Abstract. Background: Scatterometry is a fast, indirect, and nondestructive optical method for quality control in the production of lithography masks. To solve the inverse problem in compliance with the upcoming need for improved accuracy, a computationally expensive forward model that maps geometry parameters to diffracted light intensities has to be defined. Aim: To quantify the uncertainties in the reconstruction of the geometry parameters, a fast-to-evaluate surrogate for the forward model has to be introduced. Approach: We use a nonintrusive polynomial chaos-based approximation of the forward model, which increases speed and thus enables the exploration of the posterior through direct Bayesian inference. In addition, this surrogate allows for a global sensitivity analysis at no additional computational overhead. Results: This approach yields information about the complete distribution of the geometry parameters of a silicon line grating, which in return allows for quantifying the reconstruction uncertainties in the form of means, variances, and higher order moments of the parameters. Conclusions: The use of a polynomial chaos surrogate allows for quantifying both parameter influences and reconstruction uncertainties. This approach is easy to use since no adaptation of the expensive forward model is required.

中文翻译：

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光刻掩模形状重建的高效贝叶斯反演

摘要。背景：散射测量法是一种快速、间接和无损的光学方法，用于光刻掩模生产中的质量控制。为了根据即将到来的提高精度的需求来解决逆问题，必须定义一个计算成本高的正向模型，该模型将几何参数映射到衍射光强度。目的：为了量化几何参数重建中的不确定性，必须为正向模型引入一个快速评估的替代物。方法：我们使用基于非侵入式多项式混沌近似的前向模型，这提高了速度，从而能够通过直接贝叶斯推理来探索后验。此外，该代理允许在没有额外计算开销的情况下进行全局敏感性分析。结果：这种方法产生关于硅线光栅几何参数完整分布的信息，这反过来允许以参数的均值、方差和高阶矩的形式量化重建不确定性。结论：使用多项式混沌代理可以量化参数影响和重建不确定性。这种方法很容易使用，因为不需要调整昂贵的前向模型。多项式混沌代理的使用允许量化参数影响和重建不确定性。这种方法很容易使用，因为不需要调整昂贵的前向模型。多项式混沌代理的使用允许量化参数影响和重建不确定性。这种方法很容易使用，因为不需要调整昂贵的前向模型。