Matching an RF Sheath Model to a Bulk Plasma Model

IEEE Transactions on Plasma Science

Volumn 23, Issue 4, 1995, Pages 717-727

  Nitschke, Timothy E ^a   Graves, David B ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; ELECTRIC DISCHARGES; ELECTRIC IMPEDANCE; ELECTRON CYCLOTRON RESONANCE; ELECTROSTATICS; FLUIDS; IONS; MATHEMATICAL MODELS; PLASMA DENSITY; PLASMA SIMULATION; PLASMA SOURCES;

ANGULAR DISTRIBUTION FUNCTION; ELECTROSTATIC PROBE THEORY; GODYAK-STERNBERG SHEATH MODEL; SHEATH IMPEDANCE;

PLASMA SHEATHS;

EID: 0029352781     PISSN: 00933813     EISSN: 19399375     Source Type: Journal    
DOI: 10.1109/27.467994     Document Type: Article

References (33)

1. D. B. Graves and K. F. Jensen, “A continuum model of DC and RF discharges,” IEEE Trans. Plasma Sci., vol. 14, pp. 78–91, June 1986.
2. A. D. Richards, B. E. Thompson, and H. H. Sawin, “Continuum modeling of argon radio frequency glow discharges,” Appl. Phys. Lett., vol. 50, no. 9, pp. 492–494, 1987.
3. A. P. Paranjpe, J. P. McVittie, and S. A. Self, “Algorithms for numerical simulation of radio-frequency glow discharges,” Phys. Rev. A, vol. 41, no. 12, pp. 6949–6962, 1990.
4. R. K. Porteous, H. M. Wu, and D. B. Graves, “A two-dimensional, axisymmetric model of a magnetized glow discharge plasma,” Plasma Sources Sci. Technol., vol. 3, pp. 25–39, 1994.
5. K. Kondo, H. Kuroda, and T. Makabe, “Spatiotemporal characteristics determined by a relaxation continuum model of an inductively coupled plasma,” Appl. Phys. Lett., vol. 65, no. 1, pp. 31–33, 1994.
6. B. W. Yu and S. L. Girshick, “Modeling inductively coupled plasmas: The coil current boundary condition,” J. Appl. Phys., vol. 69, no. 2, pp. 656–661, 1991.
7. P. L. G. Ventzek, T. J. Sommerer, R. J. Hoekstra, and M. J. Kushner, “Two-dimensional hybrid model of inductively coupled plasma sources for etching,” Appl. Phys. Lett., vol. 63, no. 11, pp. 605–607, 1993.
8. 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, vol. 12, no. 1, pp. 478–485, 1994.
9. M. H. Cho, N. Hershkowitz, and T. Intrator, “Temporal evolution of collisionless sheaths,” J. Vac. Sci. Technol. A, vol. 6, no. 5, pp. 2978–2986, 1988.
10. J. H. Keller, J. C. Forster, and M. S. Barnes, “Novel radio-frequency induction plasma processing techniques,” J. Vac. Sci. Technol. A, vol. 11, no. 5, pp. 2487–2491, 1993.
11. V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, “Electrical characteristics of parallel plate RF discharges in argon,” IEEE Trans. Plasma Sci., vol. 19, pp. 660–676, Aug. 1991.
12. K. Kohler it et al., “Plasma potentials of 13.56-MHz RF argon glow discharges in a planar system,” J. Appl. Phys., vol. 57, no. 1, pp. 59–66, 1985.
13. C. Wild and P. Koidl, “Structured ion energy distribution in radio frequency glow-discharge systems,” Appl. Phys. Lett., vol. 54, no. 6, pp. 505–507, 1989.
14. A. Manenschijn, G. C. A. M. Janssen, E. van der Drift, and S. Radelaar, “Measurement of ion impact energy and ion flux at the RFelectrode of a parallel plate reactive ion etcher,” J. Appl. Phys., vol. 69, no. 3, pp. 1253–1262, 1991.
15. J. James, “Angular impact energy distributions of argon ions at the powered electrode of a helicon plasma source,” J. Vac. Sci. Technol. A, vol. 12, no. 1, pp. 97–105, 1994.
16. I. Langmuir and L. Tonks, “A general theory on the plasma of an arc,” Phys. Rev., vol. 34, no. 6, pp. 876–924, 1929.
17. S. A. Self, “Asymptotic plasma and sheath representations for low pressure discharges,” J. Appl. Phys., vol. 36, no. 2, pp. 456–459, 1965.
18. A. B. Wardlaw and I. M. Cohen, “Continuum analysis of the photoionization chamber in the transition from low to high rates of ionization,” Phys. Fluids, vol. 16, no. 5, pp. 637–650, 1973.
19. P. M. Chung, L. Talbot and K. J. Touryan, Electric Probes in Stationary and Flowing Plasmas: Theory and Applications. New York: Springer-Verlag, 1975.
20. H. Schlicting, Boundary Layer Theory. New York: McGraw-Hill, 1977.
21. V. A. Godyak and N. Sternberg, “Dynamic model of the electrode sheaths in symmetrically driven RFdischarges,” Phys. Rev. A, vol. 42, no. 4, pp. 2299–2312, 1990.
22. M. A. Lieberman, “Analytical solution for capacitive RF sheath,” IEEE Trans. Plasma Sci., vol. 16, pp. 638–643, Dec. 1988; and “Dynamics of a collisional, capacitive RF sheath,” vol. 17, pp. 338–341, Apr. 1989.
23. 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., to appear.
24. K. Kohler, D. E. Home, and J. W. Coburn, “Frequency dependence of ion bombardment of grounded surfaces in RF argon glow discharges in a planar system,” J. Appl. Phys., vol. 58, no. 9, pp. 3350–3355, 1985.
25. M. Surendra and D. B. Graves, “Particle simulations of radio-frequency glow discharges,” IEEE Trans. Plasma Sci., vol. 19, pp. 144–157, Apr. 1991.
26. C. B. Zarowin, “Plasma etch anisotropy—Theory and some verifying experiments relating ion transport, ion energy and etch profiles,” Solid-State Sci. and Technol., vol. 130, no. 5, pp. 1144–1152, 1983.
27. M. A. Lieberman, “Basic RF discharge model,” Electronics Research Laboratory, Univ. California, Berkeley, Memo. No. UCB/ERL M87/65, 1988.
28. A. Metze, D. W. Ernie, and H. J. Oskam, “Application of the physics of plasma sheaths to the modeling of RF plasma reactors,” J. Appl. Phys., vol. 60, no. 9, pp. 3081–3087, 1986.
29. V. A. Godyak, “Modified Bohm criterion for a collisional plasma,” Phys. Lett., vol. 89A, no. 2, pp. 80–81, 1982.
30. P. L. G. Ventzek, R. J. Hoekstra, and M. J. Kushner, “Two-dimensional modeling of high plasma density inductively coupled sources for materials processing,” J. Vac. Sci. Technol. B, vol. 12, no. 1, pp. 461–477, 1994.
31. V. Vahedi, E. Kawamura, and G. Dipeso, private communication.
32. A. E. Wendt and W. N. G. Hitchon, “Electron heating by sheaths in radio frequency discharges,” J. Appl. Phys., vol. 71, no. 10, pp. 4718–4726, 1992.
33. M. Surendra and D. Vender, “Collisionless electron heating by radio-frequency plasma sheaths,” Appl. Phys. Lett., vol. 65, no. 2, pp. 153–155, 1994.