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Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry

机译：散射中线粗糙度的建模及其对衍射强度和重构临界尺寸的影响

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摘要

We investigate the impact of line-edge and line-width roughness (LER, LWR) on the measured diffraction intensities in angular resolved extreme ultraviolet (EUV) scatterometry for a periodic line-space structure designed for EUV lithography. LER and LWR with typical amplitudes of a few nanometers were previously neglected in the course of the profile reconstruction. The two-dimensional (2D) rigorous numerical simulations of the diffraction process for periodic structures are carried out with the finite element method providing a numerical solution of the 2D Helmholtz equation. To model roughness, multiple calculations are performed for domains with large periods, containing many pairs of line and space with stochastically chosen line and space widths. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances is observed and established for different degrees of roughness. In particular, we obtain simple analytical expressions for the bias in the mean efficiencies and the additional uncertainty contribution stemming from the presence of LER and/or LWR. As a consequence this bias can easily be included into the reconstruction model to provide accurate values for the evaluated profile parameters. We resolve the sensitivity of the reconstruction from this bias by using simulated data with LER/LWR perturbed efficiencies for multiple reconstructions. If the scattering efficiencies are bias-corrected, significant improvements are found in the reconstructed bottom and top widths toward the nominal values.
机译：我们研究了线边缘和线宽粗糙度（LER，LWR）对用于EUV光刻设计的周期性线空间结构的角度分辨极紫外（EUV）散射法中测得的衍射强度的影响。在轮廓重建过程中，通常忽略了几纳米典型振幅的LER和LWR。使用提供二维Helmholtz方程数值解的有限元方法，对周期性结构的衍射过程进行了二维（2D）严格的数值模拟。为了对粗糙度建模，对周期较大的区域执行多次计算，其中包含许多对线和空间，并随机选择了线和空间的宽度。对于不同程度的粗糙度，观察到并确定了较高衍射级的平均效率的系统下降以及变化的增加。特别是，我们获得了平均效率偏差的简单分析表达式，以及由于LER和/或LWR的存在而导致的其他不确定性贡献。结果，可以容易地将该偏差包括在重建模型中，以为评估的轮廓参数提供准确的值。通过使用具有LER / LWR扰动效率的模拟数据进行多次重构，我们从该偏差解决了重构的敏感性。如果对散射效率进行了偏差校正，则重构的底部和顶部宽度朝着标称值的方向会得到显着改善。

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