Analysis of Langmuir Probe Characteristics for Measurement of Plasma Parameters in RF Discharge Plasmas

A simple method for measuring RF plasma parameters by means of a DC-biased Langmuir probe is developed. The object of this paper is to ensure the reliability of this method by using the other methods with different principles. First, Langmuir probe current e I response on RF voltage p1 V superimposed to DC p V biased probe was examined in DC plasmas. Next, probe current response of DC biased probe in RF plasmas was studied and compared with the first experiment. The results were confirmed by using an emissive prove method, an ion acoustic wave method, and a square pulse response method. The method using a simple Langmuir probe is useful and convenient for measuring electron temperature e T , electron density e n , time-averaged space potential s0 V , and amplitude of space potential oscillation s1 V in RF plasmas with a frequency of the order of pi pe 10 f f f < < .


Introduction
During the past 50 years, various techniques have been developed to determine plasma parameters in RF discharge plasmas using a Langmuir probe [1]- [5], an RF-driven probe [6]- [8], a compensated RF-driven probe [9]- [11], a tuned probe [12] [13], and optical method [14] [15].When an RF signal same as the phase and amplitude of space potential in RF (13.56 MHz) discharge plasmas is applied to a probe, RF potential between the probe and the plasma can be removed.In this case, a characteristic curve similar to a curve of DC discharge plasma is provided by this technique.By using this principle Braithwaite [6], Paranjpe [13], and others carried out detailed experiments and reported the experimental results [6]- [13].However, these techniques are complicated and troublesome for measuring the plasma parameters.For example, the driven probe method needs a phase controller, an attenuator, an oscilloscope, etc., and the tuned probe technique requires a tuning network, a low-path filter, and so forth for obtaining probe current and voltage p p -I V characteristics.In addition, these procedures need to lock the probe potential to the phase of oscillation of plasma space potential at each time whenever experimental conditions are altered; namely, gas pressure, electric power, probe position, and so on.Therefore, the methods mentioned above are rather difficult and impractical.
The same electric current flows in a probe circuit in the following two cases.The first case is that the probe potential is constant, and space potential oscillates in the plasma.
The second case is that space potential is constant, and probe potential oscillates in the plasma.In other words, both cases are totally equivalent for an electric circuit.In 1963, by using a numerical computation Boschi [3] obtained the time-averaged probe characteristic curves of a DC plasma in which a probe potential vibrated sinusoidally.If the electron distribution function is Maxwellian and the probe voltage ( ) p V t in a DC plasma is oscillating sinusoidally with a frequency f and an amplitude p1 V around the probe bias voltage p V , i.e.
( ) Here, 2πf ω = is angular frequency.For probe bias p s0 p1 , where electrons are always retarded, the electron current density ( ) p j t flowing into the probe can be expressed as follows [3] [4]: Here, s0 V is the space potential of DC plasma.The time-averaged probe characte- ristic p j can be expressed as follows: ( ) where e0 j and i0 j are saturated currents of electrons and ions for a DC plasma.0 I is the zeroth order modified Bessel function.If V ∆ is defined by the following equation, i.e.
( ) Equation (5) shows that the time-averaged probe characteristic curve shifts in parallel to more negative value V ∆ than a case of p1 0 V V = , so that the electron temperature e T is constant regardless of the frequency f and the amplitude p1 V .In the case , because the probe characteristic curve was not expressed in a numerical formula, it was derived by using a computer [Figure 2  (B) The floating potential f V is unrelated to the applied frequency f , and moves to the low potential side by V ∆ as the amplitude p1 V becomes large.
(C) The electron temperature e T is constant regardless of the frequency f and the amplitude p1 V .
He obtained the time-averaged probe characteristic curves where the sinusoidal voltage from 10 Hz to 10 MHz was applied to a probe in DC discharge plasma.As a result, the experimental data well agreed with the theory concerning to the items (B) and (C).
Both items suggest that electron temperature can be also obtained from a time-averaged characteristic curve of RF discharge plasma.Garscadden [1] also measured how a probe characteristic curve was changed by applying a sinusoidal potential covering from 50 Hz to 500 Hz to the probe.As a result, the curve as it was expected by Equation ( 5 In this paper investigations of the effects of RF potential oscillation on the Langmuir probe characteristic p p -I V curve are described, and a simple method for interpreting the plasma parameter data is presented.This method is based on using a time-averaged Langmuir probe p p -I V characteristic, and is very simple, because almost the same probe circuit which is used for DC discharge plasmas can be used.

Experimental Device for Applying a Sinusoidal Voltage to a Probe
The experimental device and measurement system for obtaining a probe characteristic curve is shown in Figure 1(a).The discharge chamber, 23 cm in diameter and 50 cm in length, is situated in a stainless steel vacuum chamber of 60 cm in diameter and 100 cm long, which is evacuated to a pressure of 10 −3 Pa by using a diffusion pump and a rotary pump.A probe tip has a plane circular surface of 3.5 mm in diameter and is spotwelded to a copper wire lead of a 50-Ω semi-rigid coaxial cable which is sleeved within a glass tube.This probe, collecting electrons on both sides, is put at the position of a radius of 3 cm.A magnetic field ( ) is added so that the high energy-tail electrons from a cathode of 2 cm in diameter cannot arrive at the probe.
The probe is biased by two dry batteries of 90V in order to prevent 50 Hz signal from spreading over the probe and discharge circuit.In addition to a DC bias voltage p V , a In order to receive a high frequency signal from plasma exactly next four items [16] [17] are considered.
1) A 50 Ω metal film resistor is put between a discharge tube and the ground.This resistor is used to match the characteristic impedance of the 50-Ω coaxial cable.The signal from plasma is received by this resistor.
2) Three lead storage batteries connected tandemly for DC discharge is put on a wooden desk.This is because the capacitance does not evolve between the batteries and the earth.
3) The power supply (P.S.) for heating the barium oxide (BaO) cathode which diameter is 2 cm is separated from the measurement circuit.
4) Sinusoidal voltage provided by a function generator is applied to a probe using a 50 Ω metal film resistor instead of a coupling transformer [2].

Time-Averaged Probe Characteristic Curves
Time-averaged probe p p -I V characteristics, which have been already reported in Refs.[18] [19], are shown in Figure 2. All of characteristics shown by dotted lines are the same p p -I V curves obtained at p1 0 V V = .From a semi-log plot of their electron currents e I space potential s0 5.6 V V = , electron temperature e 1.5 eV T = and electron density  not clear as pointed by short arrows, and their potentials seem to approach to the potential s0 V .For V V V < − of the time-averaged curve (solid line) gives the same value without depending on the applied frequency f as described in the item (C).
It is also confirmed that e T is independent of the amplitude p1 V .

Frequency Dependency of Inflection Points
Figure 3 shows frequency dependency of potential difference pd V between two inflection points observed on a time-averaged p p -I V curve, as described in Figure 2 for shown in Refs.[1] and [3].In the case of pi pi 10 f f f < < , however, pd V becomes small as frequency rises.Finally, in the case of This phenomenon occurs due to the slow motion of ions, being not able to follow the change of the high-frequency electric field within the probe-plasma sheath [20].The phenomena to occur at frequency more than pi 10 f are different from the theoretical results reported in References [1]- [3].  the lower one is equal to −1.9 V, which is also equal to s0 p1 V V − .In other words, the potential difference between these points equals the amplitude p1 7.5 V V = of the RF voltage applied to the probe.In addition, the electron saturation current sat I at the upper inflection point at s0 V is almost equal to that in the case of p1 0 V V = (dotted line).Further, the same electron temperature of e 1.5 eV T = can be estimated from two parallel straight-lines fitting to the semi-log plots in the retarding potential range . Therefore, It was confirmed that Equation ( 5) could be even applied to the case of the high frequencies more than pi f .Therefore, all plasma parameters including p1 V can be measured from the semi-log plots shown by opened circles in Figure 4.
The potential difference dif V between upper and lower inflection points measured from the semi-log plot of the time averaged e p -I V curves (see Figure 4) is plotted as a function of p1 V at 10 MHz f = , as shown in Figure 5.Both dif V and p1 V are normalized by e T which is also measured from the slope of the semi-log plot of the time averaged e p -I V curves.Here, cross symbols are obtained from a DC plasma of ).In all cases, the condition V are well agreed with each other in a wide voltage range.Therefore, p1 V can be measured precisely from dif V .

Time-Resolved Probe Characteristic Curves
The experimental setup with a sampling convertor for obtaining a time-resolved probe characteristic curve is shown in Figure 1(a).An oscillating current flowing in a probe is inputted into the sampling converter.The characteristic curve at each time phase is drawn on the X − Y recorder by changing the probe voltage p V with fixing outputphase of the sampling comverter.
Probe characteristic curves at each time phase are shown in Figure 6, where p1 V is 6.0 V. Plasma parameters are e 1.7 eV T = , 2V in Figure 6.There are four features in the probe current shown in Figure 6.First, the probe currents oscillate with the applied voltage in phase.This means that in this probe circuit only conduction current flows, but displacement current does not flow.Second, for p s0 p1 + , the amplitude of probe current at 10 MHz is larger than that at 30 kHz.This phenomenon will be discussed in section 5. Third, at 0, π and 2π t ω = , oscillating potential difference between the probe and plasma becomes 0 V, so that two characteristic curves shown by a dotted line and a solid line overlap each other.These curves also agree with a curve in the case of p1 0 V V = .
In other words, one can obtain exact plasma parameters mentioned above by using the curves at 0, π and 2π t ω = without any effect from RF electric field.It is also indicated that the time-averaged characteristics curve shown by dotted lines has two inflection points as shown in

Experimental Device for Drawing Plasma Characteristics
The experimental device and circuit for obtaining a probe characteristic in RF plasmas with space potential oscillation by using a DC-biased probe is shown in Figure 1(b), where the cylindrical chamber is grounded.RF discharge at 8.2 MHz is carried out.The experiment is performed in a cylindrical chamber of 23 cm in diameter and 50 cm in length with an cylindrical electrode (22 cm in diameter) to which RF power of 200 W is applied via matching unit.Argon is used as a working gas at pressure of 0.133 Pa.
Background pressure is 10 −3 Pa.A tantalum probe same as what is used in Figure 1(a) is placed in the center of the device.It was movable in the axial direction.The output voltage of plasma generator, which is suppressed to a one-tenth by an attenuator, is inputted to a trigger terminal of the sampling convertor.

Time-Resolved Probe Characteristic Curves in RF Discharge Plasmas
Time-resolved probe characteristic curves are shown by solid lines in Figure 7, where a time-averaged probe curve V V V > + has a large amplitude, similar to the results in Figure 6.This phenomenon will be also discussed in Section 5.     ( ) From this figure, it can be also measureed that V ∆ defined by Equation ( 4) is 11.74 V. By substituting 11.74 V V = ∆ and e 7.4 eV T = into Equation (4), p1 22.2 V V = is obtained.This value is almost equal to s1 22.0 V V = .Therefore, it is confirmed that Equation ( 5) can be also applied to RF plasmas.It should be noted that the inflection point method presented here is quite easy to obtain s1 V than a method using Equation (4).
From the technique described above, plasma parameters of RF plasmas can be easily obtained by using almost the same probe circuit as used for DC discharge plasmas, by combining a Microsoft Visual C++ software and a personal computer controlled Source Meter-2400 manufactured by Keithley Instruments.This technique is very convenient and useful for the measurement of plasma parameters of RF plasmas efficiently.

Comparison with Other Measurement Methods
As shown in Section 3, plasma parameters of RF discharge plasma were measured easily by a semi-log plot of the time-averaged characteristic curve of Langmuir probe.In order to ensure the reliability of the data provided by the probe method above, it is necessary to compare the plasma parameters with those provided using measurement procedures based on different principles.The comparison experiments were carried out for existence of inflection point at s0 s1 V V + , validity of electron temperature e T , and the mechanism of electron current enhancement and suppression at 3π 2 t ω = and π 2 , respectively, in RF plasmas (see Figure 7).

Inflection Point Measurement with Emission Probe Method
Emission probes were employed to measure the space potential of DC discharge plasma exactly [22] [23].A few researchers reported the methods for measuring the amplitude of plasma space potential by using the inflection point technique [24]- [26].Here, emission probe method is employed to confirm the existence of the inflection points at 1.5 10 cm − × , respectively.A conventional emission probe made of tantalum hair pin wire of 0.125 mm in diameter is employed in order to measure the amplitude of the RF fluctuation of space potential.The emission probe is covered with an alumina tube with outer diameter of 2 mm with two holes, except for the probe tip [22].The filament heating current is maintained by a lead storage battery to prevent 50 Hz signal from spreading over the probe and discharge circuit.Time-averaged characteristic curves of the emission probe are shown in Figure 10.In the case of probe heating current h 0 A I = , the curve similar to that plotted by dotted curve in Figure 7 is obtained.Therefore, the inflection point appears at one point tained from the semi-log plot of the time-averaged electron current.However, in the cases of h 1.06 I = and 1.12 A there appear three inflection points in both curves as pointed by arrows.The voltage of the middle point is the same as that in the case of h 0 A I = . The potential difference between upper and lower points is 40.2V as shown in Figure 10 and it is almost equal to 39.6 V which is twice of the amplitude of the space potential 19.8 V. Therefore, it is confirmed experimentally that s0 V and s1 V obtained from the emission probe method well agree with the values provided by the Langmuir probe method shown in Figures 7-9.

Electron Temperature Measurement with Ion Acoustic Wave Method
Ion acoustic wave method is one of the useful ways for obtaining an electron temperature in RF discharge plasmas [27]- [30].The plasma generation and the measurement system for ion acoustic wave are shown schematically in Figure 11.They are housed in a stainless steel vacuum chamber with an inner diameter of 60 cm and a length of 100 cm.This reactor, 7 cm in diameter and 12 cm in length, is the same as that shown in Figure 1 of Ref. [31] except that plasma is produced by an RF discharge.A cylindrical Langmuir probe P (diameter 0.6 mm, length 1.8 mm made of tantalum wire) is spotwelded to a copper core wire of a 50 Ω semi-rigid coaxial-cable (outer diameter 2.2 mm), which is sleeved with a glass tube.The gas pressure is evacuated to a pressure of 10 −3 Pa by using a diffusion pump and a rotary pump.Argon plasma is generated by RF (25 MHz) discharge.
A grid electrode G located at the outlet of the RF electrode is used for controlling the electron temperature in the downstream region of plasma [32]- [35].The grid G (16 mesh/in.) is made of 0.29-mm-diameter stainless steel wire and installed on a 4.2-cmdiameter aluminum ring flame which is connected to the earth using capacitors which exhibit low impedance to RF while allowing DC biasing of this electrode [32].These capacitors are not shown in Figure 11.
Ion acoustic waves are excited by an exciter (Exc.: 20 mesh/in., 2-cm diameter) and detected by a movable detector (Det.: 8 mesh/in., 1.5-cm diameter).Exc. and Det. are made of a grid of the stainless steel wire of 0.29 mm in diameter.The frequency of ion acoustic wave is changed by a low frequency (LF) oscillator between 50 kHz and 300 kHz.Argon pressure is 0.67 Pa.A magnetic field of is applied in order that axial electron density distribution becomes uniform and the ions suffer one-dimensional compressions in the plane waves [36] [37].A wave pattern is drawn on the X − Y recorder through a lock-in amplifier.
The dispersion relation given by Equation ( 6) for ion acoustic waves is derived from a fluid theory under the conditions ( ) Here, ex , f λ and s C are frequency, wave length, and velocity of the ion acoustic wave, respectively [38].Using argon gas, in the case of e i 1 T T  , this expression is re- ferred to Equation ( 7) Here, the units of λ , e T , and ex f are cm, eV, and kHz, respectively.Therefore, electron temperature e T can be derived by measuring the wave length λ of the ion acoustic at the frequency ex f .
Wave patterns at ex 100 kHz f = for G 0 V V = and −40 V are shown in Figure 12.
The wavelength of the ion wave becomes short with a drop of V G .The wavelengths at and −40 V are 2.0 cm and 1.25 cm, respectively.From this result, the electron temperature at G 0 V V = is calculated to be 1.64 eV by substituting ex 100 kHz f = and 2.0 λ = cm in Equation (7).The relations between ex f and 1 λ in the cases of grid voltage V G = 40 V, 0 V, and −40 V are shown in Figure 13.The slope of the straight line corresponding to the phase velocity of the ion acoustic wave becomes small with a drop of G V .This result indicates that electron temperature drops as G V decreases.
Electron temperatures calculated by the ion acoustic method with Equation ( 7) and measured by the probe method are shown in Figure 14    other.e T decreases from 4.2 eV to about 0.5 eV by a decrease in G V .Since the elec- tron temperatures obtained by two methods well fit each other, it is confirmed that electron temperature provided by the probe method is correct.

Electron Current Variations Using a Square Pulse in DC Discharge Plasmas
Since it was confirmed that probe current response on RF voltage superimposed to DC biased probe in DC plasmas was equivalent to that on DC biased probe in RF plasmas (see Figure 6 and Figure 7), a mechanism on the current enhancement and suppression for ( ) and π 2 , respectively, in RF plasmas (see  , respectively.The disc probe is put at the position of a radius of 3 cm so that high energy electrons cannot arrive at this place.Plasma parameters are obtained, i.e. e 0.64 eV T = , I with initial probe voltage dc V as a parameter.In the case of dc 1.6 V V = − , the pulsed voltage changes from dc 5 V 6.6 In this case, electron current attained immediately to the sta- tionary current without any deformation (see bottom trace).On the other hand, when , the electron current quickly overshoots in the initial response, and such overshooting of the electron current attains the maximum as dc V approaches to s0 V .Further, in this case, after overshooting the electron current dimi- nishes and returns to a minimum value, evolving an amplitude oscillation decaying in time.A period of this oscillation is about 1.71 μs, corresponding to the frequency 0.58 MHz which is lower than pi 2.6 MHz f = .From this pulse experiment, it was known that the electron current increases at  ) of the probe.Therefore, the probe would collect more electrons from the bulk plasma [39].Therefore, probe current becomes larger than that in the steady state, as shown by opened circles in Figure 16(b).On the other hand, at the current minimum time (△) the space potential becomes lower than that in the steady state as shown in Figure 16(a), indicating that there appears a potential minimum dip between z = 0 mm to 1 mm.Because of the formation of this potential dip the probe electron current is much suppressed com-pared to that in the steady state value, as also shown in Figure 16(b) [40] [41].
At the time pointed by square (□) in Figure 16(a), one can also confirm an appearance of the potential dip in front of the disc probe, resulting in a suppression of electron current, although these data are not shown in Figure 16.This result is closely related to the current suppression at 3π 2 t ω = in Figure 6 and at π 2 t ω = in Figure 7.

Discussion
In our experiments using a DC plasma, two phenomena were observed.First, when p V is higher than s0 p1 V V + , the amplitude of the oscillating probe current for 10 MHz was larger than that for 30 kHz, as shown in Figure 7. Second, instantaneous probe current does not depend on the frequency when p V is lower than s0 p1 V V − , where electrons in the ion sheath receive a retarding force during the complete cycle.Let us here discuss why these two phenomena occur.It is convenient for the explanations to divide the range of probe voltage p V into two regions, i.e., p s0 p1

Assumption
In order to explain the two phenomena mentioned above it is necessary to make the following simplified assumptions.1) Electrons do not collide with particles of neutral gas inside the probe sheath.This requirement is reduced to ( ) ( ) where σ is the collision cross section in cm 2 [4].When e 1.16 eV T = and λ .On the contrary, when the sheath thickness becomes larger than c λ by an increase of pressure, collisions of electrons in the probe sheath cannot be ignored.In this case, usual probe theory has to be modified by taking the electron collision into account.
2) For the RF frequencies f in the range electrons can completely follow the oscillating electric field in the plasma sheath, but ions cannot follow at all.Here, pe f is electron plasma frequency.Therefore, nomal sheath in the steady state cannot be formed due to the slow movement of ions at all.When the probe bias voltage ( ) p V t is changed rapidly in a DC plasma, ions move under a time-averaged electric field, similar to the case at π t ω = in Figuer 7. As long as RF frequency f is kept in the range pi pe f f f <  , probe characteristics are not changed as known from the experiments in Section 2. Actually, we confirmed the usefulness of this probe analysis even in the RF discharges at frequency of 13.56 MHz ( [32] [33] [35]).

In the Case of V p (t) < V s0
Temporal variations of potential curves near the probe are drawn schematically in Figure 17 The profiles are drawn on the basis of the results in Figure 16.
around s0 V under the constant probe voltage p s0 s1 V V V > + as schematically shown in Figure 17(c).When the space potential rapidly increases from s0 V to s0 s1 V V + between 0 t ω = and π 2 t ω = , such an abrupt drop of acceleration voltage for the electrons causes slowing down of electron speed, which causes a stagnation of electrons near the probe, and a resultant formation of a negative potential dip, as observed in Figure 16(a).Then, the electron current is suppressed, compared to the case of 30 kHz as shown in Figure 7. On the other hand, when the space potential rapidly decreases from s0 V to s0 s1 V V − between π t ω = and 3π 2 t ω = , such speed-up electrons causes a relative lack of electrons near the probe, which results in an increase in the space potential, and hence resulting in a spread of the sheath width as shown in Figure 16(a).Then, more electrons are collected by the probe and the probe electron current is enhanced compared to the case of 30 kHz as shown in Figure 7.
It is clarified that when p V is higher than in RF discharge plasma, RF current with large amplitude flows into the probe as shown in Figure 7.It is also clear that when p V is lower than s0 s1 V V − , the same RF current as shown in Figure 17(a) flows into the probe because it is decided by a potential difference ( ) s p V t V − .

Conclusions
Langmuir probe characteristic curve is examined under an influence of relative oscillating potential difference between the probe and the plasma.Sinusoidal potential p1 V ranging from 30 kHz to 10 MHz with amplitude p1 V from 0 V to 7.5 V is first applied to the probe in a direct-current (DC) discharge plasma.In the case of low frequency, which is very lower than ion plasma frequency pi f , the time-averaged probe characteristic curve has two inflection points at s0 V .It was also confirmed that the electron temperature e T is constant regardless of the frequency f and the amplitude p1 V .
These results are applied to RF discharge plasma with oscillating space potential to measure the plasma prameters by using a DC-biased Langmuir probe.As a result, it was confirmed that similar probe characteristic could be obtained in RF discharge plasmas.The amplitude of space potential oscillation s1 V , obtained from the potential difference between two inflection points on the semi-log plot of the time-averaged V V V > + in RF plasmas is clarified by the square pulse experiment.The method using a single Langmuir probe with a semi-log plot of time-averaged e p -I V curve is useful and convenient for measuring electron temperature e T , electron density e n , time-averaged space potential s0 V , and amplitude of space potential oscil- lation s1 V in RF plasmas with a frequency of the order of pi pe 10 f f f < < . This technique mitigates a great deal of troublesome measurement of plasma parameters in RF discharge plasmas.
in Ref. 3].As a result, following conclusions were derived.(A) Inflection points appear at two places of s0 p1 ) was provided [see Figure 2 in Ref. 1].

Figure 1 .
Figure 1.Experimental device and electric circuit for (a) DC and (b) RF discharges and for obtaining time-averaged and time-resolved probe characteristic curves with a sampling convertor.
Time-averaged p p -I V curves at f = 30 kHz, 0.6 MHz, and 10 MHz for p1 7.5 V V = are also shown by solid lines in Figures 2(a)-(c), respectively.For long arrows (see also Refs.3, 4 and 5).In this case, the same e T from the two p p -I V curves as expressed by Equation (5) can be obtained.However, for pi 0
these points are completely shifted to s0 V as shown in Figure 2(c).These phenomena are different from the results re- ported in Refs.3, 4 and 5. On the other hand, one can see that in the regime averaged curves shown solid lines are the same form in all cases in Figure 2. Therefore, it can be confirmed that electron temperature e T pro- vided from the range p s0 p1

Figure 4 Figure 3 .
Figure 4 shows semi-log plots of time-averaged electron currents shown in Figure 2(c).In the case of p1 7.5 V V = , two inflection points appear on the semi-log plot of the time-averaged electron current e p -I V , as shown by opened circles.The potential of the upper one is equal to the DC plasma space potential s0 5.6 V V = .The potential of

Figure 4 .
Figure 4. Semi-log plots of the time-averaged probe characteristic e p -I V curve shown in Figure 2(c).Closed and open circles correspond to the case of p1 0 V V = and 7.5 V, respectively.
in the case of 30 kHz are shown by dotted lines.On the other hand, curves in the case of 10 MHz ( as shown in an inset in Figure6.f1 V and f 2 V are floating potentials at π 2 t ω = and 3π 2 in the case of f = 30 kHz.Potential difference f 2 f1 V V − is equal to p1

Figure 5 .
Figure 5. Variation of normalized potential difference dif e V kT between upper and lower in- flection points on a semi-log plot of the timeaveraged probe characteristic curve as a function of normalized amplitude p1 e V kT applied to the probe.Three symbols are explained in the text.10 MHz f = and Ar 0.133 Pa P = .

Figure 6 .
Figure 6.Time-resolved probe characteristic curves at each time phase for 30 kHz (dotted lines) and 10 MHz (solid lines).Inset schematically shows the time phase of applied voltage to the probe.Here, voltage amplitude p1V is 6.0 V, and pi 3.1 MHz f = .

Figure 2 (
Figure 2(a).Fourth, in the retarding range p inset in Figure 7. Here, s1 V is the amplitude of RF space potential.RF potential difference between the probe and plasma vanishes at 0, π and 2π t ω = , so that e T , e n , and s0 V can be obtained from the characteristic curves at these time phases as mentioned in Figure 6. e 7.4 eV T = , s0 48.5 V V = are obtained.The time-averaged probe curve shown by dotted line has only one inflection point at p s0 V V = as also shown in Figure 2(c).Time-resolved curves shown by solid lines have also inflection point at p s0 V V = .The oscillating probe current for p s0 s1

Figure 7 .
Figure 7. Probe characteristic curves in RF discharge plasma at each time phase.Inset schematically shows the time phase of space potential.Ion plasma frequency is pi 1. Hz 0 M f = and RF frequency is Hz 8.2 M f = .

3. 3 .Figure 8 1 
Figure 8 shows semi-log plots of time-resolved electron current e I of the probe at four time phases; i.e., 3π 4, π,5π 4 and 3π 2 t ω =.The experimental condition is the same as that in Figure7.Because an RF electric field does not exist at π t ω = , the time-resolved curve has only one inflection point at p

Figure 8 .
Figure 8. Semi-log plots of time-resolved e p -I V characte- ristic curves at each time phase in RF plasma.pi 1. Hz 0 M f = and Hz 8.2 M f = .

Figure 9 .
Figure 9. Semi-log plots of electron currents and to verify the presence of lower inflection point at s0 s1 V V − on the semi-log plot of time-averaged probe characteristic curve in RF plasmas.The experiment was performed in the RF discharge tube shown in Figure 1(b).Ar P , e T , and e n are 0.67 Pa, 6.6 eV, 9 3

s0V.Figure 10 .
Figure 10.Time-averaged emissive probe e p -I V curve with heating current h I as a parameter.Allows show inflection points of the curves.s0 V is time-averaged space potential of the RF plasma.pi 1. Hz 56 M f = and Hz 8.2 M f = .

Figure 11 .
Figure 11.Experimental apparatus for a measurement of ion acoustic wave pattern with an exciter (Exc.) and a detector (Det.).P is a probe for Te measurement.G V is DC grid voltage for controlling the plasma flow.RF and LF provide RF discharge frequency 25 MHz f = and wave excitation frequency ex f , respec- tively.
as a function of G V by closed and open circles, respectively.Both electron temperatures are well agreed with each

Figure 12 .
Figure 12.Typical wave patterns at ex 100 kHz f = , measured by lock-in amplifier with DC grid voltage G V as a parameter.Ion plasma frequency is pi 1.7 MHz f = and RF discharge frequency is 25 MHz.

Figure 13 .
Figure 13.Relations between ex f and inverse of ion acoustic wavelength 1 λ with DC grid voltage G V of 40 V, 0 V, and −20 V. pi 1.7 MHz f = and f = 25 MHz.

Figure 14 .
Figure 14.Electron temperatures e T calculated from Eq- uation (7) (closed circles) and measured by a probe method (open circles) in RF plasmas, as a function of the DC grid voltage G V .pi 1.7 MHz f = and f = 25 MHz.

Figure 7 )
Figure 7) was investigated by using a square pulse voltage superimposed to DC probe voltage in DC plasma in an experimental apparatus shown in Figure 1(a).Rise time, time width, and amplitude of the square pulse voltage pu V are 0.05 μs, 10 μs, and ±5 V, respectively.The rise time 0.05 μs is equivalent to a quarter period of 5 MHz signal.This pulse voltage is applied to the DC biased probe voltage dc V .Therefore, the voltage of the disc probe changes from dc 5 V V − to dc 5 V V + [19].When pu 0 V V = , the characteristic p p -I V curve of the disc probe is shown in Figure 15(a) under the condition that Ar P and B are 0.133 Pa and pi 2.6 MHz f = .Figure 15(b) shows temporal variations of probe current p Figure 15.(a) Characteristic curve of a disc probe at pulse height of pu 0 V V = .(b) Temporal variation of electron current of the disc probe with dc V as a parameter.pi 2.6 MHz f = .

Figure 16 .
Figure 16.Axial z distributions of (a) space potential Vs and (b) saturation current ratio

.
On the other hand, electron collision mean-free path becomes c 1 mm λ  at Ar 133 Pa P = .Therefore, when Ar P is lower than 20 Pa, sheath thickness of several times D λ becomes much smaller than c

Figure 17 .
Figure 17.Schematic of space potential profiles s V near the probe in the cases of (a) p s0 p1 V V V < − in DC discharge plasmas, (b) p s0 p1 V V V > + in DC discharge plasmas, and (c) the other hand, in the case of high frequency which is higher than pi f , there appears two inflection points at s0 V and s0 p1 V V − on a semi-log plot of time-averaged e p -I V curve.Upper inflection point coincides with the space potential s0 V of DC discharge plasma, which is the same space potential at 0, π and 2π t ω = of the time-resolved p p -I V curve.Electron saturation current at upper inflection point well coincides with that of p1 0 V V = .Therefore, electron density can be derived from the electron saturation current at the upper inflection point.Potential difference between upper and lower inflection points on a semi-log plot of the time-averaged e p -I V curve shows the amplitude p1 curve in RF discharge plasmas, was confirmed by an emissive probe method.The electron temperature e T in RF plasmas is confirmed by using the ion acoustic wave method.Both electron temperatures are well agreed with each other between 4.2 eV to 0.5 eV.The mechanism for the electron current enhancement and suppression for p s0 s1