Both glow discharge optical emission and massspectrometry determine the sputtered mass rather then the sputtered depth. To determine the sputtered depth a model calculation for the density must be used to convert the sputtered mass and the elemental composition in to the sputtered volume or depth.
1. Elemental Sputtering Rates
To convert a qualitative depth profile of some coating into a quantitative depth profile, we first calculate the elemental sputtering rates, Dmij, for each element, i, at each point, j, in the depth profile. These elemental sputtering rates tell us how much of each element is being sputtered per second in g/m2/s, ie
where cij is the concentration of element i at point j in the depth profile, qMj is the sputtering rate per unit area atj, and Dtj the time increment at j.
If we integrate these elemental sputtering rates over time we have the total mass of the element removed, ie we have the coating mass of that element:
The easiest way to do this is to plot cijqMj vs time and then integrate over the time range of interest. If concentrations are in mass%, sputtering rates in g/m2/s, and time in s, then the result will be in g/m2.
Looking at the quantification procedure, we find that GDOES first determines the coating mass and than uses the elemental composition to make an assumption on the density to derive the sputtered depth. In particular, when the density of the analysed layer is not well known, the coating mass will be more reliable than the sputtered depth. Typical bad examples are oxide layers of non-stoechiometric composition.
During the calculation we also calculate the density at each point, rj. So now we can also calculate the coating mass directly from the quantitative depth profile.
First we note the relationship between depth and time:
where Dzj is the change in depth over time increment Dtj.
Substituting equation (3) into equation (1), we get
So if we integrate equation (4) over depth, we have:
The easiest way to do this is to plot cij vs depth (ie quantitative depth profile) and then have a special integration over the depth range of interest that first multiplies each cij by the density at each j. This special function might appear like magic at first until you realise what it is doing, just solving equation (5).
If concentrations are in mass%, density in g/cm3, and depth in Ám, then the result will be in g/m2.
First published on the web: 12 September 2000.
Authors: Richard Payling and Thomas Nelis.