Model of plasma source ion implantation in planar, cylindrical, and spherical geometries

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Abstract
A model has been developed that describes the propagation of the transient sheath during a pulse of high negative voltage applied to a conductor immersed in a plasma such as that present in plasma source ion implantation. This model assumes that the transient sheath obeys the Child–Langmuir law for space-charge-limited emission at each instant during the propagation of the sheath. Expressions are obtained for the sheath-edge position as a function of time. The model predicts the final sheath extent and average ion current to the target during each pulse for planar, cylindrical, and spherical geometries.