hollow risk classifiers whose performance meets the preset accuracy threshold are saved as pre-trained hollow risk estimation algorithms.

[0095] In practical implementation, during the current electroplating cycle, the impedance feature vector collected and extracted in real time is input into the trained void risk classifier, which outputs a void occurrence probability value based on the joint distribution of multi-dimensional features. The void occurrence probability value is a continuous value output by the void risk classifier, ranging from zero to one. A time decay factor is introduced to perform moving average filtering on the void occurrence probability value to generate a smooth dynamic probability curve. Moving average filtering is achieved by assigning higher weights to recent probability values ​​and lower weights to long-term probability values. The time decay factor controls the rate of weight decay. Data comparison shows that the dynamic probability curve after moving average filtering can effectively suppress the peak fluctuations in probability values ​​caused by instantaneous measurement noise. Optionally, the time decay factor is set to 0.9 to balance the dynamic response speed and curve smoothness. It can be understood that the dynamic probability curve serves as the primary constraint target for subsequent rolling optimization of pulse current waveform parameters.

[0096] See Figure 3 In one embodiment of the present invention, the process of reconstructing the three-dimensional morphology of the metal deposition front in the hole is based on the cathode potential distribution to inversely deduce the current density contour lines in the hole. The cathode potential distribution data is collected by a dual-electrode sensor array immersed in the plating solution. A transfer function between current density and deposition rate is established. This transfer function describes the quantitative relationship between current density per unit area and metal deposition rate under specific plating solution composition and temperature. The theoretical deposition thickness distribution is calculated by combining pulse plating time integration. The theoretical deposition thickness distribution is obtained by time accumulation of the instantaneous deposition rate in each pulse cycle. It can be understood that the deposition deviation caused by edge effect is corrected by the phase characteristics in the impedance characteristic vector. The phase characteristics can reflect the difference in ion transport dynamics between the hole opening and the hole bottom region, thereby compensating for the uniform field conditions assumed in the theoretical calculation.

[0097] In some embodiments, the deposition front interface is evolved using a level set method, which introduces an interface update term based on fluid shear force. The level set function defines the deposition front as a zero isosurface, and its evolution equation is jointly determined by the electric field-driven normal deposition velocity and the tangential transport term caused by fluid shear force. The output is a set of morphological data containing three-dimensional coordinates, deposition thickness, and interface curvature. The morphological data set is stored in the form of spatial grid points. Each grid point contains its three-dimensional spatial coordinates, the deposition thickness value calculated at that location, and the interface curvature value obtained by fitting a local surface.

[0098] In practice, the step of extracting the deposition thickness distribution gradient and edge steepness index involves performing spatial difference operations on the three-dimensional topographic data to calculate the thickness change rate vector for each grid point. The spatial difference operation uses the central difference method to calculate the first-order partial derivatives of the thickness in the X, Y, and Z directions of the three-dimensional grid, thus constructing the thickness change rate vector for each grid point. The magnitude distribution of the thickness change rate vector is then statistically analyzed, and the maximum magnitude is taken as the deposition thickness distribution gradient. The calculation formula is expressed as follows:

[0099]

[0100] in: Indicates the gradient of deposition thickness distribution. Indicates the deposition thickness at the grid point. , , These represent the rates of change of thickness in the X, Y, and Z directions of three-dimensional space, respectively. This indicates that the maximum value calculated from all grid points is taken. Data comparison shows that, under ideal conditions of uniform deposition, the thickness distribution gradient... The value remains at a low baseline level; when uneven deposition or the initial formation of voids begins to appear... The value will increase by an order of magnitude.

[0101] The rate of curvature change is calculated along the tangent direction of the deposition interface, and the average value of the curvature extrema is extracted as the edge steepness. The tangent direction of the deposition interface is determined by the local normal vector of the interface. The rate of curvature change is obtained by calculating the derivative of the principal curvature along the tangent direction. The thickness distribution gradient and the edge steepness are normalized and combined into a deposition uniformity index. The normalization process maps the thickness distribution gradient and the edge steepness to the range of zero to one. Optionally, the combination method adopts weighted summation, and the weight coefficients are allocated according to the contribution of the two to the final void defects in historical electroplating data. It can be understood that the deposition uniformity index is a quantitative parameter for evaluating the current deposition morphology quality and serving as a constraint condition for subsequent pulse current waveform parameter optimization.

[0102] In one embodiment of the present invention, a discrete state-space model is established using the pulse duty cycle, peak current density, and reverse pulse duration as control variables to optimize the pulse current waveform parameters. The state variables of the discrete state-space model include the deposition thickness distribution gradient, edge kurtosis index, and a filtered sequence of dynamic probability values. The pulse duty cycle ranges from 0.1 to 0.5, the peak current density ranges from 1 to 5 amperes per square decimeter, and the reverse pulse duration ranges from 1 to 10 milliseconds. Minimizing the dynamic probability value is the primary objective, with the deposition thickness distribution gradient and edge kurtosis index as constraints. The constraints are set such that the deposition thickness distribution gradient and the edge kurtosis index must not exceed a set gradient threshold and a set kurtosis threshold, respectively. A quadratic programming problem is solved within a finite time domain at each sampling time to obtain the optimal sequence of control variables. The finite time domain covers the next ten control cycles. The objective function of the quadratic programming problem is expressed as:

[0103]

[0104] in: Indicates at time The optimization objective function value, Represents dynamic probability value The weighting coefficients, Indicates the gradient of sediment thickness distribution The weighting coefficients, Indicator of edge steepness Weighting coefficients, weighting coefficients , , The sum of is one, and The value is greater than and The value is used to reflect the primary importance of minimizing the dynamic probability value. It can be understood that solving the quadratic programming problem yields an optimal setpoint sequence for the pulse duty cycle, peak current density, and reverse pulse duration over the next ten control cycles.

[0105] In some embodiments, the optimization process is performed at each sampling time, but only the optimal control quantity at the current time is implemented, and the optimization calculation is re-performed at the next sampling time. Data comparison shows that this rolling implementation strategy can better cope with random disturbances in the electroplating process than implementing the entire optimal sequence. The relaxation factor is introduced to handle constraint conflicts and ensure the feasibility of the optimization problem. When the deposition thickness distribution gradient and the edge steepness index cannot simultaneously meet the constraint threshold, the relaxation factor allows the constraint of the edge steepness index to be temporarily relaxed to ensure that the goal of minimizing the dynamic probability value is achieved and the constraint of the deposition thickness distribution gradient is satisfied.

[0106] In practical implementation, the duty cycle, peak current density, and reverse pulse duration of the pulse current are dynamically adjusted based on the optimization results. The switching sequence of the pulse power supply is adjusted according to the duty cycle command output by the optimization algorithm. The duty cycle command determines the ratio of the current conduction time to the total cycle within a pulse cycle. The output amplitude of the constant current source is adjusted according to the peak current density setting value. The peak current density setting value is converted into a specific voltage command by querying the preset current-voltage relationship table and applied to the constant current source. The duration of the anodic dissolution stage is configured according to the reverse pulse duration parameter. During the anodic dissolution stage, a small reverse current is applied within the reverse pulse duration. A cross-coupling compensation table for the three parameters is established to eliminate mutual interference between parameters. The cross-coupling compensation table stores the compensation correction value for the third parameter when any two parameters are adjusted together. For example, when the pulse duty cycle and peak current density are increased simultaneously, the reverse pulse duration needs to be increased by a compensation amount according to the compensation table to offset the deposition roughening effect that may be caused by the increase in average current. See Table 1 for a simplified cross-coupling compensation table.

[0107] Table 1: Cross-coupling compensation table

[0108] Duty cycle adjustment Peak current density adjustment Reverse pulse duration compensation +0.05 0 0 0 +0.5A / dm² +0.5ms +0.05 +0.5A / dm² +1.2ms -0.05 -0.5A / dm² -0.8ms

[0109] The parameter combination is converted into an actual electrical signal output by a digital-to-analog converter. The resolution of the digital-to-analog converter is 16 bits, the reference voltage is 5 volts, and the duty cycle command, the voltage command corresponding to the peak current density, and the reverse pulse duration command are respectively mapped to the output channel of the digital-to-analog converter. After being converted into an analog voltage signal, it is transmitted to the control terminal of the pulse power supply and the constant current source. Optionally, the update rate of the digital-to-analog converter is synchronized with the rolling optimization sampling time.

[0110] See Figure 4This is a state monitoring curve of the TGV electroplating cavity filling process before optimization. It shows the dynamic changes of core indicators and the comparison with constraint thresholds during the electroplating cycle, providing basic data support for pulse current closed-loop control. The green dashed line (gradient threshold 0.8) and the blue dashed line (steepness threshold 0.7) clearly delineate the process safety range. In the initial stage, both indicators exceeded the limit, which is the trigger condition that requires key optimization of the pulse current parameters in the subsequent stage. The decrease in dynamic void probability is strongly correlated with the improvement of deposition gradient and edge steepness, verifying the rationality of these three as core state variables for closed-loop control. The rapid decrease in gradient and steepness indicators in the first 10 cycles indicates that adjusting the pulse current parameters in the initial stage is most effective in improving deposition uniformity, providing key time-series characteristics for subsequent rolling optimization.

[0111] In one embodiment of the present invention, the rotation speed and flow direction of the plating solution stirring device are synchronously adjusted according to the dominant mode frequency of the fluid-electric field coupling state matrix in the hole. The fundamental frequency of the stirring impeller is set, which reflects the periodic characteristics of the interaction between the fluid and the electric field in the hole. In some embodiments, when the dominant mode frequency is 5 Hz, the fundamental frequency of the stirring impeller is set to 5 Hz to match the main oscillation period of the transmission process in the hole. Data comparison shows that when the fundamental frequency of the stirring impeller is consistent with the dominant mode frequency, the spectral peak energy of the flow field in the hole is more concentrated. The stirring intensity is adjusted according to the gradient of the deposition thickness distribution. The local flow velocity is increased in the region with a large gradient. The region with a large gradient of the deposition thickness distribution usually corresponds to the position where the metal ions in the hole are insufficient. The local convection is enhanced by adjusting the flow velocity of the jet nozzle in the corresponding region of the stirring device. The flow direction mode is optimized by computational fluid dynamics simulation to make the plating solution form a spiral upward flow field in the hole. The computational fluid dynamics simulation is based on the actual electroplating tank and wafer fixture geometric model. The optimization goal is to make the streamlines present a uniform spiral upward shape in the hole.

[0112] In some embodiments, the speed of the stirring motor is adjusted in real time by a frequency converter to match the periodic changes of the pulse current. The periodic changes of the pulse current are reflected by its duty cycle and frequency. The control commands of the frequency converter are synchronized with the trigger signal of the pulse power supply to monitor the flow field stability index. When the flow field stability index exceeds the threshold, the turbulence suppression mode is switched. The formula, calculated using real-time collected micro-pressure sensor data, is expressed as follows:

[0113]

[0114] in: Indicators representing flow field stability This represents the standard deviation of the flow velocity at multiple sampling points within a single time window. This represents the average flow velocity inside the orifice within the corresponding time window. Data comparison shows that when the flow field stability index... When the flow rate is below 0.15, the flow field is in a stable laminar state; when the flow field stability index... When the flow exceeds 0.15, unstable turbulence begins to appear in the flow field. At this time, the stirring mode switches to the turbulence suppression mode, which is achieved by reducing the speed of the stirring impeller and changing the impeller tilt angle.

[0115] In practice, after each electroplating cycle, the morphology data of the metal growth front is updated and the probability of voids is reassessed. New multi-frequency impedance spectroscopy signals and cathode potential signals are acquired. The new signals are acquired at the end of the current electroplating cycle and input into the updated deposition front reconstruction algorithm to generate corrected morphology data. The updated deposition front reconstruction algorithm has been calibrated with the deposition front advance rate of the previous cycle. The differences in morphology data between adjacent cycles are compared, and the deposition front advance rate is calculated. The deposition front advance rate is obtained by calculating the thickness difference of the same spatial coordinate point in the morphology data of different cycles and then dividing it by the electroplating cycle time. The deposition front advance rate is compared with the theoretical deposition front advance rate value to calibrate the model parameters of the reconstruction algorithm. The model parameters mainly refer to the proportionality coefficient in the transfer function of current density and deposition rate. It can be understood that the proportionality coefficient is corrected online by the deviation between the actual deposition front advance rate and the theoretical value.

[0116] In practice, the cavity risk estimation algorithm is retrained using the corrected topographic data to complete the self-learning process of the closed-loop control system. The corrected topographic data provides the latest and more accurate ground truth labels, which are used to incrementally update the training sample set of the gradient boosting decision tree algorithm. Optionally, each retraining uses only a certain number of recent electroplating cycle data to maintain the algorithm's adaptability to process drift. The new version of the cavity risk estimation algorithm generated after retraining will be used to calculate the dynamic probability value of the next electroplating cycle. It can be understood that this step enables the cavity risk estimation algorithm to be continuously updated in accordance with the dynamic changes of the electroplating process.

[0117] See Figure 5This is a real-time performance graph used to evaluate the closed-loop control of pulsed current in TGV electroplating, showing the dynamic correlation between void risk probability and process improvement rate over 10 electroplating cycles. The inverse fluctuations of the two curves directly verify the causal logic of "increased improvement rate → decreased void risk," proving that pulsed current parameter optimization is effective in suppressing void formation. The sharp increase in void risk probability in cycle 6 may be due to a brief decrease in the improvement rate in that cycle, indicating local fluctuations in the process, requiring close attention to parameter stability during this period in subsequent rolling optimizations. The fluctuation ranges of both the improvement rate and void risk probability narrowed significantly in cycles 8-10, indicating that the closed-loop control gradually converged in the later stages, and process stability was improved. Through the inverse linkage between "improvement rate" and "void risk probability," the effectiveness of pulsed current optimization measures in suppressing voids is directly quantitatively verified, providing data support for the engineering practicality of the algorithm.

[0118] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A pulse current closed-loop control method for self-healing voids in TGV electroplating, characterized in that, The method includes: During the TGV electroplating process, a dual-electrode sensor array immersed in the plating solution is used to collect multi-frequency impedance spectrum signals and cathode potential fluctuation signals in parallel. Frequency domain features were extracted from the acquired multi-frequency impedance spectrum signals to obtain impedance feature vectors that reflect the transport characteristics of metal ions within the pores. The cathode potential fluctuation signal was recorded synchronously, and combined with the micro-pressure sensing data of the electroplating solution and the conductivity change data, a fluid-electric field coupling state matrix in the hole was constructed. The impedance feature vector is input into a pre-trained void risk estimation algorithm to calculate the dynamic probability value of void formation in the current electroplating cycle. Based on the fluid-electric field coupling state matrix inside the pore, the three-dimensional morphology of the metal deposition front inside the pore is reconstructed, and the deposition thickness distribution gradient and edge steepness index are extracted. Using the dynamic probability value, deposition thickness distribution gradient, and edge steepness index as constraints, the pulse current waveform parameters are continuously optimized. The duty cycle, peak current density, and reverse pulse duration of the pulse current are dynamically adjusted based on the optimization results. The rotation speed and flow direction of the plating solution stirring device are adjusted synchronously so that the flow field distribution inside the hole and the optimized pulse current waveform work together. After each electroplating cycle, the morphology data of the metal growth front is updated, and the probability of void risk is reassessed to form a closed-loop control loop.

2. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 1, characterized in that, The step of extracting frequency domain features from the acquired multi-frequency impedance spectrum signal to obtain an impedance feature vector reflecting the metal ion transport characteristics within the pore includes: A fast Fourier transform is performed on the multi-frequency impedance spectrum signal within a millisecond time window to obtain the impedance amplitude-frequency characteristic curve and the phase-frequency characteristic curve. The impedance modulus at characteristic frequency points is extracted from the impedance amplitude-frequency characteristic curve, including the impedance value of the low-frequency diffusion control region, the impedance value of the mid-frequency charge transfer region, and the high-frequency solution resistance value. Extract the maximum phase angle and its corresponding frequency from the phase frequency response curve, and calculate the phase peak width and symmetry coefficient; The impedance modulus, maximum phase angle, phase peak width, and symmetry coefficient are combined into a multidimensional feature sequence. Principal component analysis is used to reduce the dimensionality of the multidimensional feature sequence, retaining the feature components whose contribution rate exceeds the threshold, and generating impedance feature vectors.

3. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 2, characterized in that, The construction of the fluid-electric field coupling state matrix within the pore includes: Dynamic pressure distribution data at different depths within the borehole are obtained using a micro-pressure sensor, and the rate of change of pressure gradient over time is calculated. The spatial distribution of conductivity in the plating solution is monitored by a conductivity sensor, and the local electric field intensity distribution is calculated by combining the pulse current density. The cathode potential fluctuation signal is decomposed into DC and AC components, and the amplitude modulation characteristics of the AC component are extracted. By integrating the pressure gradient change rate, local electric field intensity distribution and amplitude modulation characteristics, a state matrix is ​​constructed with rows corresponding to time points and columns corresponding to spatial sampling points. Singular value decomposition is performed on the state matrix to extract the dominant modes that reflect the fluid-electric field coupling strength.

4. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 1, characterized in that, The step of inputting the impedance feature vector into a pre-trained void risk estimation algorithm to calculate the dynamic probability value of void formation within the current electroplating cycle includes: A hole risk classifier is constructed using the gradient boosting decision tree algorithm, with the number of input layer nodes matching the dimension of the impedance feature vector. The impedance eigenvectors are spatiotemporally aligned with the synchronously acquired deposition rate data to form a labeled training sample set. By iteratively improving the weighted combination of weak classifiers, a nonlinear mapping relationship between impedance characteristics and void defects is established. In the current electroplating cycle, the real-time impedance feature vector is input into the trained classifier, and the output is the probability value of hole occurrence based on the joint distribution of multi-dimensional features. A time decay factor is introduced to perform a moving average filter on the probability values, generating a smooth dynamic probability curve; The training process of the hole risk estimation algorithm includes: Collect multi-frequency impedance spectrum signals and corresponding post-electroplating hole morphology detection results from historical electroplating processes. The morphology detection results are used to indicate whether void defects exist. Frequency domain features are extracted from historical multi-frequency impedance spectrum signals to generate historical impedance feature vectors. The historical impedance feature vectors are combined with the corresponding void defect labeling information to form a labeled training sample set; The gradient boosting decision tree algorithm is used to train the training sample set. By iteratively boosting the weighted combination of weak classifiers, a nonlinear mapping relationship between impedance features and void defects is established. The performance of the trained classifier was evaluated using the 10-fold cross-validation method, and the maximum depth of the decision tree and the learning rate hyperparameter were adjusted based on the validation results. Save the classifiers whose performance meets the preset accuracy threshold as pre-trained hole risk estimation algorithms.

5. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 4, characterized in that, The reconstructed three-dimensional morphology of the metal deposition front within the pore includes: Based on the cathode potential distribution, the contour lines of current density inside the borehole are deduced, and a transfer function between current density and deposition rate is established. The theoretical deposition thickness distribution is calculated by integrating the pulse electroplating time. Deposition deviations caused by edge effects are corrected by using phase characteristics in the impedance eigenvector; The depositional front interface is evolved using the level set method, and an interface update term based on fluid shear force is introduced. The output is a set of topographic data containing three-dimensional coordinates, deposition thickness, and interface curvature.

6. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 5, characterized in that, The extraction of deposition thickness distribution gradient and edge steepness indices includes: Perform spatial difference operations on the three-dimensional topography data to calculate the thickness change rate vector of each grid point; The modulus distribution of the thickness change rate vector is statistically analyzed, and the maximum modulus value is taken as the gradient of the deposition thickness distribution. The rate of curvature change is calculated along the tangent of the deposition interface, and the average value of the curvature extreme points is extracted as the edge steepness. The thickness distribution gradient and edge steepness are normalized and combined to form a deposition uniformity index.

7. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 1, characterized in that, The rolling optimized pulse current waveform parameters include: A discrete state-space model is established with pulse duty cycle, peak current density, and reverse pulse duration as control variables; The primary objective is to minimize the dynamic probability value, while the sediment thickness distribution gradient and edge steepness indices serve as constraints. Solve the quadratic programming problem in the finite time domain at each sampling time to obtain the optimal sequence of control variables; Only the optimal control value at the current moment is implemented, and the optimization calculation is re-performed at the next sampling moment; A relaxation factor is introduced to handle constraint conflicts and ensure the feasibility of the optimization problem.

8. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 7, characterized in that, The dynamic adjustment of the pulse current duty cycle, peak current density, and reverse pulse duration based on the optimization results includes: Adjust the switching timing of the pulse power supply according to the duty cycle command output by the optimization algorithm; Adjust the output amplitude of the constant current source according to the peak current density setting; Configure the duration of the anodic dissolution phase based on the reverse pulse duration parameter; Establish a cross-coupling compensation table for the three parameters to eliminate mutual interference between parameters; The parameter combination is converted into an actual electrical signal output through a digital-to-analog converter.

9. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 1, characterized in that, The synchronous adjustment of the rotation speed and flow direction of the plating solution stirring device includes: The fundamental frequency of the stirring impeller is set based on the dominant mode frequency of the fluid-electric field coupling state matrix inside the hole; The stirring intensity is adjusted according to the gradient of the deposition thickness distribution, and the local flow velocity is increased in areas with large gradients. Computational fluid dynamics simulation was used to optimize the flow pattern, so that the plating solution formed a spiral upward flow field in the hole; The speed of the stirring motor is adjusted in real time by a frequency converter to match the periodic changes of the pulse current; Monitor the flow field stability index and switch to turbulence suppression mode when the index exceeds the threshold.

10. The pulse current closed-loop control method for self-healing voids in TGV electroplating according to claim 1, characterized in that, The updating of the morphological data of the metal growth front and the reassessment of the void risk probability include: After each electroplating cycle, new multi-frequency impedance spectrum signals and cathode potential signals are collected. The new signal is input into the updated deposition front reconstruction algorithm to generate corrected morphology data; By comparing the differences in morphological data from adjacent periods, the advance rate of the depositional front is calculated. The propulsion rate is compared with the theoretical value to calibrate the model parameters of the reconstruction algorithm; The cavity risk estimation algorithm is retrained using the corrected topographic data to complete the self-learning process of the closed-loop control system.

Images