An axisymmetric model for an RF plasma in contact with a surface having a nonuniform secondary electron emission coefficient

An axisymmetric analytical model of an RF glow discharge was developed. This model allowed exploration of various effects: radial losses at the side wall, mismatch of secondary electron emission coefficients on the surface of a powered electrode, the aspect ratio and dimension of the plasma chamber, and operational parameters such as gas pressure and bias voltage. The plasma density decreased in most cases by a factor of two to three from the axis to the periphery as a consequence of the radial losses. A maximum in the radial plasma density distribution appeared when the substrate had a different secondary electron emission coefficient than the platen. A maximum in plasma density at the axis also appeared when the electrode separation was varied at constant electrode radius because the plasma diffusion loss between electrodes dominates when the electrode separation is small and plasma radial diffusion loss dominates when the electrode separation is large.