A novel and holistic approach for experimental x-ray fundamental parameter determination—the Ru L-shell

Abstract

The present work aims to improve both the experimental and the data evaluation procedures necessary for a determination of L-subshell atomic fundamental parameters (FP). The main motivation lies in the fact that the established approach, consisting of a sequential evaluation of recorded transmission and fluorescence spectra in the vicinity of the three L-absorption edges, provides relatively large uncertainties for the Coster-Kronig factors. Up to now, reliable uncertainty budgets were in the order of 15 \% to 100 \% and more.

The novel holistic evaluation procedure addresses these large uncertainties, by employing a much larger experimental dataset extending far above the L$_1$ absorption edge and a combined evaluation approach for a more reliable determination of the Coster-Kronig factors. Here, using the Ru-L shells as an example, their uncertainties are reduced to under 15 \%. In addition, this enables also the determination of other relevant FP data, such as the L-subshell Auger yields, the L-subshell photoionization cross sections as well as the L-subshell fluorescence production cross sections with significantly lower uncertainties as compared to the established approach.

Experimental determination of the hafnium L-subshell fundamental parameters using the holistic approach

“…Their works are based on a data evaluation strategy were only the region around the three L-shells is being probed. As already stated in our earlier work on the Ru-L shell parameters [2], this approach is very sensitive to extrapolation errors of the subshell photoionization cross sections. Depending on how they were determined in these works, this may explain the observed deviations.…”

“…Based on these relations, a Markov-Chain-Monte-Carlo (MCMC) [16] algorithm can be employed to find the optimal parameter set consisting of the CK factors as well as the A i parameters for the subshell photoionization contributions. For further details see [2].…”

“…Typically, the achievable uncertainties for the CK factors were at best in the order of the Krause estimates [18] and usually much larger [3,27,28]. With the holistic approach the achieveable uncertainties for the CK factors can be significantly reduced [2] as compared to the conventional data evaluation approach. For the Hf-L subshells, they are now in the 10% regime as shown in table 1, which is comparable to the Krause estimates or even lower in the case of f 12 .…”

“…At the Physikalisch-Technische Bundesanstalt (PTB), well-characterized physically calibrated XRF instrumentation is employed for dedicated FP experiments in order to update existing FP data. Recently, a new holistic data evaluation approach for accessing the FPs for the L-subshells has been demonstrated [2].…”

“…In this work, we have applied the new holistic approach to experimentally determine the L-subshell FPs of hafnium, which is an important element for state-of-the-art semiconductor applications [4][5][6] and other relevant fields [7][8][9]. The atomic FP data determined in this work can also be found on Zenodo [10].…”