Equilibrium model for two low-pressure electronegative plasmas connected by a double layer

Plihon et al. [J. Appl. Phys. 98, 023306 (2005)] have recently shown that double layers usually form during the expansion of a low pressure electronegative plasma. These double layers act as permeable internal boundaries between the source (upstream) plasma and the downstream expanding plasma; positive ions flow from upstream to downstream whereas negative ions flow in the opposite direction. So far, the detailed physical mechanisms leading to their formation have not been identified. In this paper, we develop a model for the two plasma equilibria, upstream and downstream, assuming that the double layer exists and couples the two plasmas. At very low pressure, typically 0.5 mTorr, the coupling is strong and acts both ways. The negative ions created downstream contributes to the upstream equilibrium as well as the upstream positive ions contribute to the downstream equilibrium. As the pressure increases, the situation becomes asymmetric. The source plasma is not affected by the negative ions flowing from downstream, whereas the positive ions coming from the source control the downstream plasma equilibrium, where local ionization is negligible.