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Production sequence of Si-spheres and interferometrical determination of the sphere volume

Flexible correction of non-linear, three-dimensional drift in atomic force microscopes by data fusion


In a novel approach, instead of a single, high-resolution measurement image, which is strongly influenced by drift, multiple low-resolution measurement images are recorded. These show less drift distortions each and can be used to reconstruct the temporal course of the drift. The low-resolution measurement images can be corrected using the reconstructed drift and combined to a high-resolution, almost completely drift-free data set using data fusion. 

Drift is a common disturbance in scanning probe microscopy that can lead to significant distortions of measured sample topographies. In order to achieve the highest accuracy when measuring sample topographies, software-based methods for drift correction must be used in addition to classical measures to reduce drift. Previous approaches have been capable of correcting drift either with good temporal resolution but not in all three coordinate axes, or in all three axes but only with low temporal resolution. A novel correction approach has now been developed that can correct drift in all three spatial axes with significantly improved temporal resolution. 

The basic idea of the new approach is to take a sequence of several short measurements with low lateral resolution instead of just a single high resolution measurement. To correct the drift, it can be exploited that, in addition to the distortions, spatial shifts of the measured sample topography are induced between the measurement images of a sequence. These shifts can be analyzed in all three spatial axes and used to reconstruct the temporal course of the drift. After the distortions and displacements of the low-resolution measurement images have been corrected using the reconstructed drift trajectory, they can be fused into a high-resolution image. An example of this is shown in Figure 1a) and 1b). In 1a), a 2D grating structure with 100 nm periodicity was acquired in 64 measurements with a lateral resolution of 40 nm each. In b), these 64 measurement images were fused into a single measurement image with 5 nm resolution after correction of up to 50 nm drift. Like measurement image 1c), which was acquired in a single long measurement and is thus distorted by drift, it can be used, for example, to evaluate the orthogonality of the grating structure. While the orthogonality of the lattice structure could be determined by two "conventional" measurements only as quite strongly deviating  89.29° and 89.57°, by double use of the drift correction method clearly better reproducible results of 89.99° and 90.04° were determined. 

The advantage of the new approach over other correction approaches is that a large number of short measurements can be made, which on the one hand allow the determination of three-dimensional drift with good temporal resolution, but on the other hand cause only a moderate increase in the total measurement time, since no additional measurement data needs to be recorded overall.

Figure 1: a): Single low-resolution measurement image, b): High-resolution measurement image generated by the novel drift correction method, c): High-resolution measurement image from a single long measurement influenced by drift


1) Johannes Degenhardt, Rainer Tutsch, Gaoliang Dai 2020 Flexible correction of 3D non-linear drift in SPM measurements by data fusion, to be published in the journal “Measurement Science and Technology”