Particle Formation In A DC Discharge A. Michaua, G. Lombardia, L. Colina Delacquaa, M. Redolfia, C. Arnasb, X. Bonnina and K. Hassounia a
b
LSPM, CNRS, 99 Avenue J. B. Clément, 93430 Villetaneuse, France LPIIM, CNRS-Université de Provence Centre Saint-Jérôme, Marseille Cedex, France
Abstract. We developed a model for the nucleation, growth and transport of carbonaceous dust particles in a non-reactive gas dc discharge where the carbon source is provided by cathode sputtering. In a first part, we considered only the initial phase of the discharge when the dust charge density remains small with respect to the electron density. We found that an electric field reversal at the entrance of the negative glow region promotes trapping of negatively charged clusters and dust particles, confining them for long times in the plasma and favoring molecular growth. An essential ingredient for this process is electron attachment, which negatively charges the initially neutral clusters. We also showed that the field reversal mechanism can operate to trap negative clusters and particles under both electropositive and strongly electronegative plasma.
Keywords: nanoparticles, nucleation, dusty plasmas, carbon. PACS: 52.80.Hc , 52.27.Cm , 82.33.Xj
INTRODUCTION In this paper, we investigate particle formation originating from plasma–surface interactions, e.g. sputtering and etching processes, in dc discharges generated in nonreactive rare gases. In particular, we consider whether the slight field reversal that takes place in the negative glow (NG) of a dc discharge [1] induces trapping of negative molecules and clusters, leading to an enhancement of the molecular growth of the species sputtered from the cathode surface. We then investigate the coupling phenomena induced by the presence of negative species in the discharge and the subsequent modifications induced in the discharge structure, and especially the existence and strength of field reversal.
INVESTIGATED DISCHARGE A detailed description of the studied discharge may be found in [2]. Experiments are performed in an argon dc glow discharge between two parallel electrodes of 10 cm diameter and separated by 14 cm. The argon pressure is Pg = 0.6 mbar. The bias of the graphite cathode is ~ -550 V, the current is fixed at 80 mA and the input power is ~ 40 W. The resulting carbon cathode sputtering allows the continuous injection in the plasma of carbon atoms. Nanoparticles are collected on the upper side of the anode. The discharge is maintained during 10 minutes in order to keep
discharge current constant. Electron density is determined by Langmuir probes to a few 1010 cm-3. A single generation of dust particles is obtained with a density of ~2.108 cm-3 and an average size of 54 nm after 10 minutes of discharge.
EFFECT OF DISCHARGE STRUCTURE IN THE DUST FORMATION AND TRANSPORT Model Our model describes the different phenomena that lead to particle formation in the dc discharge. In this first part, we are interested in investigating the possibility of particle formation and not in describing the entire dusty plasma phenomena. Consequently, the model considers only the early stages of molecular growth and particle formation when most of the negative charge is carried by electrons and the plasma behaves as a pristine argon discharge. This model [3] [4] describes the discharge structure, cathode sputtering, the detailed kinetics and transport of carbon clusters along with the coupled phenomena of particle nucleation, charging, growth and transport in the discharge gap, and solves for electric field reversal strength and position, cluster size and space distributions, as well as particle number densities, average charge and mass.
Results The simulations parameters are the following : cold electron temperature Te = 0.1 eV (this value was chosen from [5]), Tg = 373.15 K, ζ = 0.1, Eb = 0.225 eV and a sputtering yield at the cathode of 6.10-4. Results are given for a discharge duration of 600 s. The discharge structure is obtained from a non-local ionization model [6] taking into account three electron populations. The electron density is mainly controlled by cold electrons, while the current is carried by intermediate energy electrons (i.e. with an energy larger than the potential well but smaller than the first excitation potential of argon) and the most energetic ones contribute to the ionization. The cold electron density is several orders of magnitude larger than the intermediate and fast ones so that charging and attachment processes occurring during cluster and dust particle growth are controlled by the coldest electrons. At the considered pressure of 0.5 Torr, the sheath width was evaluated to be 3.4 mm. Figure 1 gives the electric field computed from the ionization profile obtained by a Monte-Carlo procedure and the initial electron and ion density along the discharge. The electric field reversal keeps negative particles in a region of high electron density. In contrast, neutral particles are not confined in this electrical trap and escape the discharge region.
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Figure 2 : cluster density at 600s
Carbon neutral clusters from C to C3 are sputtered from the cathode (x=0 cm). The sputtering rate can be roughly evaluated [7] from the ion energy, i.e., 80 eV at an averaged value of 5.10-3. The clusters can grow by coagulation. The transfer between neutral and negative clusters is due to attachment/detachment and charge transfer processes. Figure 2 shows the size distribution of neutral and negative clusters at the end of the discharge duration (600s). Neutral species, apart from the C to C3 which are imposed by sputtering, are very low because of the diffusive losses to the wall. Negative species exist starting from C2- and are predominant. The negative species are localized at the field reversal position (x=2 cm) where the electron density is highest and the electric field can trap them. This trapping effect enables a high enough residence time, as necessary for aggregation processes. Neutral species from C4 to C30 are not created by aggregation of smaller neutral clusters but by charge transfer between small neutral species and bigger negative clusters. A cluster growth kinetic scheme can be proposed. First, neutral clusters C, C2, C3 are emitted. Then these primary clusters grow up to C4 where electron attachment occurs and aggregation processes lead to the formation of larger negative clusters. Finally the neutral cluster population is governed by charge transfer processes (basically C2 + Cn- C2- + Cn). The third module of the model deals with particle growth and transport. Figure 3 presents the density of the solid particles at 600s. The particle cloud is localized around the field reversal position and the maximum particle density is 2x108 cm-3. The figure also shows the average diameter of the particles. It reaches a maximum of about 20 nm just at the field reversal position. The minimum diameter value is 10 nm. Finally on the same figure we show the particle average charge number. The largest charge number is around -4 and is achieved at the field reversal position. The time evolution of the particle density and diameter (Figure 4) presents 3 phases: • Before 150 s an incubation phase where we have only molecular growth on the few primary particles. • A nucleation burst where we have a strong increase of the particle density. High numbers of small particles nucleate. The averaged diameter is then decreasing.
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A nucleation and growth phase characterized by the increase of both density and diameter by molecular growth, and to a lesser extend by coagulation.
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These results are in qualitative agreement with experimental measurements. The averaged diameter is therefore about 20 nm when the experimentally observed particle size is as large as 55 nm [2].
EFFECT OF DUST ON THE DISCHARGE The model considered so far assumes that the presence of charged species does not affect the discharge structure. This assumption is only valid in the early stages of the molecular growth and particle formation. In order to investigate longer discharge durations or for a better description of the particle growth, one needs a self-consistent determination of electron, clusters, positive ions and electric field in the whole discharge. This self-consistent model is numerically quite difficult due to high coupling effects of all species in our detailed collisional model.
A simplified three species electronegative plasma model In order to evaluate the influence of the charged species on the discharge properties, and especially the field reversal effect, a very simple model was developed. The negative ions and the dust particles are lumped and treated as a single average ion. The model considers therefore 3 species: cold electrons, argon ions and an average negative ion population. The ambipolar field, electron density, positive ion density and the average negative ion density were self-consistently determined by coupling the species transport equations to a current balance equation that specifies that the total current is zero (ambipolar plasma). The electron balance is extended to include attachment on clusters and on particles but also a variable radial loss term [8] which depends of the negative ions to electron density ratio (i.e. the degree of electronegativity).
The improvement in this discharge model consists of taking into account the influence of the negative species in the charge balance for the ambipolar electric field, the consumption of electrons to particles and clusters and the loss tem corrected by the electronegativity degree of the discharge. It is worthy to emphasize that the present simple model and the one used in the previous section strongly differ by the way the electric field is determined, i.e., a Boltzmann equilibrium of the electron in the previous section and zero current in this simple model., Results of this model are given in Figure 5 and Figure 6 for different attachment frequencies (from 0 to 10-3 s-1). The results are shown in terms of the computed electronegativity degree. As the attachment rate increases (i.e. increasing electronegativity degree α), the electron density decreases by up to 2 orders of magnitude, whereas the ambipolar electric field in the bulk plasma remains quite moderate even for strong variations of the charged species densities. We still obtain a field reversal effect even for a strongly electronegative discharge 1E12
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Figure 6 : electron density profiles as function of electronegativity degree
CONCLUSION The study presented in this paper clearly shows that the dust formation observed in a dc discharge with a graphite cathode can be well interpreted in terms of molecular cluster build-up, particle nucleation, and growth. Particle production is a complex phenomenon that is governed by both molecular processes/attachment and heterogeneous processes, i.e., sticking. Despite the strong assumption of averaged valued particles, our model, nevertheless predicts particle densities and diameters in good qualitative agreement with experiment. In order to better predict the size distribution of the particles, the next step would be to include, when computing coagulation rates, the spread in sizes and charges of the dust population. We also expect that, if considering longer discharges where very large particles can grow, the coupling between the dust and the discharge will strengthen and no longer be negligible.
ACKNOWLEDGMENTS This work is supported in part by the French Agence Nationale de la Recherche under the contract CRWTH ANR-09-BLAN-0070-01 and by the FR-FCM under contract CEA TechnoFusion V3580.001.
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8]
J. P. Boeuf, L. C. Pitchford, 1995 Journal of Physics D: Applied Physics 28, p. 2083 C. Dominique, C. Arnas, 2007 Journal of Applied Physics 101, p. 123304 A. Michau, G. Lombardi, et al., 2010 Plasma Sources Science and Technology 19, p. 034023 A. Michau, G. Lombardi, et al., 2010 Plasma Physics and Controlled Fusion 52, p. 124014 U. Kortshagen, L. Tsendin, 2002 In: Electron Kinetics and Application of Glow Discharges, Springer, V. I. Kolobov, L. D. Tsendin, 1992 Physical Review A 46, p. 7837 E. Oyarzabal, R. P. Doerner, et al., 2008 Journal of Applied Physics 104, p. 043305 M. A. Lieberman, A. J. Lichtenberg, 1994 In: Principles of plasma discharges and materials processing, John Wiley & Sons, New York,
