Space Potential and Ion Energies in a Low Pressure Discharge Containing at least Two Negative Species

A Tonks-Langmuir type model for a one-dimensional low pressure (collisionless) plasma containing at least two species of Maxwellian negative charge carriers is examined. The solutions of this model yield the positive ion energy distribution at the sheath edge without needing to specify the ionization process. This distribution has a width consistent with the potential drop across the plasma, and is shown to satisfy the generalised Bohm criterion for sheath formation. However by assuming a form for the ionization rate in the plasma, the potential profile across the discharge has been calculated. It has been found that for a range of plasma parameters the solution for the potential at which quasineutrality fails becomes triple valued; the physical solution in this regime is identified.Many plasmas used for materials processing contain negative ions. It is important to understand how these ions influence the positive ion energy distribution at the substrate where the processing occurs.This work is also of relevance to the behaviour of Langmuir probes in electronegative plasmas.