Comparison of Models and Numerical Analysis Methods in Fluid Simulation of High Density Inductively Coupled Plasma Sources

고밀도 유도결합 플라즈마원 유체 수송 시뮬레이션을 위한 모델 및 수치해석 방법 비교

  • 권득철 (충북대학 전기공학과) ;
  • 윤남식 (충북대학 전기전자컴퓨터공학) ;
  • 김정형 (한국표준과학연구) ;
  • 신용현 (한국표준과학연구원)
  • Published : 2004.08.01


Various models and various boundary conditions have been suggested for fluid transport simulations of high density plasma discharges such as the inductively coupled plasma discharge. In this work, we compare the various models using one-dimensional simulations based on the FDM(finite difference method), the upwind scheme, the power-law scheme, and the dielectric relaxation scheme[l] Comparing the exactness, the numerical stability and the efficiency of the various models. the most adoptable model is suggested.




  1. S. V. Patanker, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, pp. 83-95, 1980
  2. Michael A. Lieberman, Allan J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, Wiley, pp. 154-163, 1994
  3. K. -B. Persson, Phys. Fluids, vol. 5, p. 1625 (1962)
  4. 최덕인, 플라즈마 물리학과 핵융합, 민음사, pp. 69-79, 1985
  5. D. Bohm, Characteristics of Electrical Discharges in Magnetic Field, McGraw-Hill, p. 77, 1949
  6. N. H. Choi, W. H. Koh, N. S. Yoon, H. B. Park, and D. I. Choi, 'One-Dimensional Hybrid Modeling and simulation of Eectron Cyclotron Resonance Discharge', IEEE Trans. Plasma Sci. 23, 617 (1995)
  7. J. P. Boeuf and L. C. Pitchford, 'Pseudospark discharges via computer simulation', IEEE Trans. Plasma Sci. 19, 286 (1991)
  8. T. J. Sommerer and M. J. Kushner, 'Numerical investigation of the kinetics and chemistry of rf glow discharge plasmas sustained in He, $H_2O_2,$ $He/H/O_2,$ $He/CF_4/O_2,$ and $SiH_4/NH_3$ using a Monte Carlo-fluid hybrid model', J. Appl. Phys. 71, 1654 (1992)
  9. Ming Li, Han-Ming Wu, and Yunming Chen, 'Two-Dimensional Simulation of Inductively Plasma Sources with Self-Consistent Power Deposition', IEEE Trans. Plasma Sci. 23, 558 (1995)
  10. R. A. Stewart, P. Vitello and D. B. Graves, 'Two-dimensional fluid model of high density inductively coupled plasma sources', J. Vac. Sci. Technol. B 12(1) 478 (1994)
  11. R. A. Stewart, P. Vitello, D. B. Graves, E. F. Jaeger and L. A. Berry, 'Plasma uniformity in high-density inductively coupled plasma tools', Plasms Sources Sci. Technol. 4, 36 (1995)
  12. H. H. Choe and N. S. Yoon, 'The Effect of Inertial Terms in the Momentum Equation in Fluid Simulation of High Density Plasma Discharge', J. of Korean Phys. Soc. vol. 42, s859-s866 (2003)
  13. J. D. Bukowski, D. B. Graves and P. Vitello. 'Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles', J. Appl. Phys. 80 (5) (1996)
  14. S. K. Park and D. J. Economou, 'Analysis of low pressure rf glow discharges using a continuum model', J. Appl. Phys. 80 (5) (1996)
  15. S. S. Kim, S. Hamaguchi, N. S. Yoon, C. S. Chang, Y. D. Lee and S. H. Ku, 'Numerical Investigation on Plasma and Poly-Si Etching Uniformly Control over Large Area with a Modified Inductively Coupled Plasma Source', Physics of Plasmas, 8, 1384, (2001)
  16. V. A. Godyak and N. Sternberg, 'Smooth plasmasheath transition in a hydrodynamic model', IEEE Trans. Plasma Sci. 18, 159 (1990)
  17. S. S. Kim;N. S. Yoon;C. S. Chang, 'A One-dimensional Model for a TCP discharge including the collisionless electron heating mechanism', J. Korean Phys. Soc. 29, 678 (1996)
  18. N. S. Yoon, N. H. Choi, B. H. Park, and D. I. Choi, 'One-Dimensional Fluid Model of ECR Discharge with Inhogeneity Effects of External Magnetic Field', IEEE Trans. Plasma. Sci. 23, 609 (1995)
  19. T. E. Nitschke and D. B. Graves, 'A comparison of particle in cell and fluid model simulations of low-pressure radio frequency discharges', J. Appl. Phys. 76, 5646 (1994)
  20. H. H. Choe, N. S. Yoon, S. S. Kim and D. I. Choi, 'A New Unconditionally Stable Algorithm for Steady State Fluid Simulation of High Density Plasma Discharge', Journal of Computational Physics, 170, 550-561 (2001)