Numerical Modeling of Non-equilibrium Plasma Discharge of Hydrogenated Silicon Nitride (SiH4/NH3/H2)

Document Type: Original Article


Mohamed first University, Department of Physics, LETSER Laboratory, Oujda, Morocco


In this work, we model a radiofrequency discharge of hydrogenated silicon nitride in a capacitive coupled plasma reactor using Maxwellian and non-Maxwellian electron energy distribution function. The purpose is to investigate whether there is a real advantage and a significant contribution using non-Maxwellian electron energy distribution function rather than Maxwellian one for determining the fundamental characteristics of a radiofrequency plasma discharge. The results show the evolution of the non-Maxwellian electron energy distribution function, the mobility and the diffusion coefficient required to determine the fundamental characteristics of the radiofrequency plasma discharge of a hydrogenated silicon nitride deposit at low pressure and low temperature, between the two electrodes of the capacitive coupled plasma reactor.  By comparing these results using non-Maxwellian electron energy distribution function with those calculated using the Maxwellian one, we conclude that the use of non-Maxwellian electronic energy distribution function is more efficient for describing the evolution of a radiofrequency plasma discharge in a capacitive reactor, which will improve the quality of the deposition of thin films.


  1. Su, L. W., Chen, W., Uchino, K., and Kawai, Y., “Two-dimensional simulations of multi-hollow VHF SiH4/H2 plasma”, AIP Advances, Vol. 8, No. 2, (2018), 025316. DOI: 10.1063/1.5003911.
  2. Bavafa, M., Ilati, H., Rashidian, B., “Comprehensive simulation of the effects of process conditions on plasma enhanced chemical vapor deposition of silicon nitride”, Semiconductor Science and Technology, Vol. 23, No. 9, (2008), 095023. DOI: 10.1088/0268-1242/23/9/095023.
  3. Kim, H. J., Wonkyun Y., and Junghoon J., “Effect of electrode spacing on the density distributions of electrons, ions, and metastable and radical molecules in SiH4/NH3/N2/He capacitively coupled plasmas”, Journal of Applied Physics, Vol. 118, No. 4, (2015), 043304. DOI: 10.1063/1.4927531.
  4. Kim, H. J., and Hae June L., “2D fluid model analysis for the effect of 3D gas flow on a capacitively coupled plasma deposition reactor”, Plasma Sources Science and Technology,Vol. 25, No. 3, (2016), 035006. DOI: 10.1088/0963-0252/25/3/035006
  5. Graves, D. B., and Jensen, K. F, “A continuum model of DC and RF discharges”, IEEE Transactions on Plasma Science, Vol. 14, No. 2, (1986), 78-91. DOI: 10.1109/TPS.1986.4316510.
  6. Passchier, J. D. P., and Goedheer, W. J., “A twodimensional fluid model for an argon rf discharge”, Journal of Applied Physics, Vol. 74, No. 6, (1993), 3744-3751. DOI: 10.1063/1.354487.
  7. Li, X. S., Bi, Z. H., Chang, D. L., Li, Z. Wang,C., S., Xu, X., Xu, Y., Lu, W. Q., Zhu, A. M., and Wang, Y. N., “Modulating effects of the low-frequency source on ion energy distributions in a dual frequency capacitively coupled plasma”, Applied Physics Letters, Vol. 93, (2008), No. 3, 031504. DOI: 10.1063/1.2945890.
  8. Grari, M., and Zoheir, C., “Numerical Modeling of Plasma Silicon Discharge for Photovoltaic Application”, Materials Today: Proceedings, Vol. 13, (2019), 882-888. DOI: 10.1016/j.matpr.2019.04.052.
  9. Wang, X. F., Jia, W. Z., Song, Y. H., Zhang, Y. Y., Dai, Z. L., and Wang, Y. N., “Hybrid simulation of electron energy distributions and plasma characteristics in pulsed RF CCP sustained in Ar and SiH4/Ardischarges”, Physics of Plasmas, Vol. 24, No. 11, (2017), 113503. DOI: 10.1063/1.5009416.
  10. Godyak, V. A., and Piejak, R. B., “Abnormally low electron energy and heating-mode transition in a low-pressure argon rf discharge at 13.56 MHz”, Physical Review Letters, Vol. 65, No. 8, (1990), 996. DOI: 10.1063/1.5009416.
  11. Godyak, V. A., Meytlis, V. P., and Strauss, H. R., “Tonks-Langmuir problem for a bi-Maxwellian plasma”, IEEE Transactions on Plasma Science, Vol. 23, No. 4, (1995), 728-734. DOI: 10.1109/27.467995.
  12. Hagelaar,G. J. M., and Pitchford, L. C., “Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models”, Plasma Sources Science and Technology, Vol. 14, No. 4, (2005), 722. DOI: 10.1088/0963-0252/14/4/011.
  13. Pitchford, L. C., and Phelps, A. V., “Comparative calculations of electron-swarm properties in N2 at moderate E/N values”, Physical Review A, Vol. 25, No. 1, (1982), 540. DOI: 10.1103/PhysRevA.25.540.
  14. Godyak, V. A., “Nonequilibrium EEDF in gas discharge plasmas”, IEEE Transactions on Plasma Science, Vol. 34, No. 3, (2006), 755–766. DOI: 10.1109/TPS.2006.875847.
  15. Lieberman, M. A., and Lichtenberg, A. J., “Principles of plasma discharges and materials processing”, John Wiley & Sons, 2005.
  16. Abdelaal, A. M., Attalla, E. M., and Elshemey, W. M., “Estimation of Out-of-Field Dose Variation using Markus Ionization Chamber Detector”, SciMedicine Journal, Vol. 2,No. 1, (2020), 8-15. DOI: 10.28991/SciMedJ-2020-0201-2
  17. Sanito, R. C., You, S. J., Chang, G. M., and Wang, Y. F., “Effect of shell powder on removal of metals and volatile organic compounds (VOCs) from resin in an atmospheric-pressure microwave plasma reactor”, Journal of Hazardous Materials, (2020), 122558.  DOI: 10.1016/j.jhazmat.2020.122558.
  18. Ali, A., Ejaz, N., Nasreen, S., Nasir, A., Qureshi, L. A., and Al-Sakkaf, B. M. “Enhanced Degradation of  Dyes present in Textile Effluent by Ultrasound Assisted Electrochemical Reactor”, Civil Engineering Journal, Vol. 5, No. 10, (2019),  2131-2142. DOI: 10.28991/cej-2019-03091399.
  19. Shoukat, R., and Khan, M. I., “Synthesis of nanostructured based carbon nanowalls at low temperature using inductively coupled plasma chemical vapor deposition (ICP-CVD)”. Microsystem Technologies, Vol. 25, No. 12, (2019), 4439-4444. DOI: 10.1007/s00542-019-04463-7.
  20. Archin, S., “Optimization of Process Parameters by Response Surface Methodology for Methylene Blue Removal Using Cellulose Dusts”, Civil Engineering Journal, Vol. 4, No. 3, (2018). DOI: 10.22090/JWENT.2018.02.007.
  21. Ghorbani, H., Poladi, A., and Hajian, M., “Pulsed DC-Plasma Assisted Chemical Vapor Deposition of α-rich Nanostructured Tantalum Film: Synthesis and Characterization”,  International Journal of EngineeringTransactions A: Basics, Vol. 30, No. 4 , (2017), 551-557. DOI: 10.5829/idosi.ije.2017.30.04a.13.
  22. Capitelli, M. R., Celiberto, Colonna, G., Esposito, F., Gorse, C., Hassouni, K., Laricchiuta, A., and Longo, S., “Fundamental aspects of plasma chemical physics: kinetics”, Springer Science and Business Media, 2015.
  23. Hayashi database,, retrieved on October 27, 2016.
  24. Xia, H., Xiang, D., Yang, W., Mou, P., “Multi-model simulation of 300mm silicon-nitride thin-film deposition by PECVD and experimental verification”, Surface and Coatings Technology, Vol. 297, (2016), 1-10. DOI: 10.1016/j.surfcoat.2016.04.034.
  25. Daoxin, H., Jia, C., Linhong, J. and Yuchun, S., “Simulation of cold plasma in a chamber under high-and low-frequency voltage conditions for a capacitively coupled plasma”, Journal of Semiconductors, Vol. 33, No. 10, (2012), 104004. DOI: 10.1088/1674-4926/33/10/104004.
  26. Samir, T., Liu, Y., Zhao, L.L. and Zhou, Y.W., “Effect of driving frequency on electron heating in capacitively coupled RF argon glow discharges at low pressure”, Chinese Physics B, Vol. 26, No. 11, (2017), 115201. DOI: 10.1088/1674-1056/26/11/115201.
  27. Ghorbani, H., and Poladi, A., “MD-Simulation of Duty Cycle and TaN Interlayer Effects on the Surface Properties of Ta Coatings Deposited by Pulsed-DC Plasma Assisted Chemical Vapor Deposition”, International Journal of EngineeringTransactions B: Applications Vol. 33, No. 5, (2020), 861-869.DOI: 10.5829/ije.2020.33.05b.18.
  28. Kim, H. J., and Lee, H. J. “Analysis of intermediate pressure SiH4/He capacitively coupled plasma for deposition of an amorphous hydrogenated silicon film in consideration of thermal diffusion effects”, Plasma Sources Science and Technology, Vol. 26, No. 8, (2017), 085003. DOI: 10.1088/1361-6595/aa78b4.
  29. Rastani, S., “Process Optimization of Deposition Conditions for Low Temperature Thin Film Insulators used in Thin Film Transistors Displays”, International Journal of EngineeringTransactions B: Applications, Vol. 31, No. 5, (2018), 712-718.DOI: 10.5829/ije.2018.31.05b.05.