A model is presented to describe particle growth in inductively coupled plasma. The model consists of plasma chemistry and a coagulation module that adopts a modified collision frequency function. The modified collision frequency function is modified by a collision correlation factor that reflects the repulsive force of the particle charge in plasma in order to describe the reduction of coagulation among medium size particles (around 100 nm). In this model, plasma state and concentration of nuclei are determined by a spatially averaged global model in the plasma chemistry module. Particle growth is calculated by a coagulation module. To verify the validity of the model, comparison analysis is performed between experimental data obtained with PBMS and models, some of which are modified by a collision correlation factor. The analysis is performed with respect to dependencies on synthesis time, plasma source power and chamber pressure. From the analysis, we confirm the validity of the model that adopts a modified collision frequency function for the plasma condition.
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L. Boufendi and A. Bouchoule, Industrial developments of scientific insights in dusty plasmas, Plasma Sources Sci Technol., 11 (3A) (2002) A211–A218.
A. Bouchoule, Dusty plasmas: Physics, chemistry and technological impacts in plasma processing, First Ed. John Willey & Sons, New York, USA (1999).
M. Shiratani, H. Kawasaki, T. Fukuzawa, Y. Watanabe, Y. Yamamoto, S. Suganuma, M. Hori and T. Goto, A study on the time evolution of SiH3 surface loss probability on hydrogenated amorphous silicon films in SiH4 rf discharges using infrared diodelaser aborption spectroscopy, J. Phys. D, 31 (7) (1998) 776–780.
X. D. Pi, R. W. Liptak, J. Deneen Nowak, N. P. Wells, C. B. Carter, S. A. Campbell and U. Kortshagen, Air-stable fullvisible- spectrum emission from silicon nanocrystals synthesized by an all-gas-phase plasma approach, Nanotechnology, 19 (24) (2008) 245603.
S. Seo, S. Chang, T. Yoo and J. D. Chung, Hydrophilic behavior of polymer films treated by atmospheric pressure plasma, Int. J. Air-Cond. Ref, 20 (2) (2012) 1250007.
Mark J. Kushner, A model for the discharge kinetics and plasma chemistry during plasma enhanced chemical vapor deposition of amorphous silicon, J. Appl. Phys, 63 (8) (1988) 2532.
J. Perrin, O. Leroy and M. C. Bordage, Cross-sections, rate constants and transport coefficients in silane plasma chemistry, Contrib. Plasma. Phys., 36 (1) (1996) 3–49.
M. Kawase, T. Nakai, A. Yamaguchi, T. Hakozaki and K. Hasimoto, Numerical simulation of plasma chemical vapor deposition from silane: Effects of the plasma-substrate distance and hydrogen dilution, Jpn. J. Appl. Phys., 36 (1) (1997) 3396–3407.
D. J. Kim and K. S. Kim, Analysis on nanoparticle growth by coagulation in silane plasma reactor, AlChE Journal, 48 (11) (2002) 2499–2509.
K. de Bleecker, A. Bogaerts and W. Goedheer, Modelling of nanoparticle coagulation and transport dynamics in dusty silane discharges, New Journal of Physics, 8 (9) (2006) 178–198.
D. C. Kwon, W. S. Chang, M. Park, D. H. You, M. Y. Song, S. J. You, Y. H. Im and J.-S. Yoon, A self-consistent global model of solenoidal-type inductively coupled plasma discharges including the effects of radio-frequency bias power, J. Appl. Phys., 109 (7) (2011) 3311–3318.
D. C. Kwon, Development of complex gas discharge simulators for inductively coupled plasma sources based on fluid model and finite difference method, Chungbuk University, Ph.D Thesis (2010).
S. H. Bae, D. C. Kwon and N. S. Yoon, Development of high density inductively coupled plasma sources for SiH4/O2/Ar discharge, Journal of the Korean Vacuum Society, 17 (5) (2008) 426–434.
A. Prakash, A. P. Bapat and M. R. Zachariah, A simple numerical algorithm and software for solution of nucleation, surface growth, and coagulation problems, Aerosol Science and Technology, 37 (11) (2003) 892–898.
R. N. Nowlin and R. N. Carlile, The electrostatic nature of contaminative particles in a semiconductor processing plasma, J. Vac. Sci. Technol., 9 (5) (1991) 2825.
W. G. Lee, D. C. Kwon and N.-S. Yoon, Development of a two-dimensional fluid simulator for a SiH4 discharge in transformer coupled plasma sources, Journal of the Korean Vacuum Society, 18 (6) (2003) 426–434.
R. K. Janev, D. Reiter and U. Samm, Collision processes in low-temperature hydrogen plasmas, Institut für Plasmaphysik, Trilat-eral Euregio Cluster, Jülich, Germany (2003).
S. Hideo and O. Kazyuki, Plamsa electronics, Translation Ed. Kyohak Publishing Co, Seoul, Korea (2006).
T. Matsoukas, Jouranl of colloid and Interface Science, 187 (1997) 474–483.
William C. Hinds, Aerosol technology: Properties, behavior, and measurement of airborne particles, Second Ed. Jonh Wiley & Sons, Inc, New York, USA (1998).
M. Moravej, S. E. Babayan, G. R. Nowling, X. Yang and R. F. Hicks, Plasma enhanced chemical vapour deposition of hydrogenated amorphous silicon at atmospheric pressure, Plasma Sources Sci. Technol., 13 (1) (2004).
Recommended by Associate Editor Dong Geun Lee
Yeongseok Kim received his Bachelor of Science degree in Mechanical Engineering from Sungkyunkwan University of Technology, Korea in 2012. Currently, he is a candidate of combined master’s and doctorate program in the School of Mechanical at Sungkyunkwan University. His research is focused on the modeling of nanoparticle synthesis.
Taesung Kim received his Bachelor of Science degree in Mechanical Engineering from Seoul National University of Technology, Korea in 1994. He then receive his Master of Science, and Doctor of Philosophy degrees in Mechanical Engineering from Minnesota University, USA in 1998, and 2002, respectively. Dr. Kim currently works as an associate professor in the School of Mechanical Engineering and adjunct professor in the SKKU Advanced Institute of Nano Technology at Sungkyunkwan University in Suwon, Korea. His research interests include nanoparticle synthesis, development of applications related with bio aerosol, Chemical Mechanical Polishing, and thin film synthesis.
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Kim, Y., Kim, H.U., Shin, Y. et al. Modeling of silicon nanoparticle formation in inductively coupled plasma using a modified collision frequency function. J Mech Sci Technol 28, 4693–4703 (2014). https://doi.org/10.1007/s12206-014-1036-z
- Silicon nanoparticle
- Inductively coupled plasma
- Modified collision frequency function