Method for measuring impedance of capacitive coupling plasma source

Abstract

The invention provides a method for measuring impedance of a capacitively coupled plasma source, which comprises the following steps of: under the condition that plasma is not ignited, dividing a cavity into an upper part and a lower part along an electrical middle plane, and establishing an equivalent circuit model comprising five elements to be determined; three measurement ports are defined, five independent measurement boundary conditions are set, sweep frequency measurement is carried out by using a network analyzer, and multiple groups of Z parameter data are obtained; then, on each frequency point, joint fitting is carried out on a theoretical impedance expression of the equivalent circuit and actually measured data, and parameter values of all undetermined elements are solved; and finally, outputting a parameter curve of each element along with frequency change and a cavity equivalent impedance spectrum. According to the method, the problem that equivalent parameters cannot be identified is solved through multi-working-condition data redundancy, universal, accurate and reproducible measurement of the impedance of the pure cavity is realized, and a reliable quantitative basis is provided for matching network design, process window prediction and cavity optimization.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of plasma process equipment metrology, and in particular to a method for measuring impedance of a capacitively coupled plasma source. BACKGROUND

[0002] Capacitively coupled plasma (CCP) has become one of the most popular plasma platforms in integrated circuit manufacturing, display and photovoltaic industries. From the perspective of cavity structure, a typical CCP is composed of a vacuum reaction chamber and a pair of approximately parallel electrodes (commonly a driven electrode and a grounded / bearing electrode), supplemented by insulating medium, gas distribution structure (such as showerhead / annular gas inlet), edge ring and inner liner, pumping channel and viewing window, etc. The cavity geometry, the medium coverage range of the inner liner material, the area ratio of the two electrodes, and the electrical connection path between the electrode-cavity wall-insulator, all show significantly different electrical characteristics in the unignited and ignited states; especially in the unignited state, the whole cavity is closer to the frequency-dependent R-L-C network determined by conductor loss and dielectric loss, and its specific parameters vary with structural details and material differences; therefore, the equivalent impedance of its cavity under unignited condition is a basic parameter for matching network design, energy coupling efficiency evaluation and process stability.

[0003] Due to the influence of chamber volume, structure and material differences, the existing measurement methods have many limitations. The existing measurement techniques mainly include two categories: one is to use V-I sensor to invert impedance under plasma ignited state, which is greatly affected by the time-varying and non-equilibrium of discharge process, the result is unstable, and it is difficult to characterize the inherent characteristics of the cavity body; the other is to measure and fit by combining a simplified equivalent circuit under unignited state using a single-port network analyzer. The latter is more stable, but it is usually measured under a single or a few boundary conditions, resulting in fewer fitting equations than unknown parameters, which causes the problem of parameter unidentifiability and non-unique solution. In addition, the existing methods are difficult to eliminate the system error introduced by the test fixture in the measurement, and cannot effectively distinguish between conductor loss and dielectric loss.

[0004] Therefore, there is an urgent need in the art for a method that can measure the impedance of CCP cavity under unignited condition in a general, reproducible and high-precision manner, to provide accurate and reliable "pure cavity" electrical boundary conditions. SUMMARY

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

[0006] To achieve the above purpose, the technical scheme adopted by the present application is as follows: A method for measuring the impedance of a capacitively coupled plasma source, comprising the following steps: S1. Dividing the cavity of the capacitively coupled plasma source into an upper part and a lower part along the electrical midplane under the condition that the plasma is not ignited; S2. Establishing a topologically consistent equivalent circuit model containing several undetermined elements for the upper part or the lower part; S3. Defining three measurement ports, namely a power feed-in port, an electrode sampling port and a shield shell reference port, on the upper part or the lower part; S4. Setting several independent measurement boundary conditions, and using a network analyzer to perform sweep frequency measurement in a preset frequency band to obtain the complex impedance Z parameter measurement data of each port under each boundary condition; S5. Establishing an impedance expression of the equivalent circuit model under each measurement boundary condition, and at each frequency point, jointly fitting the impedance expression with the corresponding Z parameter measurement data, and solving the parameter values of each undetermined element by a numerical optimization algorithm; S6. Collecting the fitting results of all frequency points, outputting the curve of each undetermined element varying with frequency, and calculating the equivalent impedance spectrum of the cavity part based on the solved parameters.

[0007] Further, the equivalent circuit model contains five undetermined elements, namely a first resistor R1, a first inductor L1, a capacitor C, a second inductor L2 and a second resistor R2.

[0008] Further, the topological structure of the equivalent circuit model is that one end of the series connection of the first resistor R1 and the first inductor L1 is connected to the power feed-in 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 shield shell reference port.

[0009] Further, the measurement boundary conditions include the following five conditions: Condition one: measuring at the power feed-in port, and the electrode sampling port is in an open circuit state; at this time, the impedance of the loop input by the power feed-in port and output by the shield shell reference port is measured; Condition two: measuring at the electrode sampling port, and the power feed-in port is in an open circuit state; at this time, the impedance of the loop input by the electrode sampling port and output by the shield shell reference port is measured; Condition three: measuring at the power feed-in port, and the electrode sampling port is in a short circuit ground state; at this time, the impedance of the loop input by the power feed-in port and output by the electrode sampling port and the shield shell reference port is measured; Condition four: measure at the electrode sampling port, the power feed-in port is short-circuited to ground; at this time, the measured is the impedance of the loop of the electrode sampling port input, the power feed-in port, and the shield shell reference port output; Condition five: measure at the shield shell reference port, the power feed-in port and the electrode sampling port are short-circuited to each other; at this time, the measured is the impedance of the loop of the shield shell reference port input, the power feed-in port, and the electrode sampling port output.

[0010] Further, the theoretical impedance expressions of the equivalent circuit model under the five measurement boundary conditions are as follows: (1) ; (2) ; (3) ; (4) ; (5) ; In formulas (1)-(5): , , , , respectively represent the single-port drive-point complex impedance measured under the five boundary conditions, including amplitude and phase (or real and imaginary parts) information; represents the first resistance; represents the first inductance; represents the capacitance; represents the second inductance; represents the second resistance; represents the imaginary unit, used to represent the imaginary part of impedance, i.e., the reactance part, and defines the phase relationship between alternating signals; represents the angular frequency, , represents the sweep frequency of the network analyzer.

[0011] Further, the step S4 further includes a calibration step: before measurement, the reference plane calibration is performed between the measurement port of the network analyzer and the actual feed-in point of the cavity part, and the open-circuit, short-circuit, and load calibration method is used to remove the influence of the fixture and the transmission line.

[0012] Further, the impedance expressions are jointly fitted with the corresponding Z-parameter measurement data using the least squares method, and physical constraint conditions are applied in the fitting process, including: the resistance value is greater than zero, the inductance value is greater than zero, and the capacitance value is greater than zero.

[0013] Further, the numerical optimization algorithm uses a robust regression algorithm to suppress the influence of outliers in the measurement data on the fitting result.

[0014] As can be seen from the above technical solutions, compared with the prior art, the present invention has the following technical advantages: 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. 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; 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; 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; 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

[0015] Figure 1 This is a schematic diagram of the impedance equivalent circuit construction of capacitively coupled plasma according to the present invention; 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. Figure 3 This is the fitting curve between the theoretical impedance value calculated by this invention and the measured Z-parameter.

[0016] In the diagram: 1. Power feed port; 2. Electrode sampling port; 3. Shielding shell reference port. Detailed Implementation

[0017] A preferred embodiment of the present invention will now be described in detail with reference to the accompanying drawings.

[0018] 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.

[0019] 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.

[0020] A method for measuring the impedance of a capacitively coupled plasma source includes the following steps: 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.

[0021] S2. Establish a topologically consistent equivalent circuit model for the upper part, containing five undetermined components.

[0022] 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.

[0023] 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).

[0024] 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.

[0025] S4, five kinds of independent measurement boundary conditions are set, and a network analyzer is used to perform sweep frequency measurement in a preset frequency band to obtain complex impedance Z parameter measurement data of each port under each boundary condition; the Z parameter is a complex number containing amplitude and phase (or real part and imaginary part) information.

[0026] As shown in Figure 2 Before measurement, reference plane calibration is needed between the measurement port of the network analyzer and the actual feed-in point of the cavity part (the error of the transmission line of the network analyzer and the clamp is removed), open circuit, short circuit, and load calibration method is used to remove the influence of the clamp and the transmission line, to ensure that the Z parameter measurement data only reflects the boundary of the cavity and the port, and to maximize the influence of the transition and transition structure, to improve the physical interpretability and cross-device comparability of the parameters. Specifically, the measurement boundary conditions include the following five kinds: Condition one: measurement is performed at the power feed-in port 1, and the electrode sampling port 2 is in an open circuit state; at this time, the impedance of the loop of the power feed-in port 1 input and the shielding shell reference port 3 output is measured; Condition two: measurement is performed at the electrode sampling port 2, and the power feed-in port 1 is in an open circuit state; at this time, the impedance of the loop of the electrode sampling port 2 input and the shielding shell reference port 3 output is measured; Condition three: measurement is performed at the power feed-in port 1, and the electrode sampling port 2 is in a short circuit to ground state; at this time, the impedance of the loop of the power feed-in port 1 input and the electrode sampling port 2 and the shielding shell reference port 3 output is measured; Condition four: measurement is performed at the electrode sampling port 2, and the power feed-in port 1 is in a short circuit to ground state; at this time, the impedance of the loop of the electrode sampling port 2 input and the power feed-in port 1 and the shielding shell reference port 3 output is measured; Condition five: measurement is performed at the shielding shell reference port 3, and the power feed-in port 1 and the electrode sampling port 2 are shorted to each other; at this time, the impedance of the loop of the shielding shell reference port 3 input and the power feed-in port 1 and the electrode sampling port 2 output is measured.

[0027] Wide frequency sweep and multiple boundary conditions significantly improve signal-to-noise ratio and robustness; during measurement, sweep frequency ~ (e.g. 1-30 MHz, step ), record the and curves of each working condition, which are respectively used to represent the real part (resistance component) and the imaginary part (reactance component) of the impedance, and ten data are obtained under five boundary conditions. Among them: The real part (resistance component) of the impedance comes from the resistors R1 and R2 in the equivalent circuit, representing the conductor loss (thermal loss due to resistivity) of the cavity metal parts and the dielectric loss (thermal loss due to dielectric polarization lag) of the insulating material; therefore, The curve directly quantifies the power loss capability of the cavity itself. The higher the curve, the more power the cavity consumes at this frequency; The imaginary part (reactance component) of the impedance comes from the inductors L1, L2 and the capacitor C up , which describes the impedance that does not consume energy in the circuit, but only stores and releases energy periodically between the electric field and the magnetic field, when , the impedance is inductive, and the magnetic field energy storage dominates (contributed by the inductor ); when , the impedance is capacitive, and the electric field energy storage dominates (contributed by the capacitor ); The point is the resonance point, at which the capacitive reactance and the inductive reactance cancel each other out.

[0028] S5, establish the impedance expression of the equivalent circuit model under each measurement boundary condition, and at each frequency point, combine the impedance expression with the corresponding Z parameter measurement data to solve the parameter values of each undetermined element through a numerical optimization algorithm.

[0029] The theoretical impedance expressions of the equivalent circuit model under five measurement boundary conditions are as follows: (1) ; (2) ; (3) ; (4) ; (5) ; In formulas (1)-(5): , , , , respectively represent the single-port drive-point complex impedance measured under the five boundary conditions, containing amplitude and phase (or real and imaginary part) information; represents the first resistance; represents the first inductance; represents the capacitance; represents the second inductance; represents the second resistance; represents the imaginary unit, used to represent the imaginary part of the impedance, i.e. the reactance part, and defines the phase relationship between alternating signals; ω represents the angular frequency, used to make the impedance exhibit frequency characteristics, , ω represents the sweep frequency of the network analyzer.

[0030] Specifically, as shown in Figure 3 , the impedance expression is combined with the corresponding Z parameter measurement data by a joint fitting method: at each frequency point, the theoretical value calculated by formula (1)-(5) is combined with the measured Z parameter for joint least squares fitting; to enhance robustness, weights can be set to reflect the noise level of each boundary condition, and physical constraint conditions are applied in the fitting process, including: the resistance value is greater than zero, the inductance value is greater than zero, and the capacitance value is greater than zero. The numerical optimization algorithm uses a robust regression algorithm to suppress the influence of outliers in the measurement data on the fitting results and avoid the influence of a small number of frequency points on the final results.

[0031] S6, gather the fitting results of all frequency points, output the parameter curves of the five undetermined elements (R1, L1, C up , L2, R2) varying with frequency, and calculate the equivalent impedance spectrum (amplitude / phase) of the upper cavity part based on the solved parameters. Specifically, by analyzing the frequency characteristics of the resistance parameters (R1, R2) and the capacitance parameters (C up ), the conductor loss (mainly related to the resistivity of metal parts) and the dielectric loss (mainly related to the dielectric properties of insulating materials) can be quantified, thereby providing a basis for cavity optimization design.

[0032] In specific operations, the whole process of the preferred embodiment method can be scripted, thereby unifying parameter boundaries, weights, and drawing / exporting specifications, facilitating retesting comparison, factory acceptance, and assembly change evaluation, and having strong engineering landing performance.

[0033] The above-described embodiments are merely descriptions of the preferred embodiments of the present application and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art shall fall within the protection scope determined by the claims of the present application.

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. 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. 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 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.

3. The method for measuring the impedance of a capacitively coupled plasma source according to claim 2, characterized in that, The topology of the equivalent circuit model is as follows: One end of the first resistor R1 connected in series with the first inductor L1 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; The other end of the capacitor C is connected to the reference port of the shielding shell.

4. The method for measuring the impedance of a capacitively coupled plasma source according to claim 3, characterized in that, 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 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.

5. The method for measuring the impedance of a capacitively coupled plasma source according to claim 4, 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.

6. 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.

7. 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.

8. 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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