If a pure sinusoidal RF voltage is applied to the sample, it has an amplitude *V*_{rf} (typically 700 V) and produces a DC bias potential on the inside surface of the sample *V*_{dc}. The potential on the sample surface therefore varies during each RF cycle between a small positive value, *V*_{p}, typically 30-50 V, and a large negative value, 2 x*V*_{rf} + *V*_{p}, typically -1360 V. The average is *V*_{rf} + *V*_{p}, ie 660 V, which equals *V*_{dc}.

The threshold voltage for sputtering is about 300 V, so a peak value in excess 300 V will cause sputtering. Since 300 V peak corresponds to a DC bias of about 140 V, sputtering will occur in RF at much lower voltages than in DC. An argon atom can typically travel about 1 mm during half an RF cycle. This means sputtering will only occur during that part of the cycle where *V*_{rf} > 300 V, ie during approximately 60% of the cycle. Hence, as reported, sputtering rates in RF are approximately 60% of those for DC.^{(1)}

To first order, the impedance of the GD plasma is independent of the applied RF power. This crucial result was first reported by Fabienne Canpont in 1993.^{(2)} It means, to first order, we can vary the RF power without changing the impedance. Since the emission yield depends on impedance, we can therefore vary the power without also changing the emission yield. This has consequences I will talk about later.

In an RF circuit using a matching box, the parallel capacitor *C*_{mod} varies mostly with the real part of the load impedance (resistance) and the series capacitor *C*_{pha} varies mostly with the imaginary part of the load impedance (phase). If we increase the applied RF power, both *C*_{mod} and*C*_{pha} remain nearly constant. If we increase the plasma pressure, the plasma resistance decreases and *C*_{mod} decreases while *C*_{pha} stays about the same. If we increase the gap between the sample and anode, the plasma impedance decreases, the plasma being less obstructed, and*C*_{mod} decreases.

If *R*_{g} is the source resistance, and if varying RF power does not change *R*_{g}, then

where *W*_{i} is the incident (or applied) RF power, and the factor 2 comes *V*_{rf} being defined here as peak voltage rather than rms voltage. For a fixed sample-to-anode gap, the source resistance varies with the sample matrix (ie, with the secondary electron emission yield of the sample) and the pressure. *R*_{g} is typically 20 KW.

In RF systems some power is lost in cables and through radiation. Manufacturers try to keep such losses to a minimum. The lost power can be thought of as a further resistance *R*_{loss}, in parallel with the source resistance. The power in the plasma, ie the 'effective' power *W*_{eff}, is then

where *V*_{g} is the RF peak voltage on the inside surface of the sample and *V*_{rf} is the applied RF peak voltage. For metal samples *V*_{g} = *V*_{rf}, for non-conducting samples, *V*_{g} < *V*_{rf}.

Canpont has suggested we can estimate *W*_{loss} by measuring the power without argon in the source. This is equivalent to making *R*_{g} infinite. The effective power is then the difference in power with and without argon.^{(2)}

**References**:

- R Payling, D G Jones and S Gower,
*Surf. Interface Anal.***20**(1993) 959. - F Canpont, These (Doctorat), Université Claude Bernard Lyon I, France, 1993, pp 40, 53, 70.
- Th.Nelis, M. Aeberhard, L. Rohr , J. Michler, Ph. Belenguer, Ph. Guilot, L. Thérèse; "A simple methode for measuring the plasma power in rf-GDOES instruments"; Anal. Bioanal. Chem.;
**339,3**; 2007; 763-767; DOI 10.1007/s00216-007-1509-3

First published on the web: 12 November 2002.

Authors: Richard Payling and Thomas Nelis