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Sputtering Rate Constant

The sputtering rate constant depends principally on two factors: 

  • how efficient is the transfer of energy from the incident Argon ion to the target atoms (this will vary with their relative masses)
  • how difficult is it to break atomic bonds in the target to free sputtered atoms (given by the sublimation energy)

The sputtering rate constant CQ of a pure material, expressed as a ratio to some reference material, eg pure iron, is given approximately by(1)


where mmref, and mAr are the atomic masses of the material, the reference material, and Argon (the sputtering gas), and US the sublimation energy. Hence the relative sputtering rate constant tends to increase slowly with the mass of the material and to decrease with increasing sublimation energy.

This theoretical equation involves many assumptions and works well for higher atomic mass targets (above Ni) but does not work particularly well for low atomic mass targets. So I used the following empirical version of this equation, which works better at lower masses:


where in a first study,a ~ 2.4, b ~ 1.8, andc ~ 1.5.

Relative Sputtering Rates

When several elements are present in the target, the surface will become preferentially enriched with the slower sputtering elements, and these will dominate the sputtering rate constant.

The relative sputtering rate constant for a material composed of different elements is therefore given approximately by(1)


where ci is the mass fraction of element i and CQreli is the value of CQrel for the pure material.


Strictly speaking, to determine CQrel it is necessary first to measure U0. Sometimes this is done, but mostly it is assumed U0 is constant and relative sputtering rates are used instead. Values for US are from ref. (2).

Additional sputtering rate data are available at the website of TAZ GmbH, by clicking here. Note: they express relative sputtering rates as the inverse.


  1. R Payling, in R Payling, D G Jones and A Bengtson (Eds), Glow Discharge Optical Emission Spectrometry, John Wiley, Chichester (1997), pp 260, 267.
  2. E A Brandes and G B Brook (Eds), Smithells Metals Reference Book, Butterworth-Heinemann (1992), pp 8-1 to 8-3.
  3. A Bengtson and L Danielsson, Thin Solid Films, 124 (1985) 231.
  4. T Nelis, Private communication (1999).
  5. Z Weiss, Lecture at GD-OES Seminar, Vito, Mol, Belgium, (1999).
  6. TAZ GmbH, Website (2000).
  7. M Köster, Private communication (2001).
  8. L Ohannessian, PhD Thesis, Université Claude Bernard, Lyon, France, pp 88 (1986).

First published on the web: 1 June 2000.

Author: Richard Payling