Plasma impedance matching optimization method based on backward reasoning

Abstract

The invention belongs to the technical field of plasma impedance matching, and particularly relates to a plasma impedance matching optimization method based on backward reasoning, which comprises the following steps: constructing an impedance matching circuit comprising a plasma load, a radio frequency power supply and an impedance matching network; determining a control parameter set P formed by parameters of a plurality of elements in the impedance matching network and initializing a value; acquiring preset values of other discharge parameters except the P, operating an impedance matching circuit in combination with the current value of the P, and extracting impedance Zp of the load; calculating a preset performance index of the impedance matching circuit based on the current value of the P and the current Zp; and fixing the Zp value as the current value, searching the value of the P and operating the circuit again by taking the preset performance index minimization as the target through backward reasoning until the index reaches the threshold value, obtaining the optimal value of the P and the corresponding Zp value, and completing plasma impedance matching optimization. The matching method provided by the invention has the characteristics of rapidness, accuracy and strong robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of plasma impedance matching, and more specifically, relates to a method for optimizing plasma impedance matching based on reverse reasoning. Background Art

[0002] Plasma technology plays an increasingly important role in modern industry, especially in fields such as semiconductor manufacturing, surface modification, and thin film deposition. To improve the efficiency and performance of plasma devices, it is crucial to achieve effective impedance matching between the RF power supply and the plasma load in the plasma device. Impedance matching can not only maximize power transfer but also improve the repeatability of process control, enhance plasma uniformity, and reduce energy consumption.

[0003] Traditional impedance matching methods usually rely on forward adjustment, such as using variable capacitance - inductance networks (such as L - type, π - type, or T - type matching networks) for manual or automatic tuning. However, these methods often suffer from difficulties in convergence. Especially when the initial parameters are not properly selected, even if convergence can be achieved, they often fall into local solutions. In addition, traditional methods perform poorly in multi - parameter optimization and are difficult to efficiently optimize multiple variables. More critically, traditional matching methods are usually highly coupled with the complex physical details inside the plasma and rely on complex modeling and solution processes to achieve matching optimization. This dependence makes them lack flexibility in dealing with plasma state fluctuations and is difficult to respond in real - time to dynamically changing impedance requirements. Especially at specific frequencies (such as the second - harmonic frequency, third - harmonic frequency) and in pulse modes, the impedance matching performance is significantly limited. Therefore, there is an urgent need for an impedance matching optimization method that can overcome the above limitations to achieve fast, accurate, and robust impedance matching. Summary of the Invention

[0004] In view of the above - mentioned defects or improvement requirements of the prior art, the present invention provides a method for optimizing plasma impedance matching based on reverse reasoning, aiming to propose a fast, accurate, and highly robust plasma impedance matching method.

[0005] To achieve the above object, according to one aspect of the present invention, a method for optimizing plasma impedance matching based on reverse reasoning is provided, including:

[0006] S1. Construct an impedance matching circuit for the target plasma device, which includes a plasma load and its external circuit, where the external circuit includes an RF power supply and an impedance matching network;

[0007] S2. Determine a control parameter set P for impedance matching optimization, which is composed of the parameters of multiple components in the impedance matching network, and initialize the values;

[0008] S3. Obtain the preset values of other discharge parameters other than the control parameter set P in the impedance matching circuit, combine with the current value of the control parameter set P, run the impedance matching circuit, and extract the impedance Z of the plasma load p ; Based on the current value of the control parameter set P and the current impedance Z p , calculate the preset performance index of the impedance matching circuit as the matching evaluation index;

[0009] S4. Fix the value of the impedance Z p at the current value, and by means of backward reasoning, with the goal of minimizing the preset performance index, search for and adjust the value of P and re - execute S3 until the preset performance index reaches the preset threshold, and finally obtain the optimal value of the control parameter set P and the corresponding impedance Z p value under the current value of the other discharge parameters, and complete the optimization of plasma impedance matching.

[0010] Further, in S3, run the impedance matching circuit by means of numerical simulation, obtain the voltage time - domain signal at both ends of the plasma load and the current time - domain signal flowing through the plasma load when the operation is stable, so as to obtain the impedance Z of the plasma load by an analytical method p .

[0011] Further, the preset performance index is the modulus value of the impedance matching reflection coefficient of the power reflected from the load back to the power supply by the impedance matching circuit, expressed as:

[0012]

[0013] In the formula, Γ is the impedance matching reflection coefficient, Z l is the input impedance of the impedance matching network, and Z s is the output impedance of the RF power supply.

[0014] Further, it also includes:

[0015] S5. Save the values of the other discharge parameters and their corresponding plasma load impedance Z finally obtained through backward reasoning iteration p , so as to fit out the dependency relationship between the values of the other discharge parameters and the plasma load impedance Z p ; When obtaining new preset values of the other discharge parameters, based on the dependency relationship, determine the initial value of the plasma load impedance Z p and then execute S4 to obtain the optimal value of the control parameter set P under the new preset values of the other discharge parameters.

[0016] According to another aspect of the present invention, there is provided an electronic device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the steps of the method described above are implemented.

[0017] According to another aspect of the present invention, there is provided a computer-readable storage medium, which includes a stored computer program. When the computer program is run by a processor, the device where the storage medium is located is controlled to execute the steps of the method described above.

[0018] According to another aspect of the present invention, there is provided a computer program product, including a computer program or instruction. When the computer program or instruction is executed by a processor, the steps of the method described above are implemented.

[0019] Generally speaking, compared with the prior art by the above technical solution conceived by the present invention, the technical solution provided by the present invention mainly has the following beneficial effects:

[0020] 1. The present invention proposes a plasma impedance matching optimization method based on reverse inference. First, a coupled circuit model composed of a radio frequency power supply, an impedance matching network, and a plasma load is constructed, and the control parameters of the matching network are initialized; based on the topological structure of the circuit, a matching evaluation index based on the plasma load impedance is established as the optimization objective function; during the discharge process, the equivalent impedance of the plasma load under steady-state conditions is extracted to calculate the value of the optimization objective function. If the preset convergence threshold is satisfied, the current matching network parameters are output as the optimal control parameters; otherwise, the position of the plasma load in the impedance space is fixed, and the reverse inference algorithm is used to calculate the matching network parameters that minimize the value of the optimization objective function at this position, and the matching network parameters are updated and then continue to be iteratively optimized until the convergence condition is satisfied. The present invention uses the impedance of the plasma load as a bridge to convert the impedance matching optimization process from the traditional control parameter space to the impedance space, and combines the reverse inference algorithm to reconstruct the matching problem into a function optimization problem, realizing fast and efficient matching optimization. In addition, because this method transfers the optimization process from the control parameter space to the plasma impedance space, derives new control parameters from the impedance space through reverse inference, decouples the dependence of the optimization process on the historical path, and uses the measurable plasma impedance as a bridge to shield the internal modeling details of the device, it has the characteristics of strong robustness, high decoupling of the optimization process from plasma physical details, and excellent scalability, and can be widely used in plasma impedance matching control in numerical simulations and experimental devices.

[0021] 2. The present invention further proposes that the method matching optimization further includes: saving the values of other discharge parameters and the corresponding plasma load impedance Z finally obtained through reverse inference iteration p, to fit the dependence relationship between the values of other discharge parameters and the plasma load impedance Z p ; when obtaining new preset values of other discharge parameters, based on the dependence relationship, determine the initial value of the plasma load impedance Z p and then execute S4 to obtain the optimal value of the control parameter set P under the new preset values of the other discharge parameters. Using this method can accelerate the matching optimization. Description of the Drawings

[0022] Figure 1 is a flowchart of a plasma impedance matching optimization method based on reverse reasoning provided by an embodiment of the present invention;

[0023] Figure 2 is a schematic structural diagram of an impedance matching circuit provided by an embodiment of the present invention;

[0024] Figure 3 is the optimization process of the plasma load in its corresponding impedance space provided by an embodiment of the present invention, where (a), (b), (c), and (d) respectively correspond to the results corresponding to the control parameters after the initial state, the first optimization, the second optimization, and the eighth optimization;

[0025] Figure 4 is a parameter evolution diagram during the plasma discharge process provided by an embodiment of the present invention;

[0026] Figure 5 is a schematic diagram of the changes in the matching network parameters and the plasma matching performance parameters during the impedance matching optimization process provided by an embodiment of the present invention;

[0027] Figure 6 is a structural block diagram of a self-feedback type impedance fast matching system provided by an embodiment of the present invention. Detailed Embodiments

[0028] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0029] Embodiment 1

[0030] A plasma impedance matching optimization method based on reverse reasoning, as Figure 1 shown, includes:

[0031] S1. Construct an impedance matching circuit of a target plasma device including a plasma load and its external circuit, where the external circuit includes a radio frequency power supply and an impedance matching network;

[0032] S2. Determine the control parameter set P for impedance matching optimization composed of the parameters of multiple components in the impedance matching network and initialize the values.

[0033] S3. Obtain the preset values of other discharge parameters in the impedance matching circuit other than the control parameter set P, combine with the current values of the control parameter set P, run the impedance matching circuit, and extract the impedance Z of the plasma load. p ; Based on the current values of the control parameter set P and the current impedance Z p , calculate the preset performance index of the impedance matching circuit as the matching evaluation index.

[0034] S4. Fix the value of the impedance Z p as the current value, and by means of backward reasoning, with the minimization of the preset performance index as the goal, search for and adjust the values of P and re - execute S3 until the preset performance index reaches the preset threshold, and finally obtain the optimal value of the control parameter set P and the corresponding impedance Z p value under the current values of the other discharge parameters, thus completing the optimization of the plasma impedance matching.

[0035] The plasma impedance matching optimization method proposed in this embodiment first constructs a coupled circuit model composed of a radio - frequency power supply, an impedance matching network, and a plasma load, and initializes the control parameters of the matching network; based on the topological structure of the circuit, establish a matching evaluation index (such as the modulus of the reflection coefficient) based on impedance as the optimization objective function; during the discharge process, extract the equivalent impedance of the plasma load under steady - state conditions, or directly measure the impedance of the plasma load by experimental instruments such as an impedance analyzer; calculate the value of the optimization objective function, if it meets the preset convergence threshold, output the current matching network parameters as the optimal control parameters; otherwise, fix the position of the plasma load in the impedance space, use the backward reasoning algorithm to calculate the matching network control parameters that minimize the value of the optimization objective function at this position, and update the matching network parameters and continue iterative optimization until the convergence condition is met. The present invention takes the impedance of the plasma load as a bridge, transforms the optimization process from the traditional control parameter space to the impedance space, and combines with the backward reasoning algorithm to reconstruct the matching problem into a function optimization problem, realizing fast and efficient matching optimization.

[0036] In addition, since this method transfers the optimization process from the control parameter space to the plasma impedance space, derives new control parameters from the impedance space through reverse inference, decouples the optimization process from the dependence on the historical path, and uses the measurable plasma impedance as a bridge to shield the internal modeling details of the device, it has the characteristics of strong robustness, high decoupling of the optimization process from plasma physical details, and excellent scalability. It can be widely used in plasma impedance matching control in numerical simulations and experimental devices.

[0037] Furthermore, due to its algorithm independence and flexible design based on the impedance space, this method supports seamless integration with various optimization algorithms (such as gradient descent, particle swarm optimization, etc.), and can optimize the impedance matching at multiple frequency points simultaneously by adjusting the objective function. It is not only applicable to the fundamental frequency impedance matching, but also supports the matching optimization at specific frequency points (such as the second harmonic frequency, third harmonic frequency, etc.), and can adapt to complex application scenarios such as pulsed mode discharge.

[0038] A reliable and stable matching optimization method for plasma devices proposed in this embodiment. The control parameters, other discharge parameters, and load impedance used in this method are all measurable physical quantities, so it has good generality in both numerical simulations and experimental devices; at the same time, the physical details of the plasma load are not involved in the optimization process of the present invention, so the optimization method is highly decoupled from the internal details of the plasma load; in addition, various existing reverse inference algorithms can be flexibly integrated in the optimization process of the present invention; further, through the reverse inference process, the control parameters of the matching network are effectively decoupled from their historical paths, avoiding the risk of falling into local optimal solutions. In addition, this method can generate multiple sets of saddle point reference values, providing more choice space for the optimization results, and having significant advantages compared with traditional optimization methods.

[0039] Generally speaking, the method of this embodiment can quickly and accurately find the optimal matching control parameters and maintain the optimal matching state while achieving a high degree of decoupling between the optimization method and plasma details. It is not only applicable to impedance matching at the fundamental frequency, but also can simultaneously perform matching optimization on the target harmonic frequencies (such as the second harmonic frequency, third harmonic frequency).

[0040] To better illustrate the method of this embodiment, the following will explain each step by way of example:

[0041] Regarding the step of S1 for constructing the impedance matching circuit. As Figure 2 shown is a schematic structural diagram of the impedance matching circuit in an implementation example. This circuit consists of three parts: a radio frequency power supply, an impedance matching network, and a plasma load.

[0042] Among them, the radio frequency power supply can be equivalently regarded as a radio frequency generator RF and its internal resistance R sFor the combination, the RF power supply can be a voltage source or a power source. In this embodiment, the RF power supply is set as a constant power source with an output power of 20 W, an AC frequency of 13.56 MHz, and an internal resistance R s of 50 Ω.

[0043] Among them, the specific configuration form of the impedance matching network (including component composition and topological structure) can be flexibly adjusted according to different application scenarios. In this embodiment, as Figure 2 shown, the impedance matching network adopts an "L-type" structure, which includes: a variable capacitor C m1 (connected in parallel with the RF power supply); a variable capacitor C m2 , a variable inductor L, and a loss resistance R m (the three are connected in series and form an "L-type" matching network with C m1 ). The specific connection method of the impedance matching network is: According to the circuit diagram, the modified specific connection method is: one end of the variable capacitor C m1 is connected to the output end of the RF power supply, and the other end is grounded. The output end of the RF power supply is also connected to one end of the variable capacitor C m2 , and the other end of C m2 is successively connected in series with the variable inductor L and the loss resistance R m and then connected to one end of the plasma load. The other end of the plasma load is grounded to form a complete current loop. It should be noted that the topological structure of the impedance matching network is not limited to the "L-type", and other forms such as "T-type" and "π-type" can also be adopted according to needs. In addition, the type and quantity of each component can also be flexibly configured according to specific requirements to meet different matching conditions and optimization requirements.

[0044] After establishing the impedance matching circuit, for the initial value of the control parameter P in S2, it can be set as an empirical value or randomly generated. In an implementation example, P = {C m1 , C m2 , L}, that is, it includes the three component values of the variable capacitor C m1 , the variable capacitor C m2 , and the variable inductor L, and is randomly assigned values, for example, P = {1591.90 pF, 9299.00 pF, 12.70 μH}.

[0045] In S3, regarding the matching evaluation index, it includes but is not limited to one or a combination of the following methods:

[0046] (1) The magnitude of the reflection coefficient:

[0047]

[0048] Among them, Γ is the impedance matching coefficient, Z lis the input impedance of the impedance matching network, Z s is the output impedance of the RF power supply;

[0049] (2) Impedance similarity:

[0050]

[0051] Among them, the meanings of the parameters are the same as those described above, but the complex impedance is regarded as a two-dimensional vector for calculation;

[0052] (3) Impedance vector distance (taking Euclidean distance as an example):

[0053]

[0054] The meanings of the parameters are the same as above.

[0055] The above matching evaluation indexes can be used alone according to actual needs or combined in forms such as weighted combination and hierarchical calculation to improve the accuracy and robustness of impedance matching.

[0056] As a relatively general method, preferably, the modulus value of the reflection coefficient is selected as the optimization target, and the calculation formula is:

[0057]

[0058] Among them, Γ is the impedance matching reflection coefficient, Z l is the input impedance of the impedance matching network, Z s is the output impedance of the RF power supply.

[0059] The calculation formula for calculating the input impedance of the impedance matching network is:

[0060]

[0061] Among them, Z l is the input impedance of the impedance matching network, Z1 is the branch impedance of the branch where the variable capacitor C m1 is located, Z2 is the branch impedance of the branch where the variable capacitor C m2 is located, is the impedance of the variable capacitor C m1 of, is the impedance of the variable capacitor C m2 of, Z L is the impedance of the variable inductor L, is the loss resistance R of the impedance matching network m of, Z p is the impedance of the plasma load to be determined.

[0062] The calculation formula for calculating the output impedance of the RF power supply is:

[0063]

[0064] Among them, Z s is the output impedance of the RF power supply, is the internal resistance R s of the RF power supply.

[0065] Then, under given discharge parameters, for a capacitive plasma load, the value of Equation (1) is completely determined by the control parameters and the impedance of the plasma, and thus can be written as:

[0066] |Γ| = f(P, Z p ) = f(P, C p , R p )...(4)

[0067] Among them, C p and R p are the equivalent capacitance and equivalent resistance of the capacitive plasma load, respectively. This is because for a capacitive plasma load, its impedance can be equivalent to the series connection of a resistor and a capacitor.

[0068] During S3 operation of the impedance matching circuit, actual equipment can be used for operation. Further, the impedance Z p of the plasma load can be directly measured by an instrument. It is also possible to operate the impedance matching circuit by means of numerical simulation (low cost, high speed), obtain the voltage time-domain signal across the plasma load and the current time-domain signal flowing through the plasma load when the operation is stable, so as to obtain the impedance Z p of the plasma load by an analytical method.

[0069] This embodiment takes the optimization of numerical simulation as an example. The initial values of the control parameter P have been given. In the simulation program, the plasma load is solved using a one-dimensional implicit PIC-MCC (Particle-in-Cell - Monte Carlo Collision) model, and the external circuit part is solved using an ordinary differential equation solver. The plasma load and the external circuit are coupled through the electric potential, charge density, and current at the plasma load electrode plate. The simulation time step is 1×10 -10 s, the discharge gas is pure argon, and the gas pressure is 100 mTorr. After the circuit discharge parameters (voltage, power) and control parameters are given, the system reaches a steady state after approximately 800 RF cycles (about 73 μs).

[0070] Perform Hilbert transforms on the voltage time-domain signal U p (τ) across the plasma load and the current time-domain signal Ip(τ) flowing through the plasma load corresponding to 800 to 1000 RF cycles obtained by numerical simulation, and calculate the impedance of the plasma load.

[0071] More specifically, the method for extracting the equivalent impedance of the plasma load includes:

[0072] Perform Hilbert transforms on the voltage time-domain waveform across the plasma load and the current time-domain waveform flowing through the plasma load respectively, and calculate the complex impedance of the plasma load according to the following formula.

[0073] The calculation formula for the Hilbert transform is as follows:

[0074]

[0075] where is the transformed time-domain signal, x(τ) is the time-domain expression of the waveform to be transformed, and P.V. is the principal value of the integral.

[0076] The formula for calculating the analytic signal of the voltage time-domain signal is as follows:

[0077]

[0078] where is the analytic signal corresponding to the voltage time-domain signal, represents the Hilbert transform function of the input signal u(t), and j is the imaginary unit;

[0079] The formula for calculating the amplitude of the voltage signal is as follows:

[0080]

[0081] where U m is the amplitude of the voltage signal, T is the time period, and U m (t) is the instantaneous amplitude of the voltage signal calculated from the analytic signal;

[0082] The formula for calculating the phase angle of the voltage signal is as follows:

[0083]

[0084] where φ u is the phase angle of the voltage signal, T is the time period, and φ u (t) is the instantaneous phase angle of the voltage signal calculated from the analytic signal;

[0085] Performing similar processing on the current time-domain signal i(t) can obtain the corresponding current amplitude I m and phase angle φ i , and then obtaining the phase difference between the voltage signal and the current signal:

[0086] φ = φ u - φ i ····· (9)

[0087] The formula for calculating the plasma load impedance is as follows:

[0088]

[0089] Among them, Z p is the plasma load impedance, U m is the amplitude obtained by performing a Hilbert transform on the plasma load voltage waveform, I m is the amplitude obtained by performing a Hilbert transform on the plasma load current waveform, is the phase difference between the voltage and current waveforms, and j is the imaginary unit.

[0090] The calculation formulas for the equivalent resistance and equivalent capacitance of a capacitive plasma load impedance are as follows:

[0091]

[0092] Among them, R p is the resistance value in the equivalent circuit of the plasma load, C p is the capacitance value in the equivalent circuit of the plasma load, ω = 2πf is the angular frequency of the RF power supply, and f is the frequency of the RF power supply.

[0093] After the plasma load impedance is determined, the optimization target parameter |Γ| = 0.9999 of the impedance circuit corresponding to the current impedance matching network is calculated according to Equation (1), and this position is marked with "×" in the impedance space shown in (a) of Figure 3 . It should be noted that Equation (4) equivalently represents the capacitive plasma load impedance as a series connection of a resistor and a capacitor, and this equivalence is for a more intuitive visualization of the impedance space in the form of a graph.

[0094] After the control parameters P = {1591.90 pF, 9299.00 pF, 12.70 μH} are given, Equation (4) gives the value distribution of the optimization target |Γ| in the plasma load impedance space. As shown in (a) of Figure 3 , its value distribution in the parameter space {C p ∈(0 pF, 100 pF) ∩ R p ∈(0 Ω, 80 Ω)} is shown. It can be seen that there is only a narrow matching window at this time, and the reflection coefficient in the remaining regions is close to 1.

[0095] Therefore, as can be seen from (a) of Figure 3 , the position of the current plasma load is far from the matching window and is in the mismatched region.

[0096] Set a convergence threshold ε = 0.01. If |Γ| ≤ ε, it is considered that the matching meets the requirements, and the optimal matching control parameters are output. Otherwise, the control parameter set P corresponding to the inverse inference impedance matching network is deduced, and the position Z of the plasma load in its impedance space p is fixed as a constant. At this time, the optimization objective expression (4) is simplified to a function determined only by the matching network control parameter P:

[0097] |Γ| = f(P)……(13)

[0098] To minimize the value of |Γ|, a minimization algorithm needs to be selected to search for the optimal combination of control parameters P. For the sake of simplicity in explanation, the grid search algorithm is adopted for solution: The three adjustable components C m1 , C m2 , L of the matching network are respectively divided into several discrete value points to form a multi-dimensional parameter grid, and all possible parameter combinations P = {C m1 , C m2 , L} are generated. The grid is divided for the three adjustable components included in P respectively. Thus, a series of parameter combinations including these three parameters can be given. Then, each group of parameter combinations is substituted into equation (12) to calculate its |Γ| value. By comparing all the calculation results, the parameter combination that minimizes |Γ| is selected as the new matching parameter to update the matching network, and return to step S3 to continue iterative optimization until the convergence condition is met.

[0099] Regarding the inverse inference, the inverse inference algorithm includes:

[0100] Denote the optimization objective as λ, the control parameter set as P, and the plasma load impedance as Z p , then the construction method of the optimization objective gives the relationship equation among the three:

[0101] λ = f(P, Z p )

[0102] In this equation, fix the value of Z p , and calculate the impedance matching network control parameter P that can minimize λ through the minimization algorithm new ; Take the obtained P new as the new control parameter, replace the original parameter to re-perform the discharge process, and continue iterative optimization.

[0103] The algorithms used to perform the inverse inference may include the following various methods:

[0104] Grid Search algorithm: Construct a uniformly distributed grid in the control parameter space, evaluate the objective function value λ corresponding to each group of parameter combinations one by one, and select the control parameter P that minimizes λ;

[0105] Gradient Descent Algorithm: By calculating the gradient of the objective function λ with respect to the control parameter P, adjust P in the direction of the descending gradient until it converges to the value that minimizes λ;

[0106] Particle Swarm Optimization (PSO): Simulate the position and velocity update process of multiple particles in the control parameter space. Each particle dynamically adjusts its direction and step size based on its own historical optimal position and the global optimal position, gradually approaching the control parameter P that minimizes λ;

[0107] Differential Evolution (DE) Algorithm: Generate new candidate solutions by introducing differential mutation and crossover operations in the population, and combine selection operations to retain individuals with higher fitness, evolving continuously until the control parameter P that minimizes the objective function λ is found;

[0108] Machine Learning Algorithm: Based on methods such as supervised learning, unsupervised learning, or reinforcement learning, train a model to learn the mapping relationship between the control parameter P and the target value λ, thereby predicting the control parameter P that minimizes λ.

[0109] The core of the backward inference method lies in determining the corresponding control parameter P by minimizing the optimization objective λ. The specific minimization algorithm used can be flexibly selected and implemented according to the actual application requirements and constraints.

[0110] Figure 3 It is the change in the steady-state position of the plasma load and the position of the matching window as the iteration progresses. Among them, the contour lines mark the positions of the good matching windows, and "×" marks the impedance steady-state positions of the plasma load under different control parameters. (a), (b), (c), and (d) correspond to the results corresponding to the control parameters after the initial state, the first optimization, the second optimization, and the eighth optimization, respectively. It can be seen from the figure that when the optimization objective reaches the preset convergence threshold, the steady-state impedance position of the plasma load has completely fallen into the central region of the matching window, indicating that the matching effect has reached the optimal state.

[0111] Figure 4Shows the evolution of key parameters during capacitive coupled plasma discharge. Among them, (a) shows the evolution trends of the voltage amplitude across the plasma load and the power supply voltage amplitude over time; (b) shows the time evolution trends of the plasma load current amplitude and the power supply current amplitude; (c) shows the evolution trends of the active power of the plasma load and the power supply active power over time; (d) shows the evolution trend of the electron density in the core region of the plasma over time. The abscissa represents the RF cycle, and the matching parameters are adjusted every 1000 RF cycles (about 73 μs). It can be seen from the figure that as the iteration progresses, the electron density n of the plasma e and other key parameters increase significantly, and each parameter approaches the optimal matching state after 4 iterations, and finally stabilizes at this matching state.

[0112] Figure 5 Gives the variation trends of the matching network parameters (C m1 , C m2 , L), the plasma load impedance (C p , R p ), the load power absorption efficiency η, and the modulus of the reflection coefficient |Γ| with the number of optimization iterations. The abscissa represents the number of iterations. The load power absorption efficiency is defined as the ratio of the active power of the load to the active power of the power supply. The smaller the reflection coefficient |Γ|, the less the reflected power and the better the matching effect. In this example, the set convergence threshold ε is 0.01, and the reflection coefficient reaches this threshold after 8 iterations, meeting the matching condition.

[0113] From Figure 5 it can be seen that when the reflection coefficient |Γ| and the power absorption efficiency η converge, the control parameters of the matching network (especially C m2 ) do not converge. Therefore, the following several groups of control parameters are all saddle points with similar matching performances. The appearance of this phenomenon is mainly attributed to the influence of environmental noise and random factors in the plasma system. Even if the plasma load is already in the optimal matching window of the impedance space, its position may still shift slightly, and the control parameters are inversely deduced from the impedance at this position. Therefore, the deduced control parameters will also fluctuate accordingly. Specifically, the convergence conditions of different control parameters are closely related to their sensitivities in the matching equation (1). Among them, C m1 and L are not sensitive to the fluctuations of the plasma impedance in this equation, so their values converge, while C m2 is more sensitive to the fluctuations of the plasma impedance, so its value diverges.

[0114] As a preferred implementation method, the matching optimization method of this embodiment further includes:

[0115] S5. Save the values of the other discharge parameters and the corresponding plasma load impedance Z finally obtained through reverse inference iteration p , to fit the dependence relationship between the values of the other discharge parameters and the plasma load impedance Z p ; when obtaining new preset values of the other discharge parameters, based on the dependence relationship, determine the initial value of the plasma load impedance Z p , then execute S4 to obtain the optimal value of the control parameter set P under the new preset values of the other discharge parameters. Using this method can accelerate the matching optimization.

[0116] Embodiment 2

[0117] This application also relates to an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the above method are implemented.

[0118] The electronic device may be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The so-called processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Digital Signal Processors (DSPs), Application-Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The memory can be used to store computer programs and / or modules. The processor runs or executes the computer programs and / or modules stored in the memory, and calls the data stored in the memory to implement various functions of the electronic device.

[0119] Specifically, it can be a self-feedback impedance fast matching system based on the above method. As Figure 6 shown, the system includes:

[0120] A model construction module, including a first to a second sub-module. Among them, the first sub-module is used to construct a coupled circuit model including a radio frequency power supply, an impedance matching network, and a plasma load, and the second sub-module is used to construct a matching evaluation index as an optimization target according to the topological structure of the circuit;

[0121] A component initialization module, used to set parameter values for each adjustable component in the model;

[0122] A discharge start module, used to start the discharge process and make the system run to a steady state;

[0123] The impedance extraction module includes first to third sub - modules. Among them, the first sub - module is used to collect the voltage and current time - domain signals of the plasma load, and extract the amplitude and phase information of the voltage signal and current signal through the Hilbert transform. The second sub - module is used to calculate the complex impedance of the plasma load according to the extracted voltage amplitude, current amplitude and phase difference information. The third sub - module is used to directly receive the complex impedance value of the plasma load obtained from experimental measurement, and use the received impedance value as the final impedance value extracted by the module. Among them, the third sub - module is only activated when there is an external input;

[0124] The parameter calculation module is used to calculate the numerical value of the optimization target;

[0125] The judgment module includes first to third sub - modules. Among them, the first sub - module is used to set the convergence threshold, the second sub - module is used to monitor the system state, and the third sub - module is used to judge whether the current optimization target value meets the preset convergence condition. If it meets, the optimal parameters are output; if not, the next - step optimization is triggered;

[0126] The reverse inference module includes first to third sub - modules. Among them, the first sub - module is used to select or implement the minimization optimization algorithm. The second sub - module is used to set and manage the control parameter boundaries and physical constraints of the impedance matching network to ensure that the parameters in the optimization process are reasonable and meet the actual operation requirements. The third sub - module is used to visually feedback the parameter changes and the evolution of the optimization target value during the reverse inference process, so as to facilitate the monitoring and regulation of the optimization process;

[0127] The impedance prediction module is used to accelerate the optimization efficiency and convergence speed when the system restarts or new discharge parameters are set. It includes first to third sub - modules. Among them, the first sub - module is used to collect and record the discharge parameters and the corresponding plasma load impedance values. When the newly set discharge parameters already exist in the historical record, directly transfer the corresponding plasma load impedance value to the reverse inference module. The second sub - module is used to fit the functional relationship between the historical record of discharge parameters and the corresponding plasma load impedance values. When the newly set discharge parameters do not exist in the historical record, predict a possible plasma load impedance through the fitted functional relationship and transfer it to the reverse inference module. The third sub - module is used to manually set an impedance empirical value based on the existing prior knowledge and transfer it to the reverse inference module.

[0128] Specifically, the functions of each module correspond to the above - mentioned method steps and will not be elaborated here.

[0129] The system is designed to support the discharge process in pulse mode. By adjusting the matching parameters in real time, it can meet the requirements of dynamic impedance changes and is applicable to various complex working modes. The system can quickly and accurately calculate the optimal combination of control parameters and has the ability to continuously and stably maintain the matching state of the system.

[0130] Embodiment III

[0131] This application also relates to a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0132] Specifically, the memory may include high-speed random access memory and may also include non-volatile memory, such as hard disks, memory, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one magnetic disk storage device, flash device, or other volatile solid-state storage devices.

[0133] The related technical solutions are the same as above and will not be elaborated here.

[0134] Embodiment IV

[0135] This application embodiment provides a computer program product or a computer program. The computer program product or the computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the steps of the method in the above embodiments of this application.

[0136] The related technical solutions are the same as above and will not be elaborated here.

[0137] It is easy for those skilled in the art to understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A plasma impedance matching optimization method based on backward reasoning, characterized in that Including: S1. Construct an impedance matching circuit for a target plasma device, which includes a plasma load and its external circuit. The external circuit includes a radio frequency power supply and an impedance matching network; S2. Determine a control parameter set P for impedance matching optimization, which is composed of the parameters of multiple components in the impedance matching network, and initialize the values; S3. Obtain the preset values of other discharge parameters other than the control parameter set P in the impedance matching circuit, combine with the current value of the control parameter set P, run the impedance matching circuit, and extract the impedance Z of the plasma load p ; Based on the current value of the control parameter set P and the current impedance Z p , calculate the preset performance index of the impedance matching circuit as the matching evaluation index; S4. Fix the impedance Z p Take the current value of the impedance Z, and by means of backward reasoning, with the minimization of the preset performance index as the goal, search for and adjust the value of P and re - execute S3 until the preset performance index reaches the preset threshold, and finally obtain the optimal value of the control parameter set P and the corresponding impedance Z under the current value of the other discharge parameters p value, and complete the optimization of plasma impedance matching.

2. The plasma impedance matching optimization method according to claim 1, wherein In S3, the impedance matching circuit is operated through numerical simulation to obtain the voltage time-domain signal across the plasma load and the current time-domain signal flowing through the plasma load when the operation is stable, so as to obtain the impedance Z of the plasma load by an analytical method p 。 3. The plasma impedance matching optimization method according to claim 1, characterized in that The preset performance index is the modulus of the impedance matching reflection coefficient of the impedance matching circuit's characteristic power reflected from the load back to the power supply, which is expressed as: where Γ is the impedance matching reflection coefficient, Z l is the input impedance of the impedance matching network, and Z s is the output impedance of the RF power supply.

4. The plasma impedance matching optimization method according to any one of claims 1 to 3, characterized in that, It further includes: S5. Save the values of the other discharge parameters and the corresponding plasma load impedance Z finally obtained through inverse reasoning iteration, so as to fit the dependency relationship between the values of the other discharge parameters and the plasma load impedance Z; when obtaining new preset values of the other discharge parameters, determine the initial value of the plasma load impedance Z based on the dependency relationship, and then execute S4 to obtain the optimal value of the control parameter set P under the new preset values of the other discharge parameters. p , so as to fit the dependency relationship between the values of the other discharge parameters and the plasma load impedance Z p ; when obtaining new preset values of the other discharge parameters, determine the initial value of the plasma load impedance Z based on the dependency relationship p , and then execute S4 to obtain the optimal value of the control parameter set P under the new preset values of the other discharge parameters.

5. An electronic device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program. When the computer program is run by a processor, it controls the device where the storage medium is located to execute the steps of the method described in any one of claims 1 to 4.

7. A computer program product comprising a computer program or instructions, characterized in that, When the computer program or instruction is executed by a processor, it implements the steps of the method described in any one of claims 1 to 4.

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