Radio frequency matching parameter real-time optimization method based on gradient descent

Abstract

The invention relates to the technical field of data processing, in particular to a radio frequency matching parameter real-time optimization method based on gradient descent, and the method comprises the steps: obtaining a digital measurement data set which comprises a performance index statistical measurement value; calculating a gradient estimation value of a to-be-optimized matching parameter in the target cost function based on the digital measurement data set; processing the gradient estimation value through a data processing gradient estimation algorithm to obtain an optimized matching parameter; applying a disturbance quantity matrix to the matching parameters, obtaining a performance index statistical measurement value matrix, and obtaining a data driving gradient estimation value; calculating prediction gradient information of the performance index statistical measurement value through a statistical approximation model; performing data fusion processing on the predicted gradient information and the data-driven gradient estimation value to generate a first gradient estimation value; performing time sequence data processing on the currently calculated first gradient estimation value to obtain an optimal gradient estimation value; and generating an optimization matching parameter of the next optimization iteration period based on the probability density function.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to a real-time optimization method for radio frequency matching parameters based on gradient descent. Background Art

[0002] In many areas of scientific research and industrial production, specialized digital computing and data processing methods are required to analyze data streams from complex physical systems or processes. The goal is to determine a set of optimal operating parameters that enable the system to exhibit certain desired characteristics. The determination of these parameters is of great significance for equipment characteristic analysis and process window optimization.

[0003] From the perspective of digital computing and data processing, the core of this task is a specific computational problem: receiving multiple digital inputs, executing a numerical calculation method on a data processing device, calculating one or more performance evaluation indicators based on these inputs, and then using an optimization algorithm to find a set of parameter values that optimize these indicators. These parameter values themselves are the primary output of the data processing method.

[0004] However, the numerical algorithms currently used to perform such data processing tasks face several challenges in practice. First, when the number of parameters that need to be optimized is large, the computational efficiency of many existing algorithms is not high. They may require a large number of iterative calculations or a long processing time to complete the parameter optimization calculation process, which limits their effectiveness in application scenarios where results need to be obtained quickly. Secondly, there are also deficiencies in the accuracy and reliability of the calculation results. Some widely used numerical optimization techniques may converge to a local optimal solution when processing complex objective functions derived from actual system data, that is, the parameters calculated by the algorithm are not globally optimal. In addition, the algorithm may experience numerical instability during the iterative calculation process, causing the calculation results to oscillate or diverge, and it is impossible to provide a set of definite and reliable parameter outputs. Furthermore, the ability to process input data is also a key consideration.

[0005] In practical applications, the digital data streams provided by sensors often contain noise, drift, mutations, and even data loss. This requires robust data processing methods to perform calculations stably under these imperfect data conditions and produce meaningful and reliable parameter results. While some computational methods rely on complex mathematical models, these often require precise model information or extensive prior calibration data. This not only increases the workload of initial data analysis and processing, but also places higher demands on computing resources and may struggle to adapt to changes in the target system's characteristics over time. Therefore, there is an urgent need to develop and apply new digital data processing methods specifically suited for solving multi-parameter optimization computational problems derived from real-world system data. Ideally, these methods should possess high computational efficiency, strong numerical robustness, and the reliability of finding the global optimal solution at the algorithmic level, thereby efficiently and accurately completing the parameter optimization computational task on digital processing equipment.

[0006] To this end, a real-time optimization method for RF matching parameters based on gradient descent is proposed. Summary of the Invention

[0007] The present invention aims to provide a real-time optimization method for radio frequency matching parameters based on gradient descent. The method comprises obtaining a digital measurement data set related to the target radio frequency system state, the digital measurement data set including performance indicator statistical measurement values, calculating gradient estimates of matching parameters to be optimized in a target cost function based on the digital measurement data set, processing the gradient estimates using a data processing gradient estimation algorithm, and obtaining optimized matching parameters. A perturbation matrix generated based on a preset perturbation pattern is applied to the matching parameters to obtain a performance indicator statistical measurement value matrix, and numerically calculating data-driven gradient estimates of multi-point perturbations. The performance indicator statistical measurement values are calculated using a statistical approximation model to obtain predicted gradient information. The predicted gradient information is fused with the data-driven gradient estimate to generate a first gradient estimate. Historical gradient estimation data stored in the optimization iteration cycle is accessed, and the currently calculated first gradient estimate is subjected to time series data processing to obtain an optimal gradient estimate. The optimal matching parameters for the next optimization iteration cycle are calculated using the optimal gradient estimate by numerically analyzing a preset learning rate and the optimal gradient estimate based on a probability density function.

[0008] To achieve the above object, the present invention provides the following technical solutions: A real-time optimization method for radio frequency matching parameters based on gradient descent, comprising: obtaining a digital measurement data set related to a target radio frequency system state, the digital measurement data set including statistical measurement values of performance indicators; Based on the digital measurement data set, the gradient estimation value of the matching parameter to be optimized in the target cost function is calculated; the gradient estimation value is processed by the data processing gradient estimation algorithm to obtain the optimized matching parameter; The data processing flow of the data processing gradient estimation algorithm includes: applying a perturbation matrix generated based on a preset perturbation pattern to the matching parameters, obtaining a performance indicator statistical measurement value matrix, and obtaining a data-driven gradient estimation value of multiple perturbations through numerical calculation; calculating the performance indicator statistical measurement value through a statistical approximation model to obtain predicted gradient information; performing data fusion processing on the predicted gradient information and the data-driven gradient estimation value to generate a first gradient estimation value; accessing the historical gradient estimation data stored in the optimization iteration cycle, performing time series data processing on the currently calculated first gradient estimation value, and obtaining the optimal gradient estimation value; Based on the numerical analysis of the preset learning rate and the optimal gradient estimate value based on the probability density function, the corresponding optimization matching parameters for the next optimization iteration cycle are generated by calculating the optimal gradient estimate value.

[0009] Preferably, the digital measurement data set includes at least one of a reflection coefficient, a transmission coefficient, an impedance value, a capacitance value, an inductance value, a frequency response, a power loss, a temperature, a voltage, and a current waveform of the radio frequency signal; The performance indicator statistical measurement value is at least one of the average value, variance, maximum value, minimum value, peak value of the waveform, effective value and phase difference of the data in the digital measurement data set.

[0010] Preferably, the specific process of obtaining the gradient estimate of the matching parameter to be optimized includes: defining the target cost function based on statistical measurements of performance indicators in the digital measurement data set; The current measurement value in the digital measurement data set is used to calculate the partial derivative of the target cost function with respect to each matching parameter to be optimized, and obtain a gradient estimate representing the direction and rate of change of the cost function.

[0011] Preferably, the numerical calculation process of the data-driven gradient estimate specifically includes: Applying the perturbations in the orthogonal directions and at multiple amplitude levels in the matching parameters in parallel to the current matching parameters to be optimized to form a matching parameter matrix; Calculating performance indicator statistical measurement values for the matching parameter matrix to generate a performance indicator statistical measurement value matrix; Multivariate differences are used to calculate the ratio of the performance index change and parameter perturbation in each perturbation orthogonal direction. The gradient components in the dimension of the matching parameters to be optimized are obtained by combining the difference results in each orthogonal direction, and the data-driven gradient estimation value is generated.

[0012] Preferably, the process of obtaining the predicted gradient information is as follows: based on the matching parameter values and performance indicator measurements stored in historical optimization iteration cycles, a training data set of parameter-performance mapping relationships is constructed; the statistical approximation model is fitted to the training data set based on Gaussian process regression to generate a nonlinear statistical model that can predict performance indicators as they change with parameters; and the real-time matching parameters are analyzed by the statistical approximation model to obtain predicted gradient information, which is an approximate estimate of the true gradient.

[0013] Preferably, the specific process of the first gradient estimation value includes: Normalizing the data-driven gradient estimate and the predicted gradient information respectively; obtaining a noise level assessment result of a current optimization iteration cycle, assigning weight coefficients to the data-driven gradient estimate and the predicted gradient information; and linearly combining the weighted data-driven gradient estimate and the weighted predicted gradient information to generate a first gradient estimate.

[0014] Preferably, the specific process of the optimal gradient estimation value includes: Read the gradient estimation values calculated in the historical optimization iteration cycle from the storage unit to form a gradient estimation sequence; A sliding window filtering algorithm is used to smooth the gradient estimation sequence, and the gradient estimation sequence is used to calculate a first gradient estimation value through an adaptive moment estimation algorithm; based on gradient direction consistency detection, the gradient estimation values in the window are sorted to obtain an optimal gradient estimation value.

[0015] Preferably, the specific process of generating the matching parameter value of the next optimization iteration cycle includes: Analyze the statistical distribution characteristics of the currently obtained optimal gradient estimate, including the size of the modulus, the stability and change of the direction; Analyze the historical learning rate distribution based on the probability density function and determine the confidence interval of the learning rate in the current iteration cycle; Dynamically adjust the specific value of the learning rate within the confidence interval based on the modulus and direction angle of the optimal gradient estimate; After multiplying the optimal gradient estimate by the learning rate, the current matching parameter is updated in the negative gradient direction to generate the parameter value for the next iteration cycle.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention collects multi-dimensional digital measurement data sets of the target RF system in real time, including performance indicators such as reflection coefficient, transmission coefficient, impedance, capacitance, inductance, and frequency response, and generates a multi-point disturbance matrix based on a preset disturbance pattern, and then obtains data-driven gradient estimates through numerical calculation. At the same time, the historical measurement data is subjected to Gaussian process regression fitting in combination with a statistical approximation model to predict the impact of current parameter changes on performance indicators, generate predicted gradient information, and fuse the two. After time series data processing and sliding window filtering, adaptive moment estimation and other algorithms are used to obtain more accurate and smooth optimal gradient estimates. This achieves adaptive adjustment of the RF matching network under different working conditions and external environmental changes, significantly improving real-time dynamic response capabilities and autonomous optimization efficiency.

[0017] 2. The present invention introduces a hybrid estimation mechanism that combines data-driven and model prediction, and dynamically adjusts the learning rate confidence interval based on probability density function analysis, effectively avoiding the problem of pure gradient methods easily falling into local extreme values and slow convergence. By performing normalized weighted linear combinations of the gradient components obtained by multi-amplitude and multi-directional perturbation sampling and the predicted gradient generated based on Gaussian process regression, weights can be adaptively allocated under the guidance of noise level assessment, taking into account real-time measurement noise and historical trends, significantly enhancing the robustness and convergence rate of the optimization process. In addition, the dynamic learning rate adjustment strategy can flexibly change the step size according to the gradient modulus and directional stability, further improving the global search capability of the algorithm and reducing the complexity of manual experience parameter adjustment.

[0018] 3. While achieving high-precision real-time optimization of RF matching parameters, the method of the present invention fully utilizes a large number of gradient estimation sequences and performance measurement values stored in historical optimization iteration cycles, and smoothes and sorts the gradient sequences through sliding window filtering, adaptive moment estimation, and gradient direction consistency detection technologies, thereby automatically identifying and extracting the optimal gradient estimation value. Combined with probabilistic statistical analysis, a dynamic confidence interval assessment of the learning rate distribution is performed, which achieves a significant reduction in the impact of system noise and parameter jitter while ensuring optimization speed, thereby improving matching accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A schematic structural diagram of a real-time optimization method for RF matching parameters based on gradient descent provided by the present invention; Figure 2 A schematic diagram of a process for obtaining a first gradient estimate value provided by an embodiment of the present invention; Figure 3 A schematic diagram of the optimal gradient estimation structure provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0021] Example 1 This embodiment provides a real-time optimization method for RF matching parameters based on gradient descent in a plasma etching scenario. Plasma etching is a key process in semiconductor manufacturing, and its stability and uniformity directly affect the chip yield. The RF matching network is one of the core components of the plasma equipment, responsible for efficiently transmitting the energy generated by the RF power supply to the plasma chamber to excite and maintain a stable plasma. However, during the etching process, the chamber load impedance will dynamically change due to changes in process gas, pressure, power, substrate material, etc., resulting in mismatch of matching network parameters, affecting energy transmission efficiency and plasma state. This embodiment aims to minimize the reflected power by optimizing the parameters of the matching network in real time, thereby maintaining the stability of the etching process.

[0022] See also Figure 1 The present invention provides a real-time optimization method for radio frequency matching parameters based on gradient descent, and the technical solution is as follows: obtaining a digital measurement data set related to a target radio frequency system state, the digital measurement data set including statistical measurement values of performance indicators; Based on the digital measurement data set, the gradient estimation value of the matching parameter to be optimized in the target cost function is calculated; the gradient estimation value is processed by the data processing gradient estimation algorithm to obtain the optimized matching parameter; The data processing flow of the data processing gradient estimation algorithm includes: applying a perturbation matrix generated based on a preset perturbation pattern to the matching parameters, obtaining a performance indicator statistical measurement value matrix, and obtaining a data-driven gradient estimation value of multiple perturbations through numerical calculation; calculating the performance indicator statistical measurement value through a statistical approximation model to obtain predicted gradient information; performing data fusion processing on the predicted gradient information and the data-driven gradient estimation value to generate a first gradient estimation value; accessing the historical gradient estimation data stored in the optimization iteration cycle, performing time series data processing on the currently calculated first gradient estimation value, and obtaining the optimal gradient estimation value; Based on the numerical analysis of the preset learning rate and the optimal gradient estimate value based on the probability density function, the corresponding optimization matching parameters for the next optimization iteration cycle are generated by calculating the optimal gradient estimate value.

[0023] Further, the digital measurement data set includes at least one of a reflection coefficient, a transmission coefficient, an impedance value, a capacitance value, an inductance value, a frequency response, a power loss, a temperature, a voltage, and a current waveform of the radio frequency signal; The performance indicator statistical measurement value is at least one of the average value, variance, maximum value, minimum value, peak value of the waveform, effective value and phase difference of the data in the digital measurement data set.

[0024] In this embodiment, by incorporating multiple key parameters of the RF signal into the digital measurement data set, the present invention can fully reflect the operating status of the RF system and improve the ability to perceive changes in system characteristics during the matching parameter optimization process. At the same time, combined with the statistical measurement values of multi-dimensional performance indicators, it can more accurately characterize the changing trends of signal characteristics and matching status, providing richer and more stable data support for gradient estimation and parameter optimization. It effectively enhances the adaptability of the optimization algorithm to abnormal working conditions, load fluctuations and environmental interference, improves the accuracy and real-time performance of matching parameter adjustment, thereby further ensuring the energy transmission efficiency and process stability of the plasma etching process, and promoting the improvement of chip manufacturing yield.

[0025] During the plasma etching process, multi-dimensional data related to the RF system status is collected in real time to form a digital measurement data set, including: the reflection coefficient and transmission coefficient of the RF signal, the complex impedance value at the input of the matching network, the current capacitance value of the adjustable capacitor in the matching network, the output frequency of the RF power supply, the forward power and reflected power measured by the directional coupler, the signal strength, the cavity temperature, and the gas flow and pressure. Calculate the statistics of key performance indicators based on the collected data, such as the average value, variance or maximum value within a time window. In this embodiment, we use the average value of the reflected power As a core performance indicator statistical measurement value.

[0026] Furthermore, the specific process of obtaining the gradient estimation value of the matching parameter to be optimized includes: The target cost function is defined based on the performance indicator statistical measurement values in the digital measurement data set. ; Calculate the target cost function using the current measurement value in the digital measurement data set For each matching parameter to be optimized (the matching parameter to be optimized is the adjustable capacitance value , ) to obtain the gradient estimate that represents the direction and rate of change of the cost function , the specific calculation formula is: ; Among them, the gradient vector indicates the direction in which the cost function increases fastest, and the negative gradient direction indicates the direction in which the cost function decreases fastest.

[0027] In this embodiment, by collecting multi-dimensional parameters in real time during the plasma etching process, a comprehensive digital measurement data set is constructed to effectively capture the dynamic changes in the RF system state during the etching process. By calculating the statistics of key performance indicators within a time window, especially using the average reflected power as the core performance indicator statistical measurement value, the performance change trend of the matching network can be accurately reflected, and the sensitivity to mismatch phenomena can be improved. At the same time, based on the digital measurement data, the target cost function is defined and the gradient estimate corresponding to the matching parameter to be optimized (adjustable capacitance value) is directly calculated. This makes the gradient calculation closely related to the actual measurement state, improving the real-time and accuracy of the gradient estimation. By adjusting the matching parameters in the negative gradient direction using the gradient descent principle, the reflected power can be reduced more quickly, achieving efficient optimization of the matching network.

[0028] Furthermore, the numerical calculation process of the data-driven gradient estimate specifically includes: The matching parameters Orthogonal directions and multiple amplitude levels The disturbance amount is applied in parallel to the current matching parameters to be optimized to form a matching parameter matrix ; Calculating performance indicator statistical measurement values for the matching parameter matrix to generate a performance indicator statistical measurement value matrix; Use multivariate differences to calculate the ratio of performance index changes and parameter perturbations in each perturbation orthogonal direction, combine the difference results in each orthogonal direction to obtain the gradient component in the dimension of the matching parameter to be optimized, and generate data-driven gradient estimates. , the specific calculation formula is: .

[0029] In this embodiment, by applying perturbations in orthogonal directions and multiple amplitude levels in parallel to the matching parameters to be optimized, a systematic matching parameter matrix is formed, which makes the perturbation coverage more comprehensive and can fully explore the local variation characteristics in the parameter space. Furthermore, the refined gradient components are obtained by combining the differential results to form accurate data-driven gradient estimates. Compared with the traditional single-point or single-direction perturbation method, this embodiment can significantly improve the stability and noise resistance of the gradient estimation, effectively reduce the gradient estimation error, and improve the response speed and adaptability of the optimization algorithm to parameter changes in the actual etching process, thereby speeding up the matching adjustment process and improving the energy utilization efficiency and system stability of the etching process.

[0030] Furthermore, the process of obtaining the predicted gradient information is as follows: based on the matching parameter values and performance index measurements stored in the historical optimization iteration cycle, a training data set of the parameter-performance mapping relationship is constructed; the statistical approximation model is fitted to the training data set based on Gaussian process regression to generate a nonlinear statistical model that can predict performance indicators as parameters change; Gaussian process regression can learn the nonlinear mapping relationship from parameters to performance indicators and provide prediction uncertainty. The real-time matching parameters are analyzed by the statistical approximation model to obtain predicted gradient information, which is an approximate estimate of the true gradient. Based on the trained Gaussian process regression model, the current matching parameters are input, and the model can predict the predicted gradient information of performance indicators with slight changes in parameters. ; The predicted gradient information is obtained based on historical data and statistical models, and can be regarded as an approximate estimate of the true gradient.

[0031] In this embodiment, Gaussian process regression can not only accurately fit complex nonlinear relationships, but also output the uncertainty of the prediction results, thereby improving the credibility of the prediction results. By analyzing the real-time matching parameters through this model, the predicted gradient information near the current parameter point can be obtained without additional disturbance to the actual system. Since the predicted gradient information combines historical rich data and statistical modeling results, it has better robustness and accuracy than the gradient estimation obtained by single disturbance sampling, which helps to reduce the interference of random noise on the gradient estimation during the real-time optimization process, further improve the convergence speed and stability of the matching parameter optimization, thereby continuously maintaining the high stability and high energy efficiency of the plasma etching process.

[0032] Furthermore, the specific process of the first gradient estimation value can be found in Figure 2 , specifically including: Data-driven gradient estimates and predicted gradient information Normalize them respectively; obtain the noise level evaluation result of the current optimization iteration cycle, and assign weight coefficients to the data-driven gradient estimate and the predicted gradient information and ; Linearly combine the weighted data-driven gradient estimate with the weighted predicted gradient information to generate the first gradient estimate ,in, is the normalization function.

[0033] In this embodiment, by introducing noise level assessment, the confidence in data-driven and predicted gradients is dynamically adjusted. When real-time sampled data is significantly affected by noise, the system increases the weight of predicted gradient information. Conversely, it relies more on real-time measured data-driven gradients, effectively suppressing the impact of noise interference on optimization direction judgment. This approach fully leverages the freshness of real-time measurement data and the robustness of statistical prediction models to achieve robust fusion of gradient estimates, improve directional accuracy and convergence speed during gradient descent, and further enhance the reliability of real-time optimization of RF matching parameters and the stable control capability of the plasma etching process.

[0034] Furthermore, the specific process of the optimal gradient estimation value includes: Read the gradient estimation values calculated in the historical optimization iteration cycle from the storage unit to form a gradient estimation sequence; The sliding window filtering algorithm smoothes the gradient estimation sequence, smoothes the gradient estimation sequence, reduces the impact of short-term noise fluctuations, and uses the adaptive moment estimation algorithm (such as the momentum idea in the Adam optimizer) to adjust the current gradient estimation using historical gradient information (exponential moving average of the gradient) and historical gradient square information. The gradient estimation sequence is used to calculate the first gradient estimation value; based on the gradient direction consistency detection, the gradient estimation values in the window are sorted to obtain the optimal gradient estimation value. ; Gradient direction consistency test is used to evaluate the stability of the gradient direction within the window. If the gradient direction is consistently consistent, the current gradient estimate is considered to be more reliable. The gradient estimates within the window can be sorted or weighted averaged to obtain the optimal gradient estimate for the current cycle. , see Figure 3 .

[0035] This embodiment effectively reduces the interference of short-term noise fluctuations on the gradient estimation results, improving the stability and accuracy of the gradient estimation. Furthermore, an adaptive moment estimation algorithm (e.g., a momentum optimizer) is employed to dynamically adjust historical gradient information and gradient square information, enabling the gradient estimation to balance convergence speed and jitter suppression, further enhancing the robustness of the optimization process. Gradient direction consistency detection enables real-time assessment of the stability of the gradient estimation direction, screening the optimal gradient direction, and ensuring that the optimization process proceeds in the correct and stable direction. This accelerates the convergence of RF matching parameters, reduces matching error fluctuations, and enhances the continuity and accuracy of plasma etching process control.

[0036] Furthermore, the specific process of generating the matching parameter value for the next optimization iteration cycle includes: Analyze the statistical distribution characteristics of the currently obtained optimal gradient estimate, including the size of the modulus , stability and changes in direction; Distribution of historical learning rates based on probability density function Perform analysis to determine the confidence interval of the learning rate for the current iteration cycle ; According to the modulus and direction angle of the optimal gradient estimate, the Step learning rate The specific value within the confidence interval; for example, when the gradient modulus is large and the direction is stable, the learning rate can be appropriately increased; when the modulus is small or the direction changes unsteadily, the learning rate can be reduced to stabilize the search; After multiplying the optimal gradient estimate by the learning rate, the current matching parameter is updated in the negative gradient direction to generate the parameter value for the next iteration cycle. .

[0037] In this embodiment, by analyzing the modulus and direction change characteristics of the current optimal gradient estimate, combined with the probability density function of the historical learning rate distribution, it is possible to achieve adaptive adjustment of the learning rate and enhance the flexibility and pertinence of parameter updates. When the gradient modulus is large and the direction is stable, appropriately increasing the learning rate helps to speed up the convergence speed; when the gradient modulus is small or the direction change is unstable, the learning rate is automatically reduced to avoid oscillation or deviation caused by excessive step size, thereby improving the stability and accuracy of the matching optimization process. By updating the matching parameter value in the negative gradient direction, it can be ensured that each iteration moves in the optimal descent direction, improving the overall optimization efficiency, further enabling the RF system to quickly and accurately adapt to the process requirements, and significantly improving the consistency and stability of the plasma etching process.

[0038] Table 1 Performance comparison data table Comparative performance data before and after optimization in simulation experiments for this embodiment. Taking 10Ω, 50Ω, and 100Ω load impedances as examples, the reflection coefficient amplitudes were large before optimization and significantly reduced after optimization. Furthermore, the number of convergence iterations before optimization was significantly reduced. See Table 1 for details.

[0039] The real-time optimization method of RF matching parameters based on gradient descent provided by the present invention can timely adjust the matching network parameters according to the dynamic changes of chamber load impedance during plasma etching, thereby effectively reducing the reflected power, improving energy transmission efficiency, and maintaining the stability and uniformity of the plasma state. By introducing a technical solution based on data-driven gradient estimation and statistical approximation model fusion processing of perturbation patterns, this method can achieve accurate and reliable gradient estimation under the condition of frequent changes in process environment and significant measurement noise interference, effectively improving the convergence speed and matching accuracy of the optimization process. In addition, through the time series processing of historical gradient data and the adaptive adjustment of learning rate based on probability density function, this method can further improve the stability and robustness of the optimization algorithm, avoid the problem of matching network instability caused by excessive disturbance, adapt to the real-time RF matching requirements under different etching process conditions, and significantly improve the consistency of etching process and chip yield in semiconductor manufacturing process.

[0040] Example 2 This embodiment includes all the contents of the first embodiment and proposes an iterative update method for multi-objective optimization for matching network parameter optimization. To balance different performance requirements such as low system reflected power and high stability, a vectorized objective cost function is introduced, and the gradient estimate of the Jacobian matrix is calculated to guide parameter update. The specific steps are as follows: Constructing a vector target cost function: In this embodiment, at least two performance indicators are used as components of the target cost function to form a vectorized target function. For example, the reflected power and system stability during the etching process can be selected as indicators to construct a vector target cost function. .in, represents the reflected power determined by the matching parameters, Represents the impact of matching parameters on system stability. This vector cost function can simultaneously reflect the performance of multiple performance indicators under the matching network parameter settings.

[0041] Calculate the Jacobian matrix estimate: For the above vector target cost function, calculate its matching parameters to be optimized Specifically, for each performance indicator component , calculate its partial derivatives with respect to the parameters through numerical differences or simulations, and thus construct the Jacobian matrix estimate .

[0042] Determine the parameter update direction: According to the estimated Jacobian matrix and the preset multi-objective optimization strategy, determine the update direction of the matching parameters. In this embodiment, a linear weighted method can be used to comprehensively consider the gradients of each indicator: set the weight and Corresponding to the importance of reflected power and stability, respectively, and then constructing the comprehensive gradient direction ; Comprehensive gradient direction This approach simultaneously addresses the dual goals of reducing reflected power and improving system stability. By adjusting the weights, the optimization process can achieve a balance between these objectives. If there is a conflict between performance objectives, other multi-objective strategies (such as Pareto optimal frontier search) can be used to determine the overall gradient direction.

[0043] New matching parameters: The comprehensive gradient direction determined above and historical learning rate distribution Combined, the matching parameters are iteratively updated to generate the parameter values for the next optimization cycle. The following update formula can be used ;in is the matching parameter value of the current iteration, The matching parameter value obtained for the next iteration. Historical learning rate distribution The step size of each update is controlled, typically using a small positive number to ensure convergence. After completing a parameter update, the updated parameters can be applied to the plasma etching system for simulation or experimental testing. Repeat the above steps for multiple rounds until all performance indicators converge and meet the expected requirements.

[0044] The method of this embodiment was applied to simulate and verify a plasma etching system. The experimental results, shown in Table 2, show that after using multi-objective optimization, all system performance indicators improved compared to before optimization: reflected power was significantly reduced, system stability was improved, and convergence time was shortened. This demonstrates that this method effectively improves matching optimization under multi-objective conditions.

[0045] Table 2 Comparison of performance indicators before and after multi-objective optimization While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A real-time optimization method for radio frequency matching parameters based on gradient descent, characterized in that: include: obtaining a digital measurement data set related to a target radio frequency system state, the digital measurement data set including statistical measurement values of performance indicators; Based on the digital measurement data set, the gradient estimate of the matching parameter to be optimized in the target cost function is calculated; The gradient estimation value is processed by the data processing gradient estimation algorithm to obtain the optimized matching parameters; The data processing flow of the data processing gradient estimation algorithm includes: applying a perturbation matrix generated based on a preset perturbation pattern to the matching parameters, obtaining a performance indicator statistical measurement value matrix, and obtaining a data-driven gradient estimation value of multiple perturbations through numerical calculation; calculating the performance indicator statistical measurement value through a statistical approximation model to obtain predicted gradient information; performing data fusion processing on the predicted gradient information and the data-driven gradient estimation value to generate a first gradient estimation value; accessing the historical gradient estimation data stored in the optimization iteration cycle, performing time series data processing on the currently calculated first gradient estimation value, and obtaining the optimal gradient estimation value; Based on the numerical analysis of the preset learning rate and the optimal gradient estimate value based on the probability density function, the corresponding optimization matching parameters for the next optimization iteration cycle are generated by calculating the optimal gradient estimate value.

2. The method for real-time optimization of radio frequency matching parameters based on gradient descent according to claim 1, characterized in that: The digital measurement data set includes at least one of a reflection coefficient, a transmission coefficient, an impedance value, a capacitance value, an inductance value, a frequency response, a power loss, a temperature, a voltage, and a current waveform of the radio frequency signal; The performance indicator statistical measurement value is at least one of the average value, variance, maximum value, minimum value, peak value of the waveform, effective value and phase difference of the data in the digital measurement data set.

3. The method for real-time optimization of radio frequency matching parameters based on gradient descent according to claim 1, characterized in that: The specific process of obtaining the gradient estimation value of the matching parameter to be optimized includes: defining the target cost function based on statistical measurements of performance indicators in the digital measurement data set; The current measurement value in the digital measurement data set is used to calculate the partial derivative of the target cost function with respect to each matching parameter to be optimized, and obtain a gradient estimate representing the direction and rate of change of the cost function.

4. The method for real-time optimization of radio frequency matching parameters based on gradient descent according to claim 1, characterized in that: The numerical calculation process of the data-driven gradient estimate specifically includes: Applying the perturbations in the orthogonal directions and at multiple amplitude levels in the matching parameters in parallel to the current matching parameters to be optimized to form a matching parameter matrix; Calculating performance indicator statistical measurement values for the matching parameter matrix to generate a performance indicator statistical measurement value matrix; Multivariate differences are used to calculate the ratio of the performance index change and parameter perturbation in each perturbation orthogonal direction. The gradient components in the dimension of the matching parameters to be optimized are obtained by combining the difference results in each orthogonal direction, and the data-driven gradient estimation value is generated.

5. The method for real-time optimization of radio frequency matching parameters based on gradient descent according to claim 1, characterized in that: The process of obtaining the predicted gradient information is as follows: constructing a training data set of parameter-performance mapping relationship based on the matching parameter values and performance index measurement values stored in the historical optimization iteration cycle; The statistical approximation model is fitted to the training data set based on Gaussian process regression to generate a nonlinear statistical model capable of predicting performance indicators as parameters change; The real-time matching parameters are analyzed through a statistical approximation model to obtain predicted gradient information, which is an approximate estimate of the true gradient.

6. The method for real-time optimization of radio frequency matching parameters based on gradient descent according to claim 1, characterized in that: The specific process of the first gradient estimation includes: Normalizing the data-driven gradient estimate and the predicted gradient information respectively; obtaining a noise level assessment result of a current optimization iteration cycle, assigning weight coefficients to the data-driven gradient estimate and the predicted gradient information; and linearly combining the weighted data-driven gradient estimate and the weighted predicted gradient information to generate a first gradient estimate.

7. The method for real-time optimization of radio frequency matching parameters based on gradient descent according to claim 1, characterized in that: The specific process of the optimal gradient estimation includes: Read the gradient estimation values calculated in the historical optimization iteration cycle from the storage unit to form a gradient estimation sequence; A sliding window filtering algorithm is used to smooth the gradient estimation sequence, and the gradient estimation sequence is used to calculate a first gradient estimation value through an adaptive moment estimation algorithm; based on gradient direction consistency detection, the gradient estimation values in the window are sorted to obtain an optimal gradient estimation value.

8. The method for real-time optimization of radio frequency matching parameters based on gradient descent according to claim 1, characterized in that: The specific process of generating the matching parameter value for the next optimization iteration cycle includes: Analyze the statistical distribution characteristics of the currently obtained optimal gradient estimate, including the size of the modulus, the stability and change of the direction; Analyze the historical learning rate distribution based on the probability density function and determine the confidence interval of the learning rate in the current iteration cycle; Dynamically adjust the specific value of the learning rate within the confidence interval based on the modulus and direction angle of the optimal gradient estimate; After multiplying the optimal gradient estimate by the learning rate, the current matching parameter is updated in the negative gradient direction to generate the parameter value for the next iteration cycle.

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