Scanning force microscopes may achieve uncertainties of a few nano- or sub-nanometres on very good step height standards; yet for pitch measurements even clearly less. Therefore, the contribution of the probe-sample interaction becomes more and more important in the uncertainty budget. This refers, on the one hand, to the changes of the probes during scanning or sensing of the sample as well as due to the interaction of the probe with the different materials on inhomogeneous samples. The latter is similar to problems in optical microscopy and can cause height changes which are detected as a topography of the sample. In particular, dimensional measurements of nanoparticles can be influenced by these interactions [L. Chen et al., Ultramicroscopy 107 (2007) 275–280, S. Dejima et al., to be published].

Traceability of atomic steps to the SI unit of length

To investigate the interaction of the probe tip with the surface, a special Scanning Force Microscope (SFM) has been installed. The investigation is performed within the scope of a joint project between the national metrology institutes NPL, United Kingdom, and PTB, Germany. Within the framework of this cooperation, Dr. A. Yacoot stayed for two years at PTB. The SFM shall be used to investigate effects between probe and surface which influence the topography determination [1]. For this purpose, an SFM has been realized in the case of which the movement of the cantilever can be observed with two independent detection systems.
For traceable measurements of the vertical movement of the cantilever support, a high-resolution homodyne differential interferometer is used [2]. In addition, the SFM is compatible with an X-ray interferometer of the NPL [2], which shall be used in a later extension stage to determine the lateral positions. In first investigations, Si(111) surfaces with large, even areas which had been prepared in the UHV were, among others, investigated (Figure 1). The interferometric system resolution of the SFM allowed single monoatomic steps to be safely resolved in these areas. Figure 1 shows the respective interferometer signal as a function of the place on the surface.

Foto:

Figure 1: Recorded interferometer signal of the z-movement of the cantilever of the SFM as a function of the place during measurement on a silicon (111) sample. The figure shows a section (22 µm x 22 µm) with single monoatomic steps. The single steps have a nominal step height of 0.314 nm.

The measured step height amounts to 0.31 nm. Compared to the investigations performed so far [3] on single steps with terraces of approx. 100 nm, the available samples also allow the profile of the step height to be assessed on both sides over ranges of a few micrometers. The uncertainty budged will soon be established. This would allow atomically high steps to be traced back directly to the unit of length.
After completion of the first investigations, the measuring instrument was transferred to the NPL, where the measurements will be continued within the scope of the cooperation.

[1] A. Yacoot, L. Koenders, H. Wolff, An atomic force microscope for the study of tip sample interactions, Measurement Science and technology, 2007, to be published
[2] A Yacoot, M. J. Downs, The use of x-ray interferometry to investigate the linearity of the NPL Differential Plane Mirror Optical Interferometer Meas. Sci. Technol. 11 (2000) 1126–1130.
[3] J. Fu, V. Tsai, R. Köning, R. Dixson and T. Vorburger, Algorithms for calculating single-atom step heights, Nanotechnology 10 (1999) 428–433