Statistically sound evaluation of trace element depth profiles by ion beam analysis

This paper presents the underlying physics and statistical models that are used in the newly developed program NRADC for fully automated deconvolution of trace level impurity depth profiles from ion beam data. The program applies Bayesian statistics to find the most probable depth profile given ion beam data measured at different energies and angles for a single sample. Limiting the analysis to % level amounts of material allows one to linearize the forward calculation of ion beam data which greatly improves the computation speed. This allows for the first time to apply the maximum likelihood approach to both the fitting of the experimental data and the determination of confidence intervals of the depth profiles for real world applications. The different steps during the automated deconvolution will be exemplified by applying the program to artificial and real experimental data.