Absolute measurements and modeling of radio frequency electric fields using a retarding field energy analyzer

Measurements of the rf electric field have been made along the z axis of a helicon reactor using a retarding field energy analyzer. A fluid code and a simple analytical model have been developed to analyze the ion energy distribution functions, especially in the case of bimodal distributions where the ion transit time through the sheath in front of the analyzer is comparable to the rf period. A generalized curve (and an analytical approximation to that curve) has been developed from the analytical model and confirmed by the self-consistent fluid model for high, low, and intermediate ion transit time, which can be used by experimenters to quickly convert the experimental results (energy peak separation, plasma potential and density, electron temperature), which are related to rf sheath oscillations, to absolute values of the rf electric field. An analysis of the errors involved in the derivation of the field is given. The results agree qualitatively with rf pickup measured with a floating Langmuir probe.