This paper describes the processing of three-dimensional (3D) scanning probe microscopy (SPM) data. It is shown that 3D volumetric calibration error and uncertainty data can be acquired for both metrological atomic force microscope systems and commercial SPMs. These data can be used within nearly all the standard SPM data processing algorithms to determine local values of uncertainty of the scanning system. If the error function of the scanning system is determined for the whole measurement volume of an SPM, it can be converted to yield local dimensional uncertainty values that can in turn be used for evaluation of uncertainties related to the acquired data and for further data processing applications (e.g. area, ACF, roughness) within direct or statistical measurements. These have been implemented in the software package Gwyddion.
A Si adatom on a Si(111)-(7 × 7) reconstructed surface is a typical atomic feature that can rather easily be imaged by a non-contact atomic force microscope (nc-AFM) and can be thus used to test the atomic resolution of the microscope. Based on our first principles density functional theory (DFT) calculations, we demonstrate that the structure of the termination of the AFM tip plays a decisive role in determining the appearance of the adatom image. We show how the AFM image changes depending on the tip-surface distance and the composition of the atomic apex at the end of the tip. We also demonstrate that contaminated tips may give rise to image patterns displaying so-called 'sub-atomic' features even in the attractive force regime.
Measurement of local mechanical properties is an important topic in the fields of nanoscale device fabrication, thin film deposition and composite material development. Nanoindentation instruments are commonly used to study hardness and related mechanical properties at the nanoscale. However, traceability and uncertainty aspects of the measurement process often remain left aside. In this contribution, the use of a commercial nanoindentation instrument for metrology purposes will be discussed. Full instrument traceability, provided using atomic force microscope cantilevers and a mass comparator (normal force), interferometer (depth) and atomic force microscope (area function) is described. The uncertainty of the loading/unloading curve measurements will be analyzed and the resulting uncertainties for quantities, that are computed from loading curves such as hardness or elastic modulus, are studied. For this calculation a combination of uncertainty propagation law and Monte Carlo uncertainty evaluations are used.
Nanoscale dimensional measurements are very often focused on small objects formed by only a few atomic layers in one or more dimensions. The classical convolution approach to tip-sample artifacts cannot be valid for these specimens due to the quantum-mechanical nature of small objects. As interatomic forces act on the sample and the tip of the microscope, the atoms of both relax in order to reach equilibrium positions. This leads to changes in those quantities that are finally interpreted as the atomic force microscope (AFM) tip position and influences the resultant dimensional measurements. In this paper, sources of uncertainty connected with tip-surface relaxation at the atomic level are discussed. Results of both density functional theory modeling and of classical molecular dynamics of AFM scans on typical systems used in nanometrology, e.g., fullerenes and carbon nanotubes, on highly oriented pyrolytic graphite substrates are presented. We study also the effects of tip-surface relaxation on critical measurements of the dimensions of these objects.
Nanoscale dimensional measurements are very often focused on small objects formed by only a few atomic layers in one or more dimensions. The classical convolution approach to tip–sample artifacts cannot be, on its own, sufficient for these specimens due to their quantum-mechanical nature. With growing resolution of specialized metrology scanning probe microscopes and increasing requirements of exact measurements in nanoscale range, it is necessary to make a transition from the classical picture to a quantum approach on the field of uncertainty analysis. In this paper, sources of uncertainty connected with tip–sample relaxation at the atomic level are discussed. Results of density functional theory modeling (using the tight-binding approximation software FIREBALL) of AFM scans on fullerenes are presented. In our approach we model the tip apex and the sample as systems of individual atoms. As interatomic forces act on the sample and the tip of the microscope, the atoms of both relax in order to reach equilibrium positions. This leads to changes in those quantities that are finally interpreted as the ‘atomic force microscope (AFM) tip position’ and influences the resultant dimensional measurements. The results from modeling are compared to the experimental results found in the literature.
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