Quantitative analysis of trace levels of surface contamination by X-ray photoelectron spectroscopy, Part I: statistical uncertainty near the detection limit

We discuss the problem of quantifying common sources of statistical uncertainties for analyses of trace levels of surface contamination by using X-ray photoelectron spectroscopy. We examine the propagation of error for peak-area measurements by using common forms of linear and polynomial background subtraction including the correlation of points used to determine both background and peak areas. This correlation has been neglected in previous analyses, but we show that it contributes significantly to the peak-area uncertainty near the detection limit. We introduce the concept of relative background subtraction variance (RBSV) that quantifies the uncertainty introduced by the method of background determination relative to the uncertainty of the background area itself. The uncertainties of the peak area and atomic concentration and of the detection limit are expressed using the RBSV, which separates the contributions from the acquisition parameters, the background-determination method, and the properties of the measured spectrum. These results are then combined to find acquisition strategies that minimize the total measurement time needed to achieve a desired detection limit or atomic-percentage uncertainty for a particular trace element. Minimization of data-acquisition time is important for samples that are sensitive to X-ray dose and also for laboratories that need to optimize throughput.