Bias and synergy in the self-consistent approach of data analysis of ion beam techniques.

Using multiple ion beam analysis measurements, or techniques, combined with self-consistent data processing, generally allows extracting more (or more accurate) information from the measurements than processing separately data from single measurements. Solving ambiguities, improving the final depth resolution, defining constraints and extending applicability are the main strengths of the self-consistent approach. It basically consists in formulating a multi-objective minimization problem that can be tackled by the adoption of the weighted-sum method. A simulation study is reported in order to evaluate the systematic error inserted in the analysis by the choice of a specific objective function, or even by the weights or normalization adopted in the weighted-sum method. We demonstrated that the bias of the analyzed objective functions asymptotically converges to the true value for higher statistics. We also demonstrate that the self-consistent analysis inherits the accuracy of the most accurate measurement, establishing a a rank of information content, where some combinations of measurements are more valuable than others, i.e. when processed together they provide more information by means of a better constraint for the multi-objective optimization.