Gain scaling method, dynamic impedance testing method, apparatus, and medium

Abstract

This application relates to the field of radio frequency (RF) power supply technology, and discloses a gain calibration method, a dynamic impedance testing method, equipment, and dielectric. The gain calibration method includes: acquiring multiple RF power measurements, where the RF power measurements are the output power measurements of an RF power supply in an open-loop state under multiple load impedance values; performing two-dimensional interpolation fitting in the complex plane of reflection coefficient based on the load impedance values ​​and the RF power measurements to obtain a continuous power distribution; selecting a minimum RF power value in the complex plane of reflection coefficient based on the continuous power distribution to obtain a target minimum RF power value; and calculating the gain of the RF power supply based on the target minimum RF power value, the load impedance value corresponding to the target minimum RF power value, and a preset characteristic impedance value. The embodiments of this application can improve the accuracy of RF power supply gain calibration and reduce the impact of environmental noise and small impedance fluctuations.

Description

Technical Field

[0001] This application relates to the field of radio frequency power supply technology, and in particular to a gain calibration method, a dynamic impedance testing method, equipment, and dielectric. Background Technology

[0002] The dynamic impedance of an RF power supply reflects the dynamic characteristics of the load impedance faced by the power supply output terminal as a function of parameters such as power, frequency, or time. This characteristic plays a crucial role in plasma processing, semiconductor manufacturing, and RF application systems. During testing, accurately determining the gain and maximum gradient angle of the RF power supply at its minimum output power is critical to ensuring the accuracy of dynamic impedance analysis. However, when the RF power supply operates at its minimum power output, the output signal amplitude is extremely low, making the measurement system highly susceptible to environmental noise interference, signal reflection, and minute impedance fluctuations. These interference factors significantly amplify measurement errors, leading to distorted gain calibration results and consequently reducing the overall accuracy and reliability of dynamic impedance testing. Current technologies lack effective methods for high-precision measurement under weak signal conditions, posing a significant challenge to the RF power supply gain calibration process and making it difficult to meet high-precision testing requirements. Summary of the Invention

[0003] The purpose of this application is to provide a gain calibration method, a dynamic impedance testing method, equipment, and dielectric that can improve the accuracy of RF power supply gain calibration and reduce the impact of environmental noise and small impedance fluctuations.

[0004] This application provides a gain calibration method, including: Multiple RF power measurements are acquired; the RF power measurements are the output power measurements of the RF power supply in an open-loop state under multiple load impedance values; Based on the load impedance value and the RF power measurement value, a two-dimensional interpolation fitting is performed in the complex plane of the reflection coefficient to obtain a continuous power distribution. Based on the continuous power distribution, the minimum radio frequency power value is selected in the complex plane of the reflection coefficient to obtain the target minimum radio frequency power value; The gain of the RF power supply is calculated based on the target minimum RF power value, the load impedance value corresponding to the target minimum RF power value, and the preset characteristic impedance value.

[0005] In some embodiments, the two-dimensional interpolation fitting of the RF power measurement value includes: Calculate the corresponding reflection coefficient based on the load impedance value; The complex plane of the reflection coefficient is constructed based on the real and imaginary parts of the reflection coefficient; In the complex plane of the reflection coefficient, a two-dimensional interpolation operation is performed on the discrete radio frequency power data to obtain the continuous power distribution.

[0006] In some embodiments, the two-dimensional interpolation operation is radial basis function interpolation, two-dimensional polynomial interpolation, or Gaussian interpolation.

[0007] In some embodiments, selecting the minimum radio frequency power value within the complex plane of the reflection coefficient includes: Within the target defined region, the minimum radio frequency power value in the continuous power distribution is searched to obtain the target minimum radio frequency power value; the target defined region is the region centered on the origin of the reflection coefficient complex plane, where the magnitude of the reflection coefficient is not greater than a preset reflection threshold, and the target defined region includes the reflection coefficient point corresponding to the characteristic impedance value.

[0008] In some embodiments, the reflection threshold is determined based on the magnitude of the reflection coefficient, which is determined by the load impedance stability boundary, the test system safe reflection boundary, and / or the typical plasma equivalent impedance.

[0009] In some embodiments, calculating the gain of the RF power supply based on the target minimum RF power value, the load impedance value corresponding to the target minimum RF power value, and a preset characteristic impedance value includes: Based on the reflection coefficient corresponding to the characteristic impedance value and the target minimum RF power value, calculate the load impedance value corresponding to the target minimum RF power value; The impedance change is calculated based on the load impedance value corresponding to the target minimum RF power value and the characteristic impedance value. The power change is calculated based on the RF power value corresponding to the load impedance value and the target minimum RF power value. The gain of the radio frequency power supply is determined based on the impedance change and the power change.

[0010] In some embodiments, before calculating the load impedance value corresponding to the minimum RF power value, the method further includes: Based on the impedance value of the load device of the RF power supply and the characteristic impedance value, the reflection coefficient corresponding to the minimum RF power value is calculated.

[0011] In some embodiments, the load impedance value is provided by a load traction system and a 50Ω water-cooled load, covering a VSWR range of 1.1:1 to 5:1 and covering the entire Smith circle.

[0012] In some embodiments, the open-loop state is to disconnect the closed-loop regulation circuit of the RF power supply, so that the RF power supply is equivalent to the working mode of a constant voltage source with series internal resistance.

[0013] This application also provides a method for dynamic impedance testing, including: Obtain the gain of the radio frequency power supply; the gain of the radio frequency power supply is obtained based on the gain calibration method described above; Based on the phase angle corresponding to the target minimum RF power value, calculate the maximum gradient angle of the RF power supply; Based on the gain and maximum gradient angle of the RF power supply, the dynamic impedance test results of the RF power supply are generated.

[0014] In some embodiments, calculating the maximum gradient angle of the RF power supply based on the phase angle corresponding to the target minimum RF power value includes: Determine the phase angle corresponding to the target minimum radio frequency power value; Subtract 180° from the phase angle corresponding to the target minimum RF power value to obtain the maximum gradient angle of the RF power supply.

[0015] In some embodiments, generating the dynamic impedance test results of the RF power supply based on its gain and maximum gradient angle includes: The gain and maximum gradient angle of the RF power supply are compared with the corresponding gain threshold and the corresponding maximum gradient angle threshold, respectively, and the dynamic impedance test results are generated based on the comparison results.

[0016] In some embodiments, the dynamic impedance testing method further includes: The optimal cable length for the radio frequency transmission line is calculated based on the phase difference between the maximum gradient angle and the plasma impedance trajectory angle.

[0017] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0018] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0019] The beneficial effects of this application are as follows: Based on the open-loop state of the RF power supply, two-dimensional interpolation fitting is performed in the complex plane of the reflection coefficient at multiple load impedance values ​​and corresponding RF power measurements. The target minimum RF power value is then selected based on the continuous power distribution obtained from the interpolation within the complex plane of the reflection coefficient, and the gain of the RF power supply is calculated. Therefore, by introducing two-dimensional interpolation fitting in the complex plane of the reflection coefficient, the limitations of discrete measurement points are effectively overcome. The continuous power distribution obtained from the interpolation fitting provides a more comprehensive and smoother power change trend, thereby reducing the impact of noise and measurement errors on the identification of the minimum power point. By selecting the target minimum RF power value in the complex plane of the reflection coefficient based on the continuous power distribution obtained from the interpolation, the minimum output power point of the RF power supply under specific load conditions can be accurately identified, avoiding misjudgment of the minimum power point due to insufficient sampling of discrete points or noise interference, ensuring higher reliability of the selected target minimum RF power value. Calculating the gain of the RF power supply based on this target minimum RF power value, its corresponding load impedance value, and a preset characteristic impedance value makes the gain calibration process more accurate and robust, improving the accuracy of gain calibration and reducing the impact of environmental noise and small impedance fluctuations. Attached Figure Description

[0020] Figure 1 This is a flowchart of the gain calibration method provided in the embodiments of this application.

[0021] Figure 2 This is a schematic diagram of the hardware structure of the radio frequency power supply testing device provided in the embodiments of this application.

[0022] Figure 3 This is a flowchart of a method for two-dimensional interpolation fitting of radio frequency power measurement values ​​provided in an embodiment of this application.

[0023] Figure 4 This is a flowchart of a method for calculating the gain of an RF power supply provided in an embodiment of this application.

[0024] Figure 5 This is a schematic diagram of the control of the radio frequency power supply in an open-loop state provided in the embodiments of this application.

[0025] Figure 6 This is a flowchart of the dynamic impedance testing method provided in the embodiments of this application.

[0026] Figure 7 This is a schematic diagram of the connection for plasma impedance testing provided in an embodiment of this application.

[0027] Figure 8 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0029] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and drawings are used to distinguish similar objects and are not used to describe a specific order or sequence.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application. Furthermore, the information, data, and signals involved in the embodiments of this application are all authorized by relevant parties or have been fully authorized by all parties, and the collection, use, and processing of related data comply with the relevant laws, regulations, and standards of the relevant countries and regions.

[0031] During dynamic impedance testing of RF power supplies, when calibrating the minimum RF power gain, the influence of external noise interference and reflected signals on the measurement results is significantly amplified due to the extremely low signal power level, leading to increased measurement errors and reduced gain calibration accuracy. The essence of this problem lies in the insufficient signal-to-noise ratio under low power conditions, causing minute reflection fluctuations to be misinterpreted as valid signal changes, thus failing to accurately characterize the true gain characteristics of the RF power supply. For example, in semiconductor manufacturing processes where an RF power supply drives a plasma cavity for thin film deposition, when the RF power supply output power is adjusted to the minimum operating point for gain calibration, the load impedance undergoes slight changes due to plasma state fluctuations. The reflected power caused by these changes, combined with the system's inherent noise floor, results in irregular fluctuations in the power measurement value, making it impossible to stably identify the minimum power point. In this scenario, the RF power supply in open-loop mode is equivalent to a constant voltage source with series internal resistance, and its output power measurement value is directly affected by real-time changes in load impedance. The dispersion of measurement data in the minimum power region further exacerbates the uncertainty of the calibration process.

[0032] If the above problems are not resolved, the RF power supply gain calibration results will introduce a systematic deviation, which will be transmitted to the dynamic impedance testing stage, causing the maximum gradient angle calculation to be inaccurate. Ultimately, this will prevent the RF power supply from accurately matching the impedance change characteristics of the plasma load. The resulting control parameter errors will affect the stability of the RF power supply in practical applications, increase the risk of system matching failure, and may cause abnormal operation of the load equipment.

[0033] Based on this, embodiments of this application provide a gain calibration method, a dynamic impedance testing method, an apparatus, and a medium. The method involves two-dimensional interpolation fitting between the load impedance value and the measured RF power value in the complex plane of the reflection coefficient. Based on the continuous power distribution obtained from the interpolation, the minimum target RF power value is selected in the complex plane of the reflection coefficient, and then the gain of the RF power supply is calculated. This effectively reduces measurement errors and has the advantages of improving the accuracy and reliability of RF power supply gain calibration and reducing the impact of environmental noise and small impedance fluctuations.

[0034] Figure 1 This is a flowchart of the gain calibration method provided in an embodiment of this application. See also... Figure 1 In one embodiment, the method includes, but is not limited to, steps S101 to S104.

[0035] Step S101: Obtain multiple RF power measurement values.

[0036] Radio frequency (RF) power measurements are the output power measurements of an RF power supply in an open-loop state under multiple load impedance values. In essence, RF power measurements refer to the output power data of the RF power supply acquired by a power sensor under specific voltage standing wave ratio (VSWR) conditions. Specifically, this can be achieved using a combination of a directional coupler and a power meter to reflect the power response characteristics under different load impedances.

[0037] Radio frequency (RF) power measurements are the power output data of an RF power supply in open-loop mode at multiple different load impedance values. For example, the RF power supply can be connected to a series of preset load impedance points by manually adjusting the load pulling system, and the output power of the RF power supply can be recorded at each load point using a power meter. Alternatively, an automated impedance tuner can be used to automatically scan and record the RF power value corresponding to each impedance point within a preset impedance range.

[0038] In some embodiments, the RF power measurement can be based on, for example, Figure 3 The RF power supply test setup shown was obtained. See also... Figure 2 The RF power supply testing device includes an RF power meter, a vector network analyzer, and a load device. The load device includes a load traction system and a 50Ω water-cooled load. The RF power measurement value is acquired by the RF power meter, and the vector network analyzer can directly measure the complex impedance of the load device, thereby calculating the reflection coefficient corresponding to the RF power measurement value.

[0039] Step S102: Based on the load impedance value and the RF power measurement value, perform two-dimensional interpolation fitting in the complex plane of reflection coefficient to obtain the continuous power distribution.

[0040] The complex plane of reflection coefficients is a mathematical tool used to represent the degree of mismatch between load impedance and characteristic impedance. In this complex plane, each point corresponds to a specific reflection coefficient, which consists of a real part and an imaginary part, and can comprehensively describe the reflection characteristics of electromagnetic waves on transmission lines.

[0041] Two-dimensional interpolation fitting within the complex plane of reflection coefficients can be achieved by first converting each load impedance value into its corresponding reflection coefficient, and then interpolating the discrete RF power measurement points on the complex plane. One approach is to use linear or bilinear interpolation to construct a continuous power surface using adjacent data points. Another approach is to use polynomial interpolation, constructing a higher-order polynomial to fit all discrete data points, thereby obtaining a smooth, continuous power distribution.

[0042] Step S103: Based on the continuous power distribution, the minimum radio frequency power value is selected in the complex plane of the reflection coefficient to obtain the target minimum radio frequency power value.

[0043] Selecting the minimum RF power value within the complex plane of reflection coefficients can be done across the entire complex plane or within a predefined region by traversing the continuous power distribution to find the point of minimum power. One approach is to use numerical optimization algorithms, such as gradient descent, to search for local or global minimum values ​​on the continuous power surface. Another approach is to visualize the continuous power distribution as a contour map, then manually identify the region of lowest power and extract the minimum power value from it.

[0044] Step S104: Calculate the gain of the RF power supply based on the target minimum RF power value, the load impedance value corresponding to the target minimum RF power value, and the preset characteristic impedance value.

[0045] The characteristic impedance refers to the inherent impedance of an RF transmission line or RF power supply. The characteristic impedance is typically designed to be 50Ω (Z0 = 50 + j0). When the load impedance matches the characteristic impedance, no reflection occurs on the RF transmission line, and energy transfer efficiency is maximized.

[0046] Calculating the gain of an RF power supply can be done by using a specific mathematical model to derive the gain based on the difference between the load impedance and the characteristic impedance corresponding to the target minimum RF power value, combined with the power change. One method involves first calculating the reflection coefficient at the target minimum power point, and then using the relationship between this reflection coefficient and the characteristic impedance, as well as the difference between the target minimum RF power value and a reference power value, to calculate the gain using known RF circuit theory formulas. Another method involves establishing an equivalent circuit model that includes the internal resistance of the RF power supply and the load impedance, and then substituting the target minimum RF power value and the corresponding load impedance into the model to deduce the RF power supply gain.

[0047] The following example will provide a more detailed explanation of the above technical solution: Suppose we need to perform gain calibration on an RF power supply to ensure its stable performance in plasma applications. First, the RF power supply is set to open-loop operation and connected to a load-pull system with a 50Ω water-cooled load. By adjusting the load-pull system, the output of the RF power supply is sequentially connected to multiple different load impedance points, covering, for example, VSWR ranges from 1.1:1 to 5:1 and hundreds of discrete impedance points across the entire Smith chart. At each impedance point, the output power value of the RF power supply is measured and recorded using a high-precision RF power meter. This yields multiple RF power measurements and their corresponding load impedance values.

[0048] Next, these discrete load impedance values ​​are converted into reflection coefficients, and the corresponding discrete RF power data points are plotted on the reflection coefficient complex plane. To obtain more refined power distribution information, two-dimensional interpolation fitting is performed on these discrete data points. Specifically, a radial basis function interpolation method can be used to construct a continuous power distribution surface based on all discrete data points. This surface represents the output power of the RF power supply under various load impedances on the reflection coefficient complex plane.

[0049] Subsequently, the minimum RF power value is selected on the continuous power distribution surface. For example, a target region can be defined, centered at the origin of the reflection coefficient complex plane, where the magnitude of the reflection coefficient is no greater than a preset reflection threshold, and containing the reflection coefficient points corresponding to the characteristic impedance values. Within this defined region, a numerical search algorithm, such as traversing grid points and comparing power values, is used to find the lowest point on the surface, thereby obtaining the target minimum RF power value and its corresponding reflection coefficient and load impedance value.

[0050] Finally, based on the target minimum RF power value, its corresponding load impedance value, and the preset characteristic impedance value (Z0=50+j0), the gain of the RF power supply is calculated. Specifically, the difference between the reflection coefficient corresponding to the target minimum RF power value and the reflection coefficient corresponding to the characteristic impedance can be calculated first. Then, combining the power change between the target minimum RF power value and the output power value of the RF power supply under the characteristic impedance, the gain of the RF power supply can be derived using the power transfer equation and the definition of the reflection coefficient in RF circuit theory. For example, the load impedance corresponding to the minimum power point can be calculated based on the reflection coefficient at that point. Then, based on the difference between the load impedance and the characteristic impedance, and the difference between the minimum power value and a certain reference power value (e.g., the power under the characteristic impedance), the gain of the RF power supply can be calculated using a specific mathematical model. In this way, even when the signal power is extremely low, the gain of the RF power supply can be accurately calibrated by analyzing the continuous power distribution.

[0051] Based on the above examples, the technical concept of this embodiment demonstrates a significant technical contribution in solving the problem of RF power supply gain calibration accuracy. In existing technologies, when calibrating the gain of an RF power supply at its minimum output RF power, the extremely low signal power means that even small noise or reflections can easily introduce significant errors, leading to reduced gain calibration accuracy.

[0052] This embodiment generates a continuous power distribution by acquiring multiple RF power measurements and performing two-dimensional interpolation fitting within the complex plane of the reflection coefficient, effectively overcoming the limitations of discrete measurement points. Compared to direct calculation at discrete points, the continuous power distribution provides a more comprehensive and smoother power variation trend, thereby reducing the impact of noise and measurement errors on the identification of the minimum power point. For example, in the above example, the continuous power surface constructed through radial basis function interpolation allows for more accurate localization of the true minimum power point even if there are local fluctuations at the original measurement points, through fitting the overall trend.

[0053] Furthermore, this embodiment, by selecting the minimum RF power value from a continuous power distribution, can accurately identify the minimum output power point of the RF power supply under specific load conditions. This selection method based on continuous data avoids misjudgment of the minimum power point caused by insufficient sampling of discrete points or noise interference in traditional methods. In the example, by searching for the lowest point on a continuous surface within the target defined region, the reliability of the selected minimum power value is ensured.

[0054] Finally, the gain of the RF power supply is calculated based on the target minimum RF power value, its corresponding load impedance value, and the preset characteristic impedance value, making the gain calibration process more accurate and robust. This method fully utilizes the power response characteristics of the RF power supply under different loads, significantly improving the accuracy of gain calibration by analyzing the entire power distribution rather than relying solely on a few measurement points that may be affected by noise. This is of great significance for the stable operation and precise control of RF power supplies in dynamic impedance environments, effectively solving the technical problem of low gain calibration accuracy in existing technologies.

[0055] See Figure 3 In one embodiment, the method for performing two-dimensional interpolation fitting on the radio frequency power measurement value includes, but is not limited to, steps S301 to S303.

[0056] Step S301: Calculate the corresponding reflection coefficient based on the load impedance value.

[0057] Step S302: Construct the complex plane of reflection coefficient based on the real and imaginary parts of the reflection coefficient.

[0058] Step S303: In the complex plane of reflection coefficient, perform two-dimensional interpolation on the discrete radio frequency power data to obtain continuous power distribution data.

[0059] The method for calculating the reflection coefficient can be using the formula = (Z -Z0) / (Z + Z0), where, Z represents the reflection coefficient, Z represents the load impedance, and Z0 represents the characteristic impedance (e.g., 50Ω). Another method is to use a Smith chart for graphical conversion, or to measure it directly using a vector network analyzer.

[0060] Constructing a complex plane of reflection coefficients based on the real and imaginary parts of the reflection coefficients means using the real part of each calculated reflection coefficient as the abscissa and the imaginary part as the ordinate, thereby representing these discrete reflection coefficient points in a two-dimensional coordinate system.

[0061] In the complex plane of reflection coefficients, two-dimensional interpolation of discrete RF power data transforms discrete RF power measurements into a continuous power distribution surface. Since the actual measurement points are finite, interpolation can estimate the power values ​​at unmeasured points, thus forming a smooth and complete power distribution map. Two-dimensional interpolation can be implemented using various mathematical methods. For example, in addition to radial basis function interpolation, two-dimensional polynomial interpolation, or Gaussian interpolation, bilinear interpolation, Kriging interpolation, or spline interpolation can be used to estimate the power values ​​of the entire region based on discrete data points.

[0062] This application's solution effectively addresses the challenge of obtaining continuous power distribution during gain calibration by transforming discrete RF power measurements from the impedance domain to the reflection coefficient complex plane and performing two-dimensional interpolation on this plane. Specifically, for the output power measurements of the RF power supply under multiple load impedance values, a standardized mapping from the impedance domain to the reflection coefficient domain is achieved by converting each load impedance value into its corresponding reflection coefficient. This transformation allows power data under different load conditions to be represented and analyzed on a unified complex plane. Subsequently, a reflection coefficient complex plane is constructed based on the real and imaginary parts of these reflection coefficients, locating discrete measurement points according to their positions on the complex plane. Within this complex plane, two-dimensional interpolation is performed on these discrete RF power data to generate continuous power distribution data. This method fully leverages the advantages of the reflection coefficient complex plane in describing the matching characteristics of RF systems, smoothly connecting discrete measurement points to form a complete power surface. In this way, not only can the power output characteristics of the RF power supply under different load conditions be accurately reflected, but also a reliable continuous data basis can be provided for the subsequent accurate selection of the target minimum RF power value in the complex plane of the reflection coefficient, which greatly improves the accuracy and robustness of gain calibration.

[0063] The following is a concrete example to illustrate this. When performing gain calibration, the output power measurements of the RF power supply are first obtained under multiple load impedance values. For example, assume a series of load impedance values ​​and corresponding RF power measurements are obtained. For each load impedance value, the corresponding reflection coefficient can be calculated using the formula above, based on a preset characteristic impedance value (e.g., 50 + j0Ω). Each reflection coefficient is a complex number with real and imaginary parts. Subsequently, the real parts of these reflection coefficients are used as the X-axis coordinates, and the imaginary parts as the Y-axis coordinates, constructing a complex plane of reflection coefficients. On this complex plane, each point corresponds to a discrete RF power measurement value. To obtain continuous power distribution data, two-dimensional interpolation can be performed on these discrete data points within this complex plane. For example, a bicubic spline interpolation method can be used to estimate the RF power value at any point on the complex plane by constructing a smooth surface. Through this interpolation, a continuously varying power distribution surface across the entire complex plane of reflection coefficients can be obtained, thus providing detailed data support for subsequent analysis and processing.

[0064] In some embodiments, the two-dimensional interpolation operation is radial basis function interpolation, two-dimensional polynomial interpolation, or Gaussian interpolation.

[0065] Radial basis function interpolation is a multivariate interpolation method that represents data points as a linear combination of a set of radially symmetric functions. This method is particularly suitable for handling irregularly distributed data points and can generate smooth and highly accurate interpolation surfaces. For example, multiple quadratic functions, thin-plate spline functions, or Gaussian functions can be used as radial basis functions, and the weighting coefficients of each basis function are determined by solving a system of linear equations.

[0066] Two-dimensional polynomial interpolation is a method that approximates discrete data points by fitting a two-dimensional polynomial surface. This method constructs a polynomial function containing x and y variables and their intersections, and uses least squares or other fitting techniques to determine the polynomial coefficients. For example, linear, quadratic, or higher-order polynomials can be used for fitting to accommodate power distribution data of varying complexity.

[0067] Gaussian interpolation is a method of interpolation that uses a Gaussian function as weights or basis functions. It can be achieved by weighted averaging of neighboring data points, where the weights are determined by a Gaussian kernel function based on distance, so that closer data points have a greater influence on the interpolation result. Furthermore, Gaussian interpolation can also refer to interpolation methods based on Gaussian process regression, which can provide an estimate of the uncertainty of the interpolation result and is suitable for scenarios where data noise and uncertainty need to be considered.

[0068] The solution in this application acquires multiple RF power measurements and calculates the corresponding reflection coefficient based on the load impedance value, thereby constructing a reflection coefficient complex plane. Within this complex plane, a two-dimensional interpolation operation is performed on the discrete RF power data to obtain a continuous power distribution. To ensure the accuracy and reliability of the interpolation results, this application further clarifies that the two-dimensional interpolation operation can specifically employ radial basis function interpolation, two-dimensional polynomial interpolation, or Gaussian interpolation. These specific interpolation methods all possess the ability to handle complex data distributions, effectively transforming discrete, potentially irregularly distributed RF power data into a smooth and continuous power distribution surface. For example, radial basis function interpolation can flexibly adapt to the local characteristics of data points, generating high-precision interpolation results even if the data point distribution is sparse or uneven; two-dimensional polynomial interpolation can provide a globally smooth analytical surface, suitable for scenarios with relatively regular data distributions; while Gaussian interpolation can effectively handle noise in the data through local weighted averaging or probability models, providing robust interpolation results. By selecting these mature and efficient interpolation algorithms, the accuracy and reliability of continuous power distribution can be significantly improved, thus laying a solid foundation for the subsequent accurate selection of the target minimum RF power value, and thereby ensuring the accuracy of RF power gain calculation.

[0069] In some embodiments, selecting the minimum radio frequency power value in the complex plane of reflection coefficient includes: searching for the minimum radio frequency power value in continuous power distribution data within the target defined area to obtain the target minimum radio frequency power value.

[0070] The target defined region is an area centered at the origin of the reflection coefficient complex plane, where the magnitude of the reflection coefficient is no greater than a preset reflection threshold. In essence, the target defined region refers to a specific area within the reflection coefficient complex plane used to constrain the search range for the minimum RF power value. For example, the target defined region can be a circular area whose boundary is determined by the magnitude of the reflection coefficient; or, it can be an area of ​​arbitrary shape determined based on factors such as the stability boundary of the RF power supply and the tolerance range of the load device. The reflection threshold defines the size of the region, ensuring that the load impedance within the search range does not deviate excessively from its characteristic impedance, thereby avoiding gain calibration under extreme mismatch conditions. This reflection threshold can be a fixed value, such as 0.3, corresponding to a voltage standing wave ratio (VSWR) of approximately 1.86:1; or it can be a dynamically determined value based on the performance specifications of the RF power supply, the characteristics of the load device, or system safety requirements.

[0071] The target defined region includes the reflection coefficient point corresponding to the characteristic impedance value. This means that the defined target defined region must cover the origin of the complex plane of reflection coefficients. Since the reflection coefficient corresponding to the characteristic impedance value (e.g., 50Ω) is zero, i.e., located at the origin of the complex plane of reflection coefficients, this definition ensures that the ideal matching point is always included within the search range of the minimum RF power value under any circumstances, guaranteeing the validity of the gain calibration reference.

[0072] The proposed solution defines a target region within the complex plane of reflection coefficients and restricts the search range for the minimum RF power value to this region. This target region is centered at the origin of the complex plane of reflection coefficients, its boundaries are determined by a preset reflection threshold, and it ensures that the region includes the reflection coefficient point corresponding to the characteristic impedance value. After obtaining the continuous power distribution, instead of performing an indiscriminate search across the entire complex plane of reflection coefficients, the minimum power value is sought only within this defined region. This approach ensures that the obtained target minimum RF power value necessarily corresponds to a relatively stable, safe, and practically meaningful load impedance condition. This targeted search avoids errors or risks caused by calibration at extreme or unstable impedance points, thus making the gain calibration results of the RF power supply more accurate and reliable.

[0073] The following is a concrete example to illustrate this. After completing the RF power measurement and performing two-dimensional interpolation fitting in the complex plane of reflection coefficient based on the load impedance value and the RF power measurement value to obtain the continuous power distribution, it is necessary to select the target minimum RF power value. At this point, a reflection threshold can be set, for example, 0.3. This reflection threshold defines a circular region with a radius of 0.3 centered on the origin of the complex plane of reflection coefficient as the target limited region. All points within this circular region have a reflection coefficient magnitude of no more than 0.3, and this region naturally includes the reflection coefficient point (i.e., the origin) corresponding to the characteristic impedance value (50Ω). Subsequently, the algorithm will only search the continuous power distribution within this circular target limited region to find the lowest power point within this region and determine it as the target minimum RF power value. For example, if the lowest point of the interpolated power surface within this circular region appears at a reflection coefficient of 0.1+j... 0.05 If the position is such that the power value at that position is the target minimum RF power value.

[0074] In some embodiments, the reflection threshold is determined based on the magnitude of the reflection coefficient, which is determined by the load impedance stability boundary, the test system safe reflection boundary, and / or the typical plasma equivalent impedance.

[0075] The load impedance stability boundary refers to the limit within which an RF power supply can maintain stable operation under different load impedance conditions. Exceeding this range may lead to performance degradation or damage to the RF power supply. This boundary can be determined by referring to the technical specifications provided by the RF power supply manufacturer or by precise calibration through experimental testing.

[0076] The safety reflection boundary of a test system refers to the maximum reflection coefficient that the entire test setup (including RF power supply, transmission lines, loads, etc.) can safely withstand, in order to prevent damage to the equipment due to excessive reflected power. This boundary can be determined based on calculations of the maximum power handling capacity and voltage standing wave ratio (VSWR) handling capacity of each component in the test system, with reference to relevant safety standards.

[0077] The reflection coefficient modulus of typical plasma equivalent impedance specifically refers to the reflection coefficient modulus corresponding to the representative impedance value exhibited by plasma under specific process conditions in plasma applications. Its purpose is to make the gain calibration results closer to the actual operating characteristics of the plasma load, and it can be obtained through statistical analysis of measurement data from actual plasma processes or through simulation calculations using plasma physics models.

[0078] This application's solution closely integrates the determination of the reflection threshold with actual physical boundaries and application scenarios, making the selection of the minimum RF power value during gain calibration more scientific and reliable. Specifically, by considering the load impedance stability boundary of the RF power supply itself, it can be ensured that the load conditions corresponding to the selected minimum RF power value will not lead to instability in the RF power supply operation; by considering the safety reflection boundary of the test system, damage to the test equipment due to high reflection power can be avoided during gain calibration; and by considering the reflection coefficient magnitude of typical plasma equivalent impedance, the gain calibration results can be more targeted, especially suitable for performance evaluation of RF power supplies in plasma applications. This method of determining the reflection threshold based on multiple practical constraints effectively optimizes the range of the target defined region, so that the target minimum RF power value searched in the reflection coefficient complex plane is not only a mathematical minimum, but also a physically stable, safe, and practically meaningful operating point. This significantly improves the accuracy and practicality of the gain calibration results, avoiding distortion of gain calibration results or system operation risks caused by improper threshold setting.

[0079] The following is a concrete example. For instance, when gain-calibrating an RF power supply used in a plasma etching process in semiconductor manufacturing, the reflection threshold can be determined as follows: First, the RF power supply's specifications can be consulted, which may explicitly state its stable output under load conditions with a voltage standing wave ratio (VSWR) of less than 3:1, corresponding to a specific reflection coefficient magnitude. Second, the maximum power handling capability of the entire test system, including transmission lines connecting the RF power supply and the load-pull system, directional couplers, and other components, can be evaluated. For example, the maximum VSWR these components can safely withstand is 4:1, which also corresponds to a reflection coefficient magnitude. Furthermore, based on historical data analysis or plasma simulation models of the plasma etching process, it can be known that under typical process windows, the equivalent impedance of the plasma load usually corresponds to a range of reflection coefficient magnitudes, for example, between 0.3 and 0.5. Taking all these factors into consideration, the reflection threshold can be set to the magnitude with the most stringent boundary conditions, or, based on actual application requirements, a magnitude that simultaneously satisfies stability, safety, and application relevance can be selected. For example, if the stability of the RF power supply is the primary consideration, the reflection coefficient modulus corresponding to VSWR 3:1 can be used as the reflection threshold; if the typical operating range of the plasma is the main objective, 0.3 or 0.5 can be selected as the reflection threshold.

[0080] See Figure 4 In one embodiment, the method for calculating the gain of the radio frequency power supply includes, but is not limited to, steps S401 to S404.

[0081] Step S401: Calculate the load impedance value corresponding to the target minimum RF power value based on the reflection coefficient corresponding to the characteristic impedance value and the target minimum RF power value.

[0082] Step S402: Calculate the impedance change based on the load impedance value and characteristic impedance value corresponding to the target minimum RF power value.

[0083] Step S403: Calculate the power change based on the RF power value corresponding to the load impedance value and the target minimum RF power value.

[0084] Step S404: Determine the gain of the RF power supply based on the impedance change and power change.

[0085] This application's solution aims to more accurately determine the gain of an RF power supply by introducing a series of refined calculation steps. First, by converting the reflection coefficient corresponding to the target minimum power value into a specific load impedance value, a mapping from abstract reflection characteristics to physical impedance is achieved. This conversion forms the basis for subsequent quantitative analysis. Next, by calculating the impedance change between this load impedance value and a preset characteristic impedance value, and the power change between the RF power value corresponding to this load impedance value and the target minimum power value, this solution can comprehensively capture the response characteristics of the RF power supply under different load conditions. The impedance change characterizes the degree of matching between the load and the power supply, while the power change directly reflects the power supply's output capability. Finally, by comprehensively utilizing these two key changes, this solution can establish a more accurate gain calculation model, thereby overcoming the inaccuracies caused by relying on a single parameter or rough estimation. This method ensures that gain determination is no longer a simple power ratio, but fully considers the impact of load impedance on power supply performance, thus improving the accuracy and reliability of gain calibration.

[0086] In a specific embodiment, the formula for calculating the load impedance value corresponding to the target minimum RF power value is as follows: , in, The load impedance value corresponding to the target minimum RF power value. The characteristic impedance value, The reflection coefficient corresponding to the target minimum radio frequency power value; The formula for calculating the change in impedance is: , in, This is the change in impedance; The formula for calculating the change in power is: , in, The change in power This represents the RF power value corresponding to the load impedance value. The target minimum radio frequency power value; The formula for calculating the gain of an RF power supply is: , in, The gain when the RF power supply outputs the minimum RF power.

[0087] In some embodiments, before calculating the load impedance value corresponding to the minimum RF power value, the method further includes: calculating the reflection coefficient corresponding to the minimum RF power value based on the impedance value and characteristic impedance value of the load device of the RF power supply.

[0088] This application's solution introduces a step to calculate the reflection coefficient corresponding to the minimum RF power value by using the impedance and characteristic impedance of the load device based on the RF power supply before obtaining the load impedance value corresponding to the target minimum RF power value when calculating the RF power supply gain. Specifically, firstly, a continuous power distribution is obtained by performing two-dimensional interpolation fitting on the RF power measurement values, and the target minimum RF power value is selected from it. Subsequently, in order to accurately map this minimum power point to a specific load impedance value, this application uses the actual impedance value of the load device of the RF power supply and the system-preset characteristic impedance value to calculate the reflection coefficient corresponding to the minimum RF power value. This reflection coefficient, as an intermediate parameter, accurately characterizes the impedance mismatch at the minimum power point. Once this accurate reflection coefficient is obtained, the load impedance value corresponding to the minimum RF power value can be further calculated based on the reflection coefficient and the characteristic impedance value. In this way, this application provides a clear and logically rigorous path to associate the abstract minimum power point with a specific load impedance value, so that the subsequent calculation process of determining the RF power supply gain based on impedance change and power change has a solid data foundation, thereby improving the accuracy and reliability of the entire gain calibration method.

[0089] In one specific embodiment, the formula for calculating the reflection coefficient corresponding to the minimum radio frequency power value is: , in, The reflection coefficient, The characteristic impedance of the system, The complex impedance of the load device. Let be the real part of the reflection coefficient. This represents the imaginary part of the reflection coefficient. It is the imaginary unit.

[0090] In some embodiments, the load impedance value is provided by a load traction system and a 50Ω water-cooled load, covering a VSWR range of 1.1:1 to 5:1 and covering the entire Smith circle.

[0091] This application's solution systematically provides and controls the load impedance value by combining a load pulling system with a 50Ω water-cooled load. This ensures that the output power measurement of the RF power supply during gain calibration is obtained within a carefully designed and comprehensively covered load impedance space. The load pulling system can accurately generate a wide range of load impedances from VSWR 1.1:1 to 5:1, achieving full coverage on the Smith chart. This means that not only are different degrees of impedance mismatch considered, but all possible impedance phase angles are also covered. Simultaneously, the 50Ω water-cooled load, acting as a high-power absorber, safely and effectively absorbs the RF power supply's output power while the load pulling system generates various impedances, ensuring the stability of the testing process and equipment safety. This comprehensive data acquisition strategy provides high-quality, highly reliable raw data for subsequent two-dimensional interpolation fitting in the complex plane of the reflection coefficient. This allows the final continuous power distribution to more accurately characterize the true performance of the RF power supply, laying a solid foundation for accurately selecting the target minimum RF power value and calculating the gain.

[0092] The following is a concrete example. When calibrating the gain of an RF power supply, a test platform consisting of a mechanical load puller, a power meter, a vector network analyzer, and a 50Ω water-cooled load can be used. First, the load puller is calibrated using the vector network analyzer to ensure it can accurately synthesize the required load impedance. Then, the output of the RF power supply is connected to the load puller, and the other end of the load puller is connected to the 50Ω water-cooled load. During the test, the load puller generates a series of discrete load impedance points on the Smith chart according to a preset scan path. These impedance points are carefully selected to ensure that their voltage standing wave ratio (VSWR) gradually varies from 1.1:1 to 5:1 and is distributed across various regions of the Smith chart (e.g., capacitive, inductive, and purely resistive regions), thus achieving full coverage of the Smith chart. At each load impedance point, the power meter measures the output power of the RF power supply. All measured load impedance values ​​and corresponding RF power measurements are recorded as input data for subsequent two-dimensional interpolation fitting.

[0093] In some embodiments, the open-loop state is the disconnection of the closed-loop regulation circuit of the RF power supply, making the RF power supply equivalent to a constant voltage source in series with internal resistance.

[0094] Open-loop operation refers to a situation where the output of an RF power supply is no longer subject to real-time regulation by its internal feedback mechanism. In normal operation, an RF power supply typically has a closed-loop regulation circuit to monitor output power, voltage, or current and adjust it according to preset targets to maintain output stability. However, during gain calibration, it is necessary to obtain the raw output characteristics of the RF power supply under different load conditions to accurately evaluate its gain. Therefore, disconnecting the closed-loop regulation circuit of the RF power supply is a crucial step in achieving this goal. This can be achieved in several ways, such as disabling the internal feedback control module of the power supply via software instructions or removing the feedback path from the control circuitry via hardware switching.

[0095] like Figure 5 As shown, when the closed-loop regulation circuit is disconnected, the operating mode of the RF power supply changes. At this time, the RF power supply no longer actively compensates for output fluctuations caused by load changes; its behavior can be equivalent to an ideal constant voltage source connected in series with an internal resistance. This constant voltage source represents the maximum output capability of the RF power supply under no load or a specific load, while the internal resistance reflects the output impedance characteristics of the power supply itself. This equivalent model allows the output power variation of the RF power supply under different load impedance values ​​to directly reflect the interaction between its internal characteristics and the load, providing an accurate physical basis for subsequent gain calculations.

[0096] The proposed solution explicitly defines the open-loop state of the RF power supply, i.e., disconnecting its closed-loop regulation circuit and making it equivalent to a constant voltage source with series internal resistance. This ensures that interference from the closed-loop control system is eliminated when acquiring RF power measurements. This allows the measured RF power data to accurately reflect the inherent output characteristics of the RF power supply under different load impedances. Based on these accurate measurements, subsequent two-dimensional interpolation fitting, selection of the minimum RF power value, and gain calculation will be more reliable, significantly improving the accuracy and consistency of gain calibration. This precise open-loop state control lays a solid foundation for the effective implementation of the entire gain calibration method.

[0097] The following is a concrete example to illustrate this. When implementing the gain calibration method described above, to ensure the RF power supply is in an open-loop state, the following steps can be taken: First, send a command through the RF power supply's control interface to switch the power supply to manual control mode or calibration mode. In this mode, the microcontroller or digital signal processor inside the power supply will stop executing its closed-loop power or voltage regulation algorithm, thus disconnecting the closed-loop regulation loop. At this time, the power amplifier of the power supply will receive a fixed drive signal, and its output voltage and current will be determined solely by its internal circuit characteristics and the externally connected load impedance. For example, if the power supply design has a dedicated "open-loop test" port or software option, this function can be directly activated. In this operating mode, the output behavior of the RF power supply can be considered as a constant voltage source with a specific internal resistance, whose output power varies with the load impedance, rather than attempting to maintain a constant output power.

[0098] Figure 6 This is a flowchart of the dynamic impedance testing method provided in the embodiments of this application. See also... Figure 6 In one embodiment, the method includes, but is not limited to, steps S601 to S603.

[0099] Step S601: Obtain the gain of the RF power supply.

[0100] The gain of the RF power supply is obtained based on the gain calibration method described above.

[0101] Step S602: Calculate the maximum gradient angle of the RF power supply based on the phase angle corresponding to the target minimum RF power value.

[0102] Step S603: Based on the gain and maximum gradient angle of the RF power supply, generate the dynamic impedance test results of the RF power supply.

[0103] The core innovation of this embodiment lies in combining the RF power supply gain obtained based on the above-described gain calibration method with the phase angle corresponding to the target minimum RF power value, thereby accurately calculating the maximum gradient angle of the RF power supply and improving the accuracy of dynamic impedance testing. Since the above-described gain calibration method can effectively overcome noise and reflection interference when the signal power is extremely low, ensuring high-precision acquisition of gain parameters, it provides reliable basic data for dynamic impedance testing.

[0104] In the implementation process, the gain of the RF power supply is first determined using the aforementioned gain calibration method. This gain calibration method significantly improves the accuracy of gain calculation by acquiring multiple RF power measurements, performing two-dimensional interpolation fitting in the complex plane of the reflection coefficient, and selecting the target minimum RF power value. Next, the maximum gradient angle of the RF power supply is calculated based on the phase angle corresponding to the target minimum RF power value. For example, 180° can be subtracted from the phase angle corresponding to the target minimum RF power value to obtain the maximum gradient angle. Finally, dynamic impedance test results are generated based on the RF power supply gain and the maximum gradient angle. Specifically, the gain and maximum gradient angle can be compared with the corresponding gain threshold and maximum gradient angle threshold, respectively, and the test pass / fail status can be determined based on the comparison results. Furthermore, the optimal cable length of the RF transmission line can be calculated based on the phase difference between the maximum gradient angle and the plasma impedance trajectory angle to optimize system performance.

[0105] In some embodiments, the maximum gradient angle of the RF power supply is calculated based on the phase angle corresponding to the target minimum RF power value, including: determining the phase angle corresponding to the target minimum RF power value; and subtracting 180° from the phase angle corresponding to the target minimum RF power value to obtain the maximum gradient angle of the RF power supply.

[0106] The proposed solution first determines the phase angle corresponding to the minimum RF power value selected within the complex plane of reflection coefficient. This phase angle reflects the minimum power output state of the RF power supply under a specific load. Given the distribution characteristics of RF power in the complex plane of reflection coefficient, there is typically a 180° phase difference between the minimum power point and the direction of the maximum power gradient. Therefore, by subtracting 180° from this phase angle, the location information of the minimum power point can be accurately converted into the maximum gradient angle of the RF power supply. This maximum gradient angle is a key parameter for evaluating the dynamic impedance characteristics of the RF power supply, directly indicating the direction in which the RF power supply's output power is most sensitive to dynamic load changes. This method transforms the abstract phase information of the minimum power point into a physically reasonable maximum gradient angle with practical engineering significance, thus providing a crucial input parameter for generating subsequent dynamic impedance test results, enabling dynamic impedance testing to more accurately reflect the actual performance of the RF power supply.

[0107] The following is a concrete example. Assume that after the gain calibration method has been executed, the target minimum RF power value has been determined, and the phase angle of the reflection coefficient corresponding to this target minimum RF power value is 30°. According to the scheme of this application, subtracting 180° from this phase angle of 30° yields the maximum gradient angle of the RF power supply as -150°. This phase angle can be determined by a digital signal processor (DSP) or a field-programmable gate array (FPGA), which can process complex reflection coefficient data and extract its phase information. Subsequently, the subtraction of 180° can also be implemented within the same processing unit through simple arithmetic operations.

[0108] In some embodiments, generating dynamic impedance test results for an RF power supply based on its gain and maximum gradient angle includes: comparing the RF power supply's gain and maximum gradient angle with corresponding gain thresholds and corresponding maximum gradient angle thresholds, respectively, and generating dynamic impedance test results based on the comparison results.

[0109] This application's solution generates dynamic impedance test results with clear judgment significance by comparing two key performance parameters of the RF power supply—gain and maximum gradient angle—with preset performance thresholds. The gain of the RF power supply reflects its power output capability and stability under different loads, while the maximum gradient angle characterizes its sensitivity to changes in load impedance. Systematically comparing these parameters with preset performance standards allows for a comprehensive evaluation of the RF power supply's actual performance under dynamic load environments. This comparison mechanism transforms the test results from merely a list of raw parameters into performance indicators with clear judgment significance. For example, if the gain is below the gain threshold, it may indicate insufficient power output or low efficiency; if the maximum gradient angle exceeds the maximum gradient angle threshold, it may indicate instability risks when the load changes rapidly. In this way, this application transforms complex RF power supply characteristic parameters into intuitive and operable test results, providing users with an effective means to quantitatively evaluate the dynamic performance of RF power supplies.

[0110] The following example illustrates this. After completing the gain calibration and maximum gradient angle calculation, assume that the measured gain of a certain RF power supply is 23dB and the maximum gradient angle is 50°. The preset gain threshold is 20dB to 25dB, and the maximum gradient angle threshold is no greater than 60°. A processing unit, such as an embedded controller or test software running on a PC, receives these parameters. The processing unit first compares the 23dB gain with the 20dB to 25dB gain threshold to determine if 23dB falls within this range. Since 23dB is within this range, the gain meets the requirements. Next, the processing unit compares the 50° maximum gradient angle with the maximum gradient angle threshold of no greater than 60° to determine if 50° is less than or equal to 60°. Since 50° is less than 60°, the maximum gradient angle also meets the requirements. Based on these two comparison results, the processing unit generates dynamic impedance test results, such as displaying "Test result: qualified, good performance", and can further output a detailed report indicating that the RF power supply's power output stability and sensitivity to load changes are within acceptable ranges under the current test conditions, making it suitable for subsequent practical applications.

[0111] In some embodiments, the dynamic impedance testing method further includes: calculating the optimal cable length of the radio frequency transmission line based on the phase difference between the maximum gradient angle and the plasma impedance trajectory angle.

[0112] The plasma impedance trajectory angle refers to the phase angle of the trajectory formed by the impedance of a plasma load on the complex plane of reflection coefficients during operation. Plasma impedance is typically dynamic, and its trajectory angle reflects the electrical characteristics of the plasma load, such as its capacitive or inductive properties. This trajectory angle can be obtained in various ways, such as through online monitoring of the plasma load using real-time impedance measurement equipment, or through prediction using a pre-established plasma model. For example, a vector network analyzer (VNA) or a specialized plasma impedance probe can be used to measure the plasma impedance under different process parameters and extract its phase information.

[0113] This application's solution compares the maximum gradient angle of the RF power supply with the plasma impedance trajectory angle to obtain the phase difference between the two. This phase difference directly reflects the degree of phase mismatch between the RF power supply and the plasma load. Based on this phase difference, combined with the electrical characteristics of the RF transmission line (such as propagation speed and operating frequency), the optimal cable length of the RF transmission line can be accurately calculated. By adjusting the physical length of the RF transmission line to this optimal value, the transmission line can act as an impedance transformer, transforming the actual impedance of the plasma load to the matching impedance desired by the RF power supply. This allows the RF power supply to transmit power to the plasma load with higher efficiency, minimizing reflected power and thus optimizing the entire RF power transmission system. This method combines the internal characteristics of the RF power supply with the dynamic characteristics of the external load, providing a proactive and precise impedance matching optimization strategy that goes beyond simply testing power supply performance and directly guides the optimization of the system's physical configuration.

[0114] Figure 7 This is a connection diagram of the plasma impedance test provided in an embodiment of this application. Under low-voltage, low-power process conditions, the interaction between the power-dependent plasma impedance and the load-dependent RF delivery system can cause significant instability. The system stability can be improved by changing the transmission line length.

[0115] In one specific embodiment, the formula for calculating the plasma impedance trajectory angle is: , , , , in, The plasma impedance trajectory angle, The difference in reflection coefficients. The reflection coefficient is calculated after the matcher reaches the matching state. The reflection coefficient is calculated after increasing the radio frequency power. The impedance value measured after the matching circuit reaches the matching state. The impedance value measured after increasing the RF power; The formula for calculating the phase difference between the maximum gradient angle and the plasma impedance trajectory angle is: , in, The phase difference between the maximum gradient angle and the plasma impedance trajectory angle. The phase of the plasma impedance trajectory angle. The phase of the maximum gradient angle of the RF power supply. It is an integer; The formula for calculating the additional cable length of a radio frequency transmission line is: , in, For the additional cable length of the radio frequency transmission line, The speed of light in a vacuum. For cable speed coefficient, The output frequency of the radio frequency power supply; Table 1 below shows the extra cable length values ​​calculated for integer values ​​of n, ranging from -2 to 2. The appropriate value of n should be chosen based on the specific application. Table 1 ; The calculated additional cable length for the RF transmission line can be used to increase or decrease the current cable length in the RF system, thereby improving system stability. For example, if the RF system has a cable length of 10 m and is prone to instability, to achieve more stable conditions, the cable length can be reduced by 1.74 m (n=-1) to 8.26 m; or increased by 5.56 m (n=0) to 15.56 m.

[0116] Figure 8 This is a schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application. The following refers to... Figure 8 To describe an electronic device 800 according to such an embodiment of the present disclosure. Figure 8 The electronic device 800 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0117] like Figure 8 As shown, the electronic device 800 is presented in the form of a general-purpose computing device. The components of the electronic device 800 may include, but are not limited to: at least one processing unit 810, at least one storage unit 820, a bus 830 connecting different system components (including storage unit 820 and processing unit 810), a display unit 840, etc.

[0118] The storage unit stores program code, which can be executed by the processing unit 810, causing the processing unit 810 to perform the steps described in the above-described method section of this specification according to various exemplary embodiments of this disclosure.

[0119] Storage unit 820 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 8201 and / or cache memory 8202, and may further include a read-only memory (ROM) 8203.

[0120] The storage unit 820 may also include a program / utility 8204 having a set (at least one) of program modules 8205, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0121] Bus 830 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0122] Electronic device 800 can also communicate with one or more external devices 800' (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 800, and / or with any device that enables electronic device 800 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 850. Furthermore, electronic device 800 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 860. Network adapter 860 can communicate with other modules of electronic device 800 via bus 830. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 800, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0123] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0124] The gain calibration method, dynamic impedance testing method, equipment, and dielectric provided in this application embodiment are based on an open-loop RF power supply with multiple load impedance values ​​and corresponding RF power measurements. Two-dimensional interpolation fitting is performed in the complex plane of the reflection coefficient, and the target minimum RF power value is selected based on the continuous power distribution obtained from the interpolation in the complex plane of the reflection coefficient, thereby calculating the gain of the RF power supply. Thus, by introducing two-dimensional interpolation fitting in the complex plane of the reflection coefficient, the limitations of discrete measurement points are effectively overcome. The continuous power distribution obtained from the interpolation fitting provides a more comprehensive and smoother power change trend, thereby reducing the impact of noise and measurement errors on the identification of the minimum power point. By selecting the target minimum RF power value in the complex plane of the reflection coefficient based on the continuous power distribution obtained from the interpolation, the minimum output power point of the RF power supply under specific load conditions can be accurately identified, avoiding misjudgment of the minimum power point due to insufficient sampling of discrete points or noise interference, and ensuring higher reliability of the selected target minimum RF power value. The gain of the RF power supply is calculated based on the target minimum RF power value, its corresponding load impedance value, and the preset characteristic impedance value, making the gain calibration process more accurate and robust, improving the accuracy of gain calibration, and reducing the impact of environmental noise and small impedance fluctuations.

[0125] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, or network device, etc.) to execute the methods described above according to the embodiments of this disclosure.

[0126] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0127] Computer-readable storage media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium that can transmit, propagate, or transfer a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0128] Those skilled in the art will understand that the above modules can be distributed in the device as described in the embodiments, or they can be modified accordingly and placed in one or more devices that are unique to this embodiment. The modules in the above embodiments can be combined into one module, or they can be further divided into multiple sub-modules.

[0129] Exemplary embodiments of this disclosure have been specifically shown and described above. It should be understood that this disclosure is not limited to the detailed structures, arrangements, or implementations described herein; rather, this disclosure is intended to cover various modifications and equivalent arrangements contained within the spirit and scope of the appended claims.

Claims

1. A gain calibration method, characterized in that, include: Multiple RF power measurements are acquired; the RF power measurements are the output power measurements of the RF power supply in an open-loop state under multiple load impedance values; Based on the load impedance value and the RF power measurement value, a two-dimensional interpolation fitting is performed in the complex plane of the reflection coefficient to obtain a continuous power distribution. Based on the continuous power distribution, the minimum radio frequency power value is selected in the complex plane of the reflection coefficient to obtain the target minimum radio frequency power value; The gain of the RF power supply is calculated based on the target minimum RF power value, the load impedance value corresponding to the target minimum RF power value, and the preset characteristic impedance value.

2. The gain calibration method according to claim 1, characterized in that, The two-dimensional interpolation fitting of the RF power measurement values ​​includes: Calculate the corresponding reflection coefficient based on the load impedance value; The complex plane of the reflection coefficient is constructed based on the real and imaginary parts of the reflection coefficient; In the complex plane of the reflection coefficient, a two-dimensional interpolation operation is performed on the discrete radio frequency power data to obtain the continuous power distribution.

3. The gain calibration method according to claim 2, characterized in that, The two-dimensional interpolation operation is radial basis function interpolation, two-dimensional polynomial interpolation, or Gaussian interpolation.

4. The gain calibration method according to claim 1, characterized in that, The selection of the minimum radio frequency power value within the complex plane of the reflection coefficient includes: Within the target defined region, the minimum radio frequency power value in the continuous power distribution is searched to obtain the target minimum radio frequency power value; the target defined region is the region centered on the origin of the reflection coefficient complex plane, where the magnitude of the reflection coefficient is not greater than a preset reflection threshold, and the target defined region includes the reflection coefficient point corresponding to the characteristic impedance value.

5. The gain calibration method according to claim 4, characterized in that, The reflection threshold is determined based on the magnitude of the reflection coefficient, which is determined by the load impedance stability boundary, the test system safe reflection boundary, and / or the typical plasma equivalent impedance.

6. The gain calibration method according to claim 1, characterized in that, The calculation of the gain of the RF power supply based on the target minimum RF power value, the load impedance value corresponding to the target minimum RF power value, and a preset characteristic impedance value includes: Based on the reflection coefficient corresponding to the characteristic impedance value and the target minimum RF power value, calculate the load impedance value corresponding to the target minimum RF power value; The impedance change is calculated based on the load impedance value corresponding to the target minimum RF power value and the characteristic impedance value. The power change is calculated based on the RF power value corresponding to the load impedance value and the target minimum RF power value. The gain of the radio frequency power supply is determined based on the impedance change and the power change.

7. The gain calibration method according to claim 6, characterized in that, Before calculating the load impedance value corresponding to the minimum RF power value, the method further includes: Based on the impedance value of the load device of the RF power supply and the characteristic impedance value, the reflection coefficient corresponding to the minimum RF power value is calculated.

8. The gain calibration method according to claim 1, characterized in that, The load impedance value is provided by the load traction system and a 50Ω water-cooled load, covering the VSWR range of 1.1:1 to 5:1 and the entire Smith circle.

9. The gain calibration method according to claim 1, characterized in that, The open-loop state refers to disconnecting the closed-loop regulation circuit of the RF power supply, making the RF power supply equivalent to a constant voltage source with series internal resistance in operation mode.

10. A method for testing dynamic impedance, characterized in that, include: Obtain the gain of the radio frequency power supply; the gain of the radio frequency power supply is obtained based on the gain calibration method according to any one of claims 1 to 9; Based on the phase angle corresponding to the target minimum RF power value, calculate the maximum gradient angle of the RF power supply; Based on the gain and maximum gradient angle of the RF power supply, the dynamic impedance test results of the RF power supply are generated.

11. The dynamic impedance testing method according to claim 10, characterized in that, The step of calculating the maximum gradient angle of the RF power supply based on the phase angle corresponding to the target minimum RF power value includes: Determine the phase angle corresponding to the target minimum radio frequency power value; Subtract 180° from the phase angle corresponding to the target minimum RF power value to obtain the maximum gradient angle of the RF power supply.

12. The dynamic impedance testing method according to claim 10, characterized in that, The generation of dynamic impedance test results for the RF power supply based on its gain and maximum gradient angle includes: The gain and maximum gradient angle of the RF power supply are compared with the corresponding gain threshold and the corresponding maximum gradient angle threshold, respectively, and the dynamic impedance test results are generated based on the comparison results.

13. The dynamic impedance testing method according to claim 10, characterized in that, Also includes: The optimal cable length for the radio frequency transmission line is calculated based on the phase difference between the maximum gradient angle and the plasma impedance trajectory angle.

14. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 13.

15. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 13.

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