Under certain conditions in radio-frequency (rf) plasmas, the amplitude of the low-energy peak in ion energy distributions (IEDs) measured at an electrode depends sensitively on the velocity at which ions approach the sheath. By measuring IEDs, incident ion velocities can be determined. Here, IEDs were measured in inductively coupled plasmas in 1.3 Pa of CF4, at rf sheath voltages up to 100 V at 1 MHz, obtained by biasing a counterelectrode. From measured IEDs and sheath voltages, we determined the incident velocities of all significant positive ions: CF3+, CF2+, CF+, and F+. At higher bias voltages, we detected essentially the same velocity for all four ions, suggesting that some collisional process keeps different ions at the same velocity as they emerge from the presheath. For all four ions, measured velocities were significantly lower than the Bohm velocity uB and the electropositive ion sound speed cs, because of negative ion effects. From the measured velocities, an upper bound for negative ion temperature is obtained. The velocities determined here do not agree with boundary conditions that have been previously proposed, because the latter neglect either the reduction in ion sound speed due to negative ions or the acceleration that occurs as ions pass from the point where quasineutrality is violated to the point where electron density becomes negligible. Both of these effects are treated to fair approximation, for collisionless sheaths, by setting the initial velocity to twice the ion sound speed modified by negative ions.
We tested a simple digital impedance bridge using two nominally equal resistors to
form a 1:1 ratio. We focused on resolution and stability of the detectors. Fluctuations
of the source voltages were largely removed through postprocessing of the digitized
data, and the measurement results were limited by the detector noise. This
detector-limited operating condition was first demonstrated using three modified
Keysight 3458A multimeters for measurements of the voltage ratios, achieving 0.01 μV/V
type A uncertainty in less than 15 min at 1 kHz. In an effort to extend the applicable
frequency range and develop a system with off-the-shelf components, we tested a system
using three lock-in detectors for measuring small deviations from the perfect AC ratio
of unity magnitude, achieving stabilities and resolutions of 0.1 μV/V in a few hours for
each point from 1 kHz to 5 kHz.
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