Plasma density measuring device using frequency sweep interferometer and plasma density measuring method using same

Abstract

The present invention relates to a plasma density measuring device using a frequency sweep interferometer and a plasma density measuring method using same. The plasma density measuring device using a frequency sweep interferometer according to the present invention includes: a first horn antenna for radiating frequency-modulated microwaves into a plasma chamber; a second horn antenna for receiving microwaves having passed through plasma in the plasma chamber; and a frequency sweep interferometer for generating microwaves modulated with a frequency within a preconfigured range, the microwaves being generated by linearly sweeping the entire frequency within the range within a preconfigured time, transmitting the generated microwaves to the first horn antenna, and calculating an average density and uniformity of the plasma in the plasma chamber on the basis of a phase difference between the generated microwaves and the microwaves received by the second horn antenna.

Description

Plasma density measurement device using a frequency sweep interferometer and plasma density measurement method using the same

[0001] The present invention relates to a plasma density measuring device using a frequency sweep interferometer and a plasma density measuring method using the same, and more particularly, to a plasma density measuring device using a frequency sweep interferometer capable of measuring the density of plasma without affecting the plasma in any way and a plasma density measuring method using the same.

[0002]

[0003] When a substance is heated to tens of thousands of degrees Celsius (℃), electrons are gradually removed from the molecular gas, ultimately separating into negatively charged electrons and positively charged ions, forming plasma. This plasma is used in nuclear fusion power generation, component manufacturing, and other applications.

[0004] In particular, plasma is widely used in semiconductor device manufacturing. Among these, plasma etching removes substrate materials using ions, reactive gases, or radicals generated by plasma. Etching is essential for ensuring process precision, miniaturization, and minimal damage, making it a crucial step in semiconductor device manufacturing.

[0005] As semiconductor device manufacturing continues to miniaturize and scale up wafer sizes, efforts are being made to increase plasma density and thus improve semiconductor device yield. To improve semiconductor device yield, maintaining plasma uniformity at an appropriate level and more precise condition control are essential. Therefore, measuring and monitoring plasma density to maintain plasma uniformity at an appropriate level has become a crucial issue.

[0006]

[0007] The present invention provides a plasma density measuring device using a frequency sweep interferometer capable of measuring the density of plasma without contaminating the plasma as a measurement target, and a plasma density measuring method using the same.

[0008] The present invention provides a plasma density measurement device using a frequency sweep interferometer capable of increasing density measurement accuracy by securing sufficient frequency sweep time for a steady-state plasma process device, and a plasma density measurement method using the same.

[0009] The present invention provides a plasma density measuring device using a frequency sweep interferometer capable of measuring density uniformity while increasing density measurement accuracy and reducing design costs of the measuring device, and a plasma density measuring method using the same.

[0010]

[0011] A plasma density measuring device using a frequency sweep interferometer according to the present invention includes a first horn antenna that radiates frequency-modulated microwaves into a plasma chamber, a second horn antenna that receives microwaves that have passed through plasma in the plasma chamber, and a frequency sweep interferometer that generates frequency-modulated microwaves at a frequency within a preset range, linearly sweeps the entire frequency within the range within a preset time to generate frequency-modulated microwaves, transmits the generated microwaves to the first horn antenna, and calculates an average density and uniformity of plasma within the plasma chamber based on a phase difference between the generated microwaves and the microwaves received by the second horn antenna.

[0012] In one embodiment, the plasma chamber may be a process plasma chamber.

[0013] In one embodiment, the frequency sweep interferometer measures the plasma frequency (ω) within the plasma chamber. p ) can generate microwaves having a frequency (w) higher than that of the reference band.

[0014] In one embodiment, the frequency sweep interferometer comprises an arbitrary waveform generator (AWG) for generating a predistorted voltage waveform, a voltage controlled oscillator (VCO) driver for adjusting the voltage waveform output from the arbitrary waveform generator to an input signal of a voltage controlled oscillator (VCO), a voltage controlled oscillator (VCO) for outputting a microwave in a preset range based on a signal received from the VCO driver, a divider for distributing the microwave output from the voltage controlled oscillator, a first frequency multiplier for multiplying the frequency of the first microwave distributed from the divider and outputting it to the first horn antenna, a delay for delaying the second microwave distributed from the divider, a second frequency multiplier for multiplying the second microwave delayed from the delay and outputting it, and a microwave received from the second horn antenna and the microwave received from the second frequency multiplier. It may include a frequency mixer that mixes and outputs an intermediate frequency (IF) signal, a digitizer that samples the frequency signal output from the frequency mixer and outputs sampling data, a phase analyzer that calculates the phase of the microwave received from the second horn antenna based on the data generated from the digitizer, and a plasma density calculator that calculates the average density and uniformity of the plasma within the plasma chamber based on the phase calculated from the phase analyzer.

[0015] In one embodiment, the plasma density calculator can calculate the group delay of microwaves passing through the plasma using the following mathematical expression (8).

[0016] [Equation 8]

[0017]

[0018] Here, τ g is the group delay, is the beat frequency, is the frequency sweep rate

[0019] In one embodiment, the plasma density calculator can calculate the average density of plasma within the plasma chamber through the following mathematical equation (11).

[0020] [Equation 11]

[0021]

[0022] Here, n e is the electron plasma density, i is the sample data, N is the number of sample data, ω i is the microwave frequency of the i-th sample data, τ g, i is the group delay of the i-th sample data

[0023] In one embodiment, the frequency sweep interferometer includes a microwave signal generator (microwave synthesizer) that outputs microwaves in a preset range, a divider that distributes microwaves output from the microwave signal generator, a first frequency multiplier that multiplies the frequency of the first microwave distributed from the divider and outputs it to the first horn antenna, a delayer that delays the second microwave distributed from the divider, a second frequency multiplier that multiplies the second microwave delayed from the delayer and outputs it, a frequency mixer that mixes the microwave received from the second horn antenna and the microwave received from the second frequency multiplier and outputs an intermediate frequency (IF) signal, a digitizer that samples the frequency signal output from the frequency mixer and outputs sampling data, a phase analyzer that calculates the phase of the microwave received from the second horn antenna based on the data generated from the digitizer, and a phase analyzer that calculates the phase of the microwave received from the second horn antenna based on the data generated from the digitizer. It may include a plasma density calculator that calculates the average density and uniformity of plasma within the plasma chamber based on the calculated phase.

[0024] In one embodiment, the plasma density calculator can calculate the average density and uniformity of plasma within the plasma chamber through the following mathematical expression 12.

[0025] [Equation 12]

[0026]

[0027] Here, τ g is the group delay, τ p is the delay time when there is no plasma due to phase delay.

[0028] In one embodiment, the frequency sweep interferometer may include a vector network analyzer that generates microwaves in a preset range, frequency-multiplies the microwaves, outputs the frequency-multiplying microwaves to the first horn antenna, delays the generated microwaves, frequency-multiplies the microwaves, mixes the frequency-multiplying microwaves with microwaves received from the second horn antenna, and calculates a phase of the microwaves received from the second horn antenna, and a plasma density calculator that calculates an average density and uniformity of plasma within the plasma chamber based on the phase calculated from the vector network analyzer.

[0029] In one embodiment, the plasma density calculator can calculate the average density and uniformity of plasma within the plasma chamber through the following mathematical expression 12.

[0030] [Equation 12]

[0031]

[0032] Here, τ g is the group delay, τ p is the delay time when there is no plasma due to phase delay.

[0033] A plasma density measurement method using a frequency sweep interferometer according to the present invention comprises the steps of: generating a microwave modulated with a frequency within a preset range by a frequency sweep interferometer and linearly sweeping the entire frequency within the range within a preset time to generate a frequency-modulated microwave; emitting the frequency-modulated microwave into a plasma chamber by a first horn antenna; receiving the microwave that has passed through plasma in the plasma chamber through a second horn antenna; and calculating, by the frequency sweep interferometer, an average density and uniformity of plasma within the plasma chamber based on a phase difference between the generated microwave and the microwave received from the second horn antenna.

[0034] In one embodiment, the plasma chamber may be a process plasma chamber.

[0035] In one embodiment, the step of calculating the average density and uniformity of plasma within the plasma chamber may include the step of calculating the group delay of microwaves passing through the plasma using the following mathematical expression (8).

[0036] [Equation 8]

[0037]

[0038] Here, τ g is the group delay, is the beat frequency, is the frequency sweep rate

[0039] In one embodiment, the step of calculating the average density and uniformity of plasma within the plasma chamber may include the step of calculating the average density of plasma within the plasma chamber using the following mathematical expression 11.

[0040] [Equation 11]

[0041]

[0042] Here, n e is the electron plasma density, i is the sample data, N is the number of sample data, ω i is the microwave frequency of the i-th sample data, τ g, i is the group delay of the i-th sample data

[0043] In one embodiment, the step of calculating the average density and uniformity of plasma within the plasma chamber may include the step of calculating the average density and uniformity of plasma within the plasma chamber using the following mathematical expression 12.

[0044] [Equation 12]

[0045]

[0046] Here, τ g is the group delay, τ p is the delay time when there is no plasma due to phase delay.

[0047]

[0048] As described above, the plasma density measuring device using a frequency sweep interferometer according to the present invention and the plasma density measuring method using the same can measure the density of plasma without contaminating the plasma as a measurement target.

[0049] A plasma density measuring device using a frequency sweep interferometer according to the present invention and a plasma density measuring method using the same can secure sufficient frequency sweep time for a plasma process device in a steady state, thereby increasing the accuracy of density measurement.

[0050] A plasma density measuring device using a frequency sweep interferometer according to the present invention and a plasma density measuring method using the same can increase the density measurement accuracy and reduce the design cost of the measuring device while also measuring the uniformity of the plasma.

[0051]

[0052]

[0053] FIG. 1 is a drawing showing the configuration of a plasma density measurement device using a frequency sweep interferometer according to one embodiment of the present invention.

[0054] FIG. 2 is a drawing showing a detailed configuration of a frequency sweep interferometer according to one embodiment.

[0055] FIG. 3 is a drawing showing a detailed configuration of a frequency sweep interferometer including a microwave synthesizer according to another embodiment.

[0056] FIG. 4 is a drawing showing a detailed configuration of a frequency sweep interferometer including a vector network analyzer according to another embodiment.

[0057] Figure 5 is a flowchart illustrating a plasma density measurement method using a frequency sweep interferometer according to one embodiment of the present invention.

[0058]

[0059] 100: Plasma density measurement device using frequency sweep interferometer

[0060] 110: First Horn Antenna

[0061] 120: Second horn antenna

[0062] 130: Frequency Sweep Interferometer (FSI)

[0063]

[0064] Hereinafter, specific details for implementing a plasma density measuring device using a frequency sweep interferometer according to the present invention and a plasma density measuring method using the same will be described as follows.

[0065]

[0066] FIG. 1 is a drawing showing the configuration of a plasma density measurement device using a frequency sweep interferometer according to one embodiment of the present invention.

[0067] Referring to FIG. 1, a plasma density measurement device (100) using a frequency sweep interferometer includes a first horn antenna (110), a second horn antenna (120), and a frequency sweep interferometer (130).

[0068] The frequency sweep interferometer (100) measures the plasma frequency (ω) of the plasma (142) inside the plasma chamber (140). p ) is used to measure the density of the plasma (142). For example, the frequency sweep interferometer (100) sweeps the frequency to generate a frequency-modulated microwave, passes the generated microwave through the plasma (142) or reflects the generated microwave on a mirror provided in the chamber (140) so that the microwave passes back and forth through the plasma (142), and then, based on the phase difference of the microwave, the average density and uniformity of the plasma (142) in the plasma chamber (140) can be calculated.

[0069] The first horn antenna (110) radiates frequency-modulated microwaves into the plasma chamber (140), and the second horn antenna (120) receives microwaves that have passed through the plasma (142) in the plasma chamber (or process chamber) (140). The horn antenna is a type of aperture antenna and has a structure in which the waveguide cross-section gradually widens and electromagnetic wave energy can be radially transferred between the waveguide and space. Depending on the shape of the horn, there are types of horn antennas such as pyramid horn antennas and conical horn antennas.

[0070] In one embodiment, in the case of a structure in which a microwave is emitted from a first horn antenna (110) to pass plasma, the second horn antenna (120) may be located on the opposite side of the first horn antenna (110). In another embodiment, in the case of a structure in which a microwave is emitted from the first horn antenna (110) to be reflected by a mirror located on the opposite side inside the plasma chamber (140) to pass plasma back and forth, the second horn antenna (120) may be located on the same side as the first horn antenna (110). Alternatively, in the case of a structure in which the microwaves emitted from the first horn antenna (110) are reflected by a mirror located on the opposite side inside the plasma chamber (140) and the plasma passes back and forth, a directional coupler may be installed to distinguish between the microwave output and reception of the first horn antenna (110), and the plasma density measuring device (100) may be implemented by having only one first horn antenna (110).

[0071] The frequency sweep interferometer (130) generates a microwave modulated with a frequency within a preset range and transmits it to the first horn antenna (110). In one embodiment, the frequency sweep interferometer (130) modulates the plasma frequency (ω) within the plasma chamber (140). p) can generate a microwave having a frequency (ω) higher than that of the first horn antenna (110). In one embodiment, the frequency sweep interferometer (130) can generate a modulated microwave by linearly sweeping the entire frequency within a preset range within a preset time and transmit the generated microwave to the first horn antenna (110).

[0072] The frequency sweep interferometer (130) calculates the average density and uniformity of the plasma (142) within the plasma chamber (140) based on the phase difference between the microwave generated by the interferometer (130) and the microwave received by the second horn antenna (120).

[0073] The plasma chamber (140) may correspond to a process plasma chamber applied to semiconductor device processes such as semiconductor etching processes. In the case of plasma used in the process, in order to increase process efficiency, it is necessary to maintain the uniformity of the plasma at an appropriate level so that the plasma density does not change over time and maintain a steady state.

[0074] Below, the process of measuring the density of plasma using a frequency sweep interferometer is described in detail.

[0075]

[0076] Fig. 2 is a drawing showing a detailed configuration of a frequency sweep interferometer of the plasma density measuring device of Fig. 1.

[0077] Referring to FIG. 2, the frequency sweep interferometer (130) includes an arbitrary waveform generator (AWG) (210), a voltage controlled oscillator (VCO) driver (212), a voltage controlled oscillator (VCO) (214), a divider (216), a first frequency multiplier (218), a delay (220), a second frequency multiplier (222), a frequency mixer (224), a digitizer (226), a phase analyzer (228), and a plasma density generator (230).

[0078] An arbitrary waveform generator (AWG) (210) generates a predistorted voltage waveform. In one embodiment, the arbitrary waveform generator (210) can output a predistorted voltage waveform in the range of ±10 V.

[0079] In order to accurately measure the density of the plasma (142) within the chamber (140), the frequency sweep time must be faster than the time at which the density of the plasma (142) changes. In addition, when generating a frequency-modulated microwave, the frequency must be linearly modulated to accurately measure the density of the plasma (142). However, in reality, it is difficult to obtain a completely linear frequency-modulated microwave, and more accurate and expensive components are required to obtain a more linear frequency-modulated microwave. In the plasma density measuring device according to the present invention, in order to generate a linearly frequency-modulated microwave, a distorted drive signal can be generated in advance by an arbitrary waveform generator (210) and input to a voltage-controlled oscillator (214) (microwave generator). A pre-distorted driving signal (voltage waveform) can be experimentally obtained in advance according to each condition and the shape of the final output microwave, and the arbitrary waveform generator (210) can be set to output the pre-distorted voltage waveform obtained in advance.

[0080] The VCO driver (212) adjusts the voltage waveform output from the arbitrary waveform generator (210) to an input signal of a voltage-controlled oscillator (VCO) (214), and the voltage-controlled oscillator (214) outputs a microwave within a preset range based on the signal received from the VCO driver (212).

[0081] In one embodiment, the VCO driver (212) can convert a pre-distorted voltage waveform in the range of ±10 V output from the arbitrary waveform generator (210) into a VCO tuning voltage in the range of 0 to 19 V. In one embodiment, the voltage controlled oscillator (214) outputs a frequency-modulated microwave in a preset range according to the input VCO tuning voltage. For example, the voltage controlled oscillator (214) can output a microwave in the band of 12 to 18.75 GHz.

[0082] A divider (216) divides the microwave output from the voltage-controlled oscillator (214) into two ways. A first frequency multiplier (218) multiplies the frequency of the first microwave distributed from the divider (216) by an integer and outputs the multiplied frequency to the first horn antenna (110). In one embodiment, the first frequency multiplier (218) can quadruple the frequency of the first microwave distributed from the divider (216) to output a microwave in the 50 to 75 GHz band. The microwave of the entire band (e.g., 50 to 75 GHz) output from the first frequency multiplier (218) can be linearly swept for 20 μs and output through the first horn antenna (110). The frequency of the microwave output through the first horn antenna (110) (over the entire band (e.g., 50 to 75 GHz)) can be set to be greater than the plasma frequency.

[0083] The delay unit (220) delays and outputs the second microwave distributed from the distributor (216). In one embodiment, the delay unit (220) may be implemented through a delay line, and the delay time may be adjusted by adjusting the length of the delay line. In one embodiment, the delay unit (220) may be implemented using a coaxial cable.

[0084] The second frequency multiplier (222) outputs the second microwave delayed by the delay unit (220) by an integer multiple. In one embodiment, the second frequency multiplier (222) can output a microwave in the 50 to 75 GHz band by quadruple-multiplying the frequency of the second microwave output by the delay unit (220).

[0085] The frequency mixer (224) mixes the microwave received from the second horn antenna and the microwave received from the second frequency multiplier (222) and outputs an intermediate frequency (IF) signal. The frequency mixer (224) may be configured in a homodyne manner as shown in FIG. 2, or the circuit may be configured in a heterodyne manner. The digitizer (226) samples and quantizes the intermediate frequency signal output from the frequency mixer (224) according to a preset sampling rate. In one embodiment, data sampled and output from the digitizer (226) may vary depending on the frequency sweep time and the sampling rate. For example, in the case of the digitizer (226) set to a sampling rate of 100 M samples / s, 2,000 data can be output for 20 μs.

[0086] The phase analyzer (228) calculates the phase of the microwave received from the second horn antenna based on the data generated from the digitizer (226), and the plasma density calculator (230) calculates the average density and uniformity of the plasma (142) within the plasma chamber (140) based on the phase calculated from the phase analyzer (228). In one embodiment, the phase analyzer (228) may correspond to a spectrogram analyzer based on a Morlet wavelet transform.

[0087] Below, the process of calculating the density of plasma based on the phase of microwaves passing through the plasma is described in detail.

[0088] When the microwave is polarized in O-mode, i.e., its electric field oscillates parallel to an external magnetic field or in the absence of an external magnetic field, the refractive index (n) of the plasma is the plasma frequency (ω p ) and the frequency (ω) of the microwave. The refractive index of the plasma can be expressed by the following mathematical equation 1.

[0089] [Mathematical Formula 1]

[0090]

[0091] Here, e is the electron charge, m is the electron mass, ε is the permittivity of free space, and n e represents the electron plasma density.

[0092] When a microwave of ω frequency passes through a plasma and its phase changes, the phase difference between the microwave passing through the plasma and the microwave passing through free space can be expressed by the following mathematical expression 2.

[0093] [Equation 2]

[0094]

[0095] Here, Φ represents the phase difference, c represents the speed of light, L represents the plasma length passed through, n represents the refractive index of the plasma, ω represents the frequency of the microwave, and x represents the position.

[0096] When the refractive index (n) of the plasma in mathematical expression 1 is applied to mathematical expression 2, mathematical expression 2 can be expressed as mathematical expression 3 below.

[0097] [Equation 3]

[0098]

[0099] When differentiating Equation 2 with respect to the frequency variable, Equation 2 can be expressed as Equation 4 below.

[0100] [Equation 4]

[0101]

[0102] When the refractive index (n) of the plasma in mathematical expression 1 is applied to mathematical expression 4, mathematical expression 4 can be expressed as mathematical expression 5 below.

[0103] [Equation 5]

[0104]

[0105] The frequency of the microwave (ω) is the plasma frequency (ω p ) is greater than ω ≫ω p In this case, mathematical expression 5 can be approximated to mathematical expression 6 below.

[0106] [Equation 6]

[0107]

[0108] The plasma frequency (ω) of mathematical expression 1 p ) When the square value is applied to mathematical expression 6, mathematical expression 6 can be expressed as mathematical expression 7 below.

[0109] [Equation 7]

[0110]

[0111] Here, τ g represents the group delay value. The group delay value is expressed as the beat frequency (beat frequency, as in Equation 8 below). ) for frequency sweep rate, ) can be expressed as a ratio.

[0112] [Equation 8]

[0113]

[0114] Referring to mathematical expression 7, the line integrated density (LID) of the plasma can be expressed as mathematical expression 9 below.

[0115] [Equation 9]

[0116]

[0117] Here, is a group delay, is the line average density

[0118] By applying mathematical expression 8 to mathematical expression 9, the linear average density of plasma can be expressed as mathematical expression 10 below.

[0119] [Equation 10]

[0120]

[0121] Based on mathematical expressions 8 and 10, the plasma density calculator (230) can calculate the density of plasma (142) in the chamber (140), i.e., the linear average density (LID) of plasma (142) through which microwaves pass.

[0122] The plasma density generator (230) differentiates the phase serially generated by the phase analyzer (228) with time as a variable to obtain the beat frequency (beat frequency, ) is calculated, and the frequency sweep change is differentiated with respect to time as a variable to obtain the frequency sweep rate ( ) can be calculated. The beat frequency represents the amount of phase change over time. If the frequency is swept linearly, the frequency sweep rate can be calculated as a constant value. The plasma density calculator (230) calculates the group delay (τ) using mathematical expression 8 based on the calculated beat frequency and frequency sweep rate. g ) can be produced.

[0123] The plasma density calculator (230) can calculate the linear average density (LID) of plasma in the plasma chamber by calculating the following mathematical expression 11 for each sample data sampled from the digitizer (226) based on the calculated group delay value.

[0124] [Equation 11]

[0125]

[0126] Here, i is the sample data, N is the number of sample data (e.g., 2,000 if sampled for 20 μs at a sampling rate of 100 M samples / s).

[0127] The frequency sweep interferometer (130) can display the line average density (LID) calculated through mathematical expression 11 on the screen.

[0128]

[0129] FIG. 3 is a drawing showing a detailed configuration of a frequency sweep interferometer including a microwave synthesizer according to another embodiment.

[0130] Referring to FIG. 3, the frequency sweep interferometer (130) includes a microwave synthesizer (310), a divider (312), a first frequency multiplier (314), a delay (316), a second frequency multiplier (318), a frequency mixer (320), a digitizer (322), a phase analyzer (324), and a plasma density generator (326).

[0131] In a case where sufficient frequency sweep time can be secured, such as in a steady-state plasma process device, the entire functions of the AWG, VCO driver, and VCO can be implemented with a microwave signal generator (310). The microwave signal generator (310) has the advantage of being able to perform a frequency sweep that is nearly perfectly linear, thereby improving the accuracy of density measurement. However, due to its operating principle of using a phase-locked loop (PLL), the frequency sweep speed is slower than that of a configuration including the AWG, VCO driver, and VCO, making it difficult to use for plasma that changes rapidly over time, such as a nuclear fusion plasma.

[0132] The configuration and function of the distributor (312), the first frequency multiplier (314), the delayer (316), the second frequency multiplier (318), the frequency mixer (320), the digitizer (322), the phase analyzer (324), and the plasma density generator (326) are the same as those described in FIG. 2.

[0133] In another embodiment, since an expensive microwave signal generator may include a frequency multiplier to directly generate high frequencies, the entire functions of the AWG, VCO driver, VCO, and frequency multiplier may be implemented in a single microwave signal generator. In this case, the frequency sweep interferometer (130) may include a microwave signal generator (not shown), a frequency mixer (320), a digitizer (322), a phase analyzer (324), and a plasma density calculator (326). The configuration and functions of the frequency mixer (320), the digitizer (322), the phase analyzer (324), and the plasma density calculator (326) are the same as those described in FIG. 2.

[0134] In this implementation example, sufficient frequency sweep time can be secured for a steady-state plasma process device, thereby not only increasing the density measurement accuracy but also reducing the complexity and design cost of the measurement device.

[0135]

[0136] FIG. 4 is a drawing showing a detailed configuration of a frequency sweep interferometer including a vector network analyzer according to another embodiment.

[0137] Referring to FIG. 4, the frequency sweep interferometer (130) includes a vector network analyzer (410) and a plasma density calculator (420).

[0138] In order to measure the density of the plasma, the quantity to be ultimately measured is the phase difference according to the frequency between the transmitting microwave and the receiving microwave, so by using a vector network analyzer, the entire functions of the AWG, VCO driver, VCO, frequency multiplier, frequency mixer, digitizer, and phase analyzer can be implemented in a single vector network analyzer (410). For example, the vector network analyzer (410) generates a microwave in a preset range, frequency multiplies it, outputs the frequency-multiplied microwave to the first horn antenna (110), delays the generated microwave, frequency multiplies it, and mixes the frequency-multiplied microwave with the microwave received by the second horn antenna (120) to calculate the phase of the microwave received by the second horn antenna (120). The plasma density calculator (420) can calculate the average density of the plasma (142) within the plasma chamber (140) based on the phase calculated by the vector network analyzer (410).

[0139] This implementation greatly simplifies the overall system configuration and enables a nearly linear frequency sweep, thereby enhancing density measurement accuracy. However, high-frequency vector network analyzers are very expensive, increasing the overall system implementation cost. Similarly, like microwave signal generators, their limited frequency sweep speed makes them difficult to use with plasmas with rapidly changing states, such as nuclear fusion plasmas.

[0140]

[0141] In the case where the measurement accuracy can be improved by implementing a frequency sweep close to linearity using a microwave signal generator as in the embodiment of FIG. 3 or a vector network analyzer as in the embodiment of FIG. 4, the plasma density calculator (230) calculates the average value of the plasma density using the following mathematical expression 12 rather than the approximate expression of the above mathematical expression 11. ), the mean of the square of the plasma density ( ) and the average value of the cube of the plasma density ( ) can be produced together.

[0142] [Equation 12]

[0143]

[0144] Here, τ g is the group delay, τ p is the delay time when there is no plasma due to phase delay.

[0145] The right-hand side of the above mathematical expression 12 can be expressed as a polynomial as in the following mathematical expression 13.

[0146] [Equation 13]

[0147]

[0148] Here, X = 1 / ω 2 , ω is the frequency of the microwave

[0149]

[0150]

[0151]

[0152] X, X 2 and X 3 For a cubic equation containing three terms ( ), for each of the three different micro-frequencies (ω), τ g - τ p After calculating the values ​​and obtaining three equations, the values ​​of a1, a2, and a3 can be calculated using the three equations. Using the calculated values ​​of a1, a2, and a3, the average value of the plasma density ( ), the mean of the square of the plasma density ( ) and the average value of the cube of the plasma density ( ) can be produced together.

[0153] For all micro-frequencies (ω), τ in the above equation (12) g - τp The entire graph that produced the value was fitted with a polynomial curve using the above mathematical formula 13 to directly obtain the average value of the plasma density ( ), the mean of the square of the plasma density ( ) and the average value of the cube of the plasma density ( ) can also be produced together.

[0154] The mean of plasma density, the mean of the square of the plasma density, and the mean of the cube of the plasma density are physically called the first moment M1, the second moment M2, and the third moment M3 of the density, respectively. The more high-order moments are measured, the more precisely the spatial profile of the plasma density can be calculated. For example, if the first and second moments, that is, the mean of the plasma density and the mean of the square of the plasma density, are measured together, the density uniformity can be calculated, which indicates whether the plasma is spatially distributed in a flat shape or a pointed shape.

[0155] When the plasma density is expressed by mathematical formula 14,

[0156] [Equation 14]

[0157]

[0158] n0 is the plasma density at the center. As a approaches 0, the plasma density is flat and uniform, and as a increases, the distribution becomes more pointed. a is a peak coefficient indicating the uniformity of plasma density, and can be calculated from the measured values ​​of the first and second moments as follows.

[0159] [Equation 15]

[0160]

[0161] FIG. 5 is a flowchart illustrating a method for measuring plasma density using a frequency sweep interferometer according to one embodiment of the present invention.

[0162] Referring to FIG. 5, the frequency sweep interferometer (130) generates a microwave modulated by frequency, and generates the modulated microwave by linearly sweeping the entire frequency within a preset range within a preset time (step S510). In one embodiment, the frequency sweep interferometer (130) can output a microwave in the 50 to 75 GHz band by linearly sweeping it for 20 μs.

[0163] The frequency sweep interferometer (130) transmits the generated microwave to the first horn antenna (110), and the first horn antenna (110) radiates the received microwave to the plasma chamber (140) (step S520). The second horn antenna (120) receives the microwave that has passed through the plasma (142) in the plasma chamber (140) (step S530). In one embodiment, the plasma chamber (140) may correspond to a process plasma chamber.

[0164] The frequency sweep interferometer (130) calculates the average density and uniformity of the plasma (142) within the plasma chamber (140) based on the phase difference between the generated microwave and the microwave received from the second horn antenna (120) (step S540).

[0165] In one embodiment, the frequency sweep interferometer (130) measures the group delay (τ) of microwaves passing through the plasma through the above mathematical expression 8. g) can be calculated. In one embodiment, the frequency sweep interferometer (130) can calculate the average density of plasma (142) within the plasma chamber (140) through the calculated group delay value and the above mathematical expression 11. In one embodiment, the frequency sweep interferometer (130) can calculate the uniformity of the density of plasma (142) within the plasma chamber (140) through the calculated group delay value and the above mathematical expression 15. The plasma density measuring device (100) including the frequency sweep interferometer can display the calculated average density and the uniformity of the density on the screen.

[0166]

[0167] The plasma density measurement method using a frequency sweep interferometer described through FIGS. 1 to 5 may also be implemented in the form of a recording medium including computer-executable commands, such as an application or module executed by a computer.

[0168] Computer-readable media can be any available media that can be accessed by a computer, and includes both volatile and nonvolatile media, removable and non-removable media. Additionally, computer-readable media can include both computer storage media and communication media. Computer storage media includes both volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information, such as computer-readable instructions, data structures, modules, or other data. Communication media typically includes computer-readable instructions, data structures, program modules, or other data in a modulated data signal, such as a carrier wave, or other transport mechanism, and includes any information delivery media.

[0169] A module may mean hardware capable of performing functions and operations according to each name described in the specification, or may mean computer program code capable of performing specific functions and operations, or may mean an electronic recording medium, such as a processor, on which computer program code capable of performing specific functions and operations is loaded.

[0170] Although the present invention has been described above as an embodiment, the technical idea of ​​the present invention is not limited to the above embodiment, and various plasma density measuring devices using frequency sweep interferometers and plasma density measuring methods using the same can be implemented within a scope that does not deviate from the technical idea of ​​the present invention.

Claims

1. A first horn antenna that emits frequency-modulated microwaves into a plasma chamber; A second horn antenna for receiving microwaves passing through plasma in the plasma chamber; and Generating a microwave modulated with a frequency within a preset range, linearly sweeping the entire frequency within the range within a preset time to generate the modulated microwave, and transmitting the generated microwave to the first horn antenna. A plasma density measuring device including a frequency sweep interferometer that calculates the average density and uniformity of plasma within the plasma chamber based on the phase difference between the generated microwave and the microwave received from the second horn antenna.

2. In the first paragraph, the plasma chamber is a plasma density measuring device including a frequency sweep interferometer corresponding to a process plasma chamber.

3. In the first paragraph, the frequency sweep interferometer The plasma frequency (ω) within the plasma chamber p ) A plasma density measuring device including a frequency sweep interferometer that generates microwaves having a frequency (ω) higher than a bandwidth.

4. In the first paragraph, the frequency sweep interferometer Arbitrary Waveform Generator (AWG) that generates predistorted voltage waveforms; A VCO driver that adjusts the voltage waveform output from the arbitrary waveform generator to an input signal of a voltage controlled oscillator (VCO); A voltage controlled oscillator (VCO) that outputs microwaves within a preset range based on a signal received from the VCO driver; A divider for distributing microwaves output from the voltage controlled oscillator; A first frequency multiplier that multiplies the frequency of the first microwave distributed from the above distributor by an integer and outputs it to the first horn antenna; A delay for delaying the second microwave distributed from the above distributor; A second frequency multiplier that outputs the second microwave delayed by the above delay unit by multiplying it by an integer; A frequency mixer that mixes microwaves received from the second horn antenna and microwaves received from the second frequency multiplier to output an intermediate frequency (IF) signal; A digitizer that samples the frequency signal output from the above frequency mixer and outputs sampling data; A phase analyzer for calculating the phase of a microwave received from the second horn antenna based on data generated from the digitizer; and A plasma density measuring device including a frequency sweep interferometer including a plasma density calculator that calculates the average density and uniformity of plasma within the plasma chamber based on the phase calculated from the phase analyzer.

5. In the fourth paragraph, the plasma density generator A plasma density measurement device including a frequency sweep interferometer that calculates the group delay of microwaves passing through the plasma using the following mathematical expression (8). [Mathematical formula 8] Here, τ g is group delay, is the beat frequency, is the frequency sweep rate 6. The above plasma density generator A plasma density measuring device including a frequency sweep interferometer that calculates an average density of plasma within the plasma chamber using the following mathematical expression 11. [Mathematical Formula 11] Here, n e is the electron plasma density, i is the sample data, N is the number of sample data, ω i is the microwave frequency of the i-th sample data, τ g, i is the group delay of the i-th sample data 7. In the first paragraph, the frequency sweep interferometer A microwave signal generator (microwave synthesizer) that outputs microwaves within a preset range; A divider for distributing microwaves output from the above microwave signal generating device; A first frequency multiplier that multiplies the frequency of the first microwave distributed from the above distributor by an integer and outputs it to the first horn antenna; A delay for delaying the second microwave distributed from the above distributor; A second frequency multiplier that outputs the second microwave delayed by the above delay unit by multiplying it by an integer; A frequency mixer that mixes microwaves received from the second horn antenna and microwaves received from the second frequency multiplier to output an intermediate frequency (IF) signal; A digitizer that samples the frequency signal output from the above frequency mixer and outputs sampling data; A phase analyzer for calculating the phase of a microwave received from the second horn antenna based on data generated from the digitizer; and A plasma density measuring device including a frequency sweep interferometer including a plasma density calculator that calculates the average density and uniformity of plasma within the plasma chamber based on the phase calculated from the phase analyzer.

8. In the 7th paragraph, the plasma density generator A plasma density measuring device including a frequency sweep interferometer that calculates the average density and uniformity of plasma within the plasma chamber using the following mathematical expression 12. [Mathematical formula 12] Here, τ g is the group delay, τ p is the delay time in the absence of plasma due to phase delay.

9. In the first paragraph, the frequency sweep interferometer A vector network analyzer that generates a microwave of a preset range, frequency-multiplies the microwave, outputs the frequency-multiplied microwave to the first horn antenna, delays the generated microwave, frequency-multiplies the microwave, mixes the frequency-multiplied microwave with the microwave received from the second horn antenna, and calculates the phase of the microwave received from the second horn antenna; and A plasma density measuring device including a frequency sweep interferometer including a plasma density calculator that calculates the average density and uniformity of plasma within the plasma chamber based on the phase calculated from the vector network analyzer.

10. In the 9th paragraph, the plasma density generator A plasma density measuring device including a frequency sweep interferometer that calculates the average density and uniformity of plasma within the plasma chamber using the following mathematical expression 12. [Mathematical formula 12] Here, τ g is the group delay, τ p is the delay time in the absence of plasma due to phase delay.

11. A step of generating a microwave modulated with a frequency within a preset range by a frequency sweep interferometer, wherein the modulated microwave is generated by linearly sweeping the entire frequency within the range within a preset time; A step in which a first horn antenna radiates the frequency-modulated microwave into a plasma chamber; A step of receiving a microwave passing through plasma in the plasma chamber through a second horn antenna; and A method for measuring plasma density using a frequency sweep interferometer, comprising a step of calculating an average density and uniformity of plasma within the plasma chamber based on a phase difference between the generated microwave and the microwave received from the second horn antenna.

12. In paragraph 11, The above plasma chamber is a method for measuring plasma density using a frequency sweep interferometer corresponding to a process plasma chamber.

13. In the 11th paragraph, the step of calculating the average density and uniformity of plasma within the plasma chamber A method for measuring plasma density using a frequency sweep interferometer, comprising the step of calculating the group delay of microwaves passing through the plasma using the following mathematical expression 8. [Mathematical formula 8] Here, τ g is group delay, is the beat frequency, is the frequency sweep rate 14. In the 13th paragraph, the step of calculating the average density and uniformity of plasma within the plasma chamber A method for measuring plasma density using a frequency sweep interferometer, comprising the step of calculating an average density of plasma within the plasma chamber using the following mathematical expression 11. [Mathematical Formula 11] Here, n e is the electron plasma density, i is the sample data, N is the number of sample data, ω i is the microwave frequency of the i-th sample data, τ g, i is the group delay of the i-th sample data 15. In the 13th paragraph, the step of calculating the average density and uniformity of plasma within the plasma chamber A method for measuring plasma density using a frequency sweep interferometer, comprising the step of calculating the average density and uniformity of plasma within the plasma chamber using the following mathematical expression 12. [Mathematical formula 12] Here, τ g is the group delay, τ p is the delay time in the absence of plasma due to phase delay.

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