Model of Collisional Sheath in Spherical and Cylindrical Geometries for Plasma Source Ion Implantation

A model is developed that describes the temporal evolution of the sheath during a pulse of high negative voltage applied to a spherical and cylindrical target in a plasma such as that present in plasma source ion implantation for the case in which the pressure of the neutral gas is large 4nough that the ion motion in the sheath can be assumed to he highly collisional. The analytic expressions of the sheath expanding ve1ocity are obtained. The positions of the sheath edge as a function of time predicted by the model are in agreement with those obtained by fluid equations.