AI 中文总结
本文提出贝叶斯框架结合副本交换蒙特卡洛算法，实现二维SIMS成像中痕量物种的精确定位与不确定性量化，优化后0.4μm金点相对定位误差降至1.9%。
AI 中文摘要
为实现材料表面痕量物种的精确定位，本文提出一种分析二维（2D）二次离子质谱（SIMS）成像数据的贝叶斯框架。SIMS因具有高灵敏度及优异的元素与同位素特异性，被广泛应用于半导体制造、材料科学、地质学、环境科学与生命科学领域。然而，由于一次离子束展宽、相邻离子分布重叠及离子计数有限，精确定位仍具挑战性。本文将痕量物种的潜在分布建模为二维高斯峰的叠加；为解释低计数测量的随机性，在贝叶斯框架内假设检测到的离子计数服从泊松似然分布。采用副本交换蒙特卡洛（REMC）算法估计峰参数的后验分布，可在低计数条件下实现稳定推断并进行定量不确定性量化。该方法首先通过具有已知真值的合成数据集验证，随后应用于含规则排列金（Au）点的半导体样品SIMS测量，金点直径范围为0.4至2.0μm，以扫描电子显微镜（SEM）图像作为参考。优化测量条件后，0.4μm金点的相对定位误差从5.1%降至1.9%。上述结果表明，该方法可在二维SIMS成像中实现精确的亚微米级定位，并完成统计上严谨的不确定性量化。
英文摘要
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~$μ$m, using scanning electron microscopy (SEM) images as the reference. Optimization of the measurement conditions reduced the relative localization error for 0.4~$μ$m dots from 5.1$\%$ to 1.9$\%$. These results demonstrate accurate submicrometer localization with statistically rigorous uncertainty quantification in 2D SIMS imaging.
