Sheath scaling in plasma immersion ion implantation of spherical target

It is of great practical importance to predict the sheath evolution during plasma immersion ion implantation (PIII) of spherical targets in order to properly design the vacuum chamber and treatment processes. However, owing to non-linearity, it is difficult to solve the Child-Langmuir equation to elucidate the sheath dynamics directly in practical circumstances. In this paper, sheath scaling for PIII into a spherical target is investigated using numerical methods. Our results demonstrate that the sheath thickness, including the initial ion-matrix sheath and final steady-state sheath, increases with the increase of the spherical radius or applied voltage, and decreases with increasing plasma density. The sheath scale varies to a different degree with respect to parameter change for different processing conditions. For a high plasma density and low applied voltage, the steady-state sheath thickness is more or less insensitive to variations in the spherical radius, but it is very sensitive under other conditions. The ratio of the ion-matrix sheath thickness of a planar target to that of a spherical target depends considerably on the plasma density and the spherical radius. In fact, the steady-state sheath thickness of a planar target is more than that of a spherical target regardless of changes in the plasma density of target size. Our results are important to the design of practical PIII processes.