Absolute measurements of rf fields using a retarding field energy analyzer

We present measurements of ion energy distribution functions obtained with a single Retarding Field Energy Analyzer (RFEA) along the axis of a low pressure helicon source. We have found that for high densities, the sheath thickness becomes small and sheath effects can be measured by the RFEA: a transition from a high frequency (single peak distribution) to a low frequency (bimodal distribution) sheath has been observed in the helicon source both for the capacitive and inductive modes. The energy difference between the two peaks of the bimodal distribution is related to the rf modulation of the plasma potential and to the ratio between the ion transit time in the sheath and the rf period. While the limiting cases of high and low frequency sheaths can be dealt with analytically, most of the results obtained correspond to a middle-ground where the phase mixing effect on the distribution function of the ion transit time across the sheath must be taken into account. A simple numerical model of the ion trajectories through an rf modulated sheath (assuming a known ion density and hence sheath thickness) is used to obtain V _rf, the rf amplitude of the sheath voltage, by fitting the distribution function produced by the model to measured bimodal distribution functions. By differentiating a series of V _rf values taken along the axis of the experiment, we obtain the rf electric field component in that direction.