Application of the parametric bootstrap method to determine statistical errors in quantitative X-ray microanalysis of...

Area of Science:

• Materials Science
• Analytical Chemistry
• Computational Physics

Background:

• X-ray microanalysis is crucial for determining elemental composition and film thickness in materials.
• Accurate quantification in Si-Ge binary alloys requires precise understanding of measurement uncertainties.
• Existing Monte Carlo methods provide estimations but lack robust statistical error assessment.

Purpose of the Study:

• To apply the parametric bootstrap method for assessing error dependencies in X-ray microanalysis of Si-Ge binary alloys.
• To determine statistical errors in Ge concentrations and local film thickness with a single measurement.
• To evaluate the method's utility for assessing sample homogeneity.

Main Methods:

• Parametric bootstrap applied to X-ray microanalysis data.
• Utilized previously established Monte Carlo methods for initial estimations.
• Employed bootstrap confidence intervals for homogeneity testing.

Main Results:

• The parametric bootstrap effectively quantifies statistical errors in Ge concentration and film thickness.
• Accurate error estimation is achievable across regions with varying composition and thickness.
• The method allows for homogeneity assessment using a single measurement.

Conclusions:

• The parametric bootstrap is a valuable tool for estimating precision in quantitative microanalysis.
• It enables reliable comparison of different analytical methods.
• Bootstrap confidence intervals can reliably detect sample inhomogeneity.