Nonlocal Electron Kinetics in Collisional Gas Discharge Plasmas

IEEE Transactions on Plasma Science

Volumn 23, Issue 4, 1995, Pages 503-531

  Kolobov, Vladimir I ^a   Godyak, Valery A ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b OSRAM SYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CATHODES; DIFFUSION; ELECTRIC FIELDS; ELECTRONS; GLOW DISCHARGES; IONIZATION; KINETIC THEORY; NUMERICAL ANALYSIS; RELAXATION PROCESSES;

BOLTZMANN EQUATION; COLLISIONAL GAS DISCHARGE PLASMAS; DIFFUSION COEFFICIENT; ELECTRON DISTRIBUTION FUNCTION; ELECTRON ENERGY RELAXATION; ELECTRON FLUX DENSITY; MOMENTUM TRANSFER; NONLOCAL ELECTRON KINETICS;

PLASMAS;

EID: 0029354785     PISSN: 00933813     EISSN: 19399375     Source Type: Journal    
DOI: 10.1109/27.467971     Document Type: Article

References (131)

1. I. B. Bernstein and T. Holstein, “Electron energy distributions in stationary discharges,” Phys. Rev., vol. 94, p. 1475, 1954.
2. L. D. Tsendin, “Energy distribution of electrons in a weakly ionized current-carrying plasma with a transverse inhomogeneity,” Sov. Phys. JETP, vol. 39, p. 805, 1974.
3. L. D. Tsendin and Y. B. Golubovskii, “Positive column of a low-density, low-pressure discharge. I. Electron energy distribution,” Sov. Phys. Tech. Phys., vol. 22, p. 1066, 1977.
4. T. Ruzicka and K. Rohlena, “On nonhydrodynamic properties of the electron gas in the plasma of a dc discharge,” Czech. J. Phys. B, vol. 22, p. 906, 1972.
5. L. D .Tsendin, “Electron distribution function of weakly ionized plasmas in nonuniform electric fields. I. Weak fields (energy balance determined by nearly elastic collisions),” Sov. J. Plasma Phys., vol. 8, p. 96, 1982.
6. L. D .Tsendin, “Electron distribution function of weakly ionized plasmas in nonuniform electric fields. II. Strong fields (energy balance determined by inelastic collisions),” Sov. J. Plasma Phys., vol. 8, p. 228, 1982.
7. L. D .Tsendin, “Anode region of a Glow Discharge,” Sov. Phys. Tech. Phys., vol. 31, p. 169, 1986.
8. V. I. Kolobov and L. D. Tsendin, “Analytic model of the cathode region of a short glow discharge in light gases,” Phys. Rev. A, vol. 46, p. 7837, 1992.
9. I. D. Kaganovich and L. D. Tsendin, “The Space-Time-Averaging Procedure and Modeling of the RF discharge—II. Model of collisional low-pressure RF discharge,” IEEE Trans. Plasma Sci., vol. 20, p. 66, Feb. 1992.
10. U. Kortshagen, “A non-local kinetic model applied to microwave produced plasmas in cylindrical geometry,” J. Phys. D, vol. 26, p. 1691, 1993.
11. V. I. Kolobov, D. F. Beale, L. J. Mahoney, and A. E. Wendt, “Nonlocal electron kinetics in a low-pressure inductively coupled RF discharge,” Appl. Phys. Lett., vol. 65, p. 537, 1994.
12. U. Kortshagen, I. Pukropski, and L. D. Tsendin, “Experimental investigation and fast two-dimensional self-consistent kinetic modeling of a low pressure inductively coupled RF discharge,” Phys. Rev. E, vol. 51, p. 6063, 1995.
13. U. Kortshagen and L. D. Tsendin, “Fast two-dimensional self-consistent kinetic modeling of low-pressure inductively coupled RF discharges,” Appl. Phys. Letts., vol. 65, p. 1355, 1994.
14. I. P. Shkarofsky, T. W. Johnson, and M. P. Bachinski, The Particle Kinetics of the Plasmas. Reading, MA: Addison-Wesley, 1966.
15. V. L. Ginzburg and A. V. Gurevich, “Nonlinear Phenomena in plasma in alternating electric field,” Sov. Phys. Usp., vol. 70, p. 201, 1960.
16. P. Segur, M. Yousfi, J. P. Boeuf, E. Marode, A. G. Davies, and J. G. Evans, “The microscopic treatment of nonequilibrium regions in a weakly ionized gas,” in Electrical Breakdown and Discharges in Gases, vol. 89, NATO ASI Series B., E. E. Kunhard and L. H. Luessen, Eds. New York: Plenum, 1983, p. 331.
17. L. C. Pitchford, J. P. Boeuf, P. Segur, and E. Marode, “The microscopic treatment of nonequilibrium regions in a weakly ionized gas,” in Nonequilibrium Effects in Ion and Electron Transport, J. W. Gallagher, D. F. Hudson, E. E. Kunhardt, and R. Brunt, Eds. New York: Plenum, 1990.
18. A. M. Popov, A. T. Rakhimov, and T. V. Rakhimova, “Self-consistent models of high-frequency low-pressure discharges in electropositive and electronegative gases (review),” Plasma Phys. Rep., vol. 19, no. 10, p. 651, 1993.
19. J. Ingold, “Nonequilibrium motion of electrons and ions near absorbing boundaries,” in Microwave Discharges. Fundamentals and Applications, vol. 302, NATO ASI Series B. C. M. Ferreira and M. Mosian, Eds. New York: Plenum, 1993, p. 407.
20. L. D. Tsendin, “Electron kinetics in non-uniform glow discharge plasmas,” Plasma Sources Sci. Technol., vol. 4, p. 200, 1995.
21. L. D. Landau and E. M. Lifshitz, Quantum Mechanics-Non-Relativistic Theory. Reading, MA: Addison-Wesley, 1965.
22. Y. P. Raizer, Gas Discharge Physics. Berlin: Springer-Verlag, 1991.
23. L. C. Pitchford, “Electron ionization rate coefficients at very high E/N,” in Physics and Applications of Pseudosparks, vol. 219, NATO ASI Series B, M. A. Gundersen and G. Schaefer, Eds. New York: Plenum, 1990, p. 319.
24. L. D. Tsendin, “Electron Energy distribution in an RF electric field,” Sov. Phys. Tech. Phys., vol. 22, p. 925, 1977.
25. E. A. Karoulina and Y. A. Lebedev, “The influence of the electron transport cross-sectional shape on electron energy distribution in dc and microwave plasmas,” J. Phys. D, vol. 21, p. 411, 1988.
26. S. D. Vagner, B. K. Ignat'ev, and L. D. Tsendin, “Modulation of the emission of a neon RF discharge due to time variation of the fast-electron distribution,” Sov. Phys. Tech. Phys., vol. 23, p. 665, 1978.
27. N. A. Dyatko, I. V. Kochetov, and A. P. Napartovich, “Effect of inertia of the electron energy distribution on the ionization rate in a weakly ionized RF discharge plasma,” Sov. J. Plasma Phys., vol. 11, p. 432, 1985.
28. R. Winkler, J. Wilhelm, and A. Hess, “Main features of the electron kinetics in collision dominated steady-state RF plasmas,” Annalen der Phys., vol. 42, p. 537, 1985.
29. R. Winkler, “Collision dominated electron kinetics in low and high frequency fields,” in Microwave Discharges. Fundamentals and Applications, vol. 302, NATO ASI Series B, C. M. Ferreira and M. Mosian, Eds. New York: Plenum, 1993, p. 339.
30. V. E. Golant, A. P. Zhilinsky, I. E. Sakharov, and S. C. Brown, Fundamentals of Plasma Physics. New York: Wiley, 1980.
31. A. V. Timofeev, “Hydrodynamic transport equations for a weekly ionized plasma,” Sov. Phys. Tech. Phys., vol. 15, p. 140, 1970.
32. N. L. Aleksandrov, A. P. Napartovich, and A. N. Starostin, “Transport equations in a nonequilibrium weakly ionized plasma,” Sov. J. Plasma Phys., vol. 6, p. 618, 1980.
33. V. A. Rozhanskii and L. D. Tsendin, Collisional Transport in Partially-Ionized Plasma. Moscow: Energoatomizdat, 1988.
34. L. D. Tsendin, “Ionization kinetics and ionization waves in neon,” Sov. Phys. Tech. Phys., vol. 27, p. 407, 1982.
35. V. P. Vstovskii, “Kinetics of a weakly ionized plasma in external fields,” Sov. J. Plasma Phys., vol. 12, p. 856, 1986.
36. T. Ruzicka and K. Rohlena, “Electron gas in weakly ionized plasmas,” Invited Papers ICPIG XI, Prague, Czechoslovakia, 1973, p. 61.
37. D. W. Swain and S. C. Brown, “Moving striations in a low-pressure argon discharge,” Phys. Fluids, vol. 14, p. 1383, 1971.
38. L. D. Tsendin, “Positive column of a low-density, low-pressure discharge. II. Ion motion and radial potential distribution,” Sov. Phys. Tech. Phys., vol. 23, p. 890, 1978.
39. Y. Behnke, Y. B. Golubovskii, S. U. Nisimov, and I. A. Porokhova, “Self-consistent kinetic description of the positive column of a discharge with direct and stepwise ionization,” Tech. Phys., vol. 39, p. 33, 1994.
40. N. A. Gorbunov, K. O. Iminov, and A. A. Kudryavtsev, “Formation of a nonlocal electron energy distribution in a molecular-gas discharge plasma,” Sov. Phys. Tech. Phys., vol. 33, p. 1403, 1988.
41. K. Wiesemann, “Die messung der verteilungsfunetion der electronen in der lende,” Annalen der Physik, vol. 23, p. 275, 1969.
42. D. Herrman, “Experimentelle Untersuchungen der radialen abhendigkeit der geschwindigkeitsverteilungsfunctionen der electronen im plasma der positive saule,” Beitr. Plasmaphys., vol. 11, p. 85, 1971.
43. D. Herrman, A. Rutcher, and S. Pfau, “Radiale anderungen der energiev-erteilungsfunction der electronen im plasma der positive saule electrisher entladungen,” Beitr. Plasmaphys., vol. 11, p. 75, 1971.
44. N. A. Vorob'eva, V. M. Milenin, and L. D. Tsendin, “Effect of the loss of electrons to the wall and a transverse electric field on the electron energy distribution in a low-pressure inert-gas discharge,” Sov. Phys. Tech. Phys., vol. 24, p. 442, 1978.
45. V. V. Zaitsev and V. M. Milenin, “Electrical characteristics of low-pressure discharges in argon and kripton,” Sov. Phys. Tech. Phys., vol. 45, p. 1293, 1979.
46. Y. B. Golubovskii, V. I. Kolobov, and S. H. al Hawat, “Anode region of a low-current glow discharge in neon at low pressures,” Sov. Phys. Tech. Phys., vol. 33, p. 1046, 1988.
47. V. A. Godyak and V. N. Maksimov, “Spatial distribution of a bounded plasma,” Vestnik Moskovskogo Universiteta. Fizika, vol. 32, p. 51, 1977.
48. A. V. Phelps, “The diffusion of charged particles in collisional plasmas: Free and ambipolar diffusion at low and moderate pressures,” J. Res. Natl. Inst. Stand. Technol., vol. 95, p. 407, 1990.
49. N. B. Kolokolov, A. A. Kudrjavtsev, and A. B. Blagoev, “Interaction processes with creation of fast electrons in the low temperature plasma,” Physica Scripta, vol. 50, p. 371, 1994.
50. U. Kortshagen, “Experimental evidence on the nonlocality of the electron distribution function,” Phys. Rev. E, vol. 49, no. 5, p. 4369, 1994.
51. Y. M. Aliev, A. V. Maximov, U. Kortshagen, H. Schluter, and A. Shivarova, “Modeling microwave discharges in the presence of plasma resonances,” Phys. Rev. E, vol. 51, p. 6091, 1995.
52. N. B. Kolokolov, A. A. Kudijavtsev, and V. A. Romanenko, “Control of the energy distribution of electrons and the parameters of a currentless plasma,” Sov. Phys. Tech. Phys., vol. 33, p. 1274, 1988.
53. M. J. Hartig and M. J. Kushner, “Radially dependent solutions of Boltzmann's equation in low-temperature plasma using a modified two-term expansion,” J. Appl. Phys., vol. 73, p. 1080, 1993.
54. C. Busch and U. Kortshagen, “Numerical solution of the spatially inhomogeneous Boltzmann equation and verification of the nonlocal approach for an argon plasma,” Phys. Rev. E, vol. 51, p. 280, 1995.
55. K. G. Muller and W. O. Muller, “Simulation of the electron energy relaxation in a weakly ionized plasma,” Z. Naturforsh. A, vol. 30, p. 1553, 1975.
56. G. J. Parker, W. N. G. Hitchon, and J. E. Lawler, “Numerical solution of the Boltzmann equation in cylindrical geometry,” Phys. Rev. E, vol. 50, p. 3210, 1994.
57. R. I. Lyagushchenko, “Relaxation of fast electrons in gases and semiconductors,” Sov. Phys. JETP, vol. 36, p. 901, 1973.
58. M. S. Benilov and A. V. Lyashko, “Energy relaxation of the emitted electrons in the cathode region of a high-pressure weakly ionized plasma,” Sov. Phys. Tech. Phys, vol. 36, p. 601, 1991.
59. H. Bender and K. G. Muller, “Striations as eigensolutions of the motion of electron in the electric field,” Z. Physik, vol. 263, p. 299, 1973.
60. K. G. Emeleus, “Low-current striated Townsend and transitional discharges,” Int. J. Electron., vol. 39, p. 177, 1975.
61. H. G. Lergon and K. G. Muller, “Spatial relaxation of electron energy distribution in high electric fields,” Z Physik, vol. 268, p. 157, 1974.
62. V. A. Godyak, R. Lagushenko, and J. Maya, “Spatial evolution of the electron energy distribution in the vicinity of a discharge-tube constriction,” Phys. Rev. A, vol. 38, p. 2044, 1988.
63. V. I. Kolobov and A. Fiala, “Transition from a Townsend discharge to a normal discharge via two-dimensional modeling,” Phys. Rev. E, vol. 50, p. 3018, 1994.
64. M. Hayashi, “Luminous layers in the prebreakdown region of low pressure noble gases,” J. Phys. D, vol. 15, p. 1411, 1982.
65. J.-P. Boeuf and E. Marode, “MC simulation of electron swarm motion in SF6,” J. Phys. D, vol. 17, p. 1133, 1984.
66. V. A. Shveigert, “Electron distribution function in inert gas in slightly modulated static electric field,” Sov. J. Plasma Phys., vol. 15, no. 10, p. 714, 1989.
67. Y. B. Golubovskii, V. I. Kolobov, V. O. Nekuchaev, and I. E. Suleimenov, “Electron kinetics in nonuniform electric fields at elevated pressures,” Sov. Phys. Tech. Phys., vol. 36, p. 878, 1991.
68. V. Perina, K. Rohlena, and T. Ruzicka, “Ionization waves (moving striations) in a low pressure helium discharge. Results of measurements compared with a direct solution of the electron Boltzmann equation,” Czech. J. Phys. B, vol. 25, p. 660, 1975.
69. Y. B. Golubovskii, S. U. Nisimov, and I. E. Suleimenov, “On the two-dimensional character of the striations in low-pressure discharges in rare gases,” Tech. Phys., vol. 39, p. 1005, 1994.
70. Y. M. Kagan, N. B. Kolokolov, T. A. Krylova, and V. M. Milenin, “Moving striations in neon,” Sov. Phys. Tech. Phys., vol. 16, p. 88, 1971.
71. B. N. Klyarlel'd and N. A. Neretina, “Anode region in a low-pressure gas discharge. I. Effect of anode shape on sign and magnitude of the anode fall,” Sov. Phys. Tech. Phys, vol. 3, p. 271, 1958.
72. R. E. Robson, “Boundary effects in solution of Boltzmann's equation for electron swarms,” Aust. J. Phys., vol. 34, p. 223, 1981.
73. J. J. Lowke, J. H. Parker, and C. A. Hall, “Electron diffusion under the influence of an electric field near absorbing boundaries,” Phys. Rev. A, vol. 15, p. 1237, 1977.
74. G. L. Braglia and J. J. Lowke, “Comparison of Monte Carlo and Boltzmann calculation of electron diffusion to absorbing electrodes,” J. Phys. D, vol. 12, p. 1831, 1979.
75. Y. B. Golubovskii, S. H. al Havat, and L. D. Tsendin, “Electron distribution in the anode region of a low-current discharge in neon,” Sov. Phys. Tech. Phys., vol. 32, no. 7, p. 760, 1987.
76. Y. B. Golubovskii, V. I. Kolobov, and S. H. al Hawat, “Anode region of low-current glow discharges at low and high pressures,” Sov. Phys. Tech. Phys., vol. 35, p. 747, 1990.
77. Y. B. Golubovskii and V. I. Kolobov, “Anode region of a low-current glow discharge in a rare gas,” Contributed Papers 3, ICPIG XX, Pisa, Italy, p. 663, 1991.
78. Y. B. Golubovskii and S. H. al Havat, “The near-anode region of the quasi-neutral plasma of a low-current glow discharge in neon,” Sov. Phys. Tech. Phys., vol. 32, p. 25, 1987.
79. V. A. Shveigert, “Anode region of a self-sustained glow discharge in neon,” Sov. J. Plasma Phys., vol. 14, p. 801, 1988.
80. K. G. Muller, “Structures at the electrodes of gas discharges,” Phys. Rev. A, vol. 37, p. 4836, 1988.
81. Y. S. Akishev, A. M. Volchek, A. P. Napartovich, and N. I. Trushkin, “Near-anode instability of gas flow glow discharge,” Plasma Sources Sci. Technol., vol. 1, p. 190, 1992.
82. A. I. Pavlovskii, L. P. Babich, T. V. Loiko, and L. V. Tarasova, “Runaway of electrons in gas discharges and the origin of the minimum of u(pd),” Sov. Phys. Dokl., vol. 30, p. 303, 1985.
83. L. P. Babich, T. V. Loiko, and V. A. Tsukerman, “High-voltage nanosecond discharge in a dense gas at high overvoltage with runaway electrons,” Sov. Phys. Usp., vol. 33, p. 521, 1990.
84. K. G. Muller, “Die electronen bewegung im neutralgas bei hohen electrishen feldern,” Z Physik, vol. 169, p. 432, 1962.
85. N. P. Kalashnikov, V. S. Remizovich, and M. I. Rjazanov, Collisions of Fast Charged Particles in Solids. Moscow: Atomizdat, 1980.
86. Y. M. Li, “Nonequilibrium effects in electron transport at high E/N,” in Nonequilibrium Effects in Ion and Electron Transport, J. W. Gallagher, D. F. Hudson, E. E. Kunhardt, and R. Brunt, Eds. New York: Plenum, 1990.
87. K.-U. Riemann, “Theory of the electron distribution function in a Lorentz gas at high E/N,” Phys. Rev. A, vol. 46, p. 4717, 1992.
88. R. A. Russel-Dupre, A. V. Gurevich, T. Tunnel, and G. M. Milikh, “Kinetic theory of runaway air breakdown,” Phys. Rev. E, vol. 49, p. 2257, 1994.
89. D. B. Graves and M. Surendra, “Nonequilibrium effects in dc and RF glow discharge,” in Nonequilibrium Effects in Ion and Electron Transport. J. W. Gallagher, D. F. Hudson, E. E. Kunhardt, and R. J. Van Brunt, Eds. New York: Plenum, 1990, p. 157.
90. T. G. Paulick, “Electron multiplication in the glow discharge cathode fall,” J. Appl. Phys., vol. 67, p. 2774, 1990.
91. A. B. Parker and P. C. Johnson, “The dielectric breakdown of low density gases,” Proc. R. Soc. Land. A, vol. 325, p. 511, 1971.
92. S. B. Vrhovac, S. B. Radovanov, Z. L. Petrovic, and B. M. Jelenkovic, “Electron energy distribution function in weakly ionized argon,” J. Phys. D, vol. 25, p. 217, 1992.
93. A. Phelps, B. M. Jelenkovic, and L. C. Pitchford, “Simplified models of electron excitation and ionization at very high E/N,” Phys. Rev. A, vol. 36, p. 5327, 1987.
94. V. I. Kolobov and L. D. Tsendin, “Analytic model of the Hollow Cathode effect,” Contributed Papers ICPIG XXI, Bochum, Germany, p. 329, 1993.
95. A. S. Metel, “Effect of ionization in the cathode layer on the characteristics of a Penning discharge: I. Hollow cathode discharge,” Sov. Phys. Tech. Phys., vol. 30, p. 1133, 1985.
96. H. B. Valentini, “Electron kinetics in the cathode region of a glow discharge and in hollow cathodes,” Contrib. Plasma Phys., vol. 27, p. 331, 1987.
97. S. P. Nikulin, “Characteristics of a low-pressure glow discharge in a cylindrical hollow cathode in the case of a wide cathode sheath,” Sov. Phys. Tech. Phys., vol. 37, p. 1142, 1992.
98. J. P. Boeuf and L. C. Pitchford, “Pseudospark discharges via computer simulation,” IEEE Trans. Plasma Sci., vol. 19, p. 286, 1991.
99. J. P. Boeuf, “Self-consistent models of dc and and transient glow discharges,” in Physics and Applications of Pseudosparks, vol. 219, NATO ASI Series B, M. A. Gundersen and G. Schaefer, Eds. New York: Plenum, 1990, pp. 255-276.
100. A. Fiala, L. C. Pitchford, and J. P. Boeuf, “Two-dimensional hybrid model of low-pressure glow discharges,” Phys. Rev. E, vol. 49, p. 5607, 1994.
101. E. A. Den Hartog, D. A. Doughty, and J. E. Lawler, “Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge,” Phys. Rev. A, vol. 38, p. 2471, 1988.
102. J. E. Lawler, E. A. Den Hartog, and W. N. G. Hitchon, “Power balance of negative-glow electrons,” Phys. Rev. A, vol. 43, p. 4427, 1991.
103. G. J. Parker, W. N. G. Hitchon, and J. E. Lawler, “Self-consistent kinetic model of an entire dc discharge,” Phys. Letters A, vol. 174, p. 308, 1993.
104. Y. M. Kagan, C. Cohen, and P. J. Avivi, “The Faraday dark space of a He glow discharge,” J. Appl. Phys., vol. 63, p. 60, 1988.
105. R. R. Arslanbekov, A. A. Kudryavtsev, and I. A. Movchan, “Slow electron distribution function in a cylindrical hollow-cathode discharge,” Sov. Phys. Tech. Phys, vol. 37, p. 620, 1992.
106. R. R. Arslanbekov, A. A. Kudryavtsev, and I. A. Movchan, “Electron density and temperature balance in a cylindrical hollow-cathode discharge,” Sov. Phys. Tech. Phys, vol. 37, p. 1004, 1992.
107. T. J. Sommerer, W. N. G. Hitchon, R. E. P. Harvey, and J. E. Lawler, “Self-consistent kinetic calculations of helium RF glow discharges,” Phys. Rev. A, vol. 43, p. 4452, 1991.
108. V. Vahedi, G. DiPeso, C. K. Birdsall, M. A. Lieberman, and T. D. Rognlien, “Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation,” Plasma Sources Sci. Technol., vol. 2, p. 261, 1993.
109. A. S. Smimov and L. D. Tsendin, “The space-time-averaging procedure and modeling of the RF discharge,” IEEE Trans. Plasma Sci., vol. 19, p. 130, 1991.
110. I. D. Kaganovich and L. D. Tsendin, “Low-pressure RF discharge in the free-flight regime,” IEEE Trans. Plasma Sci., vol. 20, p. 86, 1992.
111. V. A. Godyak and R. B. Piejak, “Abnormal low electron energy and heating-mode transition in a low-pressure Argon RF discharge at 13.56 MHz,” Phys. Rev. Lett., vol. 65, p. 996, 1990.
112. V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, “Measurements of electron energy distribution in low-pressure RF discharges,” Plasma Sources Sci. Technol., vol. 1, p. 36, 1992.
113. V. A. Godyak, “Statistical heating of electrons at an oscillating plasma boundary,” Sov. Phys. Tech. Phys., vol. 16, p. 1073, 1972.
114. C. E. Goedde, A. J. Lichtenberg, and M. A. Lieberman, “Self-consistent stochastic electron heating in radio frequency discharges,” J. Appl. Phys., vol. 64, p. 4375, 1988.
115. A. E. Wendt and W. N. G. Hitchon, “Electron heating by sheaths in radio frequency discharges,” J. Appl. Phys., vol. 71, p. 4718, 1992.
116. M. Surendra and D. Vender, “Collisionless electron heating by radio frequency plasma sheaths,” Appl. Phys. Lett., vol. 65, p. 153, 1994.
117. K. G. Muller, “Collisional electron hearing in a RF discharge,” J. Phys. D, vol. 26, p. 2168, 1993.
118. V. A. Godyak and R. B. Piejak, “Paradoxial spatial distribution of the electron temperature in a low pressure RF discharge,” Appl. Phys. Lett., vol. 63, p. 3137, 1993.
119. M. M. Turner and M. B. Hopkins, “Anomalous sheath heating in a low pressure RF discharge in nitrogen,” Phys. Rev. Lett., vol. 69, p. 3511, 1992.
120. M. Surendra and D. B. Graves, “Particle simulations of radio-frequency glow discharges,” IEEE Trans. Plasma. Sci., vol. 19, p. 144, 1991.
121. M. Kushner, “Mechanisms for pover deposition in Ar/SiH4 capacitively coupled RF discharges,” IEEE Trans. Plasma. Sci., vol. PS-14, p. 188, 1986.
122. J. P. Boeuf and P. Belenguer, “Fundamental properties of RF glow discharges: An approach based on self-consistent numerical models,” in Nonequilibrium Processes in Partially Ionized Gases, vol. 220, NATO ASI Series B, M. Capitelli and J. Bardsley, Eds. New York: Plenum, 1990, p. 155.
123. S. V. Berezhnoi, I. D. Kaganovich, E. L. Levin, and L. D. Tsendin, “Fast self-consistent kinetic modeling of low-pressure capacitively coupled RF discharges,” in Contributed Papers Int. Conf. Plasma Phys., P. H. Sakanaka, E. del Bosco, and M. V. Alves, Eds., Foz do Iguacu, Brasil, 1994, vol. 3, pp. 9–12
124. M. A. Lieberman and R. A. Gottscho, “Design of high density plasma sources for materials processing,” in Physics of Thin Films vol. 18, M. Francombe and J. Vossen, Eds. New York: Academic, 1994, pp. 1–119.
125. 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. Tecnol. B, vol. 12, p. 461, 1994.
126. V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, “Electrical characteristics and electron heating mechanism of an inductively coupled argon discharge,” PSST, vol. 3, p. 169, 1994.
127. V. I. Kolobov and W. N. G. Hitchon, “Electron distribution function in a low-pressure inductively coupled plasma,” Phys. Rev. E, vol. 52, p. 972, 1995
128. M. M. Turner, “Collisionless electron heating in an inductively coupled discharge,” Phys. Rev. Lett., vol. 71, p. 1844, 1993.
129. V. Vahedi, M. A. Lieberman, G. DiPeso, T. D. Rognlien, and D. Hewett, “Analytic model of power deposition in inductively coupled plasma sources,” J. Appl. Phys., vol. 78, p. 1446, 1995.
130. V. I. Kolobov, G. J. Parker, and W. N. G. Hitchon, “Modeling of electron kinetics in low-pressure inductively coupled plasmas,” invited paper presented at IEEE Int. Conf. on Plasma Sci., June 1995, Madison, WI, USA.
131. V. Godyak, R. Piejak, and B. Alexandrovich, “Magnetic and electric probe diagnostics in inductive plasmas,” invited paper at XXII Int. Conf. on Phenomena in Ionized Gases, Aug. 1995, Hoboken, NJ, USA.