Uncertainty minimization in electronic stopping cross-section measurements using the backscattering method

TL;DR

This work tackles the lack of uncertainty budgets in backscattering-based electronic stopping cross-section measurements by introducing a quantitative, uncertainty-aware framework for optimizing experimental geometry. The method leverages two paired backscattering configurations and a covariance-based uncertainty propagation to extract $[\epsilon]_{in}$ and $[\epsilon]_{out}$ with quantified random and systematic contributions, benchmarked against SRIM and ICRU-49. A key contribution is the explicit treatment of correlation between entry and exit-path measurements and a numerical geometry optimization that minimizes the total uncertainty $\sigma_{total}$. The approach enables sub-$3\%$ total uncertainties for He in Au thin films across a wide energy range, enhancing the reliability and traceability of RBS-derived stopping data for model validation and reference purposes. Practically, the framework provides a principled recipe for planning high-precision stopping-power measurements and highlights the trade-offs between random and systematic errors inherent in backscattering geometries.

Abstract

Accurate determination of electronic stopping cross sections is critical for ion beam analysis and related applications. While transmission methods are well established, backscattering approaches remain less explored from a metrological perspective, often lacking a systematic treatment of uncertainties. In this work, we present a quantitative framework to optimize experimental geometry in backscattering-based stopping measurements, explicitly accounting for both statistical and systematic errors. Applying the method to helium ions in gold thin films, we identify angular conditions that balance precision and accuracy, achieving total uncertainties below 3\% over a wide energy range. The results, benchmarked against SRIM and ICRU-49, demonstrate that our approach improves the reliability of RBS-derived stopping data and strengthens their use for reference purposes and model validation.

Figures (7)

• Figure 1: Illustrative spectrum for the RBS technique.
• Figure 2: Depth-resolution calculated using ResolNRA demonstrating the 45 nm thick film is suitable for stopping cross-section measurements in the energy range of this study.
• Figure 3: Panel showing different contributions to the final uncertainty calculated assuming the measurement of helium stopping cross-section in a $3\times10^{17}$ at./cm$^2$ (45 nm) thick gold film. The incident alpha beam energy is 1000 keV and the detector was placed at 120$^\circ$ scattering angle. Top line shows the relative random uncertainty calculated for the way-in (left) and way-out (center) the film, and the correlation factor of these both values (right). The bottom line shows systematic uncertainties for the way-in (left) and way-out (center) the film. Color scale in uncertainty plots are in logarithm scale and saturated at 10% for improved visualization. The color scale in the correlation factor map in linear and restricted between -1 and 0 since it is always negative.
• Figure 4: Heat maps showing calculated total uncertainty assuming the measurement of helium stopping cross-section in a $3\times10^{17}$ at./cm$^2$ (45 nm) thick gold film. The incident energy is 1000 keV and detector placed at 120$^\circ$ scattering angle. Total uncertainty in the way-in (left) and way-out (right). Color scale in uncertainty plots are in logarithm scale and saturated at 10% for improved visualization.
• Figure 5: Heat maps showing calculated total uncertainty assuming the measurement of helium stopping cross-section in a $3\times10^{17}$ at./cm$^2$ (45 nm) thick gold film. The incident energy is 500 keV and detector placed at 120$^\circ$ scattering angle. Total uncertainty in the way-in (left) and way-out (right). Color scale in uncertainty plots are in logarithm scale and saturated at 10% for improved visualization.