Effect of electronic states of the tip on the STM image of graphite

Surface Science Letters North-Holland

238 (1990) L439-L445

Surface Science Letters

Effect of electronic states of the tip on the STM image of graphite Nobuyuki Issbiki a, Katsuyoshi Kobayashi b and Masaru LIKao Institute for Knowledge and Intelligence Science, Kao Corporation, Bunka b Department Received

of Physics, Faculty of Science,

12 February

1990; accepted

Tsukada

b

2-l-3, Sumida-ku, Tokyo 131, Japan University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan

for publication

30 July 1990

A first-principles calculation of the STM images of graphite is performed for three different shapes of a tungsten tip. In the calculation the tip is approximated by a small cluster. One of the tips, with more than one atom at the top, produces an abnormal image, while the others, with only one atom at the top, produce normal trigonal images. The abnormal image is caused by current interference through the multi peaks of the squared amplitude of the tunnel-active orbital at the tip.

Scanning tunneling microscopy (STM) is a powerful method to investigate solid surfaces, because an atomic image can be obtained. So far the image obtained by STM has mostly been interpreted by the theory of Tersoff and Hamann [l]. In this theory the electronic state of the tip of the STM is assumed to be spherically symmetric, and the tunneling current becomes proportional to the local density of states (LDOS) of the surface at the center of the tip. Experimentally many abnormal images which do not reflect the LDOS of the surface are reported, and it is believed that such abnormal images are produced by the double tip effect. Mizes et al. [2] reproduced abnormal images of graphite by adding two normal images displaced with a certain distance between them. But their calculation neglected the interference effect in the tunneling current from each tip. Kobayashi et al. [3] calculated the STM image of graphite using a hydrogen molecule as a tip in order to clarify the relation between the shape of the tip and the STM image, and they found that the antibonding orbital of a hydrogen molecule reproduces an abnormal image because of interference. Recently they reported a numerical simulation using a W,, cluster as a tip [4]. Ohnishi et al. 0039-6028/90/$03.50

0 1990 - Elsevier

Science Publishers

[5] calculated the STM image using a cluster of a few tungsten atoms as a tip. In this Letter we examine the relation between the shape of the tip and the STM images of graphite, based on the numerical calculations for more realistic models. For this purpose we approximate the tip by a tungsten cluster. The wave function of the tungsten cluster and the graphite surface are calculated by the DV XCZ method with LCAO representation, and we identify the tunneling current using the formula derived by Tsukada and Shima [6]. In order to reduce the influence of the discreteness of the cluster levels, we broaden the energy levels of the tip by a Lorentzian function with a width A. Since it is difficult to calculate the width A with the more sophisticated Green’s function, and since A varies depending on the microscopic structure of the tip, we calculate the STM images for several values of A between 0.1 and 1.0 eV. According to the band calculation of a tungsten bulk crystal by Mattheiss [7] the peak width of the density of states (DOS) of the d band is about 0.7 eV. Also our simulation of scanning tunneling microscopy [S] shows good agreement with the experiment when the width A is set at 1.0 eV.

B.V. (North-Holland)

N. Isshiki et al. / Effect

of tip shapes on the STM image of graphite

Fig. 1. Contour map of the calculated tunneling current of a graphite surface in the logarithmic scale. The width A is set to 1.0 eV. The distance between the surface and the tip is 10 atomic units. The bias is - 0.5 V where it is defined by the surface voltage relative to the tip. The symmetry axis of the tip is perpendicular to the graphite surface, and the direction of the tip is shown at the left side. The area enclcsed by the solid line shows higher current and the dashed line shows lower current. The letters A and B are the A-site and the B-site of the graphite lattice, respectively. (a) W,, tip with [ill] protrusion of the crystal. (b) W,, tip with [110] protrusion of the crystal. (c) W,, tip, which is the same as (b) except that the apex atom is removed.

N. Isshiki et al. / Effect of tip shapes on the STM image of graphite

Moreover, the result is almost unchanged if the value of A is larger than 1.0 eV. So our assumption for the range of A is reasonable. The tunneling current for the LCAO representation is expressed in Bardeen’s formalism [9] as

[f(E)-f(E-eV)]

1=T/dE X c

c

G$rpj(E)G&Jqf(E-eV)

ri’pp’ jj’qq’ XJlpjqJ&,lqf

where f(E) 4pjq=/

)

is the Fermi

(1) distribution

function

drX,*(r-R,)V,(r)~~,(r-Rj).

In the above Vr is the potential of the xP(r - R,) and &r(r - Rj) are the atomic of the surface and the tip at Ri and Rj tively. G&,~(E) and G,zjrq(E) arethe functions of the surface and of the tip tively:

G;+(E)=

(2) tip and orbitals respecGreen’s respec-

~C;;,C,s&8(E-Ep), P

(3)

G;,~q~(E) = ~CyT,,J;Q Ab' (E-E,)'+A~' Y where the eigen functions of the surface the tip !P” are expressed as \k,(r)

= CC:,,Xp(r-Ri)?

%k;(r) = ~C&#+(r-R,). jq

and

(4)

‘k, and

(5) (6)

Three different tip shapes are adopted for the simulation of the STM image of graphite: (a) a threefold symmetric W,, cluster protruded to the [ill] direction of the crystal; (b) a twofold symmetric W,, cluster protruded to the [llO] direction; and (c) a W,, cluster, which is the same as the W,, cluster except that the apex atom is removed. These tips are shown on the left side of fig. 1. We calculate the STM images for various values of bias voltage and the energy level width A. For example, fig. 1 shows current images of graphite when the bias voltage is -0.5 V and the width A is set to 1.0 eV. The bias voltage is defined by the surface voltage relative to the tip. Since the tunneling current is considered to be

proportional to the exponent of the distance between the tip and the surface, a logarithmic plot of a current image becomes similar to a topological image. In the W,, and W,, tips, which have only one atom at the top, we obtain normal images of graphite with the trigonal lattice structure. On the other hand, the W,, tip, which has more than one atom at the top, produces abnormal images which appear linearly expanded, displaced or line-like. It should also be noted that the contrast of the abnormal image is lower than that of the normal one. In order to clarify the origin of the abnormal image, we examined the wave function of the tungsten tip. Fig. 2 shows the charge density (square of a wave function) of each tip summed over the energy range from Fermi level E, - 0.5 eV to E, + 1.0 eV. Because the tunneling current at the positive bias is considered to be mainly related to the level of the tip just below the Fermi level and in the present case we broaden the energy levels to the width of 1.0 eV, we adopt the above-mentioned energy range of summation for the bias voltage of -0.5 eV. From fig. 2 one can find that the charge densities at the top of the W,, and W,, tip are roughly composed of a single round peak, while the charge density at the top of the W,, tip is roughly composed of four peaks. Moreover, for the W,, tip, the signs of the main orbitals contributing to the respective peaks are different. To investigate the effect of the alternating signs for the peaks of the tunnel orbitals we calculated STM images produced by the tip tunnel-active orbital, which consists of four spherical atomic orbitals as shown in fig. 3. Each orbital is located at a peak of the charge density of W,,. The calculated result shows that when the sign of the orbitals is opposite for the neighboring site (fig. 3b) the image becomes line-like and the contrast is weak as in fig. lc, while in the case where all the orbitals have the same sign (fig. 3a) the image is just displaced from the normal one. This result can be qualitatively understood in the following terms. When all the peaks of the orbital have the same sign, the contribution of each peak to the current through the integral of eq. (2) is simply added to eq. (1) and the resulting image is not much differ-

znt from the normal one. On the other hand, when the signs of the peaks are changed, the contribution of each peak to the current is considerably

reduced and the resulting image becomes very different from the normal one. The line-like image of the W,, tip is not caused by a simple addition

A-

Fig. 2. Contour map of the charge density of (a) W,, tip, (b) W,, tip and (c) W,, tip summed up over the energy range from E, - 0.5 eV to E, + 1.0 eV. Left side: Charge density at the plane perpendicular to the symmetry axis and 1 atomic unit below the top. Right side: Charge density at the cross section A-B in the left side.

h? Isshiki et al. / Effect of tip shapes on the STM image of graphite

Fig. 3. Calculated STM images of graphite produced by the tip which consists of four spherical orbitals, as shown in the upper side of the figure. + and - show the sign of each orbital. (a) All four orbitals have the same sign. (b) The signs of neighboring orbitals are opposite. Expressions are the same as in fig. 2.

of the tunneling current from each peak; it is caused by an interference of the tunneling current through the multiple orbital peaks. This argument is applicable to other cases. To evaluate the effect of the width A we show the numerical result of the STM image of the W,, tip for A = 0.1 eV in fig. 4 and the corresponding charge density in fig. 5. In this case the charge density is summed up in a narrower region than that for A = 1.0 eV. If we sum up the charge density in the range from E, to E, + 1.0 eV, the profile has a rather round shape, and we get a normal image for a bias of - 1.0 V. On the other hand, an abnormal image appears for a bias of -0.5 V because the charge density of the tip summed up in the range from E, to E, + 0.5 eV has a double peak structure, and the main orbital cont~buting to the charge density has opposite signs for these peaks. By exa~ning the DOS of the apex atom near the Fermi level, we find that the ratio of 6s and 5d,z orbitals which have round shape is small, and other orbitals such as 5d,, or 5d,, cause the multi peak shape of the charge density. It should be noted that in the case of small width A an abnormal image appears under some conditions even for a tip which has only one atom at the top. In the study reported in this Letter we calculated the STM image of graphite by a first-principles method, and we found that a multi-peak charge density structure near the Fermi level causes

(4 W14

(b) WI4

Bias

=I: -1.OV

Bias = -0.5V

Fig. 4. Calculated STM images for WI, tip when the width A is 0.1 eV. (a) Bias is - 1.0 V. (b) Bias is - 0.5 V. Other conditions are the same as in fig. 2.

N. Isshiki et al. / Efject of tip shapes on the STM image

of graphite

(a) EF - EF + l.OeV

tb) EF -

EF + 0.5eV

Fig. 5. Same as fig. 4 except that charge

density

of the W,, tip is summed over the energy from E, to E, + 0.5 eV.

an abnormal image while a round charge density produces a normal image. The line-like image is caused by interference of the tunneling current through the two peaks which have opposite signs in the orbitals. Such a multi-peaked structure exists when more than one atom is located at the top of the tip. Even for the tip with only one atom at the top, such a multi-peak structure appears if we assume that A is small. According to the calculation of Mizes et al. [2], a line-lie image is created by the overlap of two normal images displacing each other at a certain special distance of the

range (a) from

E,

to E, + 1.0 eV and (h)

order of the lattice constant of graphite. However, such a simple model is plausible only to the case in which the distance between the two tips is large. and would not be applicable to the case Mizes assumed. We wish to thank Dr. R. Saito and Dr. S. Watanabe for providing the program of the DV Xa! method. The numerical calculations were performed at the Computer Center of the University of Tokyo and of the Institute for Molecular Science.

N. Isshiki et al. / Effect of tip shapes on the STM image of graphite

References [l] J. Tersoff and D.R. Hamarm, Phys. Rev. B 31 (1985) 805. (21 H.A. Mizes, Sang-i1 Park and W.A. Harrison, Phys. Rev. B 36 (1987) 4491. (31 K. Kobayashi and M. Tsukada, J. Phys. Sot. Jpn. 58 (1989) 2238. [4] K. Kobayashi and M. Tsukada, J. Vat. Sci. Technol. A 8 (1990) 170.

[5] S. Ohnishi and M. Tsukada, Solid State Commun. 71 (1989) 391. [6] M. Tsukada and N. Shima, J. Phys. Sot. Jpn. 56 (1987) 2875. [7] L.F. Mattheiss, Phys. Rev. 139 (1965) A1893. [8] K. Kobayashi, N. Isshiki and M. Tsukada, Solid State Commun. 74 (1990) 1187. [9] J. Bardeen, Phys. Rev. Lett. 6 (1961) 57.