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In a lot of systems, charge transport is governed by local features rather than being a global property as suggested by extracting a single resistance value. Consequently, techniques that resolve local structure in the electronic potential are crucial for a detailed understanding of electronic transport in realistic devices. Recently, we have introduced a new potentiometry method based on low-energy electron microscopy (LEEM) that utilizes characteristic features in the reflectivity spectra of layered materials [1]. Performing potentiometry experiments in LEEM has the advantage of being fast, offering a large field of view and the option to zoom in and out easily, and of being non-invasive compared to scanning-probe methods. However, not all materials show clear features in their reflectivity spectra. Here we, therefore, focus on a different version of low-energy electron potentiometry (LEEP) that uses the mirror mode transition, i.e. the drop in electron reflectivity around zero electron landing energy when they start to interact with the sample rather than being reflected in front of it. This transition is universal and sensitive to the local electrostatic surface potential (either workfunction or applied potential). It can consequently be used to perform LEEP experiments on a broader range of material compared to the method described in Ref. [1]. We provide a detailed description of the experimental setup and demonstrate LEEP on workfunction-related intrinsic potential variations on the Si(111) surface and for a metal-semiconductor-metal junction with an external bias applied. In the latter, we visualize the Schottky effect at the metal-semiconductor interface. Finally, we compare how robust the two LEEP techniques discussed above are against image distortions due to sample inhomogeneities or contamination.
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We present a computationally efficient method to incorporate density-functional theory into the calculation of reflectivity in low-energy electron microscopy. The reflectivity is determined by matching plane waves representing the electron beams to the Kohn-Sham wave functions calculated for a finite slab in a supercell. We show that the observed quantum interference effects in the reflectivity spectra of a few layers of graphene on a substrate can be reproduced well by the calculations using a moderate slab thickness.
The structural and electronic properties of twisted bilayer graphene are investigated from first principles and tight binding approach as a function of the twist angle (ranging from the first magic angle $theta=1.08^circ$ to $theta=3.89^circ$, with the former corresponding to the largest unit cell, comprising 11164 carbon atoms). By properly taking into account the long-range van der Waals interaction, we provide the patterns for the atomic displacements (with respect to the ideal twisted bilayer). The out-of-plane relaxation shows an oscillating (buckling) behavior, very evident for the smallest angles, with the atoms around the AA stacking regions interested by the largest displacements. The out-of-plane displacements are accompanied by a significant in-plane relaxation, showing a vortex-like pattern, where the vorticity (intended as curl of the displacement field) is reverted when moving from the top to the bottom plane and viceversa. Overall, the atomic relaxation results in the shrinking of the AA stacking regions in favor of the more energetically favorable AB/BA stacking domains. The measured flat bands emerging at the first magic angle can be accurately described only if the atomic relaxations are taken into account. Quite importantly, the experimental gaps separating the flat band manifold from the higher and lower energy bands cannot be reproduced if only in-plane or only out-of-plane relaxations are considered. The stability of the relaxed bilayer at the first magic angle is estimated to be of the order of 0.5-0.9 meV per atom (or 7-10 K). Our calculations shed light on the importance of an accurate description of the vdW interaction and of the resulting atomic relaxation to envisage the electronic structure of this really peculiar kind of vdW bilayers.
The spatial distributions of anti-bonding $pi^ast$ and $sigma^ast$ states in epitaxial graphene multilayers are mapped using electron energy-loss spectroscopy in a scanning transmission electron microscope. Inelastic channeling simulations validate the interpretation of the spatially-resolved signals in terms of electronic orbitals, and demonstrate the crucial effect of the material thickness on the experimental capability to resolve the distribution of unoccupied states. This work illustrates the current potential of core-level electron energy-loss spectroscopy towards the direct visualization of electronic orbitals in a wide range of materials, of huge interest to better understand chemical bonding among many other properties at interfaces and defects in solids.
We investigate the dependency of electrostatic interaction forces on applied potentials in Electrostatic Force Microscopy (EFM) as well as in related local potentiometry techniques like Kelvin Probe Microscopy (KPM). The approximated expression of electrostatic interaction between two conductors, usually employed in EFM and KPM, may loose its validity when probe-sample distance is not very small, as often realized when realistic nanostructured systems with complex topography are investigated. In such conditions, electrostatic interaction does not depend solely on the potential difference between probe and sample, but instead it may depend on the bias applied to each conductor. For instance, electrostatic force can change from repulsive to attractive for certain ranges of applied potentials and probe-sample distances, and this fact cannot be accounted for by approximated models. We propose a general capacitance model, even applicable to more than two conductors, considering values of potentials applied to each of the conductors to determine the resulting forces and force gradients, being able to account for the above phenomenon as well as to describe interactions at larger distances. Results from numerical simulations and experiments on metal stripe electrodes and semiconductor nanowires supporting such scenario in typical regimes of EFM investigations are presented, evidencing the importance of a more rigorous modelling for EFM data interpretation. Furthermore, physical meaning of Kelvin potential as used in KPM applications can also be clarified by means of the reported formalism.
The structure of BaMg1/3Ta2/3O3 (BMT) has been studied using X-ray scattering. The phonons have been measured and the results are similar to those of other materials with the perovskite structure such as PbMg1/3Nb2/3O3 (PMN). The acoustic and lowest energy optic branches were measured but it was not possible to measure the branches of higher energy, possibly this is because they largely consist of oxygen motions. High-resolution inelastic measurements also showed that the diffuse scattering was strictly elastic and not directly related to the phonon spectra. A diffuse scattering was observed in BMT near the (Hpm1/2, Kpm1/2, Lpm1/2) points in the Brillouin zone and this had a characteristic cube shape. This arises from ordering of the B-site ions in BMT. Additional experiments revealed a diffuse scattering in BMT similar in shape to Bragg reflections at wave-vectors of the form (Hpm1/3, Kpm1/3, Lpm1/3). Such reflections were also observed by Lufaso [Chem. Matt. 16 (2004) 2148] from powders and suggest that this structure of BMT consists of 4 differently oriented domains of a trigonal structure and results from a different ordering of the B-site ions from that responsible for the scattering at the (Hpm1/2, Kpm1/2, Lpm1/2) points. The results lead us to suggest that for BMT single crystals the bulk has the properties of a cubic perovskite, whereas the surface may have quite different structure from that of the bulk. This difference resembles the behaviour of cubic relaxors like PMN and PMN doped by PbTiO3, where significant surface effects have been reported.
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