KR102024468B1 - Crossing Frequency Diagnostic Method Using Microwaves - Google Patents

Abstract

According to an embodiment of the present invention, a method for diagnosing crossing frequency plasma comprises the steps of: radiating an ultrahigh frequency while scanning a driving frequency of the ultrahigh frequency to a radiation antenna connected to a first port of a network analyzer in the absence of plasma, and measuring a first transmission coefficient according to the frequency through a receiving antenna connected to a second port of the network analyzer; radiating the ultrahigh frequency while scanning the driving frequency of the ultrahigh frequency to the radiation antenna connected to the first port of the network analyzer in the presence of plasma, and measuring a second transmission coefficient according to the frequency through the receiving antenna connected to the second port of the network analyzer; and calculating a crossing frequency at which the first transmission coefficient and the second transmission coefficient coincide. The present invention can reduce measuring time compared with the conventional cutoff diagnosis method.

Description

Crossing Frequency Diagnostic Method Using Microwaves

The present invention relates to a plasma diagnostic method, and more particularly, to a plasma diagnostic method using a crossover frequency rather than a cutoff frequency.

Plasma processes (plasma etching, deposition, cleaning, etc.) account for about 30% of the overall process in the manufacturing industry, such as semiconductors, solar cells, and flat panel displays. At present, the importance of the plasma process is emerging. The efficiency and productivity of this plasma process is closely related to the electron density of the plasma. In particular, electron density has been known as the most intuitive among the plasma real-time process monitoring parameters. Thus, techniques for diagnosing plasma density have been continuously developed in the past. Among them, the plasma diagnostic technology using microwaves has been applied to the process and easy to interpret.

Diagnostic techniques using microwaves are largely classified as a method of measuring the reflection, absorption, and transmittance of microwaves. Representative examples include multipole resonance, which measures the reflectivity of microwaves, plasma-absorption, which measures hair-pin and absorption, and cut-off, which measures transmission. Among these, cutoff is attracting much attention as a next generation plasma real-time monitoring diagnostic device with high precision and reproducibility.

However, in the case of the existing cut-off technology, it is easy to diagnose under a low pressure environment such as plasma etching, but a problem that is difficult to diagnose under high pressure environment such as a plasma deposition process has been reported. Thus, there is a need for a technique for monitoring precise plasma density under high pressure environments.

An object of the present invention is to provide a cross-frequency measuring method for measuring the microwave transmission spectrum before and after plasma generation, and measuring the electron density in the plasma by measuring the frequency at which the two spectrums intersect.

 The technical problem to be achieved by the present invention is to overcome the limitations of plasma density measurement in a high pressure environment by the existing cut-off method.

In the cross-frequency plasma diagnosis method according to an embodiment of the present invention, in the absence of plasma, radiating the ultra-high frequency while scanning the driving frequency of the ultra-high frequency to the radiation antenna connected to the first port of the network analyzer, the second of the network analyzer Measuring a first transmission coefficient according to frequency through a receiving antenna connected to the port; While the plasma is present, the radio frequency is radiated while scanning the driving frequency of the ultra high frequency to the radiating antenna connected to the first port of the network analyzer, and the second transmission coefficient according to the frequency is obtained through the receiving antenna connected to the second port of the network analyzer. Measuring; And calculating a crossover frequency at which the first transmission coefficient and the second transmission coefficient coincide.

In one embodiment of the present invention, the range for scanning the driving frequency while measuring the second transmission coefficient may be less than the cutoff frequency.

In one embodiment of the present invention, the crossing frequency (f _crossing ) satisfies the following conditions and the electron density or plasma density (n _e ),

Here, f _pe may be a plasma frequency.

The present invention can diagnose the high-pressure plasma by using an ultra-high frequency diagnostic system.

Cross-frequency plasma diagnostic method according to an embodiment of the present invention can diagnose the high-pressure plasma, which was difficult to measure with the conventional cut-off diagnostic system.

In the cross-frequency plasma diagnosis method according to an embodiment of the present invention, the scan frequency is narrower, which may reduce the measurement time than the conventional cutoff diagnosis method.

1A and 1B show conceptual diagrams for the principle of a novel analysis method of the plasma diagnosis method proposed in the present invention.
Figure 2 is a graph showing the absolute value (S ₂₁₎ of the absolute value (S ₂₁₎ and a second transmission coefficient of a first transmission coefficient in the plasma diagnosis method according to an embodiment of the present invention.
Figure 3 is a graph showing the characteristics of the cross-frequency according to the ratio of the sheath thickness between the tips in the ultra-high frequency tower needle according to an embodiment of the present invention.
4 is a pressure-dependent method in the plasma diagnostic method according to an embodiment of the present invention
The first transmission coefficient S ₂₁ and denotes the second transmission coefficient S ₂₁ .
FIG. 5 illustrates a value obtained by dividing the cutoff frequency f _cutoff and the crossing frequency f _crossing calculated by the circuit model in the plasma diagnostic method according to the embodiment of the present invention by the plasma frequency f _pe / f _cutoff / f _pe , f _crossingf / f _pe )
FIG. 6 is a cutoff frequency (f _cutoff ) and a crossing frequency (f _crossing ) calculated by using a circuit model in the plasma diagnostic method according to an embodiment of the present invention, respectively, divided by the plasma frequency f _pe (f _cutoff / f _pe , f _crossingf / f _pe )

Hereinafter, with reference to the accompanying drawings will be described in detail the present invention. Hereinafter, the present invention will be described in more detail with reference to preferred examples. However, these examples are intended to illustrate the present invention in more detail, it will be apparent to those skilled in the art that the present invention is not limited or limited by experimental conditions, material types, and the like. The invention is not limited to the embodiments described herein but may be embodied in other forms. Rather, the embodiments introduced herein are provided so that the disclosure may be made thorough and complete, and to fully convey the spirit of the invention to those skilled in the art. In the drawings, the components are exaggerated for clarity. Portions denoted by like reference numerals denote like elements throughout the specification.

1A and 1B show conceptual diagrams for the principle of a novel analysis method of the plasma diagnosis method proposed in the present invention.

1A and 1B, the apparatus for diagnosing a cross-frequency plasma using ultra high frequency according to an embodiment of the present invention 100 includes a radiation antenna 112 and a reception antenna 114 spaced apart from the radiation antenna 112. ). The ultra-high frequency 110 may include a radiation antenna 112 connected to the coaxial cable and a reception antenna 114 disposed adjacent to the radiation antenna and connected to the coaxial cable.

The radiating antenna 112 is connected to the first port of the network analyzer 120 through a coaxial cable, and the receiving antenna 114 is connected to the second port of the network analyzer 120 via a coaxial cable. The network analyzer 120 measures the transmission coefficient between the first port and the second port while scanning the driving frequency. The scan range can be 0 GHz to 10 GHz. The radiation antenna 112 and the reception antenna may have the same structure and have a cylindrical shape having a predetermined length.

In the state where the plasma is not generated, the impedance Z _vac of the ultra-high frequency 110 may be modeled by the following circuit.

[Equation 1]

Z _vac = 1 / (j ω C _vac )

Where ω is the driving angular frequency of the network analyzer 120 and C _vac is the vacuum capacitance between the radiating antenna 112 and the receiving antenna 114.

Meanwhile, in the state where the plasma is generated, the total impedance Z _t of the ultra-high frequency 110 may be modeled by the following circuit.

[Equation 2]

Z _t = Z _p + 2 Z _sh

Where Z _sh is the sheath impedance due to the plasma sheath between the radiating antenna (or receiving antenna) and the plasma. Z _p is the plasma impedance in the plasma between the radiating antenna and the receiving antenna. Wherein in the plasma impedance (Zp) is plasma resistance (Rp) and the plasma inductor (L _p), and a plasma capacitor (C ₀₎ connected in parallel to the plasma resistance (R _p) and the plasma inductor (L _p) connected to said series-connected in series with each other Can be configured.

Conventional cutoff frequency measurement method is based on the plasma resonance phenomenon. The plasma self resonance phenomenon means that the plasma impedance Z _p has a maximum value at the plasma resonance angular frequency ω _R = 1 / sqrt (L _p C ₀ ).

Therefore, due to this resonance characteristic, the transmission coefficient S ₂₁ of the microwave has a minimum value at the resonance frequency. A typical cutoff frequency measurement method finds a frequency (or cutoff frequency, plasma resonance frequency) having a minimum value in the microwave transmission coefficient S ₂₁ . The cutoff frequency is given as a function of plasma density only.

However, in the conventional cutoff frequency measuring method, the Q-factor of the plasma resonant circuit becomes small due to the increase in the plasma resistance R _p under a high pressure environment (Q ~ 1 / ωR _p C ₀ ). As a result, it is difficult to distinguish the cutoff frequency from the microwave transmission coefficient S ₂₁ .

Conventional cutoff measurements measure the resonant frequency (or cutoff frequency) due to a plasma resonant circuit of total impedance Z _t . The cutoff frequency f _cutoff may substantially coincide with the plasma frequency f _pe when the Q-factor of the plasma resonant circuit is large. However, conventional cutoff measurement methods cannot find the resonant frequency (or cutoff frequency) when the Q-factor of the plasma resonant circuit is small. The plasma frequency f _pe is the plasma inherent frequency given by the plasma density or electron density.

In order to solve this problem, the present invention proposes a method of measuring the crossover frequency. Here, the crossing frequency (f _crossing ) is defined as the frequency at which the absolute values of the microwave transmission coefficients before and after plasma generation coincide. That is, the crossover frequency refers to a frequency that satisfies a condition in which the impedance Z _vac of the ultrahigh frequency 110 coincides with the total impedance Z _t of the ultrahigh frequency 110 in the state where the plasma is not generated. .

The present invention measures the crossover frequency using separate constraints instead of the resonant frequency (or cutoff frequency) due to the plasma resonant circuit.

Figure 2 is a graph showing the absolute value (S ₂₁₎ of the absolute value (S ₂₁₎ and a second transmission coefficient of a first transmission coefficient in the plasma diagnosis method according to an embodiment of the present invention.

Ultra-high frequency is transmitted to the radiating antenna through the first port and the coaxial cable. The protruding radiating antenna radiates the ultra-high frequency, and the ultra-high frequency enters the second port through the receiving antenna via the sheath-plasma. At this time, by calculating the ratio of the output signal V _out to the input signal V _in , the transmission coefficient can be obtained. The measurement is performed by changing the microwave frequency. A 50 Ohm load resistor R _L is connected to the second port.

The plasma sheath may be modeled as a capacitor in vacuum. When the capacitance of the plasma sheath is C _sh , the sheath impedance Z _sh may be expressed as follows.

[Equation 3]

Z _sh = 1 / (jω C _sh )

The plasma may be modeled as a capacitor that is filled with plasma. Assuming that the capacitance at this time is C _p , the plasma impedance Z _p is given as follows.

[Equation 4]

Zp = 1 / (jωC _p )

In this case, the plasma impedance Z _p may be modeled as a series resistor R _p is connected to the inductor L _p capacitor C _o resonant circuit.

[Equation 5]

는 플라즈마 전자의 관성에 의한 인덕턴스, 그리고

는 플라즈마 전자의 탄성충돌에 의한 저항, ω_pe는 플라즈마 진동의 각주파수, 그리고 ν_m은 전자-중성종 탄성충돌 주파수를 의미한다. Here, C _p is the capacitance of the plasma, the plasma C _o is the capacitance of the vacuum in the space occupied,

Is the inductance due to the inertia of the plasma electrons, and

Is the resistance due to the elastic collision of plasma electrons, ω _pe is the angular frequency of the plasma vibration, and ν _m is the electron-neutral species elastic collision frequency.

(동축 케이블 형태의 커패시턴스),

(두 전선 사이의 커패시턴스)이며,

(쉬스를 포함한 두 전선 사이의 커패시턴스), 여기서 h, t, d, s, ε₀ 는 각각 의 길이, 의 반지름, 간의 거리, 쉬스 두께, 진공에서의 유전율, 그리고

는 플라즈마의 유전율을 나타낸다. 이러한 회로에서, 플라즈마가 있을 때의 제2 투과계수(

)는 dB 단위로, 다음과 같은 식으로 나타낼 수 있다.Each capacitance is

(Capacitance in the form of coaxial cable),

(Capacitance between two wires)

(Capacitance between two wires including sheath), where h, t, d, s, ε ₀ are the length, radius of, distance between, sheath thickness, dielectric constant in vacuum, and

Represents the dielectric constant of the plasma. In such a circuit, the second transmission coefficient in the presence of plasma (

) Is expressed in dB, and can be expressed as follows.

[Equation 6]

이라 한다면, 그 때의 제1 투과 계수(

)는 다음과 같이 주어진다.In the same way, the impedance between the radiating antenna and the receiving antenna in the absence of plasma (before plasma occurs)

If so, the first transmission coefficient at that time (

) Is given by

[Equation 7]

이다.here,

to be.

)가 주파수에 따라 대수적으로 증가하고, 플라즈마 발생 후에는 제2 투과 계수(

)는 주파수에 따라 두 개의 극값을 가지며 전체적으로 증가하는 경향을 확인할 수 있다. 제2 투과 계수(

)이 최대값을 갖는 주파수는 Cp-Lp의 직렬-공진으로 해석할 수 있고, 최소값을 갖는 주파수는 Cp-Lp의 병렬-공진으로 해석할 수 있다.Before the plasma generation, the first transmission coefficient (

) Increases logarithmically with frequency, and after plasma generation, the second transmission coefficient (

) Has two extremes with frequency and can be seen to increase overall. Second transmission coefficient (

The frequency with the maximum value can be interpreted as the series-resonance of Cp-Lp, and the frequency with the minimum value can be interpreted as the parallel-resonance of Cp-Lp.

) 그래프와 제2 투과 계수의 절대값(

) 그래프가 교차가되는 지점이 존재한다. 이는 플라즈마가 발생했음에도 불구하고, 플라즈마-쉬스 임피던스간의 작용으로 인해 마치 플라즈마가 존재하지 않는 것처럼 보이는 구간을 의미한다. 이러한 주파수를 교차 주파수(crossing frequency, f_crossing)라 명명하며, 이 때의 조건은, 제2투과 계수의 절대값(

)과 제1 투과 계수(

)의 절대값(

)이 같을 때 이므로, 다음과 같이 나타낼 수 있다.Absolute value of the first transmission coefficient (

) Absolute value of the graph and the second transmission coefficient (

) There is a point where the graph intersects. This means that a section in which plasma does not seem to exist due to the action between the plasma and the sheath impedance even though the plasma is generated. This frequency is called a crossing frequency (f _crossing ), and the condition is that the absolute value of the second transmission coefficient (

) And the first transmission coefficient (

) Absolute value (

Since) is the same, it can be expressed as

[Equation 8]

로 근사할 수 있다. 따라서, 수학식 6은 다음과 같이 표시될 수 있다.From Equation 8, an analytical relationship between the angular _crossing frequency (ω _crossing ) and the plasma oscillation angular frequency (ωpe) is obtained. First, since the sheath impedance is inversely proportional to frequency, after the series-resonant frequency of Lp-Csh,

Can be approximated by Therefore, Equation 6 may be expressed as follows.

[Equation 9]

으로 근사할 수 있다. Here, Cp * means complex conjugate of Cp. Taking advantage of the fact that cross frequency is pressure independent,

Can be approximated by

α, β may be substituted as follows.

[Equation 10]

 Equation 9 can be simply expressed as follows.

[Equation 11]

The scan range of the driving frequency during the measurement of the second transmission coefficient may be equal to or less than a cutoff frequency. Accordingly, the scan range can be reduced than the cutoff frequency, thereby reducing the measurement time.

Figure 3 is a graph showing the results of calculating the cross-frequency characteristics according to the ratio of the sheath thickness between the tips in the ultra-high-frequency tower needle according to an embodiment of the present invention as a circuit model and the calculation result of Equation (8).

는 전자밀도에 의존하지 않고, 쉬스 두께에 크게 의존한다. 하지만 수학식 8은 회로 모델 결과 (도 3의 산포 데이터)와 차이가 있는데, 이것은 쉬스 임피던스를 무시한 결과(

)로 인한 차이로 보여진다.Referring to Figure 3, the dotted line represents the result of Equation 8. When checking the scatter data,

Does not depend on electron density but largely on sheath thickness. However, Equation 8 is different from the circuit model result (the scatter data in FIG. 3), which is a result of ignoring the sheath impedance.

Is seen as a difference due to

However, since sheath thickness is usually difficult to measure, it is easy to measure if the sheath change is averaged.

관계를 취하게 되면, 플라즈마 쉬스에 의한 오차 ± 15 % 정도를 감수하고,

(ne는 cm^-3 단위)로부터 전자밀도를 얻어낼 수 있다. 이에 따라, 교차 주파수(f_crossing)는 다음과 같이 주어진다.Thus, in Figure 3 the mean value, i.e.

If you take the relationship, the error caused by plasma sheath ± 15%,

It can be obtained from the electron density (ne is the unit cm ^-3). Accordingly, the crossing frequency f _crossing is given by

[Equation 12]

Where n _e is an electron density with cm ⁻³ units. However, since the average value is taken to ignore the information of the sheath thickness, an error due to the sheath thickness may be included. Thus, the crossing frequency f _crossing is due to the use of an approximation of the sheath impedance Zsh and the theoretical error is ± 15%. The theoretical error may be due to the sheath thickness of the sheath impedance Z _sh .

The crossover frequency can be extracted even at high pressures at the cutoff frequency (or resonant frequency). Thus, cross frequency measurement can extend its application.

병렬-공진을 의미하며, 이 공진 주파수를 컷오프 주파수(

)라 한다. 이 때 Zp는 최대가 되며, 따라서, S21은 최소값을 가지게 된다. 기존 연구를 통하여,

를 밝혀 냈다. 이로부터 플라즈마 밀도를 측정하는 방법을 이용해왔다. 하지만 이러한 방법은 챔버 압력이 높은 환경 하에서 플라즈마 저항(R_p)이 커짐에 따라 공진회로의 Q-인자가 작아진다. 이로부터 공진 밴드 폭이 넓어짐에 따라, 컷오프 공진을 제2 투과 계수의 절대값(S21)에서 구별해 내기가 어려워지는 문제를 야기한다. The measurement system according to an embodiment of the present invention is the same as the measurement system of the existing cutoff. The method of measuring cutoff is based on measuring plasma self resonance. Plasma self resonance phenomenon,

Means parallel-resonance, and this resonant frequency is called the cutoff frequency (

Is called. At this time, Zp becomes maximum, and therefore S21 has minimum value. Through existing research,

Revealed. From this, a method of measuring plasma density has been used. However, this method reduces the Q-factor of the resonant circuit as the plasma resistance R _p increases under high chamber pressure. From this, as the resonance band width becomes wider, it causes a problem that it is difficult to distinguish the cutoff resonance from the absolute value S21 of the second transmission coefficient.

4 is a pressure-dependent method in the plasma diagnostic method according to an embodiment of the present invention

The first transmission coefficient S ₂₁ and denotes the second transmission coefficient S ₂₁ .

Referring to FIG. 4, the circuit circuit model (circuit model) used the circuit shown in FIG. 1B. The absolute value of the first transmission coefficient of the high frequency (110) according to the change in pressure (S ₂₁₎ and the absolute value (S ₂₁₎ of the second transmission coefficient is displayed.

Both the cutoff frequency and the crossover frequency can be seen at a pressure p of 1.0 Torr and a plasma density of 5 X 10 ⁹ / cm ³ . However, if the pressure p increases to 2.0 Torr at the same plasma density (at 5 × 10 ⁹ / cm ³ ), the cutoff frequency is indistinguishable from the second transmission coefficient S ₂₁ . However, it may be extracted cross-over frequency (f _crossing).

FIG. 5 illustrates a value obtained by dividing the cutoff frequency f _cutoff and the crossing frequency f _crossing calculated by the circuit model in the plasma diagnostic method according to the embodiment of the present invention by the plasma frequency f _pe / f _cutoff / f _pe , f _crossingf / f _pe )

Referring to FIG. 5, a result of comparing cutoff frequency characteristics and cross-frequency characteristics in a low density plasma environment (n _e = 10 ⁹ / cm ³ ) is shown. The cutoff frequency f _cutoff has a slight variation in the plasma frequency f _pe according to the pressure change. The difference between the cutoff frequency f _cutoff and the plasma frequency f _pe increases the resistance R _p of the circuit constituting the plasma according to the pressure, thereby increasing the effective storage capacity as the current mainly flows into C ₀ . Therefore, the resonance frequency is interpreted to decrease. On the other hand, the cutoff frequency f _cutoff cannot be measured in the range of about 0.7 Torr or more.

However, since the crossing frequency (f _crossing ) does not depend on the Q-factor of the resonant circuit constituting the plasma, its value is constant according to the pressure change. The crossing frequency (f _crossing ) is constant with 0.85 times difference from the plasma frequency (f _pe ) according to the pressure change. In addition, the crossing frequency (f _crossing ) can be measured up to a pressure much higher than the cutoff frequency (f _cutoff ).

FIG. 6 is a cutoff frequency (f _cutoff ) and a crossing frequency (f _crossing ) calculated by using a circuit model in the plasma diagnostic method according to an embodiment of the present invention, respectively, divided by the plasma frequency f _pe (f _cutoff / f _pe , f _crossingf / f _pe )

Referring to FIG. 6, cutoff frequency characteristics and crossover frequency characteristics in a high density plasma environment (n _e = 10 ¹² / cm ³ ) are compared. The cutoff frequency _(cutoff f) is due to the reduction in the Q- factor of the resonance circuit of the plasma it can not be measured at least about 16 Torr area. It was found that f _crossing could measure pressures much higher than the cutoff frequency.

As a result of the circuit model, the cutoff frequency (f _cutoff ) in principle has a pressure limit for measuring electron density. The f _crossing has no pressure limit in the measurement. As a result, circuit model calculations resulted in measurable results in pressure ranges where the crossover frequency was much higher than the cutoff frequency within various plasma density ranges.

에서 알 수 있듯이, 같은 Rp일 때

와

가 서로 비례하기 때문이다. The results of comparing the measured frequency characteristics in the high-density plasma environment are shown, and it can be seen that the cutoff frequency cannot be measured in the region of about 16 Torr or more. Thus, the measured pressure limit of the cutoff frequency increases with the electron density. The reason is that

As you can see, when the same Rp

Wow

Is proportional to each other.

The crossover frequency can be measured up to a pressure much higher than the cutoff frequency. Circuit model results show that, in principle, the cutoff frequency has a pressure limit for electron density measurements, while the crossover frequency has no pressure limit for measurements.

As a result, circuit model calculations resulted in measurable results in pressure ranges where the crossover frequency was much higher than the cutoff frequency within various plasma density ranges.

While the invention has been shown and described with respect to certain preferred embodiments thereof, the invention is not limited to these embodiments, and has been claimed by those of ordinary skill in the art to which the invention pertains. It includes all the various forms of embodiments that can be implemented without departing from the spirit.

110: high frequency
112: radiation antenna
114: receiving antenna

Claims (3)

In the absence of plasma, the radiating high frequency is radiated while scanning the driving frequency of the ultra high frequency to the radiating antenna connected to the first port of the network analyzer, and the first transmission coefficient according to the frequency is obtained through the receiving antenna connected to the second port of the network analyzer. Measuring;
While the plasma is present, the radio frequency is radiated while scanning the driving frequency of the ultra high frequency to the radiating antenna connected to the first port of the network analyzer, and the second transmission coefficient according to the frequency is obtained through the receiving antenna connected to the second port of the network analyzer. Measuring; And
And calculating a crossover frequency at which the first permeation coefficient and the second permeation coefficient coincide with each other. According to claim 1,
And the range of scanning the drive frequency while measuring the second transmission coefficient is less than or equal to a cutoff frequency. According to claim 1,
The crossing frequency (f _crossing ) satisfies the following conditions and the electron density or plasma density (n _e ),

Here, f _pe is a plasma frequency diagnostic method, characterized in that the plasma frequency.

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