Two-dimensional modelling of CF₄rf plasmas: periodic steady state, transient response after step change of power source voltage, and comparison with one-dimensional modelling

Abstract

CF4 radio frequency (rf) (13.56 MHz) capacitively coupled plasmas were simulated using a two-dimensional fluid model of cylindrical symmetry. We investigated their periodic steady state and transient behaviour after step changes of the amplitude of a power source voltage. The results were compared with those obtained by a one-dimensional model. The two-dimensional model showed that the plasmas in a harmonic steady state have asymmetric profiles due to generation of a dc self-bias through an asymmetric electrode system with grounded wall. The transient response of the plasmas in the two-dimensional model was qualitatively similar to those of the one-dimensional model except in the powered electrode edge region where the radial component of the electric field was significant.

Electron heating and the electrical asymmetry effect in dual-frequency capacitive CF4discharges

“…The rate of electron-CF + 3 recombination is taken from Denpoh and Nanbu [31]. Different values for the ion-ion recombination rate coefficients ranging from 1 × 10 −13 m 3 s −1 to 5.5 × 10 −13 m 3 s −1 can be found in the literature [24,29,30,86,87]. We use the value provided by Rauf and Kushner [86], 1 × 10 −13 m 3 s −1 , in order to ensure consistency with our previous simulation studies of CF 4 discharges [28].…”

“…This causes the maxima of the ion Finally, we tested the sensitivity of our simulation results on the ion-ion recombination rate coefficient for θ = 0 • . In the literature different values can be found (table 3, [24,29,30,86,87]) ranging from 1 × 10 −13 to 5.5 × 10 −13 m 3 s −1 . We use the value of 1 × 10 −13 m 3 s −1 to ensure consistency with previous simulations [28].…”

Basic relationships in electronegative plasmas with a multiplicity of negative and positive ion species

“…Alternative approaches to that given above include: (i) direct integration of the relevant equations, but these are notoriously ill-conditioned and for single ion species has only recently been achieved (Kono 2002); (ii) simulations, but these are expensive of computer time particularly if one seeks to vary parameters in a systematic way (So et al 2002); (iii) matched asymptotic approximations, these led to the initial central relationships and showed the structure for a single negative ion species (Franklin et al 1993),which has been generalized above. When one or more of these techniques has been further developed it will be possible to test the accuracy and usefulness of the approach given above.…”

“…In the papers cited above the specific case of CF 4 was examined in some detail. Recent simulations by So et al (2002) have shown that such a structure exists in the steady state in CF 4 at values of pressure × plasma dimension 200 mTorr cm in rf generated plasmas.…”

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Recent simulations by So et al (2002 J. Phys. D 35 2978 have shown inter alia that in CF 4 where there are two negative ions of comparable density, the plasma is structured, in that there are essentially three regions so far as the negative ions are concerned.

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