NCAFM2023 Programme Booklet

Wednesday 1200-1220

pyFDBM: FIRST PRINCIPLES METHODS FOR AFM AND STM WITH CO TIPS

Emiliano Ventura-Macias 1* , Pablo Pou 1,2 , Ruben Perez 1,2

1 Dpt. of Condensed Matter Physics Theory, Universidad Autónoma de Madrid, Madrid, Spain Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain Email: emiliano.ventura@uam.es

Image simulations of High-Resolution AFM with a CO-functionalized tip have greatly improved as we better understand the theory of such images [1,2,3]. The Full-density-based model (FDBM) aims to replicate AFM images with the information of a single DFT calculation of the sample. As such, with the pyFDBM package, we set out to create a framework that implements automatic DFT calculations, processes them, and does FDBM simulations. Furthermore, it also incorporates methodological advancements for FDBM. One is the static approximation, which considers the potential on a deflected probe similar to that on a non-deflected probe in the same position. The other is a probe relaxation that bounds it to a spherical motion centered on the metal-tip apex. With these improvements, pyFDBM calculates the tip-sample force (F ts ) in a 3D space. With it, we took on two challenges related to CO tips: the frequency shift (Δf) interpretation and STM measurements. AFM experiments measure changes in the tip's oscillation frequency. So, we must change the F ts to Δf to compare simulated AFM to experiments. For it, we studied two Δf approximations with the typical measurement conditions of HR-AFM. The first uses the standard relationship of Δf with the force gradient Δ z F ts , while the second establishes a new relation of Δf with F ts . We compared both to the accurate numerical method presented in [4]. We found that for small oscillation amplitudes (0.3 < A < 1.0 Å), the F ts approximation works best, but for even smaller amplitudes Δ z F ts is better. Furthermore, the CO-tip deflection plays a significant role because it changes the behavior of F ts at close tip-sample distances. Consequently, we propose that HR-AFM images with CO-tips should be considered proportional to F ts . On the STM side, measurements with CO-tips provide a new straightforward procedure for intramolecular resolution [5]. Here, we lay out a methodology to simulate BRSTM images that combines the CO deflection with the approximation signal from the CO p x p y orbitals presented in [6]. This approximation uses these orbitals' Chen matrix elements to estimate the p-wave signal. Combining it with the s-wave one and the CO position leads to a suitable approximation of BRSTM images. Furthermore, as FDBM uses the DFT-calculated sample charge density, we can calculate the STM signal with the associated DFT wave function. Hence, pyFDBM is a complete framework for simulations of HRAFM and BRSTM with CO-tips, using only a single DFT calculation of the sample as input. Lastly, in a second work, we present our BRSTM simulations with experimental comparisons.

Fig. Theoretical Δf of a trimesic acid dimer. (left) Approximation based on z F ts at the mean tip-sample distance, (center) exact numerical calculation of Δf, (right) approximation based on Fts at the distance of closest approach. Tip-sample distance is 3.17 Å, amplitude is 0.55 Å, and scalebar is 1 Å.

References [1] Ellner, M., et al. (2019). ACS Nano, 13(1), 786–795.

[2] Hapala, P., et al. (2014). Physical Review B, 90(8), 085421. [3] Sakai, Y., et al. (2016). Nano Letters, 16(5), 3242–3246. [4] Giessibl, F. J. (2001). Applied Physics Letters, 78(1), 123–125. [5] Nguyen, G. D., et al. (2017). Nature Nanotechnology, 12(11), 1077–1082. [6] Gross, L., et al. (2011). Physical Review Letters, 107(8), 086101.

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