Journal of the Semiconductor & Display Technology (반도체디스플레이기술학회지)

The Korean Society Of Semiconductor & Display Technology (한국반도체디스플레이기술학회)
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Simulation of Capacitively Coupled RF Plasma; Effect of Secondary Electron Emission - Formation of Electron Shock Wave

  • Published : 2009.09.30
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Abstract

This paper presents one and two dimensional simulation results with discontinuous features (shocks) of capacitively coupled rf plasmas. The model consists of the first two and three moments of the Boltzmann equation for the ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The local field and drift-diffusion approximations are not employed, and as a result the charged species conservation equations are hyperbolic in nature. Hyperbolic equations may develop discontinuous solutions even if their initial conditions are smooth. Indeed, in this work, secondary electron emission is shown to produce transient electron shock waves. These shocks form at the boundary between the cathodic sheath (CS) and the quasi-neutral (QN) bulk region. In the CS, the electrons emitted from the electrode are accelerated to supersonic velocities due to the large electric field. On the other hand, in the QN the electric field is not significant and electrons have small directed velocities. Therefore, at the transition between these regions, the electron fluid decelerates from a supersonic to a subsonic velocity in the direction of flow and a jump in the electron velocity develops. The presented numerical results are consistent with both experimental observations and kinetic simulations.

Keywords

References

  1. Coburn, J. W., and Winters, H., “Ion- and electronassisted gas surface chemistry - an important effect in plasma processing” J. Appl. Phys., Vol. 50, pp. 3189-3196, 1979. https://doi.org/10.1063/1.326355
  2. Kim, H. C., and Manousiouthakis, V. I., “Simulation Based Plasma Reactor Design for Improved Ion Bombardment Uniformity,” J. of Vac. Sci. Technol. B, Vol. 18, pp. 841-847, 2000. https://doi.org/10.1116/1.591284
  3. Kim, H. C., and Sul, Y. T., “Development of Virtual Integrated Prototyping Simulation Environment of Plasma Chamber Analysis and Design (VIP-SEPCAD),” J. of the Korean Society of Semiconductor Equipment Technology, Vol. 2, pp. 9-12, 2003.
  4. Surrendra, M., and Graves, D. B., “Particle simulations of radio-frequency glow discharges,” IEEE Trans. Plasma. Sci., Vol. 19, pp. 144-157, 1991. https://doi.org/10.1109/27.106808
  5. Lymberopoulos, D. P. and Economou, D. J., “Fluid simulation of glow discharges; Effect of metastable atoms in argon,” J. Appl. Phys., Vol. 73, pp. 3668-3679, 1993. https://doi.org/10.1063/1.352926
  6. Kim, H. C., Sul, Y. T., and Manousiouthakis, V. I., “On Rapid Computation of Time Periodic Steady State in Simulation of Capacitively Coupled RF Plasma,” IEEE Trans. Plasma Sci., Vol. 32, pp.399-404, 2004. https://doi.org/10.1109/TPS.2004.828126
  7. Ward, A. L., “Calculations of cathode-fall characteristics,” J. Appl. Phys., Vol. 33, pp. 2789-2794, 1962. https://doi.org/10.1063/1.1702550
  8. Huppert, G. L., Sawin, H. H., and Brown, R. A., “Spectral element analysis of radio-frequency glow discharges,” Chem. Eng. Sci., Vol. 49, pp. 1601-1611, 1994. https://doi.org/10.1016/0009-2509(93)E0040-J
  9. Chen, F. F., Introduction to plasma physics and controlled fusion, New York: Plenum Press, 1984.
  10. Meyyappan, M, “A continuum model for low-pressure radio-frequency discharges,” J. Appl. Phys., Vol. 69, pp. 8047-8051, 1991. https://doi.org/10.1063/1.347451
  11. Kim, H. C., and Manousiouthakis, V. I., “Dually Driven Radio Frequency Plasma Simulation with a Three Moment Model,” J. of Vacuum Science and Technology A, Vol. 16, pp. 2162-2172, 1998. https://doi.org/10.1116/1.581324
  12. Kim, H. C., “Effects of Phase Difference between Voltage Waves Applied to Primary and Secondary Electrodes in Dual Frequency Plasma Chamber,” J. of the Semiconductor & Display Equipment Technology, Vol. 4, pp. 11-14, 2005.
  13. Vender, D., and Boswell, R., “Electron-sheath interaction in capacitive radio-frequency plasmas,” J. Vac. Sic. Technol. A, Vol. 10, pp. 1331-1338, 1992. https://doi.org/10.1116/1.578248
  14. Godyak, V. A., and Kanneh, A. S., “Ion Bombardment Secondaty Electron Maintenance of Steady RF Discharge,” IEEE Trans. Plasma. Sci., Vol. 14, p. 112-123, 1986. https://doi.org/10.1109/TPS.1986.4316513
  15. Parker, G. J., Hitchon, W. N. G., and Lawler, J. E., “Kinetic modeling of the $\alpha$ and $\gamma$ transition in radio frequency discharges,” Phys. Fluids B, Vol. 5, pp. 646-649, 1993. https://doi.org/10.1063/1.860496
  16. Blenguer, P., and Boeuf, J. P., “Transition between different regimes of rf glow discharges,” Phys. Rev. A, Vol. 41, pp. 4447-4459, 1990. https://doi.org/10.1103/PhysRevA.41.4447