Investigation of the cantilever response of non-contact atomic force microscopy for topography measurements in all three dimensions

Accurate measurements of the true three-dimensional shape of nanometre-sized structures are required as input parameters in the process of modelling and refining other (fast) measurement methods that measure indirectly such as scatterometry, scanning electron microscopy and optical microscopy. For this purpose, atomic force microscopy is a promising measurement principle, because it measures 3D spatial geometries directly in the vicinity of structures. However, the measured topography is a result of the response of a probing system to the interaction between the surfaces of the probe and the specimen. This interaction is determined by material and geometry parameters. Since the geometric conditions vary significantly, if 3D structures are measured, the interaction has to be taken into account appropriately. This paper presents the influence of the inclination angle on the interaction as a function of the distance between the probe tip and the sample surface. Nonlinear forces show bistable behaviour of the responding cantilever oscillation, which dominates measurements at sidewalls. The bistability of amplitude and phase as a function of the tip–sample distance as well as a function of the driving frequency has been investigated. It is intended to state the necessity of investigating the three-dimensional interaction force, its action in all three dimensions as well as the force changes caused by the changing size of interacting surface areas. Force and topography are non-separable features in nanometrology joining surface science and dimensional nanometrology.

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