Plasma-immersion ion implantation of the interior surface of a small cylindrical bore using an auxiliary electrode for finite rise-time voltage pulses

Plasma-immersion ion implantation (PIII) can be used to process the interior surfaces of odd-shape specimens such as a cylindrical bore. The temporal evolution of the plasma sheath in a small cylindrical bore in the presence of a grounded coaxial auxiliary electrode is derived for voltage pulses of different rise times by solving Poisson's equation and the equations of ion continuity, and motion numerically using the appropriate boundary conditions. It is found that the maximum ion impact energy and the average impact energy are improved for finite rise-time voltage pulses, and shorter rise times yield better results. Our results allow the selection of a suitable auxiliary electrode radius to improve the average impact energy for a given rise time.