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A STUDY OF THE ELECTRON ENERGY DISTRIBUTION FUNCTION IN THE CYLINDRICAL MAGNETRON DISCHARGE IN A R G O N A N D X E N O N * ) J . F . BEHNKE, E. PASSOTH, C. CSAMBAL Institute of Physics, Faculty of Mathematics and Natural Sciences, Ernst-Moritz-Arndt University, Domstrasse 10a, 17487 Grei£swald, Germany M. TICH~', P. KUDRNA Department of Electronics and Vacuum Physics, Faculty of Mathematics and Physics, Charles University, V Hole~ovi~k~ch 2, 18000 Praha 8, Czech Republic D. TRUNEC, A. BRABLEC Department of Physical Electronics, Faculty of Natural Sciences, Masaryk University, Kothifsk~ 2, 61I 37 Brno, Czech Republic Received 7 May 1998; final version 5 August 1998 We studied the behaviour of the cylindrical magnetron discharge in argon and xenon. We concentrated ourselves mainly on description of the transport of charge carriers in the region from the negative glow to the anode. We attempted to describe this transport using Monte-Carlo simulations as well as by standard transport parameters, mobility and diffusion coefficients. We also experimentally determined the radial shape of the electron energy distribution function (EEDF) including its detectable anisotropy caused by the presence of magnetic field. For the EEDF determination we used the planar probe whose collecting surface was adjustable at different angles to the direction of the magnetic field as well as movable in radial direction. The results of modelling and experiment are discussed. Introduction The low-temperature-plasma-aided creation and etching of thin films are very important parts of plasma-chemistry, due to their broad practical applications. Important drawback of many plasma enhanced surface treatments is the comparatively low growth and/or etch rate compared to classical chemical or electrochemicM processes. Many technological applications of the low-temperature plasma to the creation and etching of thin films make use of magnetic field that-helps the plasma confinement and increases growth and/or etch rate. The magnetic field in these systems can be either non-homogeneous (created typically by permanent magnets; one example is the planar unbalanced magnetron) or nearly homogeneous (created by coils) and its strength does not usually reach too high values. Cylindrical Langmuir probe is often used as a diagnostic tool in such systems. It makes possible to estimate the plasma parameters (plasma density, electron temperature and/ or *) Dedicated to Prof. Jan Jan~a on the occasion of his 60th birthday. CzechosloVak Journal of Physics, Vol. 49 (1999), No. 4

483

J.F. Behnke et

al.

EEDF) at the probe position. Planar probe can also be used for estimation of the anisotropy of plasma parameters. The collection of charged particles by the probe is, however, influenced by the presence of magnetic field. The effect of the magnetic field on plasma density estimation has been studied by many authors; an overview is given e.g. in [1, 2]. It has been shown that the effect of magnetic field on the collection of charged particles by cylindrical or spherical probe depends in general on the following two similarity parameters: - on the ratio/~e.i of probe radius to the mean Larmor radius, j3e,i = rp/re,iL, where the mean Larmor radius re,iL for electrons (ions) with Maxwellian temperature Te,i is given by re,iL = (1/qoB)v/½1rrne,ikBTe,i, where q0 is the elementary charge, B the strength of the magnetic field, rne,i mass of electron (ion) and ks the Boltzmann constant and - on the ratio B/p, where p is the working pressure. The first parameter directly relates to probe dimensions, the second one is connected with the degree of plasma anisotropy caused by the magnetic field. It is known that the diffusion coefficient of charged particles across the magnetic field lines, De,i±, is reduced as an action of the magnetic field. Most influenced are light electrons, for which holds: De± = De0/(1 +Y2~re2n) with De0 = Vt2hren, where ~e = qoB/me, ten = l/Yen and Vth are the electron cyclotron frequency, electron-neutral collision time and electron thermal velocity, respectively [2]. In case of ~2eT"en >> 1 (magnetised plasma at low pressures), which is the case of most plasmas used in technology, 2 2 the expression for De± reduces to De± ~ Vth/~2eren = r~/ren. In other words in direction perpendicular to the magnetic field the effective mean free path of electrons is roughly equal to the Larmor radius. Similar consideration holds for ions; their movement is, however, influenced by the magnetic field much less than that of the electrons. The Langmuir probe can be, in particular cases, used to assess the effect of the magnetic field to the investigated plasma. Anisotropy of the electron temperature in a magnetic field has been studied e.g. in [3-5]. Of those we shall briefly mention that by Aikawa [4]. He used two Langmuir probes to determine perpendicular and parallel components of the electron temperature, what represents the first approximation of a direction-resolved probe diagnostic. He also developed a simple theory for collection of charged particles by the probe under influence of the magnetic field. He obtained both components of the electron temperature, TII and T±, by the "conventional" method, i.e. from the slope of the semilogarithmic plot of the probe characteristic in the electron retarding regime. The temperature TII has been estimated from the current drawn by the planar probe with its surface perpendicular to the B-field-lines, T± from the characteristic of the cylindrical Langmuir probe with its axis parallel to the B-field-lines. It is interesting that the Aikawa-theories for cylindrical and planar probe are selfconsistent. Both yield the same values for space potential and plasma density, while the cylindrical probe indicates T± and the plane probe indicates Tll. His results show that with 484

Czech. J. Phys. 49 (1999)

A s t u d y of the electron energy distribution function ...

increasing the ratio B/p the T±/TII ratio increases from 1 to several units. In other words, the magnetic field influences the anisotropy of the EEDF. In our article we attempted to study directly the EEDF in magnetised discharge plasma by using the direction-resolved probe diagnostic as described below. Theoretical considerations In order to get insight into the motion of electrons in a cylindrical magnetron, the trajectories of electrons were simulated using standard Monte-Carlo method (see [6] and references therein). The discharge vessel of the cylindrical magnetron is schematically depicted in Fig. 1. The electrons started from cathode with Maxwellian

E °l

E o

o

Fig. 1. The discharge vessel of the cylindrical magnetron. energy distribution with the mean energy 2kTg (Tg is the neutral gas temperature). The classical equations of motion for electrons were solved numerically using RungeKutta method. The variation of electric field strength with the radial position r is given by a linear dependence in the cathode fall region and by the slowly changing profile in the positive column region. The null collision technique was used for the simulation of the free flight time. The total cross section for electron-argon collisions was taken from [7,8], the total and differential cross-section for elastic collisions from [9]. The excitation collisions were described by one total excitation cross section, derived from values in [10]. The ionisation cross section was taken from [11]. The electron energy remaining after an ionisation collision is shared between old and new electron with uniform distribution. The Coulomb electron-electron and electron-ion collisions were not taken into account. Czech. J. Phys. 49 (1999)

485

J.F. B e h n k e et al.

The typical trajectories of one electron in the cylindrical magnetron at two different pressures are shown in Fig. 2. The trajectory in Fig. 2a would eventually reach the anode; the calculation has been stopped due to very long calculation time. The circles in figures represent the cross-sections of the cathode (inner circle) and anode (outer circle) of the cylindrical magnetron discharge. It is seen t h a t under the men-

I

I

I

I

-3

-2

-I

o

I

I

I

I

I

1

2

3

-3

radial coordinate [cm]

t

I

I

I

I

I

I

-2

-1

0

1

2

3

radial coordinate [cm]

Fig. 2. The typical trajectories of o n e e l e c t r o n in the magnetron for first 300ns. Anode voltage U = 500V, intensity of magnetic field B = 20roT, the pressure of neutral gas p = 6 Pa (a) and 0.5 Pa (b).

tioned assumptions and lower pressure (Fig. 2b) the electrons are not likely to reach the anode at all. The presented theoretical results, however, do not correspond to the experimental facts, since in reality the discharge in the cylindrical magnetron can be ignited in a wide range of pressures and magnetic fields. The experimental facts can be summarised as follows: - Stable DC discharge can be ignited up to magnetic fields around 20 m T in all the investigated pressure range, i.e. from 0.5 Pa up to 6 Pa. - Above a certain magnetic field around 20 m T the discharge starts to be unstable. - This phenomenon does not depend significantly on the rare gas used (we used argon, krypton and xenon). The obvious discrepancy between the model and reality cannot be most probably explained by the presence of the e-e collisions which were not taken into account in the above model. Also, the slightly elevated gas t e m p e r a t u r e (370 K), found in the cylindrical magnetron discharge by optical spectroscopy [1], is not sufficient to explain it. On the other hand, preliminary evaluations of the E E D F from probe measurements made in [12] indicated the presence of non-Maxwellian E E D F in the 486

Czech. J. Phys. 49 (19g9)

A study of the electron energy distribution function ... discharge. For this reason we decided to study the EEDF in the cylindrical magnetron discharge experimentally in more detail. Since the literature data mentioned in the Introduction indicate the possibility of the presence of the anisotropy of EEDF in plasma in magnetic field, we decided to employ the experimental method that enables to determine the anisotropy of EEDF along the selected direction. E x p e r i m e n t a l m e t h o d for a s s e s s m e n t o f t h e a n i s o t r o p y o f t h e in a m a g n e t i c field

EEDF

There exist many papers that are devoted to the probe studies under variotis experimental conditions, e.g. [13-16], under the assumption that the EEDF is isotropic. For experimental study of the anisotropy of the EEDF, the method suggested by Mesentsev et al. [17-24] and by Klagge and Lunk [25] is proposed. A planar probe that can be rotated along the axis perpendicular to the normal to the probe surface is used in this method. The method is based on the expansion of the electron velocity distribution function (EVDF) into a series of spherical (Legendre) polynomials oo

f(v, O) = E

fi(v)P,(cos O) ;

(1)

i=0

here O represents the angle with its vertex at the probe position in the plane given by the preferred direction and the normal to the planar probe surface. The coefficients in the expansion series fi can be determined from the measurements by the planar Langmuir probe at different angles to the preferred direction. Basic assumptions for the implementation of the procedure are: -

collision-less movement of the particles collected by the probe inside the probe sheath,

- negligibility of reflection and secondary emission of electrons from the probe, - cylindrical symmetry of the EVDF around the preferred direction. Ill applying this procedure to the determination of the anisotropy of the EEDF in a magnetic field, the preferred direction is represented by the direction of the magnetic field vector. Generally one obtains so many coefficients fi for the EVDF expanded into Legendre polynomials as the number of probe positions used. The accuracy of the determination of the probe data does not tisually allow to determine more than the first two or three coefficients of this expansion, the first one being the isotropic one, the second one characterising the drift and the third one characterising the second order anisotropy. For determination of the first three coefficients we need the second derivative of the probe characteristic measured at three angles, 0°, 90°, and 180° , to the preferred direction, see Fig. 3. Czech. J. Phys. 49 (1999)

487


Preferred dlmecUon 0°

90 °

180 °

Fig, 3. Possible orientation of the planar probe. F r o m the probe data we get the required quantities as follows: 1. The electron density

1 2~mei 7 ,-- ,, ¥ =u ~ J

0

2. The isotropic part of the electron velocity distribution function (EVDF) ( 2q~ 2meV F0 \ V me ] = ~ (

.I,,

0 +4I~'0 +Ii's0)

or the isotropic part of EEDF 1 2m/2--~eV 1

Io(qoV) = aV

,,

+ 4I 'o +

3. The first order anisotropy of the EEDF

fl(qoV)= ~ 1S ~ ]2m]~V ~~ g x ( q ° V ) '

gl(qoV)=Gx + ~ 1

i

aide,

qoV i! where G1 = (I~I - 1180), e = qoV. 4. The second order anisotropy of the EEDF

2

f,(qoV) -- 3--~eSV~ g u ( q o V ) , where g2(qoV) = G2 + ~3

1

v~G2de,

G2 = (e L' - 21~'o + Ii~o)

qoV

In these expressions S denotes the surface collecting area of the probe, V is the probe voltage with respect to the space potential. I~~, L" 90, I~180represent the second derivatives of the probe characteristic with respect to the probe voltage obtained 488


A s t u d y of the electron energy distribution function ...

experimentally at the probe plane normal in the angle 0°, 90 °, 180° to the magnetic field lines, respectively. Other symbols have their usual meaning. For detailed description of the procedure with 5 orientations of the Langmuir probe to the magnetic field, see e.g. [18,25]. It is to be noted that the anisotropy of the EEDF in the magnetic field should be regarded in similar manner as the anisotropy of the electron temperature in [4], i.e. as the anisotropy of the electron velocity components. The expansion (1) requires the EVDF to be symmetrical around the preferred direction and hence cannot be used generally. In magneto-plasmas without drift the preferred directions B and - / ~ are equivalent. However, the measurement at O = 0° and O = 180° are advantageous for discharge end-effect studies. In our case of the measurement in a positive column of a DC magnetron discharge, where the electric field is very small, the poloidal asymmetry of the EEDF due to the E x /~ drift could be neglected. Experimental system and results The experiment has been performed on the DC cylindrical magnetron discharge system in the Institute of Physics, University of Greifswald, Germany. The cylindrical magnetron used in this experimental study was similar as that described in [1]. It is a co-axial non-magnetic-stainless-steel vacuum vessel that can be pumped by the combination of mechanical and turbomolecular pump down to the pressures of the order 10 -3 Pa. The pumping unit consists of a turbomolecular pump with Holweck stage backed by a membrane mechanical oil-free pump. The inner stainless-steel cylinder is water-cooled, isolated from the vacuum system body and serves as a cathode of the cylindrical magnetron discharge that is connected to the negative high voltage supply. The outer cylinder of the vacuum vessel is grounded and serves as anode. The discharge chamber is axially limited by two circular shields made of PTFE to the length of approximately 30 cm. The discharge vessel of our cylindrical magnetron is schematically depicted in Fig. 1. The magnetic field is created by means of a couple of Helmholz coils placed symmetrically to the middle of the discharge vessel. Tile discharge current is stabilised by the power supply operated in a constant-current mode. The current through the Helmholz coils is also electronically stabilised so that it is insensitive to the change of the coil resistance due to warming-up of the coils. The homogeneity of the magnetic field on the discharge axis has been checked by a Hall probe and found constant within 1% over the distance "4-5cm from the middle of the discharge vessel. The magnetic field strength could be varied from zero up to 5 x 10 -~ T. The cylindrical magnetron system used by us differed from that described in [1] only by the Langmuir probe and its transport mechanism. The probe transport mechanism enabled rotation of the probe as well as its radial movement. In the presented measurements the probe was planar, see Fig. 4. The 3 (or 5) orientations with regard to the magnetic field vector were adjusted by rotating the probe along its axis, which was positioned perpendicular to magnetic field lines. We actually measured only at 2 (0° and 90°) or three (0 °, 45 ° and 90 °) angular probe positions, because of the symmetry of directions/~ and Czech. J. Phys. 49 (1999)

489


probe (nickel)

dia. ]

~0.]

"~ l m m

Fig. 4. The used planar Langmuir probe, -/3. Hence f0 and f2 (in case of 5 directions also f4) were obtained in the expansion (1); fl and generally all odd terms should vanish if the plasma anisotropy is produced only by the magnetic field, see the formulae given above. Like in [1], the probe was also movable in radial direction so that the radial dependences of the probe data measured in different orientations to the magnetic field direction could be measured. Due to the comparatively large full range of our mass flow controller (20 standard cmZmin -1) we could not stabilise small flows and hence we could not make measurements at pressures lower than approximately 0.5 Pa. The probe measurements made in [12] indicated that the EEDF estimated from the second derivative of the probe characteristic in the stable region of the discharge differs significantly from the Maxwellian form. For example, in argon at lower pressure of 1 Pa and the magnetic field of 10 mT it had the form of a "double temperature" Maxwellian, where the mutual ratio of the parts with higher and lower temperatures changed with the radial co-ordinate. In the negative glow near the cathode the higher temperature part prevailed, but with increasing radius its amplitude subsequently decreased and the lower temperature part became more distinct close to the anode surface, see Fig. 5a. At higher magnetic fields when the discharge was unstable we were unable to measure the EEDF with the same precision as in the stable discharge, but still we were able to experimentally determine the radiM shape of the EEDF, see Fig. 5b. Close to the discharge axis the E E D F had almost Maxwellian shape, towards the anode its shape changes in the sense that the EEDF body contained more electrons and its tail less electrons compared to the Maxwellian shape. Figure 5 shows typical behaviour of the EEDF at lower and higher magnetic fields. In Fig. 6 we show the experimentally measured dependences of the electron mean energy E m e a n and of the parameter k of the so-called standard distribution on the radial distance from the discharge axis. The standard EEDF has the form f*(e) = constv~exp(--¢k/kskp), k > l, where ¢ is the electron energy, so is the most probable electron energy and k is the distribution parameter. The ep is related to the voltage equivalent Vp of the so-called "effective temperature" by Cp = qoVp. The mean energy Emean relates to the "effective temperature" by 490


A study of the electron energy distribution f u n c t i o n . . .

~ ............

fo

[ V'3/2]

~

J. lltlll/'17'°°

I

10"1

t '°~- 10.3 "o

•o 104

1 0 .5

,~.....

I

0

,

I

5

,

I

10 Vp [V]

,

!

15

,

20

Fig. 7. Second derivatives calculated numerically from the experimental probe characteristics at three different angles to the magnetic field. Argon, p -- 6 Pa, B --- 20 mT, ld = 50 mA. The data correspond to EEDF in Fig. 8a. free over more than 3.5 orders of magnitude. This is typical of all measurements made in the stable discharge regime, i.e. under a certain limit of the magnetic field strength (for our system this limit was slightly above 20 mT). It is also seen from the figure that the three orientations of the probe with respect to the direction of Czech. J. Phys. 49 (1999)

493

J.l;'.

Behnke et al.

the magnetic field strength do not give distinguishable results with the probe plane normal at an angle of 0 ° and 180 ° to the magnetic field lines. As an example of the experimentally determined anisotropy of the E E D F we present two sets of data, at higher and lower value of B / p . The results are presented as polar contour plots of the magnitude of the E E D F obtained from Eq. (1) at several different energies. In Fig. 8a there is the E E D F at B / p = 3.3 m T / P a . The data have been acquired in the cylindrical magnetron discharge in argon at a pressure of 6 Pa, discharge current 50 mA and the magnetic field strength 20 roT. The probe was positioned 8 m m from the cathode surface. The polar contour plots resemble circles at energies higher than approximately 3 eV. When the pressure is lowered down to 0.71 Pa then at the same magnetic field 20 m T and the same discharge current the picture

90

f(E) [(eV)"]

0.3 0.2

E = 1 eV

1 2 0 ~ 6 0 //~--~ ~~.~. // ~,~ I ~Z \\ 1 5 u ~ i~. , ~ f - a, - - ~O ' ,,-~ " "-.-.^

....... E = 2 eV ............ E = 3 eV --E=5eV __E=7eV

0.1 0.0

1 8 0 ~ \ ! \ :~ ~ / ~ ~ j .

) . / ~ 0 angl

0.1 0.2 a)

0.3

E=I

f(E) [(eV)"]

0.1

Argon, 6Pa, 20 mT B/p=33x10"3T/Pa pos = 8 mm

2 4 0 ~ 3 0 0 270

90

1

~

............ E = 3 e V E = 5 eV E = 7 eV

0.05 1, .,,,,, / , 0.0

eV

....... E = 2 e V

,~ -...~.,- ~,

, ,,,..,,,,

j /o j

E=I lay angle 0 [ ]

0.05 b)

o.1

".-.~'--...~"~'~"-.~ 240 ~ - ~ - J ~ I ~ " 3 0 0 270

Argon, 0.71Pa, 20 mT B/p = 2.8 x 10"2T/Pa pos = 5 mm

Fig. 8. Polar contour plot of the EEDF in argon; Id = 50 mA and B = 20 mT. a) p = 6 Pa, probe position 8 mm from the cathode surfax:e, b) p = 0.71 Pa, probe position 5 ram. 494


A study of the electron energy distribution fuaction . . .

changes. In Fig. 8b we present the polar contour plot constructed from the probe data acquired at such conditions. Here the probe was pos!tioned 5 m m from the cathode surface. The figure shows certain degree of anisotropy of the EEDF which can be qualitatively described as a deficit of the low energy electrons in direction perpendicular to B for electron energies lower than approximately 3-5 eV. Further difference that can be traced from Fig. 8 is the difference in the mean electron energy. In accord with the results presented in Fig. 6 the mean energy that corresponds to Fig. 8b (greater B / p ) is greater than that corresponding to Fig. 8a. Also, despite the fact that the data in Fig. 8b have been acquired at the probe position closer to the cathode surface, the amplitude of the EEDF is smaller than that in Fig. 8a. This demonstrates the magnetic field induced contraction of the discharge to the region closer to the cathode.

f(E) [(eV)1]

~E=leV ....... E=2eV

90 ~

0.6 0.4

............E=3eV

1 5 o ~ ~

~3o

~

E=5 eV

0.2 0.0

1 8 0 i ~ i i ~ i i j )

)0

angle e [ ]

0.2 0.4

a)

0.6

"-.~. ~ 240 ~

~ 300

270 f(E) [(eV)"1] 0.4 0.2 0.20"0 1

1

pos = 8 mm E = 0.6 eV

90

/

8 210~

]~f~

~..~"~

~

0

~ 3

0 3

\

)

24C

270

....... E=leV ............ E=2eV E=4eV E=6eV E = 8 eV angle O [°]

0

0.4 b)

Xenon,6Pa, 20 mT B/p = 3.3 x lOaT/Pa

300

Xenon, 0.71Pa, 20 mT B/p = 2.8 x IO'2T/Pa pos = 8 mm

Fig. 9. Polar contour plot of the EEDF in xenon at 6Pa (a) and 0.71 Pa (b); B = 20roT.


495

J.F. Behnke et ~1.

•

i

•

=

,

=

•

=

-

i

•

i

•

i

;.,

•

-

10"1 ' ~ ~ , ~'

solid

0 deg

< 10 .2

~

10 .3 0

,

0

i

2

,

i

4

,

I

6

,

i

8 10 Vp IV]

=

12

4

14

16

Fig. 10. Second derivatives of the measured probe data in 3 different orientations at the conditions of Fig. 9b. Similar results are presented in Figs. 9 and 10 for xenon. Also here we have chosen the magnetic field 20 mT at which the discharge was stable yet. Figure 9a shows the case of higher pressure 6 Pa. At this B/p the EEDF was almost isotropic. At the reduced pressure 0.71 Pa, see Fig. 10, the second derivatives at different orientations to the direction of the magnetic field strength no longer coincide and it is possible to distinguish lower slope (larger temperature) of the curve corresponding to the orientation perpendicular to the magnetic field. This result can be qualitatively compared to the course of Emean in Fig. 6. There the experimental values measured in direction perpendicular to the magnetic field (angle 90 °) systematically exceed the data measured at the other two angles (0 °, 45°). Also the corresponding polar contour plot depicted in Fig. 9b shows at this pressure somewhat larger anisotropy of the EEDF in comparison with Fig. 9a. Conclusion We attempted to describe the behaviour of the cylindrical magnetron discharge including that of the EEDF in such discharge. The Monte-Carlo simulations of electron motion in the cylindrical magnetron discharge did not resolve the problem how electrons reach the anode at sufficiently high B/p. We found experimentally that the isotropy of the EEDF in the cylindrical magnetron discharge is influenced by magnetic field. From our experimental investigations also follows that the EEDF can, at certain experimental conditions, have non-Maxwellian shape. Further modelling as well as the experimental investigation of the cylindrical magnetron discharge is in progress. The work in Germany was financially supported by the Deutsche Forschungsgemeinschaft (DFG) in frame of the project SFB 198 Greifswald "Kinetik partiell ionisierter

496


A study of the electron energy distribution function ...

Plasmen ". The work in Czech Republic was partially financially supported by the Grant Agency of Czech Republic, Grant No. GA~R-202/97/1011, GA~R-202/97/P078 and GA~R 202/98/0116 and by the Grant Agency of Charles University, Grant No. GAUK-181/96 and GAUK-75/98.

References

[1] E. Passoth, P. Kudrna, C. Csambal, J.F. Behnke, M. Tich3~, and V. Helbig: J. Phys. D: Appl. Phys. 30 (1997) 1763. [2] M. Tich¢, P. Kudrna, J.F. Behnke, C. Csambal, and S. Klagge: in Proc. X X I I I I C P I G , Toulouse (France) 1997 (Eds. M.C. Bordage and A. Gleizes), Volume of Invited Lectures (J. de Physique IV, Suppl. au J. de Physique III (1997), No. 10), p. C4-397. [3] V.A. Godyak, R.B. Piejak, and B.M. Alexandrovich: J. Appl. Phys. 73 (1993) 3657. [4] H. Aikawa: J. Phys. Soc. Jpn. 40 (1976) 1741. [5] J.C. Blancod, K.S. Golovanievski, and T.P. Kravchov: in Proc. X ICPIG, Oxford (UK) September 13-18, 1971 fEd. P.A. Davenport), Donald Parsons & Co. Publishers, p. 25. [6] M. Yousfi, A. Hennad, and A. Alkaa: Phys. Rev. E 49 (1994) 3264. [7] S.J. Buckman and B. Lohmann: J. Phys. B: At. Mol. Phys. 19 (1986) 2547. [8] J.C. Nickel, K. Imre, D.F. Register, and S. Trajmar: J. Phys. B: At. Mol. Phys. 18 [9] [10] [11] [12]

[13] [14] [15] [16] [17] [18] [19] [20] [21]

(198s) 125. S.N. Nahar and J.M. Wadehra: Phys. Rev. A 35 (1987) 2051. J. Bretagne, G. CaUede, M. Legentil, and V. Puech: J. Phys. D: Appl. Phys. 19 (1986) 761. D. Rapp and P. Englander-Golden: J. Chem. Phys. 43 (1965) 1464. E. Passoth: Investigation o] kinetics of charge carriers in cylindrical magnetron discharges (Thesis). Institute of Physics, Faculty of Mathematics and Natural Sciences, EMA University, 1997 (in German). J.G. Brown, A.B. Compher, K.W. Ehlers, D.F. Hopkins, W.B. Kunkel, and P.S. Rostler: Plasma Phys. 13 (1971) 47. Z. Zakrzewski, T. Kopiczynski, and M. Lubanski: Czech. J. Phys. B 30 (1980) 1167. R.R. Arslanbekov, N.A. Khromov, and A.A. Kudryavtsev: Plasma Sources Sci. Technol. 3 (1994) 528. J.I. Fern&ndez Palop, J. Ballesteros, V. Colomer, and M.A. Hern~mdez: Rev. Sci. Instr. 66 (1995) 1. A.P. Mesentsev, A.S. Mustafaev, and V.L. Federov: Zh. Tekh. Fiz. 55 (1985) 544. A.P. Mesentsev, A.S. Mustafaev, and V.L. Federov: Zh. Tekh. Fiz. 55 (1985) 2232. A.P. Mesentsev, A.S. Mustafaev, and V.L. Federov: J. Phys. D 21 (1988) 1464. V.L. Federov: Zh. Tekh. Fiz. 55 (1985) 926. V.F. Laphshin, A.P. Mesentsev, A.S. Mustafaev, and V.L. Federov V.L.: in Proc. ESCAMPIG-IX, Lisabon (Portugal) 1988 fed. C.M. Ferreira), p. 141.


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et al.: A study of the electron energy distribution function . . .

[22] A.P. Mesentsev, A.S. Mustafaev, V.F. Laphshin, and V.L. Federov: J. Phys. B 20 (1987) L723; J. Phys. B 20 (1987) L923. [23] V.F. Laphshin and A.S. Mustafaev: Zh. Tekh. Fiz. 59 (1989) 35. [24] V.L. Federov and A.P. Mesentsev: Zh. Tekh. Fiz. 57 (1987) 595. [25] S. Klagge and A. Lunk: J. Appl. Phys. 70 (1991) 99. [26] J. Rohmann and S. Klagge: Contrib. Plasma Phys. 33 (1993) 111. [27] W.P. Allis: M o t i o n o f Ions and Electrons, Handbuch der Physik, Vo].21 (Ed. S. Fliigge), Springer-Verlag, Berlin-Heidelberg-New York, 1956, p. 383. [28] R. Winkler: Beitr. Plasmaphys. 12 (1972) 317. [29] J.F. Behnke, E. Passoth, Y.B. Golubovski, and I.A. Porokhova: Proc. ESCAMPIG XIII, Poprad, High Tatras (Slovakia), 1996 (Eds. P. Luk~t, I. Ko~in~r, J.D. SkaJn~), Europhysics conference ~bstr~cts, Vol. 20E, part A, p. 99.

498
