Thin films generally contain depth‐dependent residual stress gradients, which influence their functional properties and stability in harsh environments. An understanding of these stress gradients and their influence is crucial for many applications. Standard methods for thin‐film stress determination only provide average strain values, thus disregarding possible variation in strain/stress across the film thickness. This work introduces a new method to derive depth‐dependent strain profiles in thin films with thicknesses in the submicrometre range by laboratory‐based in‐plane grazing X‐ray diffraction, as applied to magnetron‐sputtering‐grown polycrystalline Cu thin films with different thicknesses. By performing in‐plane grazing diffraction analysis at different incidence angles, the in‐plane lattice constant depth profile of the thin film can be resolved through a dedicated robust data processing procedure. Owing to the underlying intrinsic difficulties related to the inverse Laplace transform of discrete experimental data sets, four complementary procedures are presented to reliably extract the strain depth profile of the films from the diffraction data. Surprisingly, the strain depth profile is not monotonic and possesses a complex shape: highly compressive close to the substrate interface, more tensile within the film and relaxed close to the film surface. The same strain profile is obtained by the four different data evaluation methods, confirming the validity of the derived depth‐dependent strain profiles as a function of the film thickness. Comparison of the obtained results with the average in‐plane stresses independently derived by the standard stress analysis method in the out‐of‐plane diffraction geometry validates the solidity of the proposed method.

中文翻译：

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从平面X射线衍射提取的薄膜中的应变深度分布

薄膜通常包含取决于深度的残余应力梯度，这会影响其在恶劣环境中的功能特性和稳定性。这些应力梯度及其影响的理解对于许多应用至关重要。确定薄膜应力的标准方法仅提供平均应变值，因此忽略了整个薄膜厚度上应变/应力的可能变化。这项工作引入了一种新方法，该方法可通过基于实验室的平面内掠X射线衍射来得出亚微米范围内厚度的薄膜中与深度有关的应变曲线，该方法适用于不同厚度的磁控溅射生长多晶Cu薄膜。通过在不同入射角执行面内掠射衍射分析，薄膜的面内晶格恒定深度轮廓可以通过专用的可靠数据处理程序来解决。由于与离散实验数据集的拉普拉斯逆变换有关的潜在内在困难，提出了四种互补程序，以从衍射数据中可靠地提取薄膜的应变深度分布。出人意料的是，应变深度分布不是单调的，而是具有复杂的形状：靠近基板界面的高度压缩，薄膜内部的更大拉伸力以及靠近薄膜表面的松弛。通过四种不同的数据评估方法可以获得相同的应变曲线，从而证实了所得出的深度相关应变曲线作为膜厚函数的有效性。