In 1972, Paul Boumans introduced the following equation for the sputtering rate, *q*, in GD-OES^{(1)}

where *q* is in mass/s, *C _{Q}* is a sputtering constant which may vary with the plasma gas species but not with current, potential or pressure in the source,

*i*is the current,

_{g}*U*the voltage and

_{g}*U*a turn-on voltage, typically 300 V in DC operation.

_{0}In 1994, Payling suggested a modification to this equation when he found sputtering rates were not quite linear with voltage^{(2)}

where *N* = 0.74. With the modified equation, *U _{0}* is typically about 400 V in DC operation, so that when the two equations are plotted together they appear very similar. As a result many continue to use the original Boumans' equation.

Blue points are original equation, red points are the modified equation

The sputtering rate can also be expressed as

where *P _{g}* is the power and

*P*is a constant. Since

_{0}*P*is generally quite small, perhaps 2-3 W, the sputtering rate is nearly proportional to power. But also depends on the carrier gas pressure in the discharge source.

_{0}**References**:

- P W J M Boumans,
*Anal. Chem*.**44**, 1219 (1972). - R Payling,
*Surf. Interface Anal*.**21**, 791 (1994).

First published on the web: 15 May 2000.

Authors: Richard Payling & Thomas Nelis