V A Lisovskiy, N D Kharchenko - Modes of longitudinal combined discharge in low pressure nitrogen - страница 1
Journal of Physics D: Applied Physics
J. Phys. D: Appl. Phys. 41 (2008) 125207 (8pp) doi:10.1088/0022-3727/41/12/125207
Modes of longitudinal combined discharge in low pressure nitrogen
V A Lisovskiy, N D Kharchenko andVDYegorenkov
Kharkov National University, 4 Svobody sq., Kharkov, 61077, Ukraine
Received 28 December 2007, in final form 3 April 2008
Published 29 May 2008
Online at stacks.iop.org/JPhysD/41/125207
This paper reports the modes of a low pressure discharge in the combined (rf + dc) electric field. We propose to distinguish three modes of a longitudinal combined discharge (rf and dc voltages were applied to the same electrodes): (1) a non-self-sustained rf discharge perturbed by a dc electric field, (2) a combined discharge and (3) a non-self-sustained dc discharge perturbed by an rf electric field. The existence conditions of these modes are determined. The parameter range in which the first mode of the combined discharge may be extinguished via increasing dc voltage is shown to be limited with an rf discharge extinction curve from the low pressure side as well as with a curve of the least rf voltage corresponding to the transition of the combined discharge from the first mode to the second one. The relation between the thicknesses of the 'cathode' and 'anode' near-electrode sheaths is derived analytically for the first mode, which is in good agreement with experimental data.
The gas discharge in the combined (rf + dc) electric field is applied for determining the electron transport coefficients in low pressure gases [1, 2], as well as in a number of technological devices for spectral-chemical analysis , silicon plasma oxidation ,plasmatrons  and gas discharge lasers [6, 7]. These applications led to the emergence of a large number of experimental and theoretical papers devoted to studying the characteristics of such combined discharges in various gases (see, e.g. [8-18]). The combination of dc and rf electric fields increases the stability of gas discharge burning permitting one to introduce a large power into the discharge [6,7,10,11]. The papers [8,9] studied the transverse combined discharge in which the inner dc electrodes were located at the ends of the discharge tube and the rf electrodes were located outside the tube. Thus, crossed rf and dc electric fields were created in the discharge tube. The authors of [8, 9] presented the radial profiles of the integral glow of the transverse combined discharge. The papers [12,14] are devoted to the experimental and theoretical study of the ignition of the longitudinal combined discharge in argon and air. The breakdown curves of the combined longitudinal discharge in argon are presented in  for purely metallic electrodes as well as for electrodes coated with a dielectric layer. Employing numerical modelling, the authors of paper  made an attempt to describe the experimental breakdown curves . The author of paper  recorded with a Langmuir probe the axial profiles of plasma concentration of the longitudinal combined discharge in air; the measurements were performed with the gas pressure close to and to the right of the extinction curve minimum for the rf capacitive discharge. The paper  studies the discharge characteristics in the combined (rf + dc) electric field of a complicated configuration (triode scheme). here the distribution functions over energy were recorded for ions incident on the grounded electrode at different values of rf and dc voltages.
Though the structure and modes of the rf capacitive discharge  and dc glow discharge  are studied quite well, still the question on the modes of the longitudinal combined discharge when rf and dc voltages are applied to the same electrodes remains open.
In a combined discharge the rf electric field plays the main role in producing a dense plasma whereas the dc voltage across the electrodes increases the energy of positive ions incident on the 'cathode'. The dc voltage 'drops' mainly across the 'cathode' sheath (due to its low conductivity), whereas a considerable portion of the rf voltage applied 'drops' across the quasi-neutral plasma controlling the ionization rate of gas molecules via electron impact. in contrast to the rf capacitive discharge and the dc discharge, it is possible to independently control in the combined discharge the ion energy (with the dc voltage Udc) and the ion flow onto the electrode (controlling the plasma concentration with rf voltage Urf).
© 2008 IOP Publishing Ltd Printed in the UK
Figure 1. Scheme of the experimental device.
Low pressure discharges in nitrogen are widely applied in industrial processes for the production of hard nitride layers on steel, deposition of thin silicon nitride Si3N4 films, amorphous carbon nitride and в-C3N4 III-nitrides. Therefore, we chose nitrogen for studying the burning modes of the combined discharge.
Our paper aims to study the modes of the longitudinal combined discharge in low pressure nitrogen. It is shown that the combined discharge may exist in one of the three possible modes at different values of the ratio of the rf voltage to the dc voltage. The first mode—the rf discharge perturbed with a dc electric field—is observed at moderate dc voltages. The second mode—the combined discharge—exists in the presence of intense ionization in the 'cathode' sheath, when the dc voltage exceeds a certain critical value. The third mode— the dc discharge perturbed with rf voltage—is observed when a moderate rf voltage is applied to the burning dc discharge. It is shown that the range exists limited from the low pressure side where the first mode may be extinguished via increasing dc voltage. A relation is derived from the collisional child-Langmuir law between the thicknesses of the 'cathode' and the 'anode' sheaths furnishing a good description of the experimental data for the first mode.
2. Experimental conditions
The experiments were performed at nitrogen pressure within the range p = 0.01-5 Torr with amplitude values of the rf voltage Urf < 2000 V, the dc voltage Udc < 600 V and the rf field frequency f = 13.56 MHz. The distance between flat parallel stainless-steel electrodes was L = 30 mm. The rf potential was applied to one of the electrodes whereas the other one was grounded. The rf electrode served as a 'cathode' simultaneously, because a negative dc potential was applied to it.
Figure 1 shows our experimental device. The fused silica tube with an inner diameter of 100 mm was vacuum-sealed between the electrodes. The gas supply system fed nitrogen through a multitude of tiny orifices in the grounded electrode. The discharge vessel was evacuated through a set of orifices in the same electrode. This design permitted us to feed and pump out the gas uniformly across the electrode area, which is important in technological processes. For registering the gas pressure within the range from 10-3 Torr to the atmospheric one we employed the thermoelectric vacuum gauge. gas was pumped out with the preliminary vacuum and turbo molecular pumps providing a limiting pressure order of 10-6 Torr. An rf generator was connected to the potential electrode via a matching box of the П-type. The dc source was connected to the same electrode via a choke of Lc = 4 mH, to prevent damage to the source by the rf current.
The electron temperature Te, the plasma potential and the plasma concentration ni were established from the measurements with a single cylindrical nichrome Langmuir probe (the probe length was 5.5 mm, the probe diameter was 0.18 mm). The plasma concentration ni was calculated from the ion branch of the probe current Ipr and the electron temperature Te determined according to the technique described in the papers [21, 22]. To this end we employed the formula
^i, measured — Ii ' 1 , (1)
I* = A
I kTe . /-n\e,
I* = Y1Y2IL
where A denotes the probe collecting surface, k is the Boltzmann constant, Mi is the ion mass, e is the elementary charge, the coefficients y1 and y2 are functions of the ion concentration, electron temperature and gas pressure :
Y1,Y2 = f1,2(ni,Te, p),
IL is the Laframboise current
and n = eUp/kTe is the dimensionless probe current equalling zero at the plasma potential. Inserting (2)-(4) into (1) furnishes the equation the left-hand part of which contains the ion current that we registered with the probe and the right-hand part of which is the function of the gas pressure, electron temperature and plasma concentration. solving this equation we get the concentration of positive ions. In doing so we use the values of the electron temperature determined from the probe cVcs (employing the linear section of the graph of the electron current to the probe constructed to the semi-logarithmic scale).
3. Experimental results
We aim to study the optional modes of a longitudinal combined discharge and the existence conditions of each mode, to register the discharge current-voltage characteristics (cVcs) (with respect to dc as well as rf currents) as well as the thickness of the 'cathode' and the 'anode' sheaths under various conditions. We start with the case when only the self-sustained RF discharge is burning.
U, = 0V, dc
100 V, dc
100 V, da
153 V, dc
153 V, da
200 V, dc
200 V, da
250 V, dc
250 V, da
300 400 Udc,V
Figure 2. 'Cathode' dc and 'anode' da sheath thicknesses against the applied dc voltage with fixed values of rf voltage and N2 pressure of 0.5 Torr. Solid points are for dc and empty points are for da.
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Figure 3. 'Cathode' dc and 'anode' da sheath thickness against applied dc voltage with fixed values of rf voltage and N2 pressure of
The rf capacitive discharge possesses a layered structure and it consists of near-electrode sheaths of almost equal thickness and a region of a quasi-neutral plasma. Let us ignite the rf discharge in the weak-current a-mode, in which the ionization occurs in the region of the quasi-neutral plasma and the conductivity of near-electrode sheaths is small [19,20,23]. Now let us apply a small dc voltage across the electrodes. As a result the thickness of the sheath near the 'cathode' dc increases, and the thickness of the sheath near the 'anode' da remains almost unchanged or decreases weakly (see figures 2 and 3). In this case we observe the first mode of the longitudinal combined discharge—the rf discharge perturbed with the dc electric field. If the rf voltage does not exceed the limiting value Urf the further increase in the dc voltage decreases the plasma region width, and at some Udc value the discharge goes out. The less is the rf voltage sustained, the less dc voltage Udc is required for discharge extinguishing. However, with further growth in Udc the joint action of dc and rf voltages entails the gas breakdown, and the discharge is ignited in the second mode, which we tentatively call 'the combined discharge.
Figure 4 shows the extinction curve Urf ext (p) of a discharge. The rf discharge may exist only at rf voltage
Figure 4. Rf extinction voltage Urf ext of the self-sustained rf discharge, the minimum rf voltage Urf.min for the transition from the first mode of the combined discharge to the second one, the dc voltage Udc.tr, corresponding to this transition and the dc voltage igniting the self-sustained dc discharge Udc.br against gas pressure.
values exceeding Urf.ext. At a low gas pressure (to the left of the minimum) the extinction curve possesses a region of multi-valued dependence of the extinction voltage on the gas pressure [23, 24]. The reasons for such a behaviour of the extinction are given clearly in ; therefore we will not pay attention to it here. Figure 4 shows the critical rf voltage Urf ^n against nitrogen pressure. At Urf = Urf.min the discharge does not go out with the growth in dc voltage but experiences a transition to the second mode. The dc voltage value required for the transition from the first mode to the second one equals Udc = Udatr and it is shown in figure 4. It is clear from the figure that at a low nitrogen pressure and a high rf voltage the rf discharge extinction curve Urf.ext and the critical rf voltage curve of the transition to the second mode Urf.min merge. Therefore, the region of pressure and the rf voltage in which the first mode of the combined discharge can be extinguished by application of the dc voltage is limited from the low pressure side and it is contained between the Urf.ext and Urf.min curves. It does not mean that the existence region of the second mode of the combined discharge is located only in the gap between the Urf^xt and Ur^min curves. The first mode is also observed at the rf voltage values Urf >Urf.min, but with the dc voltage increasing the discharge experiences a transition to the second mode. Besides, whereas in the first mode the 'cathode' sheath is dark and its width grows with increasing Udc, the glow of violet tint appears in the 'cathode' sheath after the transition to the second mode (thus indicating the appearance of high energy electrons in the sheath), and its thickness decreases with the dc voltage increasing. Figures 2 and 3 clearly demonstrate the weak variation of the 'anode' sheath thickness in the first mode in contrast to its decrease with the dc voltage increasing in the second mode.
Figure 4 also shows the dc voltage required for the transition from the first mode to the second one (during which the breakdown of the 'cathode' sheath occurs judging from the variation in the discharge colour), which happens to be much less than the ignition voltage of the self-sustained dc discharge. For instance, at the nitrogen pressure of 0.14 Torr (near the minimum of the dc breakdown curve) the breakdown voltage value equals Udabr = 310 V, and the voltage value corresponding to the discharge transition to the second mode
Figure 5. Dc voltages for the transition from the first mode of the combined rf/dc discharge to the second one against the applied rf voltage at various nitrogen pressure values.
equals Udc.tr = 189 V. First, it is due to the circumstances that not only is the dc voltage drop concentrated across the 'cathode sheath, but at certain time moments almost all of the rf voltage applied to the electrodes drops across it. second, the flow of positive ions and high energy photons enters the 'cathode sheath from the plasma region (which knock out secondary electrons hitting the electrode surface), as well as metastable atoms and molecules (which enhance the flow of secondary electrons under deactivation as well as via set ionization in the 'cathode' sheath). As known , metastable electron states N2(A3£+) and N2 (a'1play an important role in sustaining the dc discharge; meanwhile ionization processes (including associative ionization) occur according to the reactions
N2(A 3£+) +N2(a' 1Eu-) — N++N2 + e
— N+ + e
N2(a' 1Eu-) +N2(a' 1Eu-) — N++ N2+ e
- N4+ +e.
These reactions may take place in the plasma volume as well as in the cathode sheath of the combined discharge, making the transition from the first mode to the second one easier. The amount of energy freed under quenching metastables N2 (a' and N2 (A 3E+) on the 'cathode' surface (8.4 eV and 6.2 eV , respectively) is sufficient to produce secondary electrons. Therefore, it is easier to break the 'cathode' sheath of the combined discharge in the first mode than to ignite the dc discharge.
Figure 5 exposes the dc voltage values at which the transition from the first mode of the combined discharge to the second one occurs against the applied rf voltage at various values of nitrogen pressure. The figure shows that the higher is the rf voltage, the lower is the dc voltage to be applied to produce the discharge transition to the second mode. At low rf voltage values the plasma concentration is small, and the application of the dc voltage induces fast growth in the 'cathode' sheath thickness. In order to break a thick 'cathode' sheath, a higher dc voltage is required, which we observe in the figure.
Uf= 0 V
600 Udc, V
Figure 6. CVCs of the combined discharges for nitrogen pressure p = 0.1 Torr.
Now consider the CVCs of the combined discharge. Figure 6 shows the direct current Idc against the direct voltage Udc at the nitrogen pressure of 0.1 Torr. At low rf voltage values (below 50 V) it is impossible to support the self-sustained discharge; therefore, we observe in the figure the CVCs for the self-sustained dc discharge (at Urf = 0 V) and for the third mode of the longitudinal combined discharge—non-self-sustained dc discharge perturbed with rf voltage. On applying the rf voltage to the dc discharge it is possible to sustain the discharge burning at a smaller dc voltage than for a self-sustained dc discharge (therefore, we call the third mode the 'non-self-sustained dc discharge'). At higher rf voltages (in the figure it corresponds to the curves for Urf > 67 V) it is possible to support a self-sustained rf discharge. First, increasing the dc voltage Udc involves a small growth in the dc current through the discharge, then the current achieves a maximum and with further growth in Udc the current decreases. This current decrease is associated with the increase in the 'cathode' sheath thickness and the decrease in the plasma region width. The number of charged particles within the plasma volume decreases thus leading to the reduction in the discharge current. Then at some dc voltage value the discharge goes out, but at higher Udc voltages it ignites again but in the second mode, and the dc voltage increase is accompanied by the increase in discharge current.
At the rf voltage above 133 V the first mode of the combined discharge does not go out, and at a sufficiently large dc voltage a breakdown of the 'cathode' sheath occurs (electron avalanches develop in the total voltage drop in rf and dc voltages across the 'cathode' sheath). This breakdown at low pressure is accomplished without a jump; the discharge current increases and the discharge experiences a smooth transition from the first mode to the second one.
Figure 7 demonstrates the CVCs of the longitudinal combined discharge at the nitrogen pressure of p = 1 Torr. In the absence of the rf voltage the self-sustained dc discharge before extinguishing burns in the normal mode, occupying only a part of the electrode area. Besides, the current increases due to the expansion of the current spot area on the electrodes with an almost unchanged value of the dc voltage (actually a small decrease in the dc voltage across the electrodes is