ReviewWhat is the orientation of the tip in a scanning tunneling microscope?
Introduction
The interpretation of scanning tunneling microscopy (STM) images is not straightforward due to the effects of the local tip apex geometry, termination and orientation. The reason is the convolution of sample and tip electronic states in a given energy window defined by the bias voltage, and the fact that in STM experiments the detailed atomic geometry around the tip apex is practically unknown and hardly controllable. On the other hand, it is clear that the electronic states and their dominating orbital characters involved in the tunneling depend very much on the local atomic structure of the tip apex.
It has been a challenge to obtain information about the relevant properties of the STM tip apex for a long time. Herz et al. performed reverse STM imaging experiments to study p, d, and f orbital characters of the tip apex atom above the Si(1 1 1)-() surface [1]. The combination of STM experiments and simulations on well characterized surfaces to obtain information on the tip structure and termination was used, e.g., by Chaika et al. [2], [3]. They considered the highly oriented pyrolytic graphite (HOPG) surface in the (0 0 0 1) crystallographic orientation in combination with W(0 0 1) tip models. Rodary et al. studied Cr/W tip apex structures by high resolution transmission electron microscopy, and they pointed out that the magnetization direction of monocrystalline nanotips cannot be controlled in spin-polarized STM [4]. Recently, the effect of the tip orbitals on the STM imaging of supported molecular structures attracted considerable attention. Gross et al. investigated pentacene and naphthalocyanine molecules on NaCl/Cu(1 1 1) surface by CO-functionalized tips, and they explained the obtained STM contrast by tunneling through the p-states of the CO molecule [5]. Siegert et al. developed a reduced density matrix formalism in combination with Chen’s derivative rule [6] to describe electron transport in STM junctions for molecular quantum dots, and studied the effect of selected tip orbital symmetries on the STM images of the hydrogen phthalocyanine molecule on a thin insulating film [7]. Lakin et al. proposed a method to deconvolute STM images and determine molecular orientations of both the sample and the functionalized tip [8]. In their work a C60–Si(1 1 1)-() surface and a C60-functionalized tip were chosen.
Even in seemingly less complicated STM junctions, only a few theoretical works focused on the effect of the tip orientation on the STM images. Hagelaar et al. demonstrated that a wide range of modeled tip terminations and orientations can reproduce the experimental images for NO adsorbed on Rh(1 1 1) [9]. This work also showed that the modeling of realistic tip structures, including nonsymmetric tips, is desirable for a good qualitative reproduction of experimental STM images. However, it is quite unlikely that the relative orientation of the sample surface and the local tip apex geometry in STM experiments is of high symmetry, which has been commonly assumed in the vast majority of STM simulations to date. Mándi et al. studied the effect of asymmetric relative tip-sample orientations on the STM contrast of the W(1 1 0) metal surface [10] and of the HOPG(0 0 0 1) surface [11] employing a three-dimensional Wentzel–Kramers–Brillouin (3D-WKB) electron tunneling theory. It was found that the STM images can be substantially distorted due to tip geometry effects. A physical explanation was provided based on the real-space shape of the electron orbitals entering the orbital-dependent tunneling transmission formula in the 3D-WKB method [10], see Eq. (A.5) in Appendix. Motivated by the ideas of Hagelaar et al. and based on the methodology of Mándi et al., in the present work a new concept of obtaining information about the local spatial orientation of the STM tip in real instruments is introduced. The concept is substantiated by a combination of STM experiments and large scale simulations taking the HOPG(0 0 0 1) surface. Concomitantly, the qualitative visual analysis of STM images is advanced by quantifying their correspondence in terms of relative brightness correlations.
The paper is organized as follows: the proposed correlation analysis method is introduced in Section 2, followed by its application to the HOPG(0 0 0 1) surface. We analyze and discuss our results in Section 3, and summarize our findings in Section 4. The appendix reports a brief summary of the 3D-WKB tunneling theory with an arbitrary tip orientation.
Section snippets
Method
To quantitatively compare the experimental (EXP) and simulated (SIM) constant-current topographs, the definition of the relative brightness of a given two-dimensional (2D) contour C at bias voltage is needed [11], [12]:where is the apparent height of the constant-current contour C above the surface lateral position at bias voltage obtained by . and respectively have the smallest and
Results and discussion
We recall that the STM contrast of the HOPG(0 0 0 1) surface can change substantially depending on the tunneling and tip parameters [2], [3], [11], [12], [21]. A selection of the possible STM contrasts in the tunneling regime is shown in Fig. 2. Here, the two nonequivalent carbon atoms of HOPG ( and ) are primarily responsible for the different STM contrasts [hexagonal contrast in Fig. 2(a) and triangular contrast in Fig. 2(b)]. Particular rotations of the STM tip were shown to result in striped
Conclusions
In scanning probe experiments the scanning tip is the source of one of the largest uncertainty as very little is known about its precise atomic structure and stability. Since the atomic structure and electronic properties of the tip apex can strongly affect the contrast of STM images, it is very difficult to experimentally obtain predictive STM images in certain systems. To tackle this problem we proposed a statistical correlation analysis method to obtain information on the local geometry and
Author contributions
G.T. and K.P. designed the research. G.T. performed the DFT calculations. G.M. performed the 3D-WKB calculations and the statistical analysis. All authors took part in the interpretation of the results. K.P. wrote the paper with the support of all co-authors.
The funding bodies were not explicitly involved in the research at any stage.
Acknowledgments
The authors thank E. Inami, J. Kanasaki, and K. Tanimura at Osaka University for the experimental brightness data. Financial support of the Magyary Foundation, EEA and Norway Grants, the Hungarian Scientific Research Fund project OTKA PD83353, the Bolyai Research Grant of the Hungarian Academy of Sciences, and the New Széchenyi Plan of Hungary (Project ID: TÁMOP-4.2.2.B-10/1-2010-0009) is gratefully acknowledged. G.T. is supported by EPSRC-UK (EP/I004483/1). Usage of the computing facilities of
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