Radio frequency sheaths—modeling and experiment

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Abstract
Measurements of ion flux and energy at a radio frequency (rf) target are given here for Ar sputtering discharges at 7 and 27 MHz, and at pressures between 1–20 Pa. These measurements allow comparison with models of the rf discharge sheath. In turn, these models can be used to correlate external observables, such as sheath voltage and height, with microscopic quantities such as sputtering rate. A numerical model of the rf sheath based upon experimentally determined glow voltage waveforms is used to calculate sheath heights, which are compared with experimental measurements. The rf sheath is modeled as a monotonic structure, permitting a simple description of ion flow in the sheath. This is an approximation because the target ion energy distribution contains a series of discrete energy peaks, superimposed upon a background caused by ion-neutral collisions. However, at high frequencies or at high pressures these peaks decrease in size relative to the background. The method used here accounts accurately for ion collision behavior in the normal sputtering regime, in between the ‘‘free-space’’ and the ‘‘collisional’’ pressure extremes. Sheath voltage waveforms are determined from the observed discharge glow voltage, and yield close agreement between theoretical and experimental sheath heights. In addition, sheath voltages are close to being self-consistent. Sine-derived waveforms are shown to yield similar self-consistency, and are appropriate at high-target voltages. The rf sheath heights at low pressure are about 1.2 times larger than would be predicted from the free-space dc sheath model, for a given ion current density and average sheath voltage. In summary, this paper shows that: (i) rf sheath voltage waveforms are distinctly nonsinusoidal, especially at low voltages; and (ii) the major features of the target ion flux can be deduced from knowledge of the discharge pressure, voltage, and sheath height.

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