Measurement of electron energy distributions in moving stiations

Physica 83C (1976) 227-230 © North-Holland Publishing Company

MEASUREMENT OF ELECTRON ENERGY DISTRIBUTIONS IN MOVING STRIATIONS G. VAN DEN BERGE Laboratorium voor Natuurkunde, Ri/ksuniversiteit, Rozier 44, B-9000 Gent, Belgium Received 24 February 1976

A sampling technique is discussed for measuring the time-resolved electron energy distribution in moving striations by means of the Langmuir-Druyvesteyn probe method. The technique is used in a neon discharge (Po = 0.79 torr; I d = 105 mA; 2r = 5.6 cm). It is found that the electron energy distribution strongly depends upon the striation phase; in the region of strong electric field it is double peaked.

1. Introduction

triggered at the frequency of the moving striations (a few kHz); it allows the undisturbed transmission of the input signal during a short time (1/30 o f the striation period) and at a well-defined striation phase. It is opened by the pulse generator PG, which is triggered by the output signal of the photomultiplier PM, mounted in front o f the measuring probe to monitor the local light intensity variations in the striated discharge. The phase o f the transmitted probe signal is determined and indicated by Z-modulation of the PM signal on the screen o f the oscilloscope O. The transmitted signal is integrated by the active semi-integrator T (time constant 0.01 s), designed in order to develop a dc output voltage proportional to the height of the

It is well known that in a low pressure discharge the electron energy distribution f ( V ) can be inferred from the properties o f a Langmuir probe current-voltage characteristic by the Druyvesteyn formula [1 ] : f(V)=BV

d2__I/

dV 2,

(1)

where Vis the potential difference between the probe and the plasma, I the electron current to the probe at the retarding potential V, and B a constant that depends upon the probe area. In the present paper a sampling technique is described for time-resolved electron energy distribution measurements in a plasma, in the presence o f moving striations. It is based on the Langmuir-Druyvesteyn probe method. The first derivative of the probe current voltage characteristic is obtained from a differentiating circuit. The second derivative is calculated using a digital computer.

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2. Electronic circuit and measurement technique

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A block diagram of the circuit is given in fig. 1. The voltage drop developed by the probe current over the resistance R is applied to the dc amplifier A 1. The amplified signal is transmitted through the bidirectional gate G to the integrating circuit T. The gate is

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D

~Jll I

Fig. l. Block diagram of the electronic circuit, measuring the first derivative of the probe characteristic at a well-defined measuring phase in the period of the moving striations. 227

228

G. Van Den Berge/Time-resolved electron energy distribution measurements

input pulse. The output signal of T, after amplification by the dc amplifier A2, is differentiated by the active differentiator with filter D (time constants of differentiator and filter: respectively 1 s and 0.01 s). Through the active filter F (rejection greater than 55 dB at 50 Hz; 0.2 s rise time), the differentiated signal is finally applied to the Y-input of the X Y recorder S. The probe potential relative to the reference electrode (in our case the cathode) is determined by the sawtooth voltage generator ST 1 (period of about 1 min). This sawtooth voltage is also connected to the X-input of the recorder. In this way the continuous dI/dV, V-curve for a well-defined measuring phase in the period of the moving striations is displayed on the XY-recorder. The second derivative and energy distribution function are then calculated using a least squares fitting program.

3. Calibration. Reliability of the calibration factor The first derivative dl/dV, determined experimentally by the output voltage Y of the differentiator D (fig. 1), is given (in A / V ) by:

~v

=KY,

(2)

where K is a constant. To obtain absolute values the measuring apparatus is calibrated by applying a sawtooth voltage S T 2 of known slope a 2 (V/s) to the resistance R (switch M 1 in position 2), the resulting differentiator output being Y0" It can easily be shown that the factor K is given by: K = ~2/~1R YO,

(3)

where ct1 (in V/s) is the slope of the sawtooth voltage S T 1. In order to study the reliability of the calibration factor we have determined experimentally the output Y0 for a number of values of ct2. The resulting values of K, given by (3), do not deviate more than 1% from the mean value of K, when the output voltage Y0 is changed by a factor up to 100.

4. Electron energy distribution and electric field measurements

The above described measuring technique has been applied to the study of a neon discharge. We have used a discharge tube in pyrex (diameter 56 mm) with a hollow cathode and a plane anode. The distance between the electrodes is 50 cm. The cathode is surrounded by an antisputtering shield; the electrodes and the shield are of nickel foil (thickness: 0.20 mm). For the energy distribution measurements we use a cylindrical tungsten probe (0.10 mm in diameter and 3 mm long) mounted along the axis of the tube (probe axis perpendicular on the tube axis) at 12.5 cm from the anode. For the measurement of the axial potential distribution a second identical probe is used, again located along the tube axis, at 1.5 cm distance from the former one. The cathode is the reference electrode. After being baked out at 400°C for 24 hours, evacuated down to 2 X 10 -9 torr and conditioned by a discharge in an inert gas (pressure of a few torr), the discharge tube has been filled with neon at 0.79 torr. The maximum impurity level of neon is 0.01% by volume. The discharge current is 105 mA. The light intensity and the axial potential at the location of the measuring probe are given in fig. 2, as a function of time (axis a). A particular striation phase can be characterized by the time to , measured along the axis of the abscissae in this diagram; the time to = 0 ms corresponds to the maximum of light intensity. The striation period is 635/as and the wavelength 14.4 cm; the phase velocity is 2.27 × 104 cm. s -1, directed from anode to cathode. According to fig. 2 (cf. axis b) the field at a given time along a given striation has a constant value of about 0.30 V. cm -1 over a distance of approximately 12 cm; the following few cm are characterized by a sharp potential rise of about 14 V. In fig. 3 we have recorded a series of seven electron energy distributions measured at the phases corresponding to the mentioned t o values. At the time where the electric field in the striation is a maximum (t o 0.55 ms; cf. fig. 2) the electron energy distribution is double peaked. The mean energy of the group of fast electrons is observed to increase from approximately 11 eV at to = 0.55 ms to approximately 16 eV at to = 0.60 ms. Simultaneously the number of fast electrons

G. Van Den Berge/Time-resolved electron energy distribution measurements

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Fig. 3. Electron energy distribution measurements at different phases of a moving striation.

Fig. 2. Light intensity and potential along a moving striation.

is observed to decrease, due to their inelastic collisions with neutral Ne atoms, resulting in the ionization or excitation o f the latter. The corresponding energy losses are respectively 21.6 eV and at least 16.6 eV. As a consequence, the number o f the slow electrons strongly increases. Moreover a large number o f slow electrons are produced b y collisions between excited atoms and slow electrons, and by mutual collisions between excited atoms. As a result o f these processes the energy distribution becomes single peaked at the time t o = 0.15 ms; the corresponding phase is characterized by a sharp decrease in the striation field. In the further striation process (to = 0.15 ms to t o = 0.50 ms) the number o f slow electrons decreases, as a result of ambipolar diffusion to the wall. The abrupt transition from the single peaked distribution at t o = 0.50 ms to the double peaked one at t o = 0.55 ms is due to the acceleration o f a number o f slow electrons in the momentarily prevailing large electric field. At the same time a new cycle of the above described striation processes is introduced.

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Fig. 4. Tests for maxwellian and Druyvesteyn distributions.

In fig. 4, log(d2I/dV 2) is plotted against the probe bias voltage V for three striation phases. The figure again illustrates the changes o f the distribution along

400

230

G. Van Den Berge/Time-resolved electron energy distribution measurements

a striation length. The straight plot obtained at t o = 0.25 ms is well known to be characteristic for a maxwellian distribution. At t o = 0.45 ms, the deficiency of high energy electrons is obvious; in this case a plot of log d 2 I / d V 2 versus V 2 yields a straight line characteristic for a Druyvesteyn distribution. It will be noticed that the results of the present work are in agreement with those obtained by Rayment and Twiddy [2] who used a different measuring technique.

5. Remark concerning the anisotropy of the distribution The use of the Druyvesteyn formula (1) is allowed if the electron energy distribution is isotrope in the neighbourhood of the measuring probe. In the discharge studied, the electrons have a directional motion and consequently a given drift velocity od. This leads to a distortion of the probe characteristic when the axis of the cylindrical probe is not parallel to the drift velocity; the discrepancy decreases with decreasing

ratio Vd/V m (v m = mean thermal velocity of the electrons). In the neon plasma studied above, the lowest mean electron energy 3.8 eV corresponds to the largest Vd/V m value: Vd/V m = 0.04. Even for this value, according to Langmuir and Mott-Smith [3], the anisotropy of the distribution can be neglected.

Acknowledgements This work has been supported by a grant from the Nationaal Fonds voor Wetenschappelijk Onderzoek, Brussels. It is a pleasure to thank Professor P. Mortier for his encouragement and criticisms.

References [1] M. J. Druyvesteyn, Z. Phys. 64 (1930) 781. [2] S. W. Rayment and N. D. Twiddy, Brit. J. Appl. Phys. (J. Phys. D) 2 (1969) 1747. [3] I. Langmuir and H. Mott-Smith, Phys. Rev. 28 (1926) 727.