Quantitative analysis of trace levels of surface contamination by X-ray photoelectron spectroscopy, Part I: statistical uncertainty near the detection limit
Shannon B. Hill, Nadir S. Faradzhev, Cedric J. Powell
We discuss the problem of quantifying common sources of statistical uncertainties for analyses of trace levels of surface contamination using X-ray photoelectron spectroscopy. We examine the propagation of error for peak-area measurements 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 for measurements near the detection limit. We introduce the concept of relative background subtraction variance (RBSV) which quantifies the uncertainty introduced by the subtraction of the background relative to the uncertainty of the background area itself. The RBSV enables uncertainties of the peak area and atomic concentration as well as the detection limit to be expressed in a form that clearly separates the contributions from the acquisition parameters, the background-subtraction method and the inherent properties of the measured spectral features. These results are then combined to determine the acquisition strategies to minimize the total measurement time to achieve a desired detection limit or uncertainty in the atomic percentage 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.