HAL Id: jpa-00226817
https://hal.archives-ouvertes.fr/jpa-00226817
Submitted on 1 Jan 1987
HAL
is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire
HAL, estdestinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
EFFECT OF TIP-SIZE ON STM IMAGES OF GRAPHITE
C. Horie, H. Miyazaki
To cite this version:
C. Horie, H. Miyazaki. EFFECT OF TIP-SIZE ON STM IMAGES OF GRAPHITE. Journal de
Physique Colloques, 1987, 48 (C6), pp.C6-85-C6-90. �10.1051/jphyscol:1987614�. �jpa-00226817�
EFFECT O F TIP-SIZE O N STM IMAGES OF. GRAPHITE
C. Horie and H. Miyazaki
Department of Applied Physics, Tohoku University, Sendai 980, Japan
Abstract. -By using our simple model of a tunneling current in the scanning tunneling microscopy (STM), we investigate how the STM images of graphite are related to the size of the tip. In our model, the tunneling current is calculated by replacing the tip and the two distinct carbon atoms in the top layer of graphite by appropriate sectional areas effective to the tunneling current, respectively. I t is shown that the STM images show a threefold symmetry, and vary depending on the effective size of the tip.
1. Introduction. G r a p h i t e is an ideal substrate for study with the scanning tunneling microscope (STM), because i t is easily cleaved to give a flat and well-ordered surface. The STM images of surface of graphite have been obtained not only in UHV C13, but also in air [2,31 and water C41 with similar results. The STM images obtained, however, do not show the expected honeycomb s t r u c t ~ r e , ~ b u t rather show a triangular lattice with a lattice constant 2.46A. Another anomalous feature of the images concerns the giant corrugation amplitudes C 1 . 2 . 6 . 6 1 observed for low bias voltages in the scanning of constant-current mode, in which the tunnel tip traces contours of constant density of states. On the other hand, in the current-
imaging mode 13,7,81, in which variations of tunneling current are recorded while the bias voltage and the gap between the tip and the surface are kept constant, there has been observed no indication of large corrugations. Recently, a microscopic theory of STM has been developed by Tersoff and Hamann C91 to investigate the relationship
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987614
C6-86 JOURNAL DE PHYSIQUE
between the STM images and the surface structure. However, since the theory is based on a simplified assumption for the character of the tip, i t is not always possible to attain any concrete conclusion about the effect of the size of tunneling tip.
In this paper, we discuss the effect of the tip-size on STM images of graphite by employing our simple model ClOl of STM, in which the tunneling current is calculated by replacing the tip and carbon atoms on the surface by effective sectional areas. Two dif- ferent areas are assigned to the two distinct atoms in the top layer of graphite, I t is shown that the STM images display threefold sym- metry coming from the inequivalence of the two atoms in the surface layer of graphite, and vary depending on the size of the tip.
2. Model. -In the two-dimensional approximation 1113 of the surface of graphite, it is well-known that the weakly coupled pZ atomic orbi- tals give rise to two n -bands, which are degenerate at the six Bril- louin zone corners at point P, and. that the Fermi level goes through this P point. On the other hand, the usual sp2 orbitals give rise to three bonding and three antibonding a -bands, which lie far below and far above the Fermi level, respectively. As a first approximation, therefore, we can assume that the electronic wave functions inherent to the top layer of graphite and relevant to the tunneling current for low bias voltages mostly originate from pZ orbitals of carbon atoms, and have large amplitude only around carbon sites. We can, therefore, assume that tunneling current flowing in or out of the surface of graphite is not uniformly distributed over the surface, but concentrated around each carbon site on the surface.
In real graphite, interlayer interactions give rise to a band overlap near the Fermi level, yielding semimetallic properties of graphite. These interactions also break the six-fold symmetry, making the two atoms in the top layer inequivalent t12,131. We denote by A those atoms which have an atom directly below in the second layer. The B atoms do not have such atoms. This inequiv- alence of the two atoms is expected to be reflected in the STM image.
Taking three-layer slab model of the surface of graphite, Batra et al. C131 have performed self-consistent calculations using local den- sity functional method, and have found that the charge density in the vacuum region coming out of B-sites is higher than that of the A- sites.
In our model, we merely assign to each carbon atom in the top layer an appropriate sectional area, through which the local tunnel- ing current with a constant density flows. In accordance with the results obtained by Batra et al. C131, we assign two different circles with radius rA and rg to A- and B-atoms, respectively. Al- though these radii are, in principle, determined by the spread and overlap of the electronic wave functions of carbon atoms with those of the tip, we leave them as parameters.
On the other hand, the electronic wave functions of the metallic tip like tungsten are considered to be extended like plane waves without being localized around each atom constituting the tip.
Fkg.1. STM images of the surface of graphite for various values of effective radius R of the tip. Each atom is placed at the peripheral corner of the hexagon. The vertical height at every point in the hexagon represents the current deviation when the center of the circle assigned to the tip is located at that point. The maximum height of the current deviation, which- is measured from the minimum current, is normalized f$r allovalue~ of R _ Theovalues of R in (a)-
(h) are 0.5A, 1.OA. 1.5A, 2.OA. 2.5A. 3.OA, 3-58, and 4.0i, respec- tively. The corresponding values of fractional deviation of current p are 1.0, 0.86, 0.27, 0.31, 0.10, 0.15, 0.06 and 0.10, respectively.
C6-88 JOURNAL DE PHYSIQUE
Therefore, we can assume that the tunneling current through the tip is determined again by the effective sectional area which is assumed to be a circle with an effective radius R. Although the value of R should be dependent on the actual geometrical shape of the tip and the gap distance from the surface, we take R as a parameter to see how the STM images depend on R.
Tunneling currents are assumed to have a constant density and flow in the direction perpendicular to the surface through the circles assigned to the carbon atoms and the tip. Thus, the total tunneling current is given by calculating the sum of partial or full areas of carbon circles, which are covered by the circle assigned to the tip when the center of the tip is located at a point above the surface. Since we consider here the current-imaging mode, in which the tip is scanned by keeping the gap distance constant, rA, rg and R are kept constant for the scan.
3. Results. I n the calculation, we take v a p e s for rA and rg to be comparable wi th or smal ler than the oatomic radius so that 2 r o = r ~ + r g is equal to or less than d=1.42A which is the distance between nearest carbons on the surface. It is sufficient to calculate the topography of tunneling currents only in one hexagon, because it is repeated over every hexagon. The typical example of the images of tunneling currents for various values of R is shown in Fig. l(a)-(h).
This is the case for rA=0.3i and rB=0.5R. The vertical height at every point in the hexagon represents the current deviation when the center of the tip is located at that point. The fractional deviation of current relative to the average current is estimated by a parameter p defined by p=(jmax-jmin)/(jmax+jmin).
For the case where R is comparable with the average radius rg=(r~+rg)/2, the atomic sites of the two distinct atoms are clearly identified, as is seen from Fig. l(a). For larger R, say, about four times rg, the portion of maximum current ceases to lie on atomic sites and is displaced toward the middle of the he$agon, forming a triangular lattice with a lattice constant fid=2.46~. For further increase in R, the portion of maximum current moves back toward the edge or corner of the hexagon, while the middle of the hexagon returns to the minimum current part. This alternation of portions of maximum and minimum currents between the middle and the corner of the hexagon repeats when R is increased further. However, since the value of fractional deviation of current p decreases significantly, it will be practically difficult to resolve the images except that the middle of the hexagon shows up as maximum or minimum currents forming a triangular lattice.
The similar feature of the tip-size dependence of the tunneling current images is found for other values of rA and rg.
4. Conclusions.
-
In the present model, the tunneling current is calculated by replacing the tip and the two distinct carbon atoms in the top layer of graphite by appropriate circular areas effective toresponds to the STM image taken with the current-imaging mode.
Since the real values of radii, r ~ , rg and R, of the circles described above should depend on the spread and overlap of electronic wave functions between the tip and the carbon atoms, and are not known in practice, the R-dependence of current images has been inves-
tigated for several cases of rA and rg.
All current images obtained display a threefold symmetry, reflecting the inequivalence of A- and B-atoms in the top layer of graphite. On the other hand, we have seen that the STM images differ depending on the effective size of the tip. In the case where the tip-size is sufficiently small so that the sectional area effective to the tunneling current is comparable with the effective areas of carbon atoms, we can clearly identify the position of the two dis- tinct atoms on the surface. In this case the middle of the hexagon corresponds to the portion of the minimum current. For larger R, the corners of the hexagon are not always positions for maximum or mini- mum currents. However, i t is noted that we always obtain the current image in which the middle of the hexagon corresponds to a portion of either maximum or minimum currents. Consequently, even if we obtain the STM image in which the portion of either maximum or minimum cuz- rent constitute a triangular lattice with a lattice constant 2.46A.
i t is not always straightforward to identify the atomic sites for A- and B-atoms in the image.
Finally, it is noted that in the case of r ~ = r g , we obtain similar images ClOl in which the middle of the hexagon corresponds to a portion of either maximum or minimum current. However, the pattern of current images within the hexagon always has a sixfold symmetry with respect to the center of the hexagon.
Acknowledgment. -The authors wish to thank T. Watanabe for fruitful discussions and comments. This work is supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan.
References.
113 Binnig, G., Fuchs, H., Gerber, Ch.. Rohrer, H., Stoll, E. and Tosatti, E., Europhysics Lett. 1, 31 (1986).
C2l Park. Sang-I1 and Quate. C. F., Appl. Phys. Lett.
a.
112 (1986).
C31 Morita, S. Tsukada. S. and Mikoshiba, N., Jpn. J. Appl.
Phys. 26, L306 (1987).
C41 Sonnenfeld, R. and Hansma, P. K., Science
w ,
211 (1986).C61 Soler. J. M.. Baro, A. M., Garcia, N. and Rohrer, H., Phys. Rev.
Lett. H . 444 (1986).
C6-90 JOURNAL DE PHYSIQUE
161 Mamin, H. J.. Ganz. E., Abraham, D. W., Thomson, R. E. and Clarke, J., Phys. Rev.
m,
9015 (1986).C71 Bryant, A., S m i t h , D . P. E. and Quate, C. F., Appl. Phys. Lett.
48, 832 (1986).
C81 Bryant, A., Smith, D. P. E., Binnig, G., Harrison, W. A. and Quate, C. F., Appl. Phys. Lett. 49, 936 (1986).
C91 Tersoff, J. and Hamann, D. R., Phys. Rev.
m,
805 (1985).t101 Horie, C. and Miyazaki, H., Jpn. J. Appl. Phys.
x ,
L995 (1987).t l l l Painter, G. S. and Ellis, D. E., Phys. Rev.
a,
4747 (1970).t123 Selloni, A., Carnevali. P., Tosatti, E. and Chen, C. D., Phys. Rev. W, 2602 (1985).
t131 Batra, I. P., Garcia, N., Rohrer, H., Salemink, H.. Stoll, E.
and Ciraci, S., Surf. Sci. 181, 126 (1987).
