Fast and accurate methods to unveil the mechanisms of contrast formation in High Resolution Force Microscopy

Resumen

Frequency Modulation Atomic Force Microscopy (FM-AFM) has become an indispensable tool in nanoscience as it allows to visualize and manipulate surfaces and molecules at the atomic scale. It has been used to characterize 2D materials like graphene on metals with images capturing impressive atomic and topographic details. The technique entered a new era with the use of metal tips decorated with CO molecules to visualize the internal structure of molecules with unprecedented resolution. The contrast enhancement provided by these functionalized tips enabled the identification of unknown organic compounds, imaging intermediate reaction states, discrimination of covalent bond orders, and the visualization of features associated with H–bonds. Great strides in theory have been made in order to understand the mechanisms responsible for the atomic-scale contrast. On one end of the spectrum, Density Function Theory (DFT) provide the framework to understand the contrast inversion observed in carbon nanostructures images, and the role of the Pauli interaction and tip flexibility in the high resolution (HR) captured by functionalized tips. However, DFT is computationally costly and only a limited number of atoms can be simulated. On the other end, theoretical images can be easily produced with methods based on pair–wise interactions. The interaction parameters are fitted to reproduce the experimental results, and thus, the resulting model can aid in the identification of molecules. In this thesis, we develop three computationally efficient methods that retain the accuracy provided by DFT calculations. First, we introduce a multi-scale potential that is able to describe the mechanical response of large areas of weakly coupled 2D materials probed by a metallic tip. Second, we develop a method to simulate 1 2 the contribution of the main interactions –van der Waals (vdW), electrostatic (ES), short-range (SR)– to AFM images taken with flexible close shell probes that includes an accurate description of the ES interaction between the electric field created by CO-metal tips and the charge density of the sample. Third, we modify the previous method to include a description of the SR interaction based on the overlap of the tip and sample charge densities. With these three approaches, we tackle several open questions in the literature regarding: (1) the mechanism behind atomic scale dissipation and atomic scale variations of the mechanical properties of 2D materials; (2) the proper ES description of CO– metal tips; (3) the role played by the ES, SR, and vdW interactions, and the associated tip tilt, on the intramolecular and intermolecular contrast observed on adsorbed molecules with CO probes. The thesis manuscript is organized as follows: The first chapter describes the basic instrumentation and operation modes of the AFM with a special focus on the ingredients needed to achieve atomic scale contrast. Subsequently, we outline the experimental works that motivate the thesis and describe the current state–of–the–art in HR imaging simulations. In the second chapter, we study the atomic scale variations of the mechanical response of weakly coupled 2D materials probed by a cantilever based AFM. We present topography and dissipation images that resolve the atoms and the moiré patterns in graphene on Pt(111), despite its extremely low geometric corrugation. The imaging mechanisms are identified with a multi–scale model based on DFT calculations, where the energy cost of global and local deformations of graphene competes with SR chemical and long-range vdW interactions. The simulations show that the atomic contrast of the carbon atoms is related to the SR tip–sample interactions, while the dissipation can be understood in terms of global deformations in the weakly coupled graphene layer. Surprisingly, the observed moiré modulation is linked with the subtle variations of the local interplanar graphene–substrate interaction. We also explore the capabilities of the AFM to achieve sub–surface resolution with a study of single defects on the Pt(111). The third chapter presents a study of the ES field of CO decorated metallic Abstract 3 tips and its relevance for HR–AFM imaging. With DFT calculations, we investigate the ES field generated by CO molecules in gas phase, as adsorbates on surfaces, and bonded to metallic tips. We postulate that CO tips cannot be described by single dipoles; a proper description takes into account the positive dipole behavior of the metallic apex and the negative charge cloud strongly localized in front of the oxygen atom. This description is incorporated into a model developed in this chapter to simulate rapidly interaction–decomposed AFM images with flexible close shell probes. We validate the model of the tip by reproducing experimental qPlus based images of localized ionic defects (Cl vacancies on a metal–supported NaCl bilayer). In the next chapter, we focus on H–bonded layers of triazine molecules as probed by CO tips. We describe the changes require in the methodology developed in chapter 3 (for studying surfaces) to simulate molecules. With interaction decomposed images generated by the model, we identify the interplay of the ES, SR, and vdW forces on the contrast formation and discuss the intra– and intermolecular features commonly observed in the images. We also demonstrate the existence of different potential energy surface (PES) minima for the CO tilt and discuss its influence on imaging. In the fifth chapter, we develop a new methodology to simulate HR–AFM images that puts on equal footing the SR and ES interaction. Whereas the previous method used pair–wise potentials to describe the SR, this one uses the overlap of the charge densities of the tip and the sample. With this, we investigate intra– and intermolecular features observed in AFM images that are closely related to subtle effects in the charge density of the sample. First, we demonstrate that not only structural similar molecules with different stoichiometry provide qualitatively different AFM images, but that the chemical environment (i.e., bonding structure) is also relevant. Second, we pinpoint the Pauli repulsion as the underlying mechanism responsible for the discrimination of covalent bond orders with CO tips. Lastly, the probing of H-bonds with CO tips is investigated.