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Application of the physics of plasma sheaths to the modeling of rf plasma reactors
1.The results described in this paper are also relevant for plasma reactors of different geometries as long as the thickness of the plasma sheaths is small compared to the electrode dimensions. Calculations show that for the electron (ion) number densities typical in low‐pressure plasma reactors, the thickness of the plasma sheath is of the order of 1 mm. The model calculations presented here can also be extended to take into account the effect of reactor walls, etc., on the electrical characteristics of the reactor by adding circuit elements to the equivalent electric circuit model discussed in Sec. III.
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12.This assumption is valid for electron energy modulation due to elastic interactions of electrons with atoms. [H. J. Oskam, Philips Res. Repts. 13, 335 (1958)].The energy modulation due to mutual charged particle interactions can be neglected for the assumed charge particle number densities of about Inelastic interactions between electrons and atoms involve only the small fraction of electrons in the high‐energy tail of the electron energy distribution.
13.The time constant related to charged particle loss by ambipolar diffusion is, for an active plasma, given by where L is the distance between the electrodes, is the diffusion coefficient of the ions, and and are the electron and gas temperatures, respectively.
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15.An extension of the Bohm sheath criterium to a surface biased slightly negative with respect to a plasma showed that this assumption is valid to within 5% for the smallest sheath voltage encountered in the present model (R. W. Carlson, Ph.D. thesis, Univerity of Minnesota 1966).
16.The ion current density is determined by the plasma density at the interface between the plasma and the pre‐sheath, the electron temperature, and the ion velocity, which is given by Bohm’s criterium. The electron current density is determined by the plasma density the electron temperature, and the voltage across the sheath. Therefore, for a fixed potential between the plasma and the electrode, a nonzero value of the electric field at the sheath edge will only result in a slightly thinner plasma sheath and, thus, in a smaller transit time of the positive ions across the sheath.
17.The fraction of electrons able to reach the electrodes for the sheath voltages encountered in the model is very small. The influence of this electron loss on the Boltzmann density distribution of the electrons in the sheath is very small (R. W. Carlson, Ph.D. thesis, University of Minnesota 1966).
18.The potential difference between the electrode and the plasma is Therefore, the potential across the plasma sheath is where is the potential across the pre‐sheath in Bohm’s model (Fig. 2). In the present model it is assumed that is independent of time. Therefore, can be omitted in Eqs. (1) and (2).
19.R. H. Bruce, J. Appl. Phys. 52, 7064 (1981).
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