A method of measuring the impedance of a capacitively coupled plasma source

Abstract

The application provides a method for measuring the impedance of a capacitive coupling plasma source, which comprises the following steps: under the condition that no plasma is ignited, a cavity is divided into an upper part and a lower part along an electrical median plane, and an equivalent circuit model containing five undetermined elements is established; three measurement ports are defined, five kinds of independent measurement boundary conditions are set, sweep measurement is carried out by using a network analyzer, and multiple sets of Z parameter data are obtained; then at each frequency point, a theoretical impedance expression of the equivalent circuit is combined with the measured data for joint fitting, and the parameter values of all the undetermined elements are solved; finally, the parameter curves of each element varying with frequency and the equivalent impedance spectrum of the cavity are output. The application solves the problem of indistinguishable equivalent parameters through redundant multi-working condition data, realizes general, accurate and reproducible measurement of the pure cavity impedance, and provides a reliable quantitative basis for matching network design, process window prediction and cavity optimization.

Description

Technical Field

[0001] This invention relates to the field of metrology technology for plasma process equipment, and specifically to a method for measuring the impedance of a capacitively coupled plasma source. Background Technology

[0002] Capacitively coupled plasma (CCP) has become one of the most widely used plasma platforms in integrated circuit manufacturing, display, and photovoltaic industries. From a cavity structure perspective, a typical CCP consists of a vacuum reaction chamber and a pair of nearly parallel electrodes (commonly a driving electrode and a ground / carrying electrode), supplemented by insulating dielectric, gas distribution structures (such as a showerhead / annular air intake), edge rings and linings, evacuation channels, and viewing windows. The cavity geometry, lining material and dielectric coverage, the area ratio of the two electrodes, and the electrical connection path between the electrodes, cavity wall, and insulator all exhibit significantly different electrical characteristics in the unlit and lit states. Especially in the unlit state, the cavity as a whole more closely resembles a frequency-dependent RLC network determined by both conductor and dielectric losses, with specific parameters varying depending on structural details and material differences. Therefore, the equivalent impedance of the cavity under unlit conditions is a fundamental parameter for matching network design, energy coupling efficiency evaluation, and process stability.

[0003] Existing measurement methods suffer from numerous limitations due to variations in chamber volume, structure, and materials. Current measurement techniques mainly fall into two categories: one involves impedance inversion using a VI sensor under plasma ignition conditions. This method is heavily influenced by the time-varying and non-equilibrium nature of the discharge process, resulting in unstable results and difficulty in characterizing the inherent properties of the chamber itself. The other involves measurement using a single-port network analyzer combined with a simplified equivalent circuit for fitting under unignition conditions. While the latter is more stable, it typically only measures under single or a few boundary conditions, leading to a smaller number of fitting equations than unknown parameters, resulting in unidentifiable parameters and non-unique solutions. Furthermore, existing methods struggle to eliminate systematic errors introduced by the test fixtures during measurement and cannot effectively distinguish between conductor losses and dielectric losses.

[0004] Therefore, there is an urgent need in the field for a method that can perform universal, reproducible, and high-precision impedance measurements of CCP cavities under unignited conditions, in order to provide accurate and reliable electrical boundary conditions for "pure cavities". Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a capacitively coupled plasma cavity impedance measurement method based on multi-condition joint fitting, which can accurately and uniquely determine the equivalent circuit parameters of the cavity in the unignited state and effectively distinguish different types of losses.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for measuring the impedance of a capacitively coupled plasma source includes the following steps:

[0008] S1. Under the condition of unignited plasma, the cavity of capacitively coupled plasma is divided into upper and lower parts along the electrical plane;

[0009] S2. Establish a topologically consistent equivalent circuit model for the upper or lower part, containing several undetermined components.

[0010] S3. Define three measurement ports on the upper or lower part: power feed port, electrode sampling port, and shielding shell reference port.

[0011] S4. Set several independent measurement boundary conditions, and use a network analyzer to perform frequency sweep measurement within a preset frequency band to obtain the complex impedance Z parameter measurement data of each port under each boundary condition.

[0012] S5. Establish the impedance expression of the equivalent circuit model under each measurement boundary condition, and at each frequency point, jointly fit the impedance expression with the corresponding Z parameter measurement data, and solve the parameter value of each undetermined component through a numerical optimization algorithm.

[0013] S6. Collect the fitting results of all frequency points, output the curve of each unknown element as a function of frequency, and calculate the equivalent impedance spectrum of the cavity part based on the solved parameters.

[0014] Furthermore, the equivalent circuit model includes five undetermined components: a first resistor R1, a first inductor L1, a capacitor C, a second inductor L2, and a second resistor R2.

[0015] Furthermore, the topology of the equivalent circuit model is as follows: one end of the first resistor R1 and the first inductor L1 connected in series is connected to the power feed port, and the other end is connected to one end of the capacitor C and the second resistor R2; the other end of the second resistor R2 is connected to one end of the second inductor L2; the other end of the second inductor L2 is connected to the electrode sampling port; and the other end of the capacitor C is connected to the shielding shell reference port.

[0016] Furthermore, the measurement boundary conditions include the following five types:

[0017] Condition 1: The measurement is performed at the power feed port, and the electrode sampling port is in an open circuit state; at this time, the impedance of the circuit between the power feed port input and the shielded shell reference port output is measured.

[0018] Condition 2: Measurement is performed at the electrode sampling port, with the power feed port in an open circuit state; at this time, the impedance of the circuit between the electrode sampling port input and the shielding shell reference port output is measured.

[0019] Condition 3: The measurement is performed at the power feed port, and the electrode sampling port is in a short-circuit ground state; at this time, the impedance of the circuit from the power feed port input to the electrode sampling port and the shielding shell reference port output is measured.

[0020] Condition 4: The measurement is performed at the electrode sampling port, and the power feed port is in a short-circuit ground state; at this time, the impedance of the loop between the electrode sampling port input, the power feed port, and the shielding shell reference port output is measured.

[0021] Condition 5: The measurement is performed at the shielded housing reference port, with the power feed port and electrode sampling port short-circuited. At this time, the impedance of the circuit from the shielded housing reference port input to the power feed port and the electrode sampling port output is measured.

[0022] Furthermore, the theoretical impedance expression of the equivalent circuit model under the five measurement boundary conditions is as follows:

[0023] (1);

[0024] (2);

[0025] (3);

[0026] (4);

[0027] (5);

[0028] In formulas (1)-(5): , , , , These represent the complex impedances of the single-port drive point measured under five different boundary conditions, including amplitude and phase (or real and imaginary parts) information; Indicates the first resistor; Indicates the first inductance; Indicates capacitance; Indicates the second inductor; Indicates the second resistor; The imaginary unit is used to represent the imaginary part of impedance, i.e., the reactance, and defines the phase relationship between AC signals. Represents angular frequency. , This indicates the sweep frequency of the network analyzer.

[0029] Furthermore, step S4 also includes a calibration step: before measurement, a reference surface calibration is performed between the measurement port of the network analyzer and the actual feed point of the cavity part, and the influence of the fixture and transmission line is removed by using open circuit, short circuit, and load calibration methods.

[0030] Furthermore, the impedance expression is jointly fitted with the corresponding Z-parameter measurement data using the least squares method, and physical constraints are applied during the fitting process. These physical constraints include: resistance value greater than zero, inductance value greater than zero, and capacitance value greater than zero.

[0031] Furthermore, the numerical optimization algorithm employs a robust regression algorithm to suppress the influence of outliers in the measurement data on the fitting results.

[0032] As can be seen from the above technical solutions, compared with the prior art, the present invention has the following technical advantages:

[0033] 1. This invention provides sufficient data redundancy through five independent operating conditions, forming a closed set of solution equations, which ensures the identifiability and solution accuracy of all parameters of the equivalent circuit.

[0034] 2. The method of the present invention does not depend on a specific cavity size or internal structure, the process is standardized, and the results can be reproduced and compared on different devices and at different time points;

[0035] 3. This invention effectively reduces system errors and improves the physical authenticity and cross-platform comparability of parameters through reference surface calibration and de-embedding processing;

[0036] 4. By accurately solving the resistance and capacitance parameters, this invention can further analyze and quantify the contributions of conductor loss and dielectric loss, providing guidance for cavity optimization design;

[0037] 5. The entire measurement and fitting process of this invention can be scripted and automated, and is applicable to engineering scenarios such as equipment debugging, factory acceptance, and process window prediction. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the impedance equivalent circuit construction of capacitively coupled plasma according to the present invention;

[0039] Figure 2 This is a schematic diagram showing the connection between the network analyzer of the present invention and the upper part of the capacitively coupled plasma.

[0040] Figure 3 This is the fitting curve between the theoretical impedance value calculated by this invention and the measured Z-parameter.

[0041] In the diagram: 1. Power feed port; 2. Electrode sampling port; 3. Shielding shell reference port. Detailed Implementation

[0042] A preferred embodiment of the present invention will now be described in detail with reference to the accompanying drawings.

[0043] like Figure 1 As shown, the capacitively coupled plasma (CCP) of this preferred embodiment consists of a cylindrical vacuum chamber and two circular parallel plate electrodes, with plasma generated between the two electrodes. The chamber shell and electrode body are made of stainless steel (aluminum or other conductive materials can also be selected). The outer wall of the cylindrical chamber and the upper electrode are grounded, and the lower electrode serves as the radio frequency feed terminal. Process gas enters from the upper "spray head" type inlet electrode and exits from the lower exhaust port. This preferred embodiment performs electrical characterization of a "pure chamber" under unignited, room temperature conditions, effectively avoiding contamination of the results by time-varying / non-equilibrium conditions in the ignition state.

[0044] This invention divides the complex cavity into two relatively independent parts along its natural electrical midplane (usually ground potential or a plane of symmetry), and establishes an independent, topologically consistent equivalent circuit model for each part. The measurement method described in this invention is self-consistent and complete for each independent cavity part; therefore, in practical applications, it is possible to select to measure only one part or both parts as needed.

[0045] A method for measuring the impedance of a capacitively coupled plasma source includes the following steps:

[0046] S1. Under conditions of unignited plasma and room temperature, the cavity of capacitively coupled plasma is divided into upper and lower parts along the electrical plane (ground potential or symmetry plane). The measurement method of the present invention will be described below using the upper part as an example.

[0047] S2. Establish a topologically consistent equivalent circuit model for the upper part, containing five undetermined components.

[0048] In this step, the five components to be determined are the first resistor R1, the first inductor L1, and the capacitor C. up The second inductor L2 and the second resistor R2. Specifically, such as... Figure 1 As shown, the copper rod, upper electrode plate, insulator (Peek), and outer shielding shell are equivalent to an RLC network along the conductive path of the main circuit, with the parameter set being {R1, L1, C}. up L1 and L2 represent the equivalent inductance of the metal loop and return path, respectively; C up Characterizes the parasitic capacitance between the copper rod and the shielding shell and surrounding metal; R1 and R2 represent conductor and dielectric losses. For the lower cavity, a homogeneous network {R3, L3, C} is used. down The equivalent circuit modeling of L4 and R4 is completely consistent with the subsequent solution process.

[0049] S3. The upper part defines three measurement ports: power feed port 1, electrode sampling port 2, and shielding shell reference port 3 (with the cavity ground as a reference).

[0050] The topology of the equivalent circuit model is as follows: one end of the series connection between the first resistor R1 and the first inductor L1 is connected to the power input port 1, and the other end is connected to the capacitor C. up One end of the second resistor R2; the other end of the second resistor R2 is connected to one end of the second inductor L2; the other end of the second inductor L2 is connected to the electrode sampling port 2; the capacitor C up The other end is connected to the shielding shell reference port 3.

[0051] S4. Set five independent measurement boundary conditions, and use a network analyzer to perform frequency sweep measurement within a preset frequency band to obtain the complex impedance Z parameter measurement data of each port under each boundary condition; the Z parameter is a complex number that contains amplitude and phase (or real part and imaginary part) information.

[0052] like Figure 2 As shown, before measurement, reference surface calibration needs to be performed between the measurement port of the network analyzer and the actual feed point of the cavity (to remove errors from the network analyzer's transmission lines and fixtures). Open-circuit, short-circuit, and load calibration methods are used to eliminate the influence of fixtures and transmission lines, ensuring that the Z-parameter measurement data only reflects the cavity and port boundaries, minimizing the influence of adapters and transition structures, and improving the physical interpretability and cross-device comparability of the parameters. Specifically, the measurement boundary conditions include the following five types:

[0053] Condition 1: The measurement is performed at power feed port 1, and electrode sampling port 2 is in an open circuit state; at this time, the impedance of the circuit input at power feed port 1 and output at shielded shell reference port 3 is measured.

[0054] Condition 2: Measurement is performed at electrode sampling port 2, while power feed port 1 is in an open circuit state; at this time, the impedance of the circuit input at electrode sampling port 2 and output at shielding reference port 3 is measured.

[0055] Condition 3: The measurement is performed at power feed port 1, and electrode sampling port 2 is in a short-circuit ground state; at this time, the impedance of the circuit that is input at power feed port 1 and output at electrode sampling port 2 and shielding reference port 3 is measured.

[0056] Condition 4: Measurement is performed at electrode sampling port 2, while power feed port 1 is in a short-circuit grounded state; at this time, the impedance of the circuit input at electrode sampling port 2, power feed port 1, and shielded shell reference port 3 is measured.

[0057] Condition 5: The measurement is performed at the shielded reference port 3, with the power feed port 1 and the electrode sampling port 2 shorted together. At this time, the impedance of the circuit from the input of the shielded reference port 3 to the output of the power feed port 1 and the electrode sampling port 2 is measured.

[0058] Wideband frequency sweep and multiple boundary condition redundancy significantly improve signal-to-noise ratio and robustness; during measurement, frequency sweep is performed according to operating conditions. ~ (e.g., 1–30MHz, in steps) Record each working condition and The curves represent the real part (resistive component) and imaginary part (reactant component) of the impedance, respectively, with ten data points for five boundary conditions. Among them:

[0059] The real part (resistive component) of the impedance originates from the resistances R1 and R2 in the equivalent circuit, representing the conductor loss (heat loss due to resistivity) of the cavity metal component and the dielectric loss (heat loss due to dielectric polarization hysteresis) of the insulating material; therefore, The curve directly quantifies the power dissipation capability of the cavity itself. The higher the curve, the more power the cavity consumes at that frequency;

[0060] The imaginary part (reactant component) of the impedance comes from the inductances L1 and L2 and the capacitance C in the equivalent circuit. up It describes the impedance in a circuit that does not consume energy but only periodically stores and releases energy between electric and magnetic fields. At this time, the impedance is inductive, and the energy stored in the magnetic field is dominant (due to the inductance). Contribution); when At this time, the impedance is capacitive, and the energy stored in the electric field is dominant (due to the capacitance). contribute); The point is the resonant point, at which point the capacitive reactance and inductive reactance cancel each other out.

[0061] S5. Establish the impedance expression of the equivalent circuit model under each measurement boundary condition, and at each frequency point, jointly fit the impedance expression with the corresponding Z parameter measurement data, and solve the parameter value of each undetermined component through a numerical optimization algorithm.

[0062] The theoretical impedance expression for the equivalent circuit model under the five measurement boundary conditions is as follows:

[0063] (1);

[0064] (2);

[0065] (3);

[0066] (4);

[0067] (5);

[0068] In formulas (1)-(5): , , , , These represent the complex impedances of the single-port drive point measured under five different boundary conditions, including amplitude and phase (or real and imaginary parts) information; Indicates the first resistor; Indicates the first inductance; Indicates capacitance; Indicates the second inductor; Indicates the second resistor; The imaginary unit is used to represent the imaginary part of impedance, i.e., the reactance, and defines the phase relationship between AC signals. This indicates the angular frequency, used to make the impedance exhibit frequency characteristics. , This indicates the sweep frequency of the network analyzer.

[0069] Specifically, such as Figure 3 As shown, the method for jointly fitting the impedance expression with the corresponding Z-parameter measurement data is as follows: at each frequency point, the theoretical value calculated by formulas (1)-(5) is jointly fitted with the measured Z-parameters using least squares; to enhance robustness, weights can be set to reflect the noise level of each boundary condition, and physical constraints are applied during the fitting process. The physical constraints include: resistance value greater than zero, inductance value greater than zero, and capacitance value greater than zero. The numerical optimization algorithm adopts a robust regression algorithm to suppress the influence of outliers in the measurement data on the fitting results and avoid a small number of frequency points affecting the final result.

[0070] S6. Compile the fitting results for all frequency points and output the five undetermined elements (R1, L1, C). up The parameter curves of L2, R2) as a function of frequency are obtained, and the equivalent impedance spectrum (amplitude / phase) of the upper cavity is calculated based on the solved parameters. Specifically, this is achieved by analyzing the resistance parameters (R1, R2) and capacitance parameters (C). up The frequency characteristics of the cavity can be used to quantify conductor loss (mainly related to the resistivity of metal components) and dielectric loss (mainly related to the dielectric properties of insulating materials), thus providing a basis for cavity optimization design.

[0071] In practical operation, the entire process of this preferred embodiment can be scripted, thereby unifying parameter boundaries, weights and drawing / export specifications, facilitating retesting and comparison, factory acceptance and assembly change evaluation, and making it highly applicable to engineering projects.

[0072] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for measuring the impedance of a capacitively coupled plasma source, characterized in that, Includes the following steps: S1. Under the condition of unignited plasma, the cavity of capacitively coupled plasma is divided into upper and lower parts along the electrical plane; S2. Establish a topologically consistent equivalent circuit model for the upper or lower part, containing several undetermined components. The equivalent circuit model includes five undetermined components: a first resistor (R1), a first inductor (L1), a capacitor (C), a second inductor (L2), and a second resistor (R2). The topology of the equivalent circuit model is as follows: one end of the first resistor (R1) and the first inductor (L1) connected in series is connected to the power feed port, and the other end is connected to one end of the capacitor (C) and the second resistor (R2); the other end of the second resistor (R2) is connected to one end of the second inductor (L2); the other end of the second inductor (L2) is connected to the electrode sampling port; and the other end of the capacitor (C) is connected to the shielding reference port. S3. Define three measurement ports on the upper or lower part: power feed port, electrode sampling port, and shielding shell reference port. S4. Set several independent measurement boundary conditions, and use a network analyzer to perform frequency sweep measurement within a preset frequency band to obtain the complex impedance Z parameter measurement data of each port under each boundary condition. The measurement boundary conditions include the following five types: Condition 1: The measurement is performed at the power feed port, and the electrode sampling port is in an open circuit state; at this time, the impedance of the circuit between the power feed port input and the shielded shell reference port output is measured. Condition 2: Measurement is performed at the electrode sampling port, with the power feed port in an open circuit state; at this time, the impedance of the circuit between the electrode sampling port input and the shielding shell reference port output is measured. Condition 3: The measurement is performed at the power feed port, and the electrode sampling port is in a short-circuit ground state; at this time, the impedance of the circuit from the power feed port input to the electrode sampling port and the shielding shell reference port output is measured. Condition 4: The measurement is performed at the electrode sampling port, and the power feed port is in a short-circuit ground state; at this time, the impedance of the loop between the electrode sampling port input, the power feed port, and the shielding shell reference port output is measured. Condition 5: The measurement is performed at the shielded shell reference port, with the power feed port and electrode sampling port short-circuited. At this time, the impedance of the circuit from the shielded shell reference port input to the power feed port and the electrode sampling port output is measured. S5. Establish the impedance expression of the equivalent circuit model under each measurement boundary condition, and at each frequency point, jointly fit the impedance expression with the corresponding Z parameter measurement data, and solve the parameter value of each undetermined component through a numerical optimization algorithm. S6. Collect the fitting results of all frequency points, output the curve of each unknown element as a function of frequency, and calculate the equivalent impedance spectrum of the cavity part based on the solved parameters.

2. The method for measuring the impedance of a capacitively coupled plasma source according to claim 1, characterized in that, The theoretical impedance expression for the equivalent circuit model under the five measurement boundary conditions is as follows: （1）； （2）； （3）； （4）； （5）； In formulas (1)-(5): , , , , These represent the complex impedances of the single-port drive point measured under five different boundary conditions, including amplitude and phase (or real and imaginary parts) information; Indicates the first resistor; Indicates the first inductance; Indicates capacitance; Indicates the second inductor; Indicates the second resistor; The imaginary unit is used to represent the imaginary part of impedance, i.e., the reactance, and defines the phase relationship between AC signals. Represents angular frequency. , This indicates the sweep frequency of the network analyzer.

3. The method for measuring the impedance of a capacitively coupled plasma source according to claim 1, characterized in that, Step S4 further includes a calibration step: before measurement, a reference surface calibration is performed between the measurement port of the network analyzer and the actual feed point of the cavity part, and the influence of the fixture and transmission line is removed by using open circuit, short circuit, and load calibration methods.

4. The method for measuring the impedance of a capacitively coupled plasma source according to claim 1, characterized in that, The impedance expression is combined with the corresponding Z-parameter measurement data using the least squares method, and physical constraints are applied during the fitting process. These physical constraints include: resistance value greater than zero, inductance value greater than zero, and capacitance value greater than zero.

5. The method for measuring the impedance of a capacitively coupled plasma source according to claim 1, characterized in that, The numerical optimization algorithm employs a robust regression algorithm to suppress the influence of outliers in the measurement data on the fitting results.

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