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首页> 外文期刊>Journal of Physics, D. Applied Physics: A Europhysics Journal >Fitness function and nonunique solutions in x-ray reflectivity curve fitting: crosserror between surface roughness and mass density
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Fitness function and nonunique solutions in x-ray reflectivity curve fitting: crosserror between surface roughness and mass density

机译：X射线反射率曲线拟合中的适应度函数和非唯一解：表面粗糙度和质量密度之间的交叉误差

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摘要

Nonunique solutions of the x-ray reflectivity (XRR) curve fitting problem were studied by modelling layer structures with neural networks and designing a fitness function to handle the nonidealities of measurements. Modelled atomic-layer-deposited aluminium oxide film structures were used in the simulations to calculate XRR curves based on Parratt's formalism. This approach reduced the dimensionality of the parameter space and allowed the use of fitness landscapes in the study of nonunique solutions. Fitness landscapes, where the height in a map represents the fitness value as a function of the process parameters, revealed tracks where the local fitness optima lie. The tracks were projected on the physical parameter space thus allowing the construction of the crosserror equation between weakly determined parameters, i.e. between the mass density and the surface roughness of a layer. The equation gives the minimum error for the other parameters which is a consequence of the nonuniqueness of the solution if noise is present. Furthermore, the existence of a possible unique solution in a certain parameter range was found to be dependent on the layer thickness and the signal-to-noise ratio.
机译：通过使用神经网络对层结构建模并设计适应度函数来处理非理想测量，研究了X射线反射率（XRR）曲线拟合问题的非唯一解。在仿真中，使用了模拟的原子层沉积氧化铝膜结构来计算基于Parratt形式主义的XRR曲线。这种方法减少了参数空间的维数，并允许在非唯一解的研究中使用适应度景观。适应度景观（其中地图中的高度表示适应度值作为过程参数的函数）显示了局部适应性最佳值所在的轨迹。轨道被投影在物理参数空间上，从而允许在弱确定的参数之间，即在层的质量密度和表面粗糙度之间，构造交叉误差方程。该公式给出了其他参数的最小误差，这是存在噪声时解决方案不唯一性的结果。此外，发现在特定参数范围内可能存在的唯一解决方案的存在取决于层厚度和信噪比。

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