Bayesian Localization and Uncertainty Quantification of Trace Species in Two-Dimensional SIMS Imaging
To enable accurate localization of trace species on material surfaces, we propose a Bayesian framework for analyzing two-dimensional (2D) secondary ion mass spectrometry (SIMS) imaging data. SIMS is widely used in semiconductor manufacturing, materials science, geology, environmental science, and life sciences because of its high sensitivity and excellent elemental and isotopic specificity. However, precise localization remains challenging because of primary ion beam broadening, overlap between neighboring ion distributions, and limited ion counts. The underlying distribution of trace species is modeled as a superposition of two-dimensional Gaussian peaks. To account for the stochastic nature of low-count measurements, the detected ion counts are assumed to follow a Poisson likelihood within a Bayesian framework. Posterior distributions of the peak parameters are estimated using replica-exchange Monte Carlo (REMC), enabling stable inference together with quantitative uncertainty estimation under low-count conditions. The proposed method is first validated using synthetic datasets with known ground truth and is then applied to SIMS measurements of semiconductor samples containing regularly arranged gold (Au) dots with diameters ranging from 0.4 to 2.0~$\mu$m, using scanning electron microscopy (SEM) images as the reference. Optimization of the measurement conditions reduced the relative localization error for 0.4~$\mu$m dots from 5.1$\%$ to 1.9$\%$. These results demonstrate accurate submicrometer localization with statistically rigorous uncertainty quantification in 2D SIMS imaging.