Multiple harmonic compensation of Langmuir probes in rf discharges

We report on the use of an active Langmuir probe with three-harmonic compensation to diagnose rf discharge plasmas driven at 13.56 MHz. The plasma generates many harmonics on the fundamental, the first few being strongest. This gives a multi-harmonic rf voltage across the probe sheath that is removed by applying a rf signal to the probe that is matched both in amplitude and in phase for each harmonic. The probe I–V characteristic can then be analysed using dc theory. We show here that only when the rf harmonic amplitude approaches about 2Te is it necessary to compensate for that harmonic. For the commercial processing rig used this only occurs for the second harmonic at low pressures, <5 × 10−3 mbar. Here the addition of second-harmonic compensation shifts the probe I–V curve, making it markedly more positive than for fundamental-only compensation. Despite this the values obtained for the electron density ne and temperature Te changed by less than 10%. For most plasmas in which the harmonics have amplitudes below Te the use of fundamental-only compensation is adequate for all but the most precise measurements.