Electron scattering in scanning probe microscopy experiments

It has been shown that electron transitions, as measured in a scanning tunnelling microscope, are related to chemical interactions in a tunnelling barrier. Here, we show that the shape and apparent height of subatomic features in both, measurements of the attractive forces in an atomic force microscope, and measurements of the tunneling current between the Si(111) surface and an oscillating cantilever, depend directly on the available electron states of the silicon surface and the silicon tip. Simulations and experiments confirm that forces and currents show similar subatomic variations for tip-sample distances approaching the bulk bonding length. 2005 Elsevier B.V. All rights reserved. The intense research into improving the local and energy resolution in scanning probe microscopes (SPM) over the last two decades have made the assignment of atomic features to the position of surface ions attainable in many cases by comparing experimental data to high level numerical simulations. The very high resolution of individual features in the experiments, today below the limit of 1 Å, makes it possible to carry out detailed studies of the electronic structure and their local extension, which a decade ago have been thought impossible. The greater simplicity of physical processes in an scanning tunnelling microscope (STM), where long-range forces and the dynamics of an oscillating cantilever do not enter the picture, seemed to allow accurate comparisons between STM experiments and theory quite early. However, also in this case interactions and atomic displacements in a tunneling junction may decisively alter the image [1]. The advent of the atomic force microscope (AFM) extended the range of experiments substantially, since AFM experiments do not rely on the transition of electrons through the tunnelling barrier, and can therefore in principle be performed on all materials [2]. Today, AFM is able to reveal finer details than STM [3–6]. Theoretically, the advance in quantitative 0009-2614/$ see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.12.065 * Corresponding author. E-mail address: [email protected] (W.A. Hofer). models of AFM and their predictive power made it possible to analyze the differences between simple theoretical models and the obtained experimental results: by gradually obtaining a more realistic view of the experimental situation, the role of different interactions and their effects on SPM images was determined [7–9]. The simple initial models could thus be corrected, e.g., for the effects of atomic relaxations, of ionic charge, or dissipation processes during AFM scans [10]. In this Letter, we show that the subatomic features, observed by AFM and STM measurements with oscillating cantilevers on Si(111) (7 · 7), which have been the subject of intense debate [3,4,11], are due to the scattering of electrons from a very narrow energy range at the surface into double dangling bonds of the silicon tip. The Si(111) surface was simulated by a four layer silicon film, the bottom layer was passivated with hydrogen. The ionic positions were determined by fully relaxing the surface layers until the Hellman–Feynman forces on individual ions were less than 0.01 eV/Å. The electronic groundstate was then calculated using ultrasoft pseudopotentials for the ionic cores with the VIENNA AB INITIO SIMULATION Program [12,13]. Due to the size of the system, which comprises 249 ions in the unit cell, the calculation was limited to only one k-point, the C point. The energy cutoff for the plane-wave expansion was set to 250 eV. 178 L.A. Zotti et al. / Chemical Physics Letters 420 (2006) 177–182 The atomic arrangement in the final iteration and the (7 · 7) unit cell is shown in Fig. 1a. After the electronic groundstate structure had been calculated the Kohn–Sham states in the energy interval EF ± 3 eV were extracted. Testing the resolution of the ensuing images based on the electronic surface structure alone we found that the detailed features are quite sensitive to the cutoff in the two dimensional Fourier expansion of the single electron states. To obtain high resolution images it was necessary to expand every state with close to 500 reciprocal lattice vectors. The density of electron charge within the interval [Ee 2 eV, EF] in a horizontal plane above the surface is shown in Fig. 1b. The contributions to the charge density at 2 eV are shown in (c). It can be seen that the differential contributions show a double feature at the position of the adatoms, which is missing in the density contour over the whole bias interval. This indicates that the double features are due to electron states with an energy close to 2 eV relative to the Fermi level. An integration over the whole bias range sums up a large number of individual states, the double feature, which we attribute to single electron states, is then no longer observable. The tip model in our simulations is a (2 · 2) Si(001) surface with a single silicon atom, as suggested by an analysis of high resolution AFM experiments [3]. The tip was simulated by an eight layer film with a hydrogen passivated bottom layer. Since the tip system is somewhat smaller we increased the number of k-points of the tip system to nine k-points near the center of the tip Brillouin zone, including the C point. The single silicon atom at the tip apex leads to two dangling bonds protruding from the tip apex. We simulated two STM tips, obtained by rotating the atoms of the original cell by 90 while keeping the lattice vectors constant. To obtain the current maps and the locally resolved dI/dV spectra of the surface we employed a newly developed method, described in [15,16]. The Fig. 1. (a) Position of atoms in the surface layer (blue) and adatoms (red) in t interval [EF 2 eV, EF] at a median distance of 3.5 Å. Atoms are seen as sin EF 2 eV. Double features of states at the silicon surface in this case are clearl the reader is referred to the web version of this article.) scattering method, calculated to first order in the interface Green’s function accounts for the bias dependency with the help of an additional term, which depends on the bias potential eV and the exponential decay of surface and tip states ji(k), according to [16]: IðV Þ 1⁄4 4pe h X