Morphometric Roughness of Nanostructured Surfaces

描述复杂的、非重复的地形是具有挑战性的，像快速傅立叶变换和均方根粗糙度（RMS）这样的经典方法在捕捉其复杂性方面存在不足。然而，特定的地形极大地影响了物理、化学和生物特性。因此，地形的准确表征和精确描述是必不可少的。针对不同的材料特性，已经设计了许多具有特定形貌的不同纳米结构，但仍然缺乏直观的、跨学科接受的和全面的粗糙度描述。这个由实验（生物）物理学、理论物理学和数学科学家组成的团队旨在填补这一空白，并为自己设定了为纳米技术中使用的一系列非常不同的样品开发最合适的分析和表征方法的目标。原子力显微镜是在纳米尺度上记录形貌的主要实验方法。数学工具包括基于Minkowski泛函数的高级形状描述符，以及新开发的（纳米）粗糙表面的空间模型和使用分形和随机几何方法的聚集模型。

Describing complex, non-recurring topographies is challenging and classical methods like Fast Fourier Transform and root mean square roughness (RMS) fall short in capturing their intricacies. However, the specific topography greatly influences physical, chemical, and biological properties. An accurate characterization and precise description of topographies are therefore essential. Numerous different nanostructures with specific topographies have been designed for various material properties, yet the lack of an intuitive, interdisciplinary accepted and comprehensive description of roughness persists. The team of scientists from experimental (bio)physics, theoretical physics and mathematics aims to fill this gap and has set itself the goal of developing the most suitable analysis and characterization methods for a range of very different samples used in nanotechnology. Atomic force microscopy is the main experimental method for recording topographies on the nanoscale. The mathematical tools include advanced shape descriptors, based on Minkowski functionals, and newly developed spatial models for (nano)rough surfaces and aggregation models using methods from fractal and stochastic geometry.