Modeling positive ion current to a planar probe in low-pressure electronegative discharges

A fluid model is utilized to describe the plasma-sheath boundary for a negatively biased planar probe immersed in electronegative plasmas. The model equations are solved on the scale of the electron Debye length and calculate the spatial distributions of electric potential, velocity, and density of positive ions in front of the probe. The position of sheath edge, the positive ion velocity at sheath edge (the Bohm velocity), and the positive ion flux collected by the probe are determined and compared with analytic (or scaling) formulas. Effects of control parameters on the Bohm velocity, the sheath thickness, and on the positive ion flux are investigated. A larger thermal motion of negative ions causes the Bohm velocity to increase, the sheath to increase, and the positive ion flux collected by the probe to increase. An increase in collision causes the Bohm velocity to decrease and the sheath to decrease resulting in a decrease in the positive ion flux. An increase in electronegativity causes both the Bohm velocity and the sheath thickness to decrease, resulting in an increase in the positive ion flux. As the value of the non-neutrality parameter q increases, the Bohm velocity and the sheath thickness are found to decrease, and the positive ion flux collected by the probe increases. The behavior of the positive ion flux entering the sheath is discussed as functions of control parameters. A careful comparison of theoretical positive ion flux with the experimental flux can allow us to obtain the electronegativity, the plasma ionization rate (q), and the collision parameter (delta).