Evaluation of Langmuir probe ion density measurement in weakly ionized discharges using plasma oscillation probes and microwave interferometry

A comparison study is made of the classical theories of the determination of the ion density Ni from the ion current Ii to a cylindrical Langmuir probe vs bias voltage Vb in weakly ionized RF plasmas. A broad parameter range is examined in a commercial inductively coupled plasma (ICP). Accurate local electron density Ne values (Ne,MWI) obtained from Abel inversion of chord-averaged microwave interferometry (MWI) measurements using radial profiles Ni(R) from Langmuir probes, are verified by comparison with Ne from a plasma oscillation probe, and then compared with Ni obtained from theoretical interpretations of the probe current Ip(Vb) characteristics using a Hiden  Langmuir probe. Observed agreement between Ne,MWI and Ni thus obtained ranges from poor to fair; best agreement is observed at low pressure and RF power. A heuristic alternative approach based upon the ChildLangmuir law of ion sheath expansion (Ii ∝ Vb) is described, whereby Ni is determined by extrapolation of a linear regression fit to Ip, in the ion saturation regime, to its value Ii(Vf) at Vb = Vf, the floating potential. Good to excellent agreement with Ne,MWI is thus obtained, far superior to that using conventional analyses, despite the nonrigorous foundation for this “floating potential” method. 2