JPH0711992B2 - Electron temperature measurement method with asymmetric double probe - Google Patents

Description

TECHNICAL FIELD The present invention relates to measurement of electron temperature in plasma, and in particular, insertion of two asymmetric probes (electrodes) having different shapes or sizes in plasma. The present invention relates to an electron temperature measuring method using an asymmetric double probe for measuring electron temperature at high speed.

(Prior Art) In recent years, in weakly ionized plasma such as plasma processing, it has become important to monitor various parameters when the gas pressure, flow rate, input power intensity, or the like in the plasma changes. In particular, there is a strong demand for high-speed and high-accuracy measurement of electron temperature, which is related to the reaction rate between electrons and atomic molecules.

FIG. 7 is a circuit diagram of a conventionally used electron temperature measuring method. 2 which has the same symmetry as the shape in the plasma
When two probes P ₁ and P ₂ are inserted, a varying voltage V _P is applied, and the current i _P corresponding to V _P flowing from the plasma is measured, a voltage-current characteristic symmetrical to the origin 0 as shown in Fig. 6 is obtained. A curve is obtained. Inclination at origin 0 on this curve (di _P /
dV _P) and probe saturation current value i _S is the electron temperature T _e, when the Boltzmann constant kappa, holds the relational expression _{/ κT e / e = 2i S} (di P / dV P), the kT _e from the above equation It was a reward. However, in this method, the probe voltage V _P must be swept in order to obtain the slope and saturation value of the characteristic curve, which requires time for measurement, and the slope and saturation value must be applied by the method of least squares. It took time to obtain it with a certain accuracy. Furthermore, since it is difficult to make the surface areas of the two probes completely equal, there is an imbalance in the probe surface areas, the characteristic curve does not pass through the zero point, and there is an imbalance in the saturation value. There was a problem with the data analysis method. Therefore, the measurement result includes a large error. For high-speed measurement of electron temperature, a method using two symmetrical probes and a reference electrode has been previously devised "K.Hi.
rao and K. Oyama: J. Geomag, Geoeles 22 (1970) 393].
In this method, an alternating current is applied to one of the two symmetrical probes, and the electron temperature is obtained from the difference in the floating potentials of both electrodes. However, this method essentially requires three electrodes, and it is difficult to manufacture the two probe electrodes in perfect symmetry.

(Problems to be Solved by the Invention) In order to control the plasma with high accuracy, it is necessary to monitor the electron temperature in the plasma, which changes from moment to moment, at high speed and accurately. For this reason, the above-mentioned conventional method has a problem that it takes a long time for measurement, and the apparatus is large in size, and a large amount of cost is required. An object of the present invention is to insert an asymmetrical probe into the plasma, follow the constantly changing plasma state, and grasp the electron temperature thereof in real time. This technology controls gas pressure, gas flow rate, input power, etc., which are elements for forming plasma promptly according to the measured electron temperature value,
It is essential for setting and maintaining the plasma parameters at the desired values.

(Means for Solving the Problems) In order to solve the above problems, the present invention immerses a double probe composed of two asymmetric probes in plasma,
The current flowing during that time is maintained so as to be 0, and the voltage at that time (hereinafter referred to as an open circuit voltage) is monitored. Then
By applying an alternating current between the two probes, the change amount of the open circuit voltage, that is, the difference from when the open circuit voltage is not applied is monitored. Since this potential difference is related to the electron temperature,
A signal is measured by applying a telegraph signal that interrupts an alternating current between the probes and extracting an open circuit voltage that changes according to the interrupt.

(Operation) The present invention will be described in detail below.

The current-voltage characteristic i _P (V _P ) of the asymmetric double probe is given by the following equation.

i _P (V _P ) = C ₁ + C ₂ tanh {(η−β) / 2} (1) Here, if _Te is the electron temperature and α = I _e2 / I _e1 , then η = ev _P / ΚT _e , β = l _n (α), C ₁ = (I _i2 −I _i1 ) / 2, C ₂ = (I _i1 + I _i2 ) / 2 I _ej , I _ij (j = 1,2) respectively It is the saturation current of electrons and positive ions. Where l _n is the natural logarithm. The characteristic of the equation (1) becomes a diagram as shown in FIG. In the figure, point P is a symmetry point of the characteristic curve, and from the origin 0 (κT _e l _n α,
Only C ₁ ). The voltage offset Vf is given by the following equation.

Vf = l _n [(I _e2 / I _e1 ) / (I _i2 / I _i1 ) ... (2) If the electron and positive ion saturation currents are proportional to the probe surface area.

Since (I _e2 / I _e1 ) = (I _i2 / I _i1 ), Vf = 0. This Vf corresponds to an open circuit voltage when two asymmetric probe electrodes are inserted in plasma and placed in a currentless state.

When the AC voltage asin ωt is applied to the probe voltage for modulation, the probe current-voltage characteristic changes as shown by the dotted line curve in FIG. Therefore, the currentless open circuit voltage is displaced from Vf in the original solid line to Vf '. The offset voltage Vf ′ when AC modulation is applied is determined by the following equation.

Where Δη = ΔV / κT _e = (Vf′−Vf) / κT _e , s = β
−η ₀ , (η ₀ = Vf / κT _e ), r = ea / κT _e .

The conditions under which the surface area ratios of the asymmetric double probes differ will be considered based on the above principle.

(I) When the probe surface area ratio κ is very large. This is because s is large and exp (−s) << 1 (β = 1
_n κ). Expression (3) can be expanded to Becomes Now get _{Δη = -l n {I 0 (} r)} ··· (5). Here, I ₀ (r) is a zero-order modified Bessel function. When selecting the amplitude of the applied AC signal to be sufficiently small, I ₀
Because ^{(r) = 1 + r 2} /4 becomes approximate expression can be applied, from ^{Δη = -r 2/4 ··· (} 6) i.e. ^{(6), | ΔV | = ea 2 /} 4κT e ··· (7 ) Is obtained. This shows an inverse proportional function of the offset voltage displacement ΔV with respect to the electron temperature T _e , and the electron temperature can be immediately obtained from the measurement of the offset amount.

(Ii) When the probe surface area ratio κ is arbitrary In this case, Δη can be determined by numerically integrating equation (3). The relationship between −Δη and r≡ea / κT _e is shown in FIG. As is clear from the figure, when the surface area ratio of the probes P ₁ and P ₂ changes from 2: 1 to 10: 1, the value of Δη gradually increases and the sensitivity of electron temperature measurement increases. However, practically, 4 to 1 to 8 to 1 are preferable, and there is no great advantage if the number is further increased. From the figure, the relationship between the AC amplitude a and the electron temperature T _e can be obtained.

The frequency of the AC signal is the ion plasma frequency of the plasma (eg, H ₂ plasma, 14 MH at a plasma density of 10 ¹⁰ cm ^-3 ).
z) Choose below. Therefore, a time response of at least 1 msec or more can be obtained.

(Effects of the Invention) As described above, according to the present invention, it is not necessary to manufacture the two probes in the same shape, that is, their surface areas are exactly the same. The resulting circuit, and the circuit that obtains its output, can be easily manufactured, thus significantly reducing the cost. Therefore, compared with the conventional method, the electronic temperature measurement is improved in time responsiveness, cost saving and the like.

(Example) Hereinafter, the present invention will be described in more detail with reference to the accompanying drawings.

FIG. 1 is a block circuit diagram showing an embodiment of the present invention, and FIGS. 2A to 2D are diagrams showing an output signal wave system from a main part in FIG.

The respective outputs of the high frequency oscillator 1 and the square wave generating circuit 2 are modulated by the modulating circuit 3 and then applied via the transformer T and the DC blocking capacitor C between the probe electrodes of P ₁ and P ₂ . The filter 4 is for removing higher harmonic components in the output signal of the modulation circuit, and the detection circuit 5 is a detection circuit that uses the output of the square generation circuit 2 as a reference signal. The input resistance when looking at the measurement system from both probe sides is very high,
Therefore, in any case, no current flows between the probes of P ₁ and P ₂ . FIGS. 2A to 2D show the relationship between the output signals of the high frequency oscillator 1, the square wave generation circuit 2 and the modulation circuit 3, and T ₁ during the period when the high frequency signal is generated at the output of the modulation circuit. , The voltage between the probes P ₁ and P ₂ is the voltage corresponding to the point Vf ′ in FIG.
Further, during the period T ₂ in which no high frequency output is generated, this is the point Vf in FIG. Therefore, the detection output becomes a square wave with an amplitude of (Vf-Vf ') as shown in FIG. 2D. The magnitude of (Vf-Vf ') depends on the amplitude of the modulated output signal as shown in FIG. 2C, and the electron temperature can be determined from these relationships.

[Brief description of drawings]

FIG. 1 is a block circuit diagram showing an embodiment according to the present invention, and FIGS. 2A, 2B, 2C and 2D are waveforms of signals generated from the main circuits shown in FIG. FIG. 2A is a waveform diagram of a signal output from a high frequency signal generator, FIG.
The figure shows a signal waveform diagram output from a square wave generator, FIG. 2C shows a waveform diagram output from a modulation circuit, FIG. 2D shows a waveform diagram showing the potential difference between two probes, and FIG. A graph showing the relationship between Δη and ea / κT _e when the surface area ratios of the two probes are arbitrarily different. Fig. 4 shows the characteristics of Fig. 5 in which an AC voltage was applied to the probe voltage for modulation. Fig. 5 is a graph showing a current-voltage characteristic curve (dotted line) obtained in this case, Fig. 5 is a current-voltage characteristic curve diagram when an asymmetric double probe is used, and Fig. 6 is a case where a conventional symmetrical double probe is used. FIG. 7 is a current-voltage characteristic curve diagram of FIG. 7, and FIG. 7 is an electronic temperature measurement circuit diagram using a conventional symmetrical double probe. (Description of symbols) 1 ...... high-frequency oscillator, 2 ...... square wave generator circuit, 3 ...... modulation circuit, 4 ...... filter, 5 ...... detection circuit, P _1, P ₂ ...
… Probe electrode, C… DC blocking capacitor, T…
Transformer, X ... A signal that gives the electronic temperature.

Claims (1)

[Claims] 1. An asymmetry in which an electron temperature is determined by intermittently applying an AC voltage between two asymmetric probes installed in a plasma, and measuring a change in the voltage caused by the AC voltage in a current-free state. Electronic temperature measurement method with double probe.