Abstract
A theoretical global model is presented for describing the kinetics of generation and growth of clusters and nanoparticles in low-pressure plasmas, where important processes for clusters and grains are collisions with monomers, electrons, and ions and particle coagulation and loss because of diffusion and gas flow drag. Simple equations are given for calculations of monomer density, particle-size distribution function, critical cluster size, the rate of particle production and particle density and mean size, and plasma characteristics (the densities and average energies of “cold” and “hot” electrons and the density of positively charged ions). The model is self-consistent; that is, the above-mentioned properties of clusters, nanoparticles, electrons, and ions are calculated jointly from coupled equations as functions of a small number of radio frequency (RF) discharge parameters (discharge geometry; absorbed electric power; voltage across the RF sheath; gas pressure; composition; and flow rate). Comparisons are made with the experimental data on SiH4-Ar mixtures.
Similar content being viewed by others
References
Dusty Plasma, Ed. by A. Bouchoule (Wiley, New York, 2000).
Special issue: Plasma Sources Sci. Technol. 3(3) (1994).
L. Boufendi, A. Plain, J. Ph. Blondeau, et al., Appl. Phys. Lett. 60, 169 (1992).
A. Bouchoule and L. Boufendi, Plasma Sources Sci. Technol. 2, 204 (1993).
L. Boufendi, J. Hermann, A. Bouchoule, et al., J. Appl. Phys. 76, 148 (1994).
L. Boufendi and A. Bouchoule, Plasma Sources Sci. Technol. 3, 262 (1994).
L. Boufendi, A. Bouchoule, and T. Hbid, J. Vac. Sci. Technol., A 14(2), 572 (1996).
H. Kawasaki, K. Sakamoto, S. Maeda, et al., Jpn. J. Appl. Phys. 37, 5757 (1998).
Ch. Hollenstein, J.-L. Dorier, J. Dutta, et al., Plasma Sources Sci. Technol. 3, 278 (1994).
C. Courteille, Ch. Hollenstein, J.-L. Dorier, et al., J. Appl. Phys. 80, 2069 (1996).
M. Kushner, J. Appl. Phys. 63, 2532 (1998).
J. Perrin, C. Bohm, R. Etemadi, and A. Lloret, Plasma Sources Sci. Technol. 3, 252 (1994).
S. Choi and M. Kushner, J. Appl. Phys. 74, 853 (1993).
A. Fridman, L. Boufendi, T. Hbid, et al., J. Appl. Phys. 79, 1303 (1996).
D. Lemons, R. Keinigs, D. Winske, and M. Jones, Appl. Phys. Lett. 68, 613 (1996).
V. Schweigert and I. Schweigert, J. Phys. D: Appl. Phys. 29, 655 (1996).
T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995).
V. Fortov, A. Khrapak, S. Khrapak, et al., Usp. Fiz. Nauk 174, 495 (2004).
B. Gordiets and C. M. Ferreira, J. Appl. Phys. 84, 1231 (1998).
B. Gordiets and C. M. Ferreira, J. Appl. Phys. 86, 4118 (1999).
U. Kortshagen and U. Bhandarkar, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 60, 887 (1999).
U. Bhandarkar, M. Swihart, S. Girshik, and U. Kortshagen, J. Phys. D: Appl. Phys. 33, 2731 (2000).
K. de Bleecker, A. Bogaerts, and W. Gijbels, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 69, 056409 (2004).
A. Gallagher, A. Howling, and Ch. Hollenstein, J. Appl. Phys. 91, 5571 (2002).
U. Bhandarkar, U. Kortshagen, and S. Girshik, J. Phys. D: Appl. Phys. 36, 1399 (2003).
K. de Bleecker, A. Bogaerts, and W. Gijbels, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 70, 056407 (2004).
A. Gallagher, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 62, 2690 (2000).
B. Gordiets, L. Shelepin, and Yu. Shmotkin, Tr. Fiz. Inst. im. P. N. Lebedeva Ross. Akad. Nauk 145, 1391 (1984).
B. Gordiets and Yu. Shmotkin, Khim. Fiz. 4(4), 484 (1985).
B. Gordiets, A. Osipov, and L. Shelepin, Kinetic Processes in Gases and Molecular Lasers (Gordon and Breach, New York, 1986).
B. Gordiets and E. Bertran, Chem. Phys. Lett. 414, 423 (2005).
D. Frank-Kamenetskii, Diffusion and Heat Conductivity in Chemical Kinetics (Nauka, Moscow, 1967) [in Russian].
M. Capitelli, C. M. Ferreira, B. Gordiets, and A. Osipov, Plasma Kinetics in Atmospheric Gases (Springer, Berlin, 2000).
V. Godyak and A. Khanneh, IEEE Trans. Plasma Sci. PS-14, 112 (1986).
Yu. Raizer, M. Shneider, and N. Yatsenko, High-Frequency Capacitive Discharges (Mosk. Fiz.-Tekh. Inst., Moscow, 1995) [in Russian].
A. Lichtenberg, V. Vaheni, and M. Lieberman, J. Appl. Phys. 75, 2339 (1994).
Physico-Chemical Processes in Gas Dynamics: A Handbook, Ed. by G. Chernyi and S. A. Losev (Mosk. Gos. Univ., Moscow, 1995) [in Russian].
J. Perrin, J. Schmitt, G. de Rosny, et al., Chem. Phys. 73, 383 (1982).
H. Chatham, D. Hils, R. Robertson, and A. Gallagher, J. Chem. Phys. 81, 1770 (1984).
Author information
Authors and Affiliations
Additional information
Published in Russian in Khimicheskaya Fizika, 2008, Vol. 27, No. 4, pp. 79–93.
The article was translated by the authors.
Rights and permissions
About this article
Cite this article
Gordiets, B.F., Bertran, E. A self-consistent model for the production and growth of nanoparticles in low-temperature plasmas. Russ. J. Phys. Chem. B 2, 315–328 (2008). https://doi.org/10.1134/S1990793108020243
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1990793108020243