Radio frequency sheaths—adjustable waveform model

Abstract

An approximate analytic description of radio frequency (rf) discharge sheaths is given here. This description employs simple power-law equations, obtaining results for a family of sheath voltage waveforms. Both low-pressure (‘‘free space’’) and high-pressure (‘‘collisional’’) regimes are analyzed, yielding power-law dependences of voltages, fields, and charges on distance into the sheath. The resulting sheath model yields asymmetric discharge sheath heights 1.1–1.3 times the corresponding dc sheath model. This family of sheath voltage waveforms is shown to be consistent with experimental sheath voltage waveforms, through experimental measurements of particle arrival times at rf sputtering targets with various electrode area ratios and chamber pressures. The imposition of a nonsinusoidal waveform on the sheath has interesting implications for voltages and ion flows in the remaining regions of the discharge. Ions may be accelerated from the ‘‘presheath’’ region both toward and away from the sheath around a negatively biased target. This is in contrast with dc sheaths, where ions are accelerated only toward the more negative electrode. Thus, ion bombardment of both the target and the counterelectrode is indicated by this model of asymmetric rf discharges. Final sections of this paper consider the velocity of the glow electron wavefront in the sheath, and the close correspondence between these power-law solutions and sine waveforms.