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Electron drift velocity in      in strong electric fields determined from rf breakdown curves

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Journal of Physics D: Applied Physics

J. Phys. D: Appl. Phys. 43 (2010) 385203 (7pp) doi:10.1088/0022-3727/43/38/385203

Electron drift velocity in SF6 in strong electric fields determined from rf breakdown curves

V Lisovskiy1, V Yegorenkov1, J-P Booth2, K Landry3, D Douai4 and

V Cassagne5

1 Department of Physics and Technology, Kharkov National University, Svobody sq.4, Kharkov 61077, Ukraine

2 Laboratoire de Physique des Plasmas, Ecole Polytechnique, Palaiseau 91128, France

3 Unaxis Displays Division France SAS, 5, Rue Leon Blum, Palaiseau 91120, France

4 Physical Sciences Division, Institute for Magnetic Fusion Research, CEA Centre de Cadarache, F-13108 saint Paul lez Durance cedex, France

5 Developpement Photovoltaique Couches Minces, Total, 2, place Jean Millier, La Defense 6, 92400 Courbevoie, France

E-mail: lisovskiy@yahoo.com

Received 29 November 2009, in final form 3 August 2010

Published 9 September 2010

Online at stacks.iop.org/JPhysD/43/385203

Abstract

This paper presents measurements of the electron drift velocity Vdr in SF6 gas for high reduced electric fields (E/N = 330-5655Td (1 Td = 10—17 Vcm2)). The drift velocities were obtained using the method of Lisovskiy and Yegorenkov (1998 J. Phys. D: Appl. Phys. 31 3349) based on the determination of the pressure and voltage of the turning points of rf capacitive discharge breakdown curves for a range of electrode spacings. The Vdr values thus obtained were in good agreement with those calculated from the cross-sections of Phelps and Van Brunt (1988 J. Appl. Phys. 64 4269) using the BOLSIG code. The validity of the Lisovskiy-Yegorenkov method is discussed and we show that it is applicable over the entire E/N range where rf discharge ignition at breakdown occurs for rf frequencies of 13.56 MHz or above.

1. Introduction

Sulfur hexafluoride (SF6) is a man-made gas with excellent dielectric properties and is widely used as an insulating gas in various electric devices [1,2]. Mixtures of SF6 with oxygen are employed for plasma etching semiconductor materials [3,4] and for plasma cleaning of technological chambers [5]. It is also used in rare gas-halide excimer lasers, AWACS radar domes, x-ray machines, airplane tires, etc. [6]. Therefore, considerable attention has been devoted to studying the physical properties of this gas.

The drift velocity Vdr of electrons moving in an electric field is one of the most important characteristics of an ionized gas. It describes the electrical conductivity of a weakly ionized gas (the current carried by positive ions can be neglected due to their small drift velocity). The electron cloud in an ionized gas moves with a broad velocity spectrum, but the drift velocity describes the average movement of the electrons under the influence of an electric field. The electron drift velocity is a key transport coefficient and is required for fluid modelling of technological discharge plasmas, gas-filled counters of ionizing radiation, the Earth's atmosphere, etc.

Several methods have been developed to determine the electron drift velocity, including the pulsed Townsend method [7-9], the time-of-flight method [10-12], monitoring of the velocity of the optical emission of the moving electron cloud [13] and the shutter method [7,14,15]. However, as a rule, these methods can only be used for relatively low reduced electric fields (E/N lower than about 1000 Td). At high E/N the average energy of electrons is high; therefore, the efficiency of shutters is lower. For accurate Vdr measurements one may observe single avalanches but at higher E/N the probability of secondary avalanches increases. Therefore, conventional methods can only be applied at д = у x (eaL1) <C 1, where Y is the ion induced secondary electron emission coefficient, a is the first Townsend coefficient, L is the inter-electrode

0022-3727/10/385203+07$30.00

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Pumping

Figure 1. Schematic of our experimental set-up.

spacing. However, Lisovskiy and Yegorenkov [16,17]have proposed a method based on analysing rf breakdown curves, which allows Vdr to be determined in stronger electric fields. Recently Petrovic et al [18] have criticized this method; we will address these criticisms in the final section of this paper.

In this paper we have used the Lisovskiy-Yegorenkov method to determine the electron drift velocity in SF6. Measurements were made in the range E/N = 330-5655 Td. With the help of the 'Bolsig' numerical code and published cross-sections [19] we have calculated the electron transport parameters in SF6 in the range E/p = 1-5000 Vcm—1 Torr—1, and the drift velocity values obtained from our experiment agree well with the calculated values.

2. Experimental

The ignition of rf capacitive discharges in SF6 was studied over the pressure range p ss 0.02-4 Torr. A large number of rf breakdown curves were recorded at the frequency f = 13.56 MHz, but some experiments were also performed at the frequency f = 27.12 MHz. The distance between the flat circular aluminium electrodes (143 mm in diameter) was varied overtherangeL = 5-25 mm. Therfvoltage(amplitude Urf < 1500 V) was fed to one of the electrodes, while the other was grounded. The electrodes were located inside a fused silica tube with an inner diameter of 145 mm (see figure 1). The gas was supplied through small orifices in the powered electrode. The orifices in the rf electrode served only for gas supply into the inter-electrode gap, the diameter of each orifice being 0.5 mm. Such narrow orifices would not let electrons perform long path breakdown. Gas was pumped out via a narrow gap between the grounded electrode and the wall of the fused silica tube. The gap width was also equal to 0.5 mm.

The gas flow was fixed with a mass flow controller to 5 sccm, and the pressure regulated by throttling the outlet to the pump. The rf voltage was measured with an rf probe (Advanced Energy Z'SCAN). Gas pressure was measured with a capacitive manometer (MKS Instruments), attached near the grounded electrode (between this electrode and the vacuum pump). For pressure gauging we attached the second capacitive manometer directly to the gap between the electrodes (chamber design permitted us to do so). We knew exactly what was the gas pressure in the inter-electrode gap over the whole gas pressure range studied.

By 'breakdown voltage' we mean the maximum rf voltage that can be applied across the electrodes without discharge ignition. The addition of even a small fraction of a volt leads to gas breakdown, the rf voltage drop across the electrodes decreases abruptly, a glow appears within the gap, a conductance current flows in the discharge circuit and the phase shift angle between rf current and voltage becomes less than ж/2. All these changes, which appear simultaneously, are reliable indications of the gas breakdown and they are easily observed. The rf voltage was varied (before the breakdown) in steps of AUrf s 0.3 V (because the generator had stepwise control). The gas pressure was monitored with capacitive manometers with a smallest step of Ap ss 0.001 Torr. The inter-electrode distance was measured with an accuracy of AL ss 0.01 mm. The rates of increase in the pressure (while measuring to the left of rf breakdown curve minimum in the multi-valued region) and in the rf voltage (right-hand branch) were very small. For example, after increasing the rf voltage by a minimum step AUrf s 0.3 V we waited several seconds for a possible breakdown and, if not, made the following step AUrf.

The residence time for atoms and molecules in our chamber within all the range of gas pressure studied was less than 1 min, as the gas was renewed continuously. The time between successive breakdowns in our chamber was not less than 5 min; therefore, the excited atoms and molecules after previous breakdown were swept out of the chamber and did not affect the next breakdown. Consequently, no 'memory effect' [20] influenced the discharge ignition in our experiment.

We used the technique proposed by Levitskii [21]to measure the breakdown curves of the rf discharge. Near to, and to the high-pressure side of the minimum in the breakdown curve the SF6 pressure was fixed before slowly increasing the rf voltage until gas breakdown occurs. To the low pressure side of the minimum the curve may be multi-valued, i.e. the curve turns back to higher pressures, and breakdown can occur at two different values of the rf voltage. Therefore, in this range we first decreased the SF6 pressure, then fixed the rf voltage value and only then increased the SF6 pressure slowly until discharge ignition occurred. At the moment of discharge ignition the rf voltage shows a sharp decrease, and a glow appears between the electrodes serving as the indicator of the onset of gas breakdown. The uncertainty in the measured breakdown voltages did not exceed 1-2 V over the whole Urf range under study.

2.1. Determination of the electron drift velocity from rf breakdown curves and the data for SF6

Breakdown curves for the rf capacitive discharges can be divided into three regions: the drift-diffusion region, the Paschen region and the multipactor region [16]. In this method we are interested in the drift-diffusion region. In the drift-diffusion region the charged particles are principally created

given by

Figure 2. Rf breakdown voltage Urf against SF6 pressure p for various inter-electrode gap values, f = 13.56 MHz.

Figure 3. Rf breakdown voltage Urf against SF6 pressure for f = 13.56 MHz, and f = 27.12MHz, L = 11.9mm.

by the ionization of gas molecules via electron impact, and lost by the drift motion of electrons in the rf electric field, diffusion to the electrodes and discharge chamber walls, and attachment of free electrons to gas molecules (if a discharge is ignited in a electronegative gas). Electron-induced secondary electron emission from the electrode surface may play an auxiliary role. The drift-diffusion region is dominant for large inter-electrode gaps and sufficiently high frequencies f of rf field (see figures 2 and 3), but becomes weakly expressed with narrow gaps (less than 1 cm) and frequencies below 10 MHz. It is this branch that is of principal importance for us because the method we employ for determining Vdr is based on recording the coordinates (rf voltage Ut and gas pressure pt) of the turning point of this branch. The mechanisms of generation and loss of charged particles for the other (Paschen and multipactor) regions are discussed elsewhere [16].

Let us briefly describe the Lisovskiy-Yegorenkov [16,22, 23] method for determining the electron drift velocity from rf breakdown curves. The equation of motion of the centre of the electron swarm in a uniform rf electric field Erf sin mi is

dV

m-      = —eErf sin mi mVv,

di

(1)

where V is the electron velocity, e and m are the electron charge and mass, respectively, Erf is the rf field amplitude, vme is the momentum transfer frequency of collisions between electrons and gas molecules (the quantity vme is assumed to be constant), m = 2nf is the angular frequency of the rf field. Integrating this expression gives the following expressions for the velocity V and displacement r of electrons:

eEVrf

m^/m2 + Vj

= cos(mi + ф),

eEVrf

mm^Jm2 + vt

sin(mi + ф),

(2)

(3)

where ф = arctan(vme/m). These equations were obtained earlier, e.g. in [24]. The amplitude, A, of the electron displacement in an rf electric field is given by

A

eErf

Vdr

mm^/m2 + vt

2

me

(4)

where the maximum instantaneous drift velocity of electrons, Vdr,isgivenby

eErf

Vdr =-, /  „ . (5)

m^/m2 + v,

2

me

If Urf = Urf(p) is the amplitude of the rf voltage at breakdown, a turning point occurs when d Urf (p)/dp -—coo. At the turning point of the breakdown curve (corresponding to p = pt and Urf = Ut) the amplitude of the electron displacement is equal to half of the gap width L between the electrodes [22]:

A

Vdr

L 2 .

(6)

Hence the electron drift velocity Vdr at the turning point of the rf breakdown curve is equal to

Vdr

mL

Lnf.

(7)

It follows from equation (7) that the value of the electron drift velocity at the turning point of the breakdown curve depends only on the values of the inter-electrode gap and the frequency of the rf field. At the same time it is independent of the gas species. However, the corresponding value of E/N (or E/p) at this point will be different for each gas.

The coordinates of the turning point permit us to determine the reduced field, E/p (or E/N), corresponding to this electron drift velocity. For example, from figure 2 we determine the coordinates of the turning point of the rf breakdown curve for the gap of 2.5 cm: pt = 0.024Torr and Ut = 113.1V. Then we find that E/p = U/(L x pt) = 1885 Vcm— 1 Torr—1, E/N = 5655Td and Vdr = 2.5 x ж x 13.56 x 106 = 1.06 x 108cms—1. In order to obtain a set of Vdr values over a wide range of E/N, rf breakdown curves must be recorded at various values of the inter-electrode gap L.

r

m

m

Figure 4. Electron drift velocity in SF6 against E/N.

We may also vary the rf field frequency f with L fixed. The rf breakdown curves for L > 11.9 mm and f = 13.56 MHz, as well as for f = 27.12 MHz (presented in figures 2 and 3), show a diffusion-drift branch with multi-valued dependence of the rf breakdown voltage on gas pressure, so we may use them for determining the electron drift velocity values from the location of the turning points.

The values of the electron drift velocity determined from our measured breakdown curves are presented in figure 4. There have been a number of previous measurements of the electron drift velocity in SF6 [17, 25-31]. Our data are in good agreement with the data of other authors within the range E/N = 300-600 Td. Christophorou and Olthoff [6]have reviewed the previous work, and state that only Lisovskiy and Yegorenkov [17] and Aschwanden [28] have report values for reduced electric fields above 1000 Td. Christophorou and Olthoff suggest 'recommended data' at high reduced field, obtained by fitting a line through the data of Aschwanden, due to the better agreement of these data with the other measurements at lower reduced field. In this paper we report our measurements of rf breakdown curves for SF6 at a variety of electrode spacings, from which we have determined the electron drift velocity within the range E/N = 300-5655 Td. At E/N ss 300 Td our results practically coincide with those of Aschwanden and other workers. However, our values are lower than those of Aschwanden for higher reduced fields. At E/N = 3000 Td we found values 20% lower, and with further increase in E/N this discrepancy increases.

We also calculated values of the electron drift velocity from the experimental cross-sections of Phelps and Van Brunt [19] for elastic and inelastic collisions between electrons and SF6 molecules, using the BOLSIG code (www.siglo-kinema.com/bolsig.htm). The BOLSIG code allows numerical solution of the Boltzmann equation for electrons in weakly ionized gases and in steady-state, uniform fields. Figure 4 shows that our electron drift velocity values are in good agreement with the calculated values over the entire range of E/N. In contrast, the values of Aschwanden are higher, particularly at high reduced field. The previous measurements of Lisovskiy and Yegorenkov [17] (using the same method as here) are close to the present measurements and the calculated values. For strong reduced fields the values reported by Lisovskiy and Yegorenkov are slightly higher, but this could be attributed to lower gas purity in the older measurements.

As the values of the electron drift velocity obtained here are in good agreement with the results of other authors at low E/N and are also in good agreement with values calculated from collision cross-sections at high E/N, we consider that they are more reliable than those of Aschwanden [28]. This should be confirmed by further calculations and measurements (using other techniques) in the high reduced field region.

2.2. Validity ofthe determination ofelectron drift velocity from rfbreakdown curves

Now let us consider the validity of the Lisovskiy-Yegorenkov method to determine the electron drift velocity. This method is based on the assumption that, when a sinusoidal rf electric field is applied, the electron drift velocity Vdr (i) also oscillates sinusoidally, with an amplitude given by equation (4). It should be noted that at high rf frequencies there can be a phase shift between the field and the drift velocity, but this does not affect the measurement. The method is simple and gives good agreement with the data obtained by other techniques and numerical calculations (see, e.g., [16, 17, 22, 23, 32, 33]). The Lisovskiy-Yegorenkov method is accessible to many researchers. As far as we know, few installations exist for accurate Vdr determination. However, the number of rf discharge chambers at universities and research centres of companies can be counted in hundreds, if not thousands. The Lisovskiy-Yegorenkov method enables one to determine Vdr in situ within the E/N range and in the gas (or their mixtures) which are of interest to researchers.

We also remark that the spread of Vdr values determined with Lisovskiy-Yegorenkov method does not exceed that obtained with other methods. Figure 4 demonstrates that at E/N s 500 Td the measured Vdr values lie within the range from 3.12 x 107cms—1 [27]to2.21 x 107cms—1 [30]. Our result Vdr = 2.56 x 107 cms—1 at this E/N value is within the Vdr spread presented in above papers.

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V Lisovskiy, V Yegorenkov, J-p Booth - Electron drift velocity in sf6 in strong electric fields determined from rf breakdown curves