The electron distribution function at an RF planar probe due to an incident electron beam

Abstract

Experiments with a planar probe embedded in the grounded electrode of the GEC cell run in the capacitive mode suggest the presence of extra-energetic electrons. In particular, under a wide range of filling pressure and power the I–V characteristic rises linearly towards the ion saturation current. To model this analytically, an electron beam is taken to be incident at the plasma–sheath boundary of the planar probe. The beam electrons are retarded, as they approach the probe surface, by a combination of a steady component of potential and that fraction of applied RF which is distributed between the plasma and ground; the electron transit time is assumed short compared to the RF period. The electron distribution function received at the probe is expressed in terms of a convolution integral. The distribution received at the probe is used to calculate the resulting component of beam current at the probe surface for the special case that the incident beam distribution has a top hat form. Combining this current with the ion sound and electron thermal currents leads to the I–V characteristic. Given a specified range of energies for the incident beam it is shown that the characteristic rises linearly towards the ion saturation current. It is concluded that this feature of the characteristic can be plausibly interpreted as due to extra-energetic electrons.