Inversion of the Electron Energy Distribution in Hollow Cathode Glow Discharge
I.A.Soloshenko, V.Yu.Bazhenov, V.A.Khomich, V.V.Tsiolko, A.F.Tarasenko,
A.G.Terent’eva, A.G.Kalyuzhnaya, A.I.Shchedrin
Institute of Physics of National Academy of Sciences of Ukraine, 46 Nauki Ave., 03028, Kiev, Ukraine,
Abstract. Experimental and theoretical studies of the electron energy distribution function (EEDF) in glow discharge with
hollow cathode in the mixture of N2 and SF6 are accomplished. It is shown that at adding of 5-6% SF6 to nitrogen, electron
concentration at inverse region of EEDF (2-4 eV) increases by about one order of magnitude. The reason for such effect
consists in intensive adherence of low-energy electrons to electronegative molecules which promotes the decrease of their
amount in the discharge and, consequently, the increase of relative amount of electrons in the inverse region.
Keywords: hollow cathode, EDF, inversion, sulfur hexafluoride.
PACS: 52.80.He, 52.25.Dg.
The phenomenon of inverse electron energy distribution function (EDF) in low-temperature plasma is of
considerable interest because such media can be used for obtaining inverse population of the atomic and molecular
electron levels. The results of our previous experimental and theoretical investigations  showed that such
distribution can be realized in hollow cathode (HC) glow discharge in nitrogen. The EDF inversion in pure nitrogen
is related to certain features of the interaction of N2 molecules with electrons. In the region 2 – 4 eV electrons quite
rapidly lose their energy for the excitation of vibrational levels of nitrogen molecules, which results in the
appearance of a trough in the corresponding region of the EDF. Unfortunately, the absolute majority of electrons
occur in the region of lower energy (< 2 eV), and their density in the region of EDF inversion in rather insignificant.
In  we theoretically predicted the possibility of increasing the fraction of electron in the region of EDF inversion
by adding a small amount of electronegative gases (SF6 or CCl4) into nitrogen. It was suggested, that the attachment
of low energy electrons to the electronegative molecules would lead to a decrease in the number of such electrons in
the discharge and, accordingly, to an increase in the relative fraction of electron with higher energies including those
corresponding to the region of inversion.
This paper presents the results of experimental investigation of the EDF in a mixture of N2 and SF6 and
theoretical calculation using parameters corresponding to the experimental conditions.
EXPERIMENTAL SETUP AND MEASUREMENTS RESULTS
The experiments were carried out with the hollow cylindrical cathode 280 mm in diameter and 400 mm in length.
A 230 mm-diameter anode was placed near one end of the cathode. The hollow cathode was evacuated by a
forepump to a residual pressure of ≈2× 10-3 Torr. Since pumping rate was virtually independent of the pressure in
the range from 2 × 10-3 to 2× 10-1 Torr, the working mixture of N2 and SF6 in the hollow cathode was prepared using
the follow procedure. After evacuation of HC to residual pressure, the necessary amount of SF6 was introduced and
the HC was filled with N2 to total pressure of 0.1 Torr. The partial pressure of SF6 in our experiments was varied
within (1-10)× 10-3 Torr, which amounted to 1-10% of total gas pressure. The plasma density and EDF were
measured with the use of Langmuir probes, which were made of a tungsten wire with diameter of 50-100 μm and
had a charge collector length of 10-12 mm. The probes could be moved in the radial and axial direction. In order to
eliminate the influence of surface contamination on the current-voltage (I-V) characteristics of the probes, they were
cleaned after each measurement by heating up to 8000C.
The I-V curves were measured using an automated system controlled by a personal computer provided with a
special software. The system provided programmed variation of the probe current (which was set with an accuracy
of 0.1 μA) and simultaneously measured the probe potential (relative to anode), the anode voltage and the discharge
current. The results of measurements were digitized and stored in the computer memory in the form of an I-V curves
for a given discharge current and voltage. The measurements at the fixed set of parameters were repeated up to 30
times and obtained data were averaged. The plasma potential was determined as corresponding point where the
second derivation of probe current with respect to the voltage was zero.
During the EDF measurements, the systematic error in the region of small electron energies (≤0.2-0.3 eV) was
decreased using the method based on the combination of the first and second derivatives of electron current to the
probe . In this case, the EDF had the following form:
( ) 1 ( “( ) ‘ ( ) )
0 f eV C j eV j eV eV e e
≈ − Ψ
where 0 C is the normalization constant, e j is the density of the electron current to the probe, V is the potential
relative to the plasma potential, γ λ i 0 Ψ = ac is the diffusion parameter of the probe, a is the probe diameter, λ
is the electron mean free path, c ln( l 4a) i = π , l is the probe length and 4 / 3 0 γ = (for a << λ ). For
determination of the derivatives we used the total current to the probe instead of electron current, because
estimations had shown that the contribution of ion current to total probe current could be ignored in the range of
energies up to ~ 10 eV.
The partial pressure of SF6 in our experiments
did not exceed 6× 10-3 Torr. Higher densities of this
gas in the discharge plasma led to the excitation of
intense relaxation oscillations with frequencies in
the range from 10 to 105 Hz, which hindered correct
measurements of the plasma characteristics. The
introduction of SF6 into nitrogen led to an increase
in the discharge voltage. In pure N2, the discharge
voltage was 520-540 V at the discharge current 1 A.
In a mixture of N2 with SF6 at a partial pressure of
6× 10-3 Torr the discharge voltage for the same
current reached 700-800 V. The presence of SF6 in
the gas mixture also led to an increase in the
electric field strength in the discharge plasma: at
partial pressure of SF6 on a level of (5-6)× 10-3 Torr
the longitudinal electric field strength reached
≈0.1 V/cm, which was almost ten times as strong as
the value in the case of pure N2. The radial electric
field Er also exhibited an increase and moreover the
radial field profile became more complicated as
compared to that in the pure nitrogen plasma
(Fig.1). In this figure the dependencies of radial
electric field on the system radius are presented for different partial pressures of SF6. One can see from the figure
that SF6 adding leads to rapid growth of radial electric strength Er in the paraxial region and at the periphery of
discharge plasma, whereas in the intermediate region Er growth is essentially smaller. At SF6 partial pressure of
4× 10-3 Torr, Er reached ≈ 0.5 V/cm in paraxial region
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