JPH0711991B2 - Electronic temperature measurement method with double probe - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to measurement of electron temperature in plasma, and particularly, measurement of electron temperature with high accuracy by inserting two probes (electrodes) into plasma. The present invention relates to a method for measuring an electron temperature using a double probe.

(Prior Art) In recent years, along with the development of plasma chemistry, technological developments such as modification of surface of solids, cleaning, synthesis and decomposition of substances using plasma have been conducted. In various devices using such plasma, in order to control the plasma with high accuracy, it is important to accurately grasp information such as potential distribution, electron density, and electron temperature in the medium. The present invention particularly relates to a method for measuring an electron temperature from various information in plasma.

Conventionally, the probe measurement method of inserting the probe into the plasma and measuring the plasma in a system independent from the discharge electrode is most suitable not only for the high frequency discharge and the microwave discharge but also for the direct current discharge. A double probe measurement method is known in which two probes having the same size (surface area of the probe) are inserted into plasma for measurement for the purpose of electron temperature measurement.

FIG. 8 is a measurement circuit diagram by the double probe method.
The DC voltage V is applied between the two probes, the current flowing between the probe i and saturation current value i _s is The current-voltage characteristic curve represented by the equations (1) and (2) and shown by the solid line in FIG. 9 is obtained from the measurement results. (Where, κ: Boltzmann constant, T _e : electron temperature, n _e : electron density, A: probe surface area, ε: natural logarithm base, tan h: sinusoidal hyperbolic function, M: positive ion mass, e: charge Origin) V
The slope S at = 0 is The electron temperature is calculated from the slope S and the saturation current value i _s.
T _e is required. Further, by substituting the electron temperature T _e and the saturation current value i _s obtained in (2), to obtain a current density n _e was conventional double probe measurement method.

(Problems to be Solved by the Invention) However, a drawback of the above-mentioned conventional method is that when obtaining the electron temperature,
This is because the error due to the method of drawing the tangent line on the current-voltage characteristic curve and the error due to the determination of the saturation current value are taken in double, so that the error is added and becomes large. Another drawback is
It is very difficult to make the surface areas of the two probes completely the same, and the open-circuit voltage (voltage when the current is zero) does not become 0 due to the slight difference in shape and the asymmetry that appears in the current-voltage characteristic curve. An offset voltage V ₀ that maintains a certain constant voltage is generated, and the current-voltage characteristic shown by the solid line in FIG. 9 becomes a distorted curve as shown by the dotted line in FIG. Therefore, in such a case, there is a problem that the electron temperature T _e and the electron density n _e cannot be accurately determined because it is unclear where to consider the origin in the above-mentioned analysis method. Furthermore, the result of the actual measurement in FIG. 8 is a curve having a further inclination from the saturated state to the saturated state as shown by the dashed line in FIG.
It is represented by an expression in which the term S · V is added to the right side of expression (1). There is a problem in this slope processing, that is, how to consider the saturation value, and the conventional method has a problem that a measurement error increases.

(Means for Solving the Problems) The present invention has been made to overcome the above problems, and two probes are inserted in the plasma medium so that two DC current-voltage characteristics of the two probes can be obtained. The secondary differential coefficient is detected, the voltage interval between the peaks of the secondary differential coefficient is measured, and the electron temperature is determined. The secondary differential coefficient can be obtained by superimposing an alternating current on the DC current-voltage characteristic and detecting a double harmonic, a change in DC component, or a beat component corresponding to the secondary differential coefficient. .

(Operation) FIG. 3 shows the difference V between the electric potentials V ₁ and V ₂ of the _two probes with respect to the electric potential V _s of the plasma.

The currents i ₁ and i ₂ flowing through each probe are i ₁ = I _e1 exp (-eV ₁ / κT _e ) -I _i1 (4) i ₂ = I _e2 exp (-eV ₂ / κT _e ) -I _i2 …… (5) is given. The relational expression of the probe current i is given by i = i ₁ = -i ₂ , i ₁ + i ₂ = 0 (6). Where I _e1 and I _e2 are electron saturation currents I _i1 and I _{i2, respectively.}
Is the positive ion saturation current. From equations (4)-(6), i = C ₁ + C ₂ tanh {(η−β) / 2} (7) is obtained. Where C ₁ and C ₂ are the amount of bias shift in the asymmetric probe, η is the amount that eV is normalized by κT _e , β is the symmetry point of the voltage-current characteristic that occurs in the asymmetric probe, and l _n is the natural logarithm of log _e. Then, C ₁ = (I _i1 -I _i2 ) / 2, C ₂ = (I _i1 + I _i2 ) / 2 β ＝ l _n (α) ＝ l _n (I _e2 / I _e1 ), η ＝ eV / The relationship of κT _e holds.

FIG. 4 shows the characteristic curve of the equation (7), and the coordinate point source (β,
C ₁ ) is the symmetry point of the characteristic curve. That is, it can be seen that the characteristics of the double probe in the case where the shapes of the two probes are broken and the characteristic curves are asymmetrical are reduced to a characteristic expression of the symmetrical probe by coordinate conversion. Also, for a truly symmetric double probe, I
_{Since e2} = I _e1 , β = 0 and C ₁ = 0, and the equation (7) is reduced to the equation (1). From the above, the characteristic of the double probe is similar to that of the parallel translation of the coordinates regardless of the symmetry or asymmetry of the probe.

Next, when the second derivative i ″ is calculated for the probe current i in equation (7), i ″ = 2C ₂ exp (η + β) {exp (2β) −exp (2
β)} / {exp (η) + exp (β)} ⁴ (8) is obtained. This formula is i ″ = 2C ₂ exp (ξ) {1-exp (ξ)} / {1 + exp by coordinate transformation of ξ = η−β
(Β)} ⁴ (9), but the formula (9) has the same form as the formula (8) with β = 0. That is, the shape of the characteristic curve of i _p ″ is similar to that of parallel movement of coordinates regardless of the symmetry or asymmetry of the probe (see FIG. 5).

In FIG. 5, P ₁ and P ₂ are peaks of the second derivative, but their positions are obtained at the point of the third derivative i ″ ′ = 0, Is. That is, the distance between the two peaks is 2.63κ
It becomes T _e .

The above is the case where the velocity distribution of electrons in the plasma follows the Maxwell distribution in thermal equilibrium. When the distribution deviates from the thermal equilibrium, the shape of the peak of i ″ deviates from the shape given by the equation (9). This deviation indicates the degree of thermal disequilibrium. An example is shown in FIG. Indicates.

Further, when there is a flow of electrons in the plasma or a microscopic spatial change (wave, etc.), the symmetry of the waveform of the secondary differential coefficient is lost as shown in an example in FIG. By detecting such asymmetry, the degree of local nonuniformity of plasma can be detected.

(Effects of the Invention) As described above, in the method of measuring the electron temperature by inserting two probes into the plasma medium, the present invention can measure the electron temperature in the plasma regardless of the symmetrical asymmetry of the probe shape. It is possible to measure with high accuracy, and it is also possible to easily obtain information from the plasma medium such as electron density, non-uniformity of electrons or ions, and deviation between Maxwell distribution and velocity distribution. Therefore, according to the present invention, it becomes possible to control various devices using plasma with high accuracy.

(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.
FIG. 2 is a diagram showing operation waveforms of main parts in FIG.

The sweep voltage generating circuit 1 whose output voltage rises linearly with time is used, and the output signal of the AC voltage generator 2 is superposed on the sweep voltage generating circuit 1 according to the principle of the AC superposition differential method, and the two are inserted into the plasma. It is applied to the probe electrodes A and B. Of the probe current flowing at this time, a signal of a frequency component flowing in proportion to the second derivative of the probe characteristic is amplified by the selective amplifier 3, and then in the phase sensitive detection circuit 5, the signal of the reference signal generation circuit 4 is used. , This is extracted at a predetermined phase.
Here, there are the following three methods for detecting the second derivative. (1) A double harmonic method in which the AC signal generator 2 generates a sin sine wave signal of sin ωt, the selective amplifier 3 amplifies only the 2 ω component, and the reference signal generation circuit 4 generates a 2 ω signal.
(2) A direct current variation method in which the AC signal generator 2 generates a waveform obtained by modulating sinωt with a square wave of ω, the selective amplifier 3 detects a modulation component, and the reference signal generation circuit 4 generates a modulation frequency component. .

(3) The AC signal generator 2 generates [sin ω ₁ t + sin ω ₂ t], and the selective amplifier 3 detects the beat wave [ω ₁ −ω ₂ ],
The beat method in which the reference signal generation circuit 4 generates the reference signal of [ω ₁ −ω ₂ ] can be used.

The voltage interval V between the two positive and negative maximum values P ₁ and P ₂ existing in the extracted signal is detected by the peak value detection circuit 6 as a time interval T. The reference pulse generating circuit 7, the gate circuit 8 and the counter 9 together form a time interval measuring circuit, and the gate circuit 8 is driven by the output signal of the peak value detecting circuit to reach the maximum value P ₁ . The counter 9 counts the output pulses of the reference pulse generating circuit 7 from the time to the time when it reaches P ₂ . As a result, the electron temperature T _e can be directly read from the counter count value n (= T _e ).

Further, by outputting the shape of i ″ to the oscillograph or the XY recorder 10 and displaying it, when the shape of the peak is monitored, if the left and right peaks are asymmetrical, the degree of non-uniformity of plasma is indicated. In addition, when the peak is divided into two or when it is deviated from the equation (8), it means that the plasma velocity distribution deviates from the Maxwell distribution.

[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 diagrams showing waveforms generated from each circuit block used in the present invention. FIG. 2A is a waveform diagram output from the sweep voltage generator, FIG. 2B is a waveform diagram output from the phase sensitive detection circuit, and FIG. 2C is a waveform diagram output from the peak value detection circuit. , FIG. 2D is a waveform diagram output from the gate circuit, FIG. 3 is a conceptual diagram showing probe potentials when two probes are inserted into plasma, and FIG. 4 is FIGS. 3 and (7). Asymmetrical DC voltage / current characteristic curve diagram based on the equation, FIG. 5 is a characteristic curve diagram obtained by calculating the second derivative of equation (7) (FIG. 4), and shows the peak of the second derivative value. Is the secondary fineness when the velocity distribution of electrons in the plasma does not follow the Maxwell distribution in thermal equilibrium. FIG. 7 is a diagram showing a characteristic curve, FIG. 7 is a second derivative characteristic curve diagram when electrons in the plasma have a flow or a spatial change, and FIG. 8 is a measurement circuit diagram by the conventional double probe method, FIG. 9 is a DC current-voltage characteristic curve diagram measured by the measurement circuit shown in FIG. 8. The solid line shows characteristics when two probes have symmetry, and the dotted line shows characteristics when two probes are asymmetric. It is a curve figure. (Explanation of symbols) 1 ... Sweep voltage generator, 2 ... AC signal generator, 3 ...
Selective amplifier, 4 ... Reference signal generation circuit, 5 ... Phase sensitive detection circuit, 6 ... Peak value detection circuit, 7 ... Reference pulse generation circuit, 8 ... Gate circuit, 9 ... Counter, 10 ...
… Oscilloscope or XY recorder, A, B… Probe electrodes.

Claims (5)

[Claims] 1. An electron temperature is determined by detecting a second derivative of a direct current-voltage characteristic between two probes installed in plasma and measuring a voltage interval between peaks of the second derivative. Electronic temperature measurement method with double probe. 2. The detection of the secondary differential coefficient comprises superimposing an alternating current on the DC current-voltage characteristic to detect a double harmonic, a change in the DC component or a beat component corresponding to the secondary differential coefficient. The electronic temperature measuring method according to claim 1, characterized in that 3. The electron temperature measuring method according to claim 1, wherein the electron density is determined from the area of the peak of the second derivative. 4. The electron temperature measuring method according to claim 1, wherein the nonuniformity of the plasma is detected from the difference between the shapes of the two peaks of the second derivative. 5. The electronic temperature measuring method according to claim 1, wherein the deviation of the velocity distribution from the Maxwell distribution is measured from the shape of each peak of the second derivative.