ANALYSIS OF A KINEMATIC MODEL FOR ION-TRANSPORT IN RF PLASMA SHEATHS

An idealized model for ion transport across an oscillating plasma sheath is analyzed-to obtain insight into qualitative features of the ion energy distributions observed in low-pressure rf discharges. The sheath is characterized by a constant electric field over an extent that varies sinusoidally with time, and ions incident on it correspond to a monoenergetic flux independent of phase-phi in the rf cycle. The dimensionless parameters alpha = qV(s)/m-omega-2d2 and beta = upsilon-0/omega-d (where d and V(s) are the mean sheath thickness and potential drop, omega is the excitation frequency, and upsilon-0 and q/m are the incoming ion speed and charge-to-mass ratio) govern the ion trajectories, which are found to divide into groups, delimited by two "critical" values of phi, that undergo N and N + 1 encounters with the field. The first critical phase depends only weakly on beta, whereas the second is sensitive to both alpha and beta and cycles continuously as these parameters diminish. Correspondingly, within the "transition regime" where alpha and beta are neither very small nor greater than (or comparable to) unity, the precise form of the incident-ion energy spectrum exhibits rapid variations, superposed on a systematic narrowing, as the frequency-omega is increased.