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首页> 外文期刊>Journal of Physics, D. Applied Physics: A Europhysics Journal >Novel method for error limit determination in x-ray reflectivity analysis
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Novel method for error limit determination in x-ray reflectivity analysis

机译：X射线反射率分析中误差极限确定的新方法

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摘要

A novel error limit determination method for x-ray reflectivity (XRR) analysis is developed and applied to data measured from atomic-layer-deposited aluminium oxide on silicon. The analysis here is based on Parratt's formalism and on a fitness defined as a mean-squared error between a measurement and a fit in logarithmic scales. The mathematically derived upper bound for an error uses a trick which divides the fitness into two parts. The divided original fitness equals the fitness between a measurement and a numerically optimal but unknown fit (the first part) plus the fitness between the unknown optimal fit and the known original fit (the second part). In practical error determination, the fitness in the first part is the fitness of noise and it is approximated using a separate simulation and in the second part, the unknown optimal fit is considered as a variable to be optimized. An efficient implementation is presented for the error determination and the determined parameters were 42.4 +/- 0.12 nm (0.3%), 3.15 +/- 0.11 g cm(-3) (3.5%) and 0.80 +/- 0.06 nm (7.5%) for the thickness, the mass density and the surface roughness, respectively. Although the formalized error may need some fine tuning as future work since it gives an asymptotic estimate, it still gave reasonable results in the case of systematic error caused by nonideal fit.
机译：开发了一种新颖的用于X射线反射率（XRR）分析的误差极限确定方法，并将其应用于从在硅上沉积原子层的氧化铝测量的数据。此处的分析基于帕拉特的形式主义和适应度，适应度定义为度量与对数刻度的拟合之间的均方误差。从数学上得出错误的上限使用了一个技巧，该技巧将适应度分为两部分。划分后的原始适应度等于测量值和数值最佳但未知的拟合度（第一部分）之间的适应度，加上未知的最佳拟合度与已知的原始拟合度（第二部分）之间的适应度。在实际误差确定中，第一部分的适应度为噪声的适应度，使用单独的模拟对其进行近似，在第二部分中，未知的最佳拟合被视为要优化的变量。提出了一种有效的误差确定方法，确定的参数为42.4 +/- 0.12 nm（0.3％），3.15 +/- 0.11 g cm（-3）（3.5％）和0.80 +/- 0.06 nm（7.5％） ）分别表示厚度，质量密度和表面粗糙度。尽管形式化误差可能会进行渐近估计，因此可能需要做一些微调，以备将来之用，但在非理想拟合引起的系统误差的情况下，它仍能给出合理的结果。

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