A gradient descent-based real-time optimization method for radio frequency matching parameters

Abstract

The application relates to the technical field of data processing, in particular to a radio frequency matching parameter real-time optimization method based on gradient descent, a digital measurement data set is acquired, and performance index statistical measurement values are included; based on the digital measurement data set, gradient estimation values of to-be-optimized matching parameters in a target cost function are calculated; the gradient estimation values are processed through a data processing gradient estimation algorithm, and optimized matching parameters are obtained; a disturbance quantity matrix is applied to the matching parameters, performance index statistical measurement value matrices are acquired, data-driven gradient estimation values are obtained; prediction gradient information is calculated through a statistical approximation model based on the performance index statistical measurement values; the prediction gradient information and the data-driven gradient estimation values are subjected to data fusion processing, and first gradient estimation values are generated; the currently calculated first gradient estimation values are subjected to time sequence data processing, and optimal gradient estimation values are obtained; and optimization matching parameters of a next optimization iteration cycle are generated based on a probability density function.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, specifically to a real-time optimization method for radio frequency matching parameters based on gradient descent. Background Technology

[0002] In many fields of scientific research and industrial production, specialized digital computing and data processing methods are required to analyze data streams originating from complex physical systems or processes. The aim 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 input data streams, executing a numerical computation method on a data processing device, calculating one or more performance evaluation indicators based on these input data, and finding a set of parameter values ​​that optimize these indicators through an optimization algorithm. These parameter values ​​themselves are the main output of the data processing method.

[0004] However, current numerical algorithms used to perform such data processing tasks face several challenges in practice. First, many existing algorithms are computationally inefficient when the number of parameters to be optimized is large. They may require numerous iterative calculations or long processing times to complete the parameter optimization process, limiting their effectiveness in applications requiring rapid results. Second, there are also shortcomings in the accuracy and reliability of the computational results. Some widely used numerical optimization techniques may converge to local optima when dealing with complex objective functions derived from real-world system data, meaning the parameters calculated by the algorithm are not globally optimal. Furthermore, numerical instability may occur during iterative calculations, leading to oscillations or divergence in the results, failing to provide a definite and reliable set of parameter outputs. Finally, the ability to process input data is also a critical consideration.

[0005] In practical applications, the digital data streams provided by sensors often contain noise, drift, or abrupt changes, and may even experience data loss. This necessitates that the data processing methods employed possess strong robustness, capable of stably performing calculations and yielding meaningful and reliable parameter results under such imperfect data conditions. While some computational methods rely on complex mathematical models, these methods typically require precise model information or a large amount of prior calibration data. This not only increases the workload of preliminary data analysis and processing but also places higher demands on computational 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 computation problems derived from real-world system data. Ideally, such methods should possess high computational efficiency, strong numerical robustness, and the reliability to find the global optimum at the algorithmic level, thereby efficiently and accurately completing parameter optimization computation tasks on digital processing devices.

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

[0007] The purpose of this invention is to provide a real-time optimization method for radio frequency (RF) matching parameters based on gradient descent. This method involves acquiring a digital measurement dataset related to the state of the target RF system, including statistical measurements of performance indicators. Based on this dataset, the gradient estimates of the matching parameters to be optimized in the target cost function are calculated. The gradient estimates are then processed using a data processing gradient estimation algorithm to obtain the optimized matching parameters. A perturbation matrix generated based on a preset perturbation mode is applied to the matching parameters to obtain a matrix of statistical measurements of performance indicators. Data-driven gradient estimates of multi-point perturbations are obtained through numerical calculation. Predicted gradient information is calculated from the statistical measurements of performance indicators using a statistical approximation model. The predicted gradient information and the data-driven gradient estimates are fused to generate a first gradient estimate. Historical gradient estimates from the stored optimization iteration cycle are accessed, and the currently calculated first gradient estimate is processed using time-series data to obtain the optimal gradient estimate. Finally, based on a probability density function, numerical analysis of the preset learning rate and the optimal gradient estimate is performed, and the optimal matching parameters for the next optimization iteration cycle are calculated using the optimal gradient estimate.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A real-time optimization method for radio frequency matching parameters based on gradient descent includes:

[0010] Acquire a digital measurement dataset related to the state of the target RF system, which includes statistical measurements of performance indicators.

[0011] Based on a digital measurement dataset, the gradient estimate of the matching parameter to be optimized in the objective cost function is calculated; the gradient estimate is then processed using a data processing gradient estimation algorithm to obtain the optimized matching parameter.

[0012] The data processing flow of the gradient estimation algorithm includes: applying a perturbation matrix generated based on a preset perturbation mode to the matching parameters, obtaining a matrix of statistical measurement values ​​of performance indicators, and obtaining data-driven gradient estimates of multi-point perturbation through numerical calculation; calculating predicted gradient information from the statistical measurement values ​​of performance indicators through a statistical approximation model; performing data fusion processing on the predicted gradient information and the data-driven gradient estimates to generate a first gradient estimate; accessing historical gradient estimation data in the stored optimization iteration cycle, performing time-series data processing on the currently calculated first gradient estimate, and obtaining the optimal gradient estimate.

[0013] Based on the numerical analysis of the preset learning rate and the optimal gradient estimate using the probability density function, the corresponding optimization matching parameters for the next optimization iteration cycle are generated by calculating the optimal gradient estimate.

[0014] Preferably, the digital measurement dataset includes at least one of the following: the reflection coefficient, transmission coefficient, impedance value, capacitance value, inductance value, frequency response, power loss, temperature, voltage, and current waveforms of the radio frequency signal.

[0015] The statistical measurement value of the performance index is at least one of the mean, variance, maximum value, minimum value, peak value, effective value, and phase difference of the data in the digital measurement dataset.

[0016] Preferably, the specific process for obtaining the gradient estimate of the matching parameter to be optimized includes:

[0017] The target cost function is defined based on the statistical measurement values ​​of the performance indicators in the digital measurement dataset.

[0018] Using the current measurement values ​​in the digital measurement dataset, the partial derivatives of the target cost function with respect to each matching parameter to be optimized are calculated to obtain gradient estimates that characterize the direction and rate of change of the cost function.

[0019] Preferably, the numerical calculation process of the data-driven gradient estimate specifically includes:

[0020] The perturbations of orthogonal direction and multiple amplitude levels in the matching parameters are applied in parallel to the current matching parameters to be optimized, forming a matching parameter matrix;

[0021] Calculate the statistical measurement values ​​of performance indicators for the matching parameter matrix, and generate a matrix of statistical measurement values ​​of performance indicators;

[0022] Multivariate difference is used to calculate the ratio of performance index change and parameter perturbation in each perturbation orthogonal direction. The gradient components in the dimension of the matching parameter to be optimized are obtained by combining the difference results of each orthogonal direction, and data-driven gradient estimates are generated.

[0023] Preferably, the process of obtaining the predicted gradient information is as follows: a training dataset of parameter-performance mapping relationship is constructed based on the matching parameter values ​​and performance index measurement values ​​stored in the historical optimization iteration cycle; the statistical approximation model fits the training dataset based on Gaussian process regression to generate a nonlinear statistical model that can predict the performance index changes with parameters; the real-time matching parameters are analyzed through the statistical approximation model to obtain the predicted gradient information, which is an approximate estimate of the true gradient.

[0024] Preferably, the specific process of the first gradient estimate includes:

[0025] The data-driven gradient estimate and the predicted gradient information are normalized respectively; the noise level assessment result of the current optimization iteration cycle is obtained, and weight coefficients are assigned to the data-driven gradient estimate and the predicted gradient information; the weighted data-driven gradient estimate and the weighted predicted gradient information are linearly combined to generate the first gradient estimate.

[0026] Preferably, the specific process of obtaining the optimal gradient estimate includes:

[0027] Gradient estimates calculated from historical optimization iterations are read from the storage unit to form a gradient estimation sequence;

[0028] The sliding window filtering algorithm smooths the gradient estimation sequence, and the adaptive moment estimation algorithm uses the gradient estimation sequence to calculate the first gradient estimate. Based on gradient direction consistency detection, the gradient estimates within the window are sorted to obtain the optimal gradient estimate.

[0029] Preferably, the specific process for generating the matching parameter values ​​in the next optimization iteration includes:

[0030] Analyze the statistical distribution characteristics of the currently obtained optimal gradient estimate, including the magnitude of the modulus, the stability of the direction, and the variation of the gradient.

[0031] The historical learning rate distribution is analyzed based on the probability density function to determine the learning rate confidence interval for the current iteration cycle;

[0032] Based on the magnitude and orientation angle of the optimal gradient estimate, the learning rate is dynamically adjusted within the confidence interval.

[0033] After multiplying the optimal gradient estimate by the learning rate, the current matching parameters are updated in the direction of the negative gradient to generate the parameter values ​​for the next iteration.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] 1. This invention acquires multi-dimensional digital measurement datasets of the target RF system in real time, including performance indicators such as reflection coefficient, transmission coefficient, impedance, capacitance, inductance, and frequency response. A multi-point perturbation matrix is ​​generated based on a preset perturbation mode, and then data-driven gradient estimates are obtained through numerical calculations. Simultaneously, a statistical approximation model is used to fit Gaussian process regression to historical measurement data to predict the impact of current parameter changes on performance indicators, generating predicted gradient information. These two predictions are then fused and processed using time-series data processing, sliding window filtering, and adaptive moment estimation algorithms to obtain more accurate and smoother optimal gradient estimates. This enables adaptive adjustment of the RF matching network under different operating states and external environmental changes, significantly improving real-time dynamic response capabilities and autonomous optimization efficiency.

[0036] 2. This invention introduces a hybrid estimation mechanism combining data-driven and model-predictive approaches, and dynamically adjusts the learning rate confidence interval based on probability density function analysis, effectively avoiding the problems of local extrema and slow convergence inherent in pure gradient methods. By normalizing and weighting the gradient components obtained from multi-amplitude and multi-directional perturbations and the predicted gradient generated based on Gaussian process regression, weights can be adaptively allocated under noise level assessment indicators, taking into account both real-time measurement noise and historical trends, significantly enhancing the robustness and convergence rate of the optimization process. Furthermore, the dynamic learning rate adjustment strategy can flexibly change the step size according to the gradient magnitude and directional stability, further improving the algorithm's global search capability and reducing the complexity of manual parameter adjustment.

[0037] 3. The method of this invention achieves high-precision real-time optimization of RF matching parameters, while making full use of a large number of gradient estimation sequences and performance measurement values ​​stored in the historical optimization iteration cycle. Through techniques such as sliding window filtering, adaptive moment estimation, and gradient direction consistency detection, the gradient sequence is smoothed and sorted, thereby automatically identifying and extracting the optimal gradient estimation value. Then, combined with probabilistic statistical analysis, the learning rate distribution is dynamically evaluated with confidence intervals. This significantly reduces the impact of system noise and parameter jitter while ensuring optimization speed, thereby improving matching accuracy and stability. Attached Figure Description

[0038] Figure 1 A schematic diagram of the structure of a real-time optimization method for radio frequency matching parameters based on gradient descent provided by the present invention;

[0039] Figure 2 This is a schematic diagram of the process for obtaining the first gradient estimate provided in an embodiment of the present invention;

[0040] Figure 3This is a schematic diagram of the optimal gradient estimation structure provided in an embodiment of the present invention. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] Example 1

[0043] 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 critical process in semiconductor manufacturing, and its stability and uniformity directly affect 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 dynamically changes due to variations in process gas, pressure, power, substrate material, etc., leading to mismatch in the matching network parameters and affecting energy transmission efficiency and plasma state. This embodiment aims to minimize reflected power by optimizing the matching network parameters in real time, thereby maintaining the stability of the etching process.

[0044] Please see Figure 1 This invention provides a real-time optimization method for radio frequency matching parameters based on gradient descent, the technical solution of which is as follows:

[0045] Acquire a digital measurement dataset related to the state of the target RF system, which includes statistical measurements of performance indicators.

[0046] Based on a digital measurement dataset, the gradient estimate of the matching parameter to be optimized in the objective cost function is calculated; the gradient estimate is then processed using a data processing gradient estimation algorithm to obtain the optimized matching parameter.

[0047] The data processing flow of the gradient estimation algorithm includes: applying a perturbation matrix generated based on a preset perturbation mode to the matching parameters, obtaining a matrix of statistical measurement values ​​of performance indicators, and obtaining data-driven gradient estimates of multi-point perturbation through numerical calculation; calculating predicted gradient information from the statistical measurement values ​​of performance indicators through a statistical approximation model; performing data fusion processing on the predicted gradient information and the data-driven gradient estimates to generate a first gradient estimate; accessing historical gradient estimation data in the stored optimization iteration cycle, performing time-series data processing on the currently calculated first gradient estimate, and obtaining the optimal gradient estimate.

[0048] Based on the numerical analysis of the preset learning rate and the optimal gradient estimate using the probability density function, the corresponding optimization matching parameters for the next optimization iteration cycle are generated by calculating the optimal gradient estimate.

[0049] Furthermore, the digital measurement dataset includes at least one of the following: the reflection coefficient, transmission coefficient, impedance value, capacitance value, inductance value, frequency response, power loss, temperature, voltage, and current waveforms of the radio frequency signal.

[0050] The statistical measurement value of the performance index is at least one of the mean, variance, maximum value, minimum value, peak value, effective value, and phase difference of the data in the digital measurement dataset.

[0051] In this embodiment, by incorporating multiple key parameters of the radio frequency (RF) signal into a digital measurement dataset, the present invention can comprehensively reflect the operating status of the RF system and enhance the ability to perceive changes in system characteristics during the matching parameter optimization process. Simultaneously, by combining multi-dimensional performance index statistical measurements, 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. This effectively enhances the optimization algorithm's adaptability to abnormal operating conditions, load fluctuations, and environmental interference, improves the accuracy and real-time performance of matching parameter adjustments, thereby further ensuring the energy transfer efficiency and process stability of the plasma etching process and promoting improved chip manufacturing yield.

[0052] During the plasma etching process, multidimensional data related to the RF system status are collected in real time to form a digital measurement dataset, 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, the gas flow rate and pressure.

[0053] Based on the collected data, statistical measures of key performance indicators are calculated, including the average, variance, or maximum value within a time window. In this embodiment, we will calculate the average value of the reflected power. As a statistical measurement value of core performance indicators.

[0054] Furthermore, the specific process for obtaining the gradient estimate of the matching parameter to be optimized includes:

[0055] The objective cost function is defined based on the statistical measurement values ​​of the performance indicators in the digital measurement dataset. ;

[0056] The target cost function is calculated using the current measurement values ​​in the digital measurement dataset. For each matching parameter to be optimized (the matching parameter to be optimized is the adjustable capacitor value) , The partial derivatives of the cost function are used to obtain gradient estimates that characterize the direction and rate of change of the cost function. The specific calculation formula is as follows:

[0057] ;

[0058] The gradient vector indicates the direction in which the cost function increases the fastest, while the negative gradient direction indicates the direction in which it decreases the fastest.

[0059] In this embodiment, by acquiring multi-dimensional parameters in real time during plasma etching, a comprehensive digital measurement dataset is constructed, effectively capturing the dynamic changes in the RF system state during etching. By calculating the statistics of key performance indicators within a time window, especially using the average reflected power as the core performance indicator, the performance trend of the matching network can be accurately reflected, improving the sensitivity to mismatch phenomena. Simultaneously, based on the digital measurement data, a target cost function is defined, and the gradient estimate corresponding to the matching parameter to be optimized (adjustable capacitance value) is directly calculated. This ensures that gradient calculation is closely related to the actual measurement state, improving the real-time performance and accuracy of gradient estimation. By utilizing the gradient descent principle to adjust the matching parameters along the negative gradient direction, the reflected power can be reduced more quickly, achieving efficient optimization of the matching network.

[0060] Furthermore, the numerical calculation process of the data-driven gradient estimate specifically includes:

[0061] The matching parameters Orthogonal direction and multiple amplitude levels The perturbations are applied in parallel to the current matching parameters to be optimized, forming a matching parameter matrix. ;

[0062] Calculate the statistical measurement values ​​of performance indicators for the matching parameter matrix, and generate a matrix of statistical measurement values ​​of performance indicators;

[0063] Multivariate differencing is used to calculate the ratio of performance index change to parameter perturbation in each perturbation orthogonal direction. By combining the differencing results in each orthogonal direction, the gradient components in the dimension of the matching parameter to be optimized are obtained, generating data-driven gradient estimates. The specific calculation formula is as follows:

[0064] .

[0065] In this embodiment, a systematic matching parameter matrix is ​​formed by applying orthogonal directions and multiple amplitude levels of perturbations in parallel to the matching parameters to be optimized. This results in more comprehensive perturbation coverage and allows for a full exploration of local variation characteristics within the parameter space. Furthermore, refined gradient components are obtained by combining the difference results, forming accurate data-driven gradient estimates. Compared with traditional single-point or single-direction perturbation methods, this embodiment significantly improves the stability and noise resistance of gradient estimation, effectively reduces gradient estimation errors, and enhances the response speed and adaptability of the optimization algorithm to parameter changes during actual etching. This accelerates the matching adjustment process and improves the energy utilization efficiency and system stability of the etching process.

[0066] Further, the process of obtaining the predicted gradient information is as follows: A training dataset for the parameter-performance mapping relationship is constructed based on the matching parameter values ​​and performance index measurements stored in historical optimization iteration cycles; the statistical approximation model fits the training dataset based on Gaussian process regression to generate a nonlinear statistical model capable of predicting performance index changes with parameters; Gaussian process regression can learn the nonlinear mapping relationship from parameters to performance indexes and provide the uncertainty of the prediction. The predicted gradient information is obtained by analyzing the real-time matching parameters through the statistical approximation model; this predicted gradient information is an approximate estimate of the true gradient. Based on the trained Gaussian process regression model, and inputting the current matching parameters, the model can predict the predicted gradient information of the performance index as the parameters change slightly. 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.

[0067] In this embodiment, Gaussian process regression can not only accurately fit complex nonlinear relationships but also output the uncertainty of the prediction results, thus improving the reliability 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 perturbation to the actual system. Since the predicted gradient information combines rich historical data and statistical modeling results, it has better robustness and accuracy compared to the gradient estimation obtained by single perturbation sampling. This helps to reduce the interference of random noise on gradient estimation during real-time optimization, further improving the convergence speed and stability of matching parameter optimization, thereby continuously maintaining the high stability and high energy efficiency of the plasma etching process.

[0068] Furthermore, for the specific process of the first gradient estimate, please refer to [link / reference needed]. Figure 2 Specifically, it includes:

[0069] Data-driven gradient estimation With predicted gradient information Normalization is performed separately; the noise level assessment result of the current optimization iteration cycle is obtained, and weight coefficients are assigned to the data-driven gradient estimate and the predicted gradient information. and The weighted data-driven gradient estimate is linearly combined with the weighted predicted gradient information to generate the first gradient estimate. ,in, This is the normalization function.

[0070] In this embodiment, by introducing a noise level assessment, the trust level of the data-driven gradient and the predicted gradient is dynamically adjusted. When the real-time sampled data is significantly affected by noise, the system can increase the weight of the predicted gradient information; conversely, it relies more on the real-time measured data-driven gradient, thereby effectively suppressing the impact of noise interference on the optimization direction judgment. This approach can fully utilize the freshness of real-time measurement data and the robustness of the statistical prediction model to achieve robust fusion of gradient estimation, improve the 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.

[0071] Furthermore, the specific process of obtaining the optimal gradient estimate includes:

[0072] Gradient estimates calculated from historical optimization iterations are read from the storage unit to form a gradient estimation sequence;

[0073] The sliding window filtering algorithm smooths the gradient estimation sequence to reduce the impact of short-term noise fluctuations. It then uses an adaptive moment estimation algorithm (such as the momentum concept in the Adam optimizer) to adjust the current gradient estimate using historical gradient information (exponential moving average of the gradient) and historical gradient squared information, applying the gradient estimation sequence to the calculation of the first gradient estimate. Based on gradient direction consistency detection, the gradient estimates within the window are sorted to obtain the optimal gradient estimate. The stability of gradient directions within a window is evaluated through gradient direction consistency detection. If the gradient directions remain consistent, the current gradient estimate is considered relatively reliable. The gradient estimates within the window can be sorted or weighted to obtain the optimal gradient estimate for the current period. For details, please refer to Figure 3 .

[0074] In this embodiment, the interference of short-term noise fluctuations on gradient estimation results is effectively reduced, improving the stability and accuracy of gradient estimation. Simultaneously, an adaptive moment estimation algorithm (such as the momentum optimizer concept) is employed to dynamically adjust historical gradient information and gradient squared information, enabling gradient estimation to balance convergence speed and jitter suppression, further enhancing the robustness of the optimization process. Through gradient direction consistency detection, the stability of the gradient estimation direction can be evaluated in real time, selecting the optimal gradient direction and ensuring that the optimization process proceeds along the correct and stable direction. This accelerates the convergence speed of RF matching parameters, reduces matching error fluctuations, and enhances the continuity and accuracy of plasma etching process control.

[0075] Furthermore, the specific process for generating the matching parameter values ​​in the next optimization iteration includes:

[0076] Analyze the statistical distribution characteristics of the currently obtained optimal gradient estimate, including the magnitude of the modulus. The stability and changes in direction;

[0077] Based on the probability density function of historical learning rate distribution Perform analysis to determine the confidence interval of the learning rate for the current iteration cycle. ;

[0078] Based on the magnitude and orientation angle of the optimal gradient estimate, the first... Step learning rate The specific values ​​to be taken within the confidence interval; for example, when the gradient magnitude is large and the direction is stable, the learning rate can be increased appropriately; when the magnitude is small or the direction changes erratically, the learning rate should be decreased to stabilize the search.

[0079] After multiplying the optimal gradient estimate by the learning rate, the current matching parameters are updated in the direction of the negative gradient to generate the parameter values ​​for the next iteration. .

[0080] In this embodiment, by analyzing the magnitude and direction variation characteristics of the current optimal gradient estimate and combining it with the probability density function of the historical learning rate distribution, adaptive adjustment of the learning rate can be achieved, enhancing the flexibility and targeting of parameter updates. When the gradient magnitude is large and the direction is stable, appropriately increasing the learning rate helps to accelerate the convergence speed; while when the gradient magnitude is small or the direction variation is unstable, the learning rate is automatically reduced to avoid oscillations or deviations caused by excessively large step sizes, thereby improving the stability and accuracy of the matching optimization process. By updating the matching parameter values ​​in the negative gradient direction, it can be ensured that each iteration moves along the optimal descent direction, improving the overall optimization efficiency, further enabling the RF system to quickly and accurately adapt to process requirements, and significantly improving the consistency and stability of the plasma etching process.

[0081] Table 1 Performance Comparison Data Table

[0082]

[0083] This embodiment presents performance comparison data before and after optimization in a simulation experiment. Taking load impedances of 10Ω, 50Ω, and 100Ω as examples, the amplitude of the reflection coefficient was relatively large before optimization, and significantly reduced after optimization. Simultaneously, the number of convergence iterations was greatly shortened before optimization, as detailed in Table 1.

[0084] The gradient descent-based real-time optimization method for RF matching parameters provided in this invention can adjust the matching network parameters in a timely manner to address the dynamic changes in the chamber load impedance during plasma etching, thereby effectively reducing reflected power, improving energy transfer efficiency, and maintaining the stability and uniformity of the plasma state. By introducing a technical solution that integrates data-driven gradient estimation based on perturbation modes with a statistical approximation model, this method can achieve accurate and reliable gradient estimation even under conditions of frequent process environment changes and significant measurement noise interference, effectively improving the convergence speed and matching accuracy of the optimization process. Furthermore, through time-series processing of historical gradient data and adaptive adjustment of the learning rate based on the probability density function, this method can further enhance the stability and robustness of the optimization algorithm, avoid the instability of the matching network caused by excessive perturbation, adapt to the real-time RF matching requirements under different etching process conditions, and significantly improve the consistency of etching processes and chip yield in semiconductor manufacturing.

[0085] Example 2

[0086] This embodiment includes all the content of Embodiment 1, and proposes a multi-objective optimization iterative update method for the matching network parameter optimization problem. To balance different performance requirements such as low system reflection power and high stability, a vectorized objective cost function is introduced, and the parameter update is guided by calculating the gradient estimate of the Jacobian matrix. The specific steps are as follows:

[0087] Constructing a vector objective cost function: In this embodiment, at least two performance metrics are used as components of the objective cost function to form a vectorized objective function. For example, reflection power and system stability during the etching process can be selected as metrics to construct the vector objective cost function. .in, This represents the reflected power determined by the matching parameters. This represents the impact of matching parameters on system stability. This vector cost function can simultaneously reflect the performance of multiple performance metrics under the matching network parameter settings.

[0088] Calculate the Jacobian matrix estimate: For the above vector objective cost function, calculate its matching parameters to be optimized. The estimated value of the Jacobian matrix. Specifically, for each performance index component... The partial derivatives of the Jacobian matrix with respect to the parameters are calculated through numerical differencing or simulation, thereby constructing an estimate of the Jacobian matrix. .

[0089] Determine the parameter update direction: Based on 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 various indicators: set weights. and The importance of reflection power and stability are respectively considered, and then the comprehensive gradient direction is constructed. ;

[0090] Comprehensive gradient direction This approach simultaneously addresses the dual objectives of reducing reflection power and improving system stability. By adjusting the weight ratios, a balance can be achieved between these different objectives in the optimization process. If there are conflicts between performance objectives, other multi-objective strategies (such as Pareto optimal front search) can be employed to determine the overall gradient direction.

[0091] New matching parameters: the combined gradient direction determined above. Historical learning rate distribution By combining and iteratively updating the matching parameters, the parameter values ​​for the next optimization cycle can be generated. The following update formula can be used. ;in The matching parameter value for the current iteration. The matching parameter values ​​obtained for the next iteration. Historical learning rate distribution. Control the step size of each update, typically using a small positive number to ensure convergence. After completing one parameter update, the updated parameters can be applied to the plasma etching system for simulation or experimental testing. Repeat the above steps for multiple iterations until all performance indicators converge and meet the expected requirements.

[0092] The method described in this embodiment was applied to the plasma etching system for simulation verification. The experimental results are shown in Table 2. Compared with the unoptimized system, the system's performance indicators were improved after multi-objective optimization: the reflection power was significantly reduced, the system stability was improved, and the convergence time was shortened. This indicates that the method effectively improves the matching optimization effect under multi-objective conditions.

[0093] Table 2 Comparison of performance indicators before and after multi-objective optimization

[0094]

[0095] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which 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: Acquire a digital measurement dataset related to the state of the target RF system, which includes statistical measurements of performance indicators. Based on the digital measurement dataset, the gradient estimate of the matching parameter to be optimized in the objective cost function is calculated; The gradient estimates are processed using a data processing gradient estimation algorithm to obtain the optimal matching parameters. The data processing flow of the gradient estimation algorithm includes: applying a perturbation matrix generated based on a preset perturbation mode to the matching parameters, obtaining a matrix of statistical measurement values ​​of performance indicators, and obtaining data-driven gradient estimates of multi-point perturbation through numerical calculation; calculating predicted gradient information from the statistical measurement values ​​of performance indicators through a statistical approximation model; performing data fusion processing on the predicted gradient information and the data-driven gradient estimates to generate a first gradient estimate; accessing historical gradient estimation data in the stored optimization iteration cycle, performing time-series data processing on the currently calculated first gradient estimate, and obtaining the optimal gradient estimate. Based on the numerical analysis of the preset learning rate and the optimal gradient estimate using the probability density function, the corresponding optimization matching parameters for the next optimization iteration cycle are generated by calculating the optimal gradient estimate.

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 dataset includes at least one of the following: the reflection coefficient, transmission coefficient, impedance value, capacitance value, inductance value, frequency response, power loss, temperature, voltage, and current waveforms of the radio frequency signal. The statistical measurement value of the performance index is at least one of the mean, variance, maximum value, minimum value, peak value, effective value, and phase difference of the data in the digital measurement dataset.

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 for obtaining the gradient estimate of the matching parameter to be optimized includes: The target cost function is defined based on the statistical measurement values ​​of the performance indicators in the digital measurement dataset. Using the current measurement values ​​in the digital measurement dataset, the partial derivatives of the target cost function with respect to each matching parameter to be optimized are calculated to obtain gradient estimates that characterize 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: The perturbations of orthogonal direction and multiple amplitude levels in the matching parameters are applied in parallel to the current matching parameters to be optimized, forming a matching parameter matrix; Calculate the statistical measurement values ​​of performance indicators for the matching parameter matrix, and generate a matrix of statistical measurement values ​​of performance indicators; Multivariate difference is used to calculate the ratio of performance index change and parameter perturbation in each perturbation orthogonal direction. The gradient components in the dimension of the matching parameter to be optimized are obtained by combining the difference results of each orthogonal direction, and data-driven gradient estimates are 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: a training dataset for parameter-performance mapping is constructed based on the matching parameter values ​​and performance index measurements stored in the historical optimization iteration cycle. The statistical approximation model fits the training dataset based on Gaussian process regression to generate a nonlinear statistical model that can predict performance indicators as parameters change. The real-time matching parameters are analyzed by 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 estimate includes: The data-driven gradient estimate and the predicted gradient information are normalized respectively; the noise level assessment result of the current optimization iteration cycle is obtained, and weight coefficients are assigned to the data-driven gradient estimate and the predicted gradient information; the weighted data-driven gradient estimate and the weighted predicted gradient information are linearly combined to generate the 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 for obtaining the optimal gradient estimate includes: Gradient estimates calculated from historical optimization iterations are read from the storage unit to form a gradient estimation sequence; The sliding window filtering algorithm smooths the gradient estimation sequence, and the adaptive moment estimation algorithm uses the gradient estimation sequence to calculate the first gradient estimate. Based on gradient direction consistency detection, the gradient estimates within the window are sorted to obtain the optimal gradient estimate.

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 for generating the matching parameter values ​​for the next optimization iteration includes: Analyze the statistical distribution characteristics of the currently obtained optimal gradient estimate, including the magnitude of the modulus, the stability of the direction, and the variation of the gradient. The historical learning rate distribution is analyzed based on the probability density function to determine the learning rate confidence interval for the current iteration cycle; Based on the magnitude and orientation angle of the optimal gradient estimate, the learning rate is dynamically adjusted within the confidence interval. After multiplying the optimal gradient estimate by the learning rate, the current matching parameters are updated in the direction of the negative gradient to generate the parameter values ​​for the next iteration.

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