Modelling plasma discharges at high electronegativity

Abstract

Macroscopic models for the equilibrium of a three-component electronegative gas discharge are developed. Assuming the electrons and the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is derived. Such a discharge can consist of an electronegative core and may have electropositive edge regions, but the electropositive regions become small for the highly electronegative plasma considered here. In the parameter range for which the negative ions are Boltzmann, the electron density in the core is nearly uniform, allowing the nonlinear diffusion equation to be solved in terms of elliptic integrals. If the loss of positive ions to the walls dominates the recombination loss, a simpler parabolic solution can be obtained. If recombination loss dominates the loss to the walls, the assumption that the negative ions are in Boltzmann equilibrium is not justified, requiring coupled differential equations for positive and negative ions. Three parameter ranges are distinguished corresponding to a range in which a parabolic approximation is appropriate, a range for which the recombination significantly modifies the ion profiles, but the electron profile is essentially flat, and a range where the electron density variation influences the solution. The more complete solution of the coupled ion equations with the electrons in Boltzmann equilibrium, but not at constant density, is numerically obtained and compared with the more approximate solutions. The theoretical considerations are illustrated using a plane parallel discharge with chlorine feedstock gas of p = 30, 300 and 2000 mTorr and n e0 = 10 10 cm −3 , corresponding to the three parameter regimes. A heuristic model is constructed which gives reasonably accurate values of the plasma parameters in regimes for which the parabolic profile is not adequate.

1-D fluid model of atmospheric-pressure rf He+O2 cold plasmas: Parametric study and critical evaluation

“…The ion density profiles are flat in the bulk and steep in the sheaths, as predicted for moderate-pressure electronegative discharges. 38 The preferential power deposition on the sheath edges during the expansion and contraction of the sheaths results on the observed double hump ionic profiles. 27 It is noted that the electronegativity (n À =n e ) is around 1 even though the oxygen concentration is only 0.5%.…”

Experimental Observation and Computational Analysis of Striations in Electronegative Capacitively Coupled Radio-Frequency Plasmas

“…These "striations" are found to be generated by the resonance between the driving radio-frequency and the eigenfrequency of the ion-ion plasma (derived from an analytical model) that establishes a modulation of the electric field, the ion densities, as well as the energy gain and loss processes of electrons in the plasma. The growth of the instability is followed by the numerical simulations.Plasmas in electronegative gases exhibit complex physical and chemical kinetics [1][2][3][4][5][6][7][8][9][10][11]. Their main constituents are typically positive and negative ions, and electrons are only present as a minor species.…”

“…Plasmas in electronegative gases exhibit complex physical and chemical kinetics [1][2][3][4][5][6][7][8][9][10][11]. Their main constituents are typically positive and negative ions, and electrons are only present as a minor species.…”

Role of plasma-aided manufacturing in semiconductor fabrication

“…Tsendin [45] was the first to suggest that negative ions are not distributed uniformly throughout the plasma but had negative ions in its core and positive ions on the edge. Lichtenberg et al [46] solved the nonlinear diffusion equation for a positive ion, negative ion, electron plasma for a variety of assumptions. Three parameter ranges were distinguished corresponding to a range in which a parabolic approximation is appropriate, a range for which the recombination significantly modifies the ion profiles, but the electron profile is essentially flat, and a range where the electron density variation influences the solution.…”