Limitations

The limitations of the ARXPS technique have been laid out in detail by Cumpson. Here we'll just summarize:

1) In the depth profile, one has to trade off certainty in the composition for depth resolution, or vice-versa.

Even for a generous uncertainty in composition of ± 50%, the best fractional depth resolution one can hope for is 0.8.

2) The problem of inverting the Laplace transform (calculating a depth profile) is "ill-conditioned".

Depth profiles that are only broadly similar will give very similar ARXPS results, which means that one needs very exact ARXPS data to arrive at a unique depth profile. Let's look at an example :

In the lower graph below the points are real ARXPS data taken from a polystyrene sample exposed to a helium/oxygen plasma. The upper graph shows the best-fit profiles derived from four model depth profile types. The 'Cumpson', exponential and maybe the triangle profiles are broadly similar, but the boxcar profile looks rather different, and yet, they all reproduce the experimental data reasonably well (lines on the graph at the bottom)

comparison of the fit of the different models

It can be seen that in order to distinguish between these depth profiles on the basis of ARXPS data one would require a high degree of precision in the at. % values.

3) For typical ARXPS data one is limited to three degrees of freedom.

For a precision in the peak intensity measurement of 3%, one can only extract three independent parameters from the data. In order to justify the extraction of a fourth parameter, we'd need to increase the precision to 0.3%. Any calculations we do on the ARXPS data, therefore, must fix or link all but three parameters. In a substrate / overlayer model, for example, we might attempt to optimize the layer thickness and two composition parameters. If we wish to posit the existence of two layers on the substrate, and to optimize the thickness of each, we only have one composition parameter left to play with. The chunkiness of the three model profiles constructed from linear segments, shown in the graph above, results from this limitation.