In this work, a simple method to follow the evolution of the surface of thin films during growth on substrates characterised by high roughness is detailed. To account for real cases as much as possible, the approach presented is based on the hypothesis that deposition takes place under nonstochastic conditions, such as those typical of many thin film processes in industry and technology. In this context, previous models for roughness replication, which are mainly based on idealised deposition conditions, cannot be applied and thus ad hoc approaches are required for achieving quantitative predictions. Here it is suggested that under nonstochastic conditions a phenomenological relation can be proposed, mainly based on local roughening of surface, to monitor the statistical similarity between the film and the substrate during growth or, in other words, to detect changes of the bare substrate morphological profile occurring during the film growth on top. Such approximation is based on surface representation in terms of power spectral density of surface heights, derived from topographic images; in this work, such method will be tested on two separate batches of synthetic images which simulate thin films growth onto a real rough substrate. In particular, two growth models will be implemented: the first reproduces the surface profile obtained during an atomic force microscopy measurement by using a simple geometrical envelope of surface, regardless the thin film growth mechanism; the second reproduces the columnar growth expected under nonstochastic deposition conditions. It will be shown that the approach introduced is capable to highlight differences between the two batches and, in the second case, to quantitatively account for the replication of the substrate roughness during growth. The results obtained here are potentially interesting in that they account essentially for the geometrical features of the surfaces, and as such they can be applied to synthetic depositions that reproduce different thin film depositions and experimental contexts.

中文翻译：

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评估非随机沉积条件下的保形薄膜沉积：粗糙度复制的现象学模型在合成地形图像中的应用

在这项工作中，详细介绍了一种在具有高粗糙度的基板上生长过程中跟踪薄膜表面演变的简单方法。为了尽可能多地考虑实际情况，所提出的方法基于以下假设：沉积发生在非随机条件下，例如工业和技术中许多薄膜工艺的典型条件。在这种情况下，以前主要基于理想化沉积条件的粗糙度复制模型无法应用，因此需要临时方法来实现定量预测。这里建议在非随机条件下，可以提出一种现象学关系，主要基于表面的局部粗糙化，以监测生长过程中薄膜和基材之间的统计相似性，或者，换句话说，检测在顶部薄膜生长期间发生的裸基板形态轮廓的变化。这种近似是基于表面高度的功率谱密度方面的表面表示，源自地形图像；在这项工作中，这种方法将在两批独立的合成图像上进行测试，这些图像模拟了薄膜在真实粗糙基材上的生长。特别是，将实施两个生长模型：第一个通过使用简单的表面几何包络重现原子力显微镜测量期间获得的表面轮廓，而不管薄膜生长机制如何；第二个再现了在非随机沉积条件下预期的柱状生长。将证明引入的方法能够突出两个批次之间的差异，并且，在第二种情况下，定量解释生长过程中衬底粗糙度的复制。这里获得的结果可能很有趣，因为它们基本上解释了表面的几何特征，因此它们可以应用于重现不同薄膜沉积和实验环境的合成沉积。