Quantification of GD results for CDPWhen performing a Depth Profile Analysis with GDOES, the intensity  time profile measured by the GD spectrometer must be converted into a Content Depth profile, expressing the elemental composition as function of depth. This process is commonly called quantification of a GD analysis, or Quantitative Depth Profile Analysis (QDP or QDPA) Atoms in the PlasmaThe atoms sputtered from the surface of the sample enter the plasma where they are excited and emit photons. Imagine the number of photons per atom is constant. Then by counting the number of photons we are effectively counting the number of atoms. Typically one photon is emitted for about every 10 000 atoms entering the plasma. Hence if we measure 1000 photons we have really counted 1000x10 000=10 million atoms. (The graphic is supplied by courtesy of Alwyn Anfone, Clemson University, USA) By measuring photons at different energies (different emission lines) we can tell what proportion of these atoms are Al atoms or Fe atoms or Na atoms, etc. And the total number of atoms per second tells us the sputtering rate. So from measuring the intensities we know both the concentrations and thesputtering rate simultaneously. From the sputtering rate we can then tell how much material we have removed from the sample surface. This allows us to plot concentrations versus depth in the sample. It sounds simple, and in fact it really is, though it has taken us many years to get to this simple picture. The problem is that people start to think it must be more complicated or we make approximations which are not valid. So, going back to the plasma, we could easily imagine that the number of photons will vary from element to element (and from line to line), so we have an equation relating photons (measured as Intensity, I_{i}, of element i) and the number of atoms of element i in the plasma (given as the product of concentration c_{i} in mass % and sputtering rate q_{M} in g/m^{2}): Some ComplicationsUnfortunately there are four known complications. First, and most serious, there is always some unwanted background signal, so our equation becomes:^{(1)} where b_{i} is known as the background equivalent concentration (or BEC, for short). If you are wondering why we make c_{i}q_{M} the dependent variable rather than I_{i}, click here. Secondly, there is the possibility, though usually small in GDOES, that some nearby emission lines from some other elements j will interfere with our line from element i, giving some additional unwanted signal: Thirdly, there is the possibility, though only for resonance lines, that our photon will be absorbed by some other atom. The likelihood of this increases exponentially with the number of atoms. It therefore can make our equation nonlinear, see selfabsorption for more details:^{(2)} Fourthly, and most annoying, the number of photons per atom does change by a small amount. This change in emission is called the 'relative emission yield', and is the most controversial parameter in GDOES. For mathematical convenience we take the inverse of the relative emission yield, give it the symbol R_{i} and call it, naturally, the 'inverse relative emission yield'. GDOES EquationHence our equation finally becomes: So our simple equation is not so simple anymore. Fortunately it represents few problems for a computer. The final equation can be used both for bulk analysis and for quantitative depth profiling. The only real difference between bulk and depth profiling is in the presentation of the results. References: (1) T Nelis, Colloq. Spectrosc. Intnl. York (1993). (2) R Payling, Spectroscopy 13, 36 (1998). further and more publications related to the subject :  Z. Weiss, Surf. Interface Anal., 1992, 18, 691.
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First published on the web: 1 June 2000. Author: Richard Payling
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