Spatially resolved local electronic structure on graphite surface: a scanning tunneling spectroscopy investigation

Surface Science Letters 293 (1993) L871-L875 North-Holland

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surface science letters

Surface Science Letters

Spatially resolved local electronic structure on graphite surface: a scanning tunneling spectroscopy investigation

Nan Li and Sishen Xie Institute of Physics, Chinese Academy of Sciences, Beijing, 100080, China

Received 30 March 1993; accepted for publication 1 June 1993

An experimental measurement of the local electronic structure on graphite surface with a combined STS/STM system has been performed. STS spectra were measured step by step along a line on the surface, and spatial variations of the energy bands at about the Fermi level were obtained from the measurements. By an assumption of different local electronic structures around the inequivalent A and B sites on the surface, a simple model calculation of the spatial variation of the energy bands has been performed. Because of the consistency of the calculated results with those of the STS measurements, positions of type A carbon atoms on the surface were determined.

The peculiar structure and electronic states of graphite have attracted much attention in the last few years, especially because of their specific contribution to the understanding of STM theory for imaging surface local electronic structures [1- 5]. In layered material, carbon atoms in each single layer can be divided into two sets, in which those with neighbor atoms in the adjacent layers can be denoted as type A atoms, while those just above and below the hollow sites in the adjacent layers can be denoted as type B. The two atom types behave differently to STM imaging, as has been shown by a series of STM results on the graphite surface in which only one of the two atom types appears with scanning energy around the Fermi level. This result has been explained in terms of the difference in the local electronic states between the two types of structural inequivalent carbon atoms [3-5].

As indicated by Batra and Ciraci [4], due to the weak interaction of the A-type atoms in the graphite surface top layer to the atoms in the layer beneath, the local charge density would deviate from the surface and concentrate in between the two layers. Both Batra and Ciraci [4], and Mizes and Harrison [5] also indicated, due to

the interaction, the electronic states around the A-type atoms coinciding with the Fermi energy level would split into bonding and antibonding states, and their energies would deviate from the Fermi level. For the local electronic states around the B-type atoms on the other hand, there would be no such deviation. In this case, the bands at the Fermi energy involve only B-type atoms, and those are more readily visible to the STM imaging at an energy of approximately the Fermi level, than those of the A type.

In this work, we present an experimental investigation of the local electronic structure on the graphite surface with scanning tunneling spectroscopy (STS). Spatially resolved energy bands are derived from the measurements, and a simple model calculation based on the above assumption is given to simulate the spatial variation of the surface bands. The results show an agreement between the calculation and the STS measurements, which presents evidence to the above assumption about the local electronic structures on the graphite surface.

The STS measurements were performed with a combined STS/STM system which was devel- oped from an STM system operating in air. The

0039-6028/93/$06.00 © 1993 - Elsevier science Publishers B.V. All rights reserved

L872 Nan Li, Sishen Xie / STS of the local electronic structure of graphite

details of the experimental system were described elsewhere [6]. The sample was a natural graphite single crystal, which was cleaved in air and mounted to the sample holder of the measurement system as the surface was fresh. The tip for the STM scanning and STS measurements was made of tungsten wire of 0.5 mm in diameter. It was electrochemically etched for sharpening enough to give atomic resolution. That was determined by STM imaging immediately after the tip was mounted onto the system.

As the first step of the experiment, STM scanning was performed and repeated on the graphite surface until the system got very stable and a reproducible atomic resolved image was obtained. Then, the scanning was controlled, by an IBM PC, to stop at the desired site on the sample surface for STS measurements. By sweeping the bias voltage in a range of + 2.5 V, In I-V curves were measured step by step along a line in the scanning direction with a step distance of ~ 0.5 A. The row data were processed then to give (d l n I / d In V)-V curves, in which the peaks were considered to be representatives of resonants in the density of states of materials [7,8].

In fi~g. 1, the STM image obtained over an area of 30 A x 30 ,~ in the constant current mode is given. The bias voltage was V m = - 2 4 7 mV, and the tunneling current was It = 0.6 nA. The attached white line in the image indicates the place along which the experimental STS measurements were performed. It can be seen from the figure that the line is along the diagonal of a 2 x 5 lattice in the probed structure. The curve shown below indicates the surface corrugation along the line. In fig. 2, several typical (dlnI/dlnV)-V curves obtained at some points along the line are shown. The top curve in the figure refers to the theoretical calculation of the density of states for the graphite 7r and 7r* bands, given by Tatar and Rabii [9].

In fig. 2, a rough agreement between the STS results and the theoretical density of states can be observed. The strong peak at ~ 2.1 eV above the Fermi level in the measured (d In I/d In V)-V curves shows a basic agreement with that in the density of empty states. This peak can be as- signed as due to the contribution of the antibond-

Fig. 1.oSTM image of the graphite surface. The scanning area is 30 A x 3 0 A. The bias is V m = - 2 4 7 mV and the tunneling current 1 i = - 0 . 6 nA. The white line attached indicates the positions for the STS measurements. The curve below shows

the surface corrugation along the line.

ing ~-* band of the graphite in the vicinity of the M point at the border of the Brillouin zone [10,11]. In the lower energy range of the conduc-

G r a p h i t e

~ \ ,' ,

I i I

-a.o -z.o - I . o o.'o 1Jo e.'o a.o Binding Energy (eV)

Fig. 2. STS curves of ( d l n I / d l n V ) - V obtained with the experiment. The top curve is the density of states relating to

~- and ~r * bands of graphite from Tatar and Rabii [9].

Nan Li, Sishen Xie / STS of the local electronic structure of graphite L873

tion band, weak peak features appeared in the experimental STS curves with their positions varying around 0.5 and 1.5 eV above E F for each curve of the calculated density of states. For the valent states, the agreement was not so good, as the broad density peak at ~ -1.5 to -2 .4 eV from the Fermi energy was not clearly shown in the experimental curves. It only appeared as several weak features and varied in a wider energy range, for different curves, from -0.6 down to -2.5 eV about the Fermi level. In the present study, the reason for the reduction of the broad peak is still not very dear. A clue for a possible interpretation may be given by considering a difference between the calculated density of states and the measured STS curves, i.e. the former was calculated for bulk graphite, while the latter were taken from local electronic states on the surface. A further investigation should be considered.

As the spatial variation of the local electronic structure is the basic interest of this paper, we plotted the energy position of each peak in the measured (d In I/d In V)-V curves versus the surface positions of the corresponding STS measurements shown along the white line on the image of fig. 1). Two of such plots are given in fig. 3 as the curves V and C, which are representatives of the spatial distribution of the valence and conduction

2.0

;>

..=..

1.0

I f~ o.o

-1 .0 '

'0 eO

-2 .0 .

-3.0

~ C

• .., /.. i ..... ......-.. / .../ ---s

' ' i , , i , , i , , i , . i . ,

A

v

4.0~

s.o,~

o *pq

2.0 "~

1.0 ~ r~

o.o o.o s.o 8.0 2.o 12.0 (.15.OA) 1o.o

Rela t ive Pos i t i on

Fig. 3. Spatial variations of the surface bands (+) derived from the STS spectra. The bottom curve (e) shows the surface corrugation along the line for the STS measurements as a reference. The dashed lines are model calculation results as

indicated in the text.

band, respectively, coming nearest to the Fermi level. For reference, the surface corrugation along the measurement positions was also included at the bottom of the figure. It can be seen directly from the figure that the spatial variation of the energy bands oscillates at an atomic scale, and the oscillation exhibits a certain correlation with the surface atomic arrangement via the surface corrugation. By a further analysis, it is shown that details of the local electronic structure on the graphite surface can be revealed by the correlation of the spatial band structures and the surface atomic arrangement.

Now let us consider the asymmetry between the A sites (those atoms which are above an atom in the adjacent plane beneath) and B sites (those above a hollow in the lower plane) on the graphite surface, as given by Batra et al. [4,5], as a starting point. For the surface monolayer, there are four degenerate wave functions at the Fermi energy. Two wave functions can be noted as ~bA(r, E F) and OB(r, E F) which contain contributions only from the A site or from the B site, respectively. The other two wave functions are their conju- gates. When the second layer is included, it cou- ples to the first plane only through A-type atoms. Hence ~bA(r, E F) will interact with its counterpart in the layer below, forming bonding and antibonding states, and its energy will move away from E F. For ~bB(r, E F) the energy will not change as no coupling occurred to it. Therefore, the Fermi-energy states will only come from those localized at the B site. Furthermore, the imaged surface corrugations, such as shown in fig. 1, can be considered as the contours of the local states around the B site when they were detected at the small bias voltage of V m ----0.25 V. For the valence states localized around the B-type atoms, it can be supposed that they have a small binding energy, Ea a. For the bonding states around the A-type atoms, which did not appear in the STM image, on the other hand, the binding energy E A must be larger than E~, as it deviates from the Fermi level.

Keeping the above consideration in mind, now let us turn to the STS probing procedure. It is clear that the density of states probed instanta- neously by the tip at surface position r must

L874 Nan Li, Sishen Xie / STS of the local electronic structure of graphite

come from contributions of all local electronic states around the atoms in the probing area. This area can be defined by an effective radius in which the wave functions of the tip overlap with those of the local states on the surface. Thus, the energy positions of the probed density peaks will be defined by all of the simultaneously detected local states. By a first-order approximation, the contribution from each of the local states can be assumed to have a Gaussian-form relation to the distance from the individual atom to the tip center r, i.e. it is proportional to e x p [ - ( r - R,)2/4o-2], where 4o- 2 is a parameter of the effective probing area, and R i is the ith atom position in the area. Then, the peak energy FB(r) of the probed density of states at tip position r can be approximated as

Ea(r)=(~i exp[-(r-RAi)a/4o-2]EA

+~j exp[-(r-RB/)2/4o'2]E~)

×(~i exp[-(r-RAi)2/4o-2] -1

+ Y'~exp[--(r--RBj)2/4o'2]) , (1) )

where the summation is over the probing area, RAi and Rai refer to the A and B sites, respectively. Given an atomic arrangement on the surface, the spatial energy band can then be simu- lated with the relation.

In fig. 4a we illustrate the surface atomic arrangement related to the STS measurements. The illustration shows two possible positions for the A-type atoms on the surface by small black and empty circles, respectively. These two positions are equivalent in symmetry operations, and there is an inverse center between the two. For this reason, calculated EB(r)-r curves for the two positions must also have such a symmetry. By assuming that the small black circles in Fig. 4a represent the A-type atoms, and with a set of values of the parameter 4o .2 , we calculated the Ea(r)-r curves by eq. (1). The results are shown in fig. 4b. The results indicate that the positions

ta) 0

- - " B type C a toms on top layer

• ~__ . p o ~ b l e posit ions for A type

0 ) C a toms on the top layer

0.6

0.4,

A

0.2-

0 . 0 - I ~ -

~ - 0 . 2 -

I~1-0.4-

"~ - 0 . 0 -

- 0 . 8 -

- 1 . 0 -

-1 .2 O,

S

' 4 :0 ' a :0 ' l z ' . 0 ' ' r e . 0 R e l a t i v e P o s i t i o n (J~)

Fig. 4. (a) Surface atomic structure related to the STS measurements. The dashed circle represents a probing area. (b) Set of EB(r)-r curves calculated by eq. (1). The parameter 4o.2 (,~2) is taken as: a - 0.5; b - 1.0; c - 1.5; d - 2.0; e - 2.5; f - 3.0; g - 3.5, h - 4.0. The insert shows the influence of the tip shapes with small (S) 40. 2 and large (L) 40. 2 on the

detection of the local electronic structures.

of the oscillating peaks in the EB(r)-r curves have a negligible relation to 4o "2. But the magni- tude of the oscillating peaks will be decreased with increasing 4o .2 . This means that when the probing area is enlarged, the number of connected atoms in the area will be increased. The measured density of states will then be the spatial average of all states around the connected atoms in the probing area. The information about the

Nan L~ Sishen Xie / STS of the local electronic structure of graphite L875

local electronic states around a particular atom will be merged into the average.

In fig. 3, one of the above calculation results is shown as a dashed curve labeled S. This curve was obtained with the parameter 4o "2-~ 1.0 A.

Comparing it to the results of the STS measurements, it is seen that the peak positions in the spatial valence band V agree basically to that in the calculated curve. Because of this result, it can be presumed that the positions of the small black circles in fig. 4a represent the A-type atoms on the graphite surface. With the same method, we calculated the spatial variations of the peak energy in the conduction band in the vicinity of the Fermi level, and the result was also shown in fig. 3 by a dashed line labeled S'. Comparing it to the experimental results, it can be seen that only a partial agreement between the measurements and the calculation was obtained.

The disagreement between the STS measurement results and the result of the calculation can be attributed to the following factors: (1) Experi- mental error: it can be imagined that any negligible minor drift of the tip in the STS measurement, due to a small vibration or other distur- bance, may cause a shift of the peak position in the measured curves. (2) Influence of the surface circumstances: the strong field of ~ 10 8 V/cm in the tunneling gap, when the bias was ~ 2.0 V and the width of the gap was ~ 2/~, would be suffi- cient to cause molecules in air or adsorbed on the surface to excite with a certain probability. This will put some influence to the density of states on the surface, especially to the empty states. That might be one of the reasons for the poor agreement between the results of the measurements and of the calculation for the conduction band. (3) Simple model: since only a qualitative mean- ing exists in the first step analysis of the experimental results, detailed calculations, including convolutions of the local density of states of the tip and sample surface, were not performed. These problems should be solved by an improve-

ment of the experimental conditions and with precise calculations.

In summary, we have performed an experimental measurement on the local electronic structure on graphite surface by using STS/STM. Along a line on the imaged surface the (din I / d i n V)-V curves were measured step by step, and spatial variations of the energy bands in the vicinity of the Fermi level were derived from the measurements. With the analysis of the local electronic structure around the inequivalent A and B sites in the surface monolayer, a simple model calculation was performed which pre- sented a simulation of the spatial variation of the energy bands. A consistency of the calculated results with those of the STS measurements was obtained, and with that position of A-type carbon atoms on the surface were determined. This work presents a possibility for investigating surface local electronic structures with a spatial resolution at an atomic scale by a combined STS/STM system.

References

[1] A. Selloni, P. Carnevali, E. Tosatti and C.D. Chen, Phys. Rev. B 31 (1985) 2602.

[2] J. Tersoff, Phys. Rev. Lett. 57 (1986) 440. [3] I.P. Batra, N. Garcia, H. Rohrer, H. Salemink, E. Stoil

and S. Ciraci, Surf. Sci. 181 (1987) 126. [4] I.P. Batra and S. Ciraci, J. Vac. Sci. Technol. A 6 (1988)

313. [5] H.A. Mizes and W.A. Harrison, J. Vac. Sci. Technol. A 6

(1988) 300. [6] Nan Li, Shengfa Qian, Youfeng Zheng, Chunsheng Fu

and Sishen Xie, J. Vac. Sci. Technol., submitted. [7] R.M. Feenstra, J.A. Stroscio and A.P. Fein, Surf. Sci. 181

(1987) 295; R.M. Feenstra, J.A. Stroscio, J. Tersoff and A.P. Fein, Phys. Rev. Lett. 58 (1987) 1192.

[8] C.J. Chen, J. Vac. Sci. Technol. A 6 (1988) 319. [9] R.C. Tatar and S. Rabii, Phys. Rev. B 25 (1982) 4126.

[10] R. Claessen, H. Carstensen and M. Skibowski, Phys. Rev. B 38 (1988) 12582.

[11] I.R. Collins, P.T. Andrews and A.R. Law, Phys. Rev. B 38 (1988) 13348.

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Spatially resolved local electronic structure on graphite surface: a scanning tunneling spectroscopy investigation