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Formation of superperiodic patterns on highly oriented pyrolytic graphite by manipulation of nanosized graphite sheets with the STM tip
Surface Science 408 (1998) 86–94
Formation of superperiodic patterns on highly oriented pyrolytic graphite by manipulation of nanosized graphite sheets with the STM tip T.M. Bernhardt, B. Kaiser *, K. Rademann Walther-Nernst-Institut fu¨r Physikalische und Theoretische Chemie der Humboldt-Universita¨t zu Berlin, Bunsenstraße 1, 10117 Berlin, Germany Received 13 November 1997; accepted for publication 11 February 1998
Abstract Scanning tunneling microscopy investigations of superperiodic lattices on graphite (0001) are reported. The origin of these superperiodic features is still uncertain. In this investigation particular attention is paid to unusual superstructures with a spatially varying periodicity, because this sort of superstructures refers to the presence of in plane bending forces which affect the topmost graphite layer. We use the tip of the scanning tunneling microscope to manipulate single weakly bound nanometer-sized sheets on the graphite surface in order to directly induce intralayer strain and interlayer mismatch. By this means it has been possible to fold a graphite sheet onto a step or a boundary region and thus create superstructures with hexagonal symmetry. The observed lattice ˚ . The giant pattern vanished as the topmost layer was forced constants in the stressed area varied continuously between 50 and 80 A to break up. These observations also point to the important role of intralayer strain in the formation of the observed superstructures on graphite surfaces and are discussed in terms of the rotational moire´ pattern hypothesis and a dislocation network model. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Graphite; Scanning tunneling microscopy; Surface structure
1. Introduction The (0001) basal plane of graphite is one of the most often investigated substrates in scanning tunneling microscopy, mainly because of its versatility as a weakly interacting substrate for molecular imaging and deposition experiments. On this surface regular superlattices with periodicities on the ˚ ngstrøms can be order of tens or hundreds of A observed occasionally. Several authors have conducted closer investigations of these superperiodic * Corresponding author. Fax: (+49) 30 20935559; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 98 ) 0 01 5 2 -6
patterns [1–12] and their major findings are: (1) The superstructures appear as giant hexagonal lattices superimposed on the atomic lattice of graphite, (2) the periodicities of the observed giant lattices show a large variety of values ranging from ˚ [7], (3) the vertical amplitudes of 7.4 [3] to 440 A the superstructures are considerably larger than ˚ the atomic corrugation of graphite (up to 15 A [4,8]), (4) the superlattices can extend over thou˚ ngstrøms and they are usually termisands of A nated by sharp boundaries [10]. It has been noted [3,4] that these hexagonal superperiodic structures strongly resemble rotational moire´ patterns. Moire´ patterns are generally
T.M. Bernhardt et al. / Surface Science 408 (1998) 86–94
known as interference structures of two periodic lattices which are slightly rotated against each other [13]. Proposed explanations for the generation of such moire´ type structures on a graphite surface are as follows. (1) Double tip effects, i.e. the giant lattices are due to a superposition of atomic images taken by two minitips tunneling simultaneously on differently oriented graphite grains [3]. (2) Rotational misorientation, which means that the topmost graphite layer is rotated by a defined angle with respect to the underlying bulk atomic orientation. The influence of the sublayers may result in a periodic modulation of the surface density of states which appears as an electronic superlattice with a periodicity dependent on the rotation angle of the graphite layers [4,8–11]. (3) Finally, recent theoretical calculations show that the nanoscale patterns observed with the STM could also be due to lattice imperfections which are buried deep in subsurfaces [14,15]. However, a complete understanding of the mechanisms that lead to the formation of such moire´ type superstructures has not yet been achieved. Instead there are several recent observations by Beebe and co-workers [16,17] which are in marked contradiction with the most widely accepted rotational misorientation moire´ pattern hypothesis. This shows the need for further investigations of the formation mechanisms of superperiodic patterns. In the present paper we focus our attention on superstructures on highly oriented pyrolytic graphite (HOPG) with a non-constant periodicity in order to obtain a deeper insight into other possible formation mechanisms. This is the first report on the observation of such unusual superperiodic patterns. In particular we describe a possibility for the carefully directed generation of these superstructures by manipulation of nanosized graphite sheets with the tip of the STM.
2. Experimental A commercial ‘‘beetle-type’’ STM (Besocke Delta Phi, Ju¨lich and Omicron, Taunusstein,
87
Germany; [18]) operating at room temperature in an UHV environment (4×10−11 mbar) was used to image the HOPG substrates. The graphite samples (ZYH grade from Advanced Ceramics, Cleveland, USA) were prepared by cleaving with adhesive tape in air and subsequent heating to 600°C for several hours in ultrahigh vacuum [19]. The STM is operated in the constant current mode. Typical tunneling parameters for imaging are 50–1000 mV and 0.2–1 nA, and typical scan rates are 5–8 Hz. The STM images shown have been electronically differentiated to enhance vertical resolution and to compensate for a possible tilt of the whole surface area. They therefore represent the surface as it appears when illuminated from the left.
3. Results Superperiodic lattices on the (0001) basal plane of graphite have been detected generally in the vicinity of grain boundaries or steps. Fig. 1 shows a superstructured region between two boundary
˚ 2 STM image of a superperiodic pattern on Fig. 1. 787×787 A HOPG. Tunneling parameters: 480 mV, 0.6 nA. The superstructured region is terminated by sharp boundaries on the left and ˚ on the right. The distance between the boundary lines is 440 A and this feature extends over a length of more than 1 mm.
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lines. Similar features have been observed quite often during our investigation of different HOPG samples with the STM and this is in agreement with observations by other authors. The superperiodic structure is superimposed on the atomic lattice of graphite which appears in a STM image commonly as a lattice with three-fold symmetry, where only every second atom of the uppermost graphite layer is visible. The observation of half the carbon atoms of a graphite (0001) plane has been attributed to the abab-type stacking of hexagonal graphite [20]. Therefore only every second carbon atom of the (0001) plane has a direct neighbor in the underlying graphite layer (a sites). The b site carbon atoms are located above the center of the atomic hexagonal rings of the second graphite layer. Theoretical investigations indicate that the local density of states (DOS), which determines the measured tunneling current, is larger at the b sites than at the a sites, i.e. only b site carbon atoms are visible in the STM image [21]. In Fig. 2 an atom-resolved view of the center of the superstructured region in Fig. 1 is shown. The three-fold symmetry of both the atomic and the
˚ 2 STM image of the centre region of the Fig. 2. 104×104 A superperiodic pattern in Fig. 1. Tunneling parameters: 210 mV, 0.6 nA. The atomic corrugation of graphite as well as the super˚ are visible. The orientastructure with a periodicity of 40±1 A tion angle w of the superperiodic lattice relative to the atomic lattice is measured from this image to be 28±1°.
superperiodic lattice is clearly visible. The periodic˚, ity D of the observed superstructure is 40±1 A whereas the spacing d of the atomic corrugation ˚ . If one applies of graphite is known to be 2.46 A the hypothesis that in this case a moire´ type pattern is observed which is caused by rotation of the topmost graphite layer, then the relative rotation angle h is given by D=
d 2 sin(h/2)
,
(1)
and one finds that the atomic lattices of the two uppermost graphite layers must be rotated against each other by an angle of h=3.5±1° [4]. This implies, that the orientation angle w of the superstructure in comparison with the atomic lattice of the graphite top layer amounts to h w=30°− #28°, 2
(2)
which is in good agreement with the experimental observation (cf. Fig. 2). A quite different appearance of a superstructured region is shown in Fig. 3. This stable superlattice deviates from previously reported superperiodic features in the way that its periodicity changes spatially, i.e. the spacing between the bright maxima of the superstructure increases from the lower left to the upper right corner of the image. In order to demonstrate this further, a line scan between the arrow markers in Fig. 3 is drawn in Fig. 4a. The corresponding spacings D between adjacent corrugation maxima of the superstructure are shown in Fig. 4b. It can be seen that D ˚ over a distance increases by approximately 40 A ˚ . If one again applies the moire´ rotation of 1500 A hypothesis and assumes that the superstructure in Fig. 3 is caused by rotation of a graphite layer with respect to the underlying bulk, then as a consequence of the varying lattice spacing D the relative rotation angle h must also change with distance. Fig. 4c shows h as a function of the distance, calculated according to Eq. (1). This implies that in the region where this superstructure appears the graphite layer (probably the uppermost) is not only rotated, but also bent in the lateral plane. Hence, an intralayer bending or
T.M. Bernhardt et al. / Surface Science 408 (1998) 86–94
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˚ 2 STM image of a superstructure with nonFig. 3. 2480×2480 A constant periodicity. Tunneling parameters: 60 mV, 0.6 nA. The superstructure appears on a graphite sheet, one monolayer in height, which is pinned in a valley between a strong surface distortion on the left and a multiatomic step on the right hand side. A line scan between the arrow markers is shown in Fig. 4.
shearing strain has to be assumed which could possibly originate from the distorted graphite surface on the left side of the superstructured region in Fig. 3. In order to investigate further the role of intralayer strain as well as interlayer mismatch in the formation mechanism of superstructures on graphite surfaces, we tried to manipulate nanometersized graphite sheets consisting of only one or a few graphite monolayers (such as that shown in Fig. 5a) with the STM tip. For this purpose we located the tip over quite stepped and structured regions on the graphite substrate and searched for appropriate graphite flakes. In this first step the tunneling voltage was held at about 800–1000 mV (current, 1 nA) in order to minimize tip–sample interaction. It is known that the tip–sample interaction on graphite increases drastically if the tunneling voltage is below 500 mV (current, 1 nA) [22–24]. In a second step we use this effect to influence the surface topography by scanning over weakly bound graphite sheets with decreased tunneling voltage, i.e. small tip–sample distance through the lowered tunneling resistance.
Fig. 4. (a) Height profile along the line defined by the two arrow markers in Fig. 3. (b) Values of the spacing D between adjacent corrugation maxima in (a). (c) Moire´ rotational misorientation angle h between two successive graphite layers necessary to produce the observed superstructure calculated form D and Eq. (1). Lines in (b) and (c) are drawn to guide the eye.
Surprisingly, the generally observed reaction of these sheets on the tip-induced force was folding. Folding of parts of a graphite sheet occurred quite easily, when the height of a sheet was one to three monolayers, whilst we were not able to fold for ˚ height (six monolayers). example islands of 20 A During the whole procedure the sampling feedback had not been interrupted. The surface structure was manipulated during the normal scanning process. The folding direction could be influenced to a certain extent by variation of the scan direction. Fig. 5 shows a sequence of images of a nanosized graphite sheet two monolayers in height. Each image was acquired with a tunneling voltage of 370 mV (current, 1 nA). Image (a) represents the first scan of this region. Initially no surface modification can be observed. However, apparently during tip repositioning for the next scan, a folding has occurred. From image (b), a slightly enlarged
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Fig. 5. Manipulation of a weakly bound nanosized graphite sheet with the STM tip. The sequence of images shows the influence of the tip on the structure of the sheet and the formation of a superstructure. Tunnelling parameters: 370 mV, 1 nA. (a) ˚ 2 STM image. (b) 2480×2480 A ˚ 2 STM image. A folding of a part of the sheet appeared apparently during repositioning 4960×4960 A ˚ 2 STM image of the whole folded area. The apparent pinning points of the folded sheet are of the tip for this scan. (c) 2480×2480 A ˚ 2 magnification of image (c). The inset shows line scans between the arrow markers AA and BB, denoted A and B. (d) 1550×1550 A ˚ 2 STM image. New scan of the area. Arrows demonstrating the giant lattice and the non constant periodicity. (e) 1550×1550 A ˚ 2 STM image showing the broken sheet. indicate the scan line during which the folded part of the sheet breaks off. (f ) 1550×1550 A The superstructure has totally disappeared.
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view, it can be seen that the end of the sheet has been folded toward the lower left corner on top of the boundary line propagating diagonally from the lower left to the upper right corner of the images. A superperiodic pattern is clearly visible on that part of the folded sheet which is positioned to the right of the boundary line. Image (c) is the result of a new scan, showing the whole folded part of the graphite sheet. The periodicity of the observed superstructure becomes larger with increasing distance from the folding edge and the boundary line. As stated above, this is an indication of a bending force that influences this part of the folded sheet. The resultant intralayer strain decreases with increasing lattice constant from the upper right part in the vicinity of the folding edge (marked by the arrow A) to the lower left end, where the sheet is pinned to a distortion of the graphite surface (arrow B). A magnification of image (c) is shown in image (d ) together with two line scans across the superstructure illustrating the ˚ ). varying lattice periodicity (D between 50 and 80 A The presence of intralayer strain and its strong relation to the observed superstructure finally becomes evident, when during one of the subsequent scans, exactly at the scan line marked with two arrows in image (e), the stressed layer breaks up and immediately, apparently as a result of the relaxation of the folded sheet, the superstructure vanishes. In the following image (f ) the whole rupture propagating along the boundary line is visible and no superperiodic pattern can be identified, either on the island which has been detached from the original sheet or on the remaining part of the sheet which is still in contact with the folding edge.
4. Discussion The purpose of the following discussion is to clarify the atomic origin of the observed superstructures and to show that, dependent on the presence of bending or shearing forces, different mechanisms can lead to the formation of superstructures. It is now widely accepted that the image contrast in superstructured regions observed with the STM on graphite is due to areas of different stacking sequences which result in a different local
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DOS [9,11]. The measured asymmetry between a and b sites in the different parts of a superstructure [11] and tight-binding DOS calculations for different graphite modifications [25] lead to the following assignment. The bright areas of the hexagonal superstructure correspond to regions of aab-type stacking, whereas aba- and abc-stacked regions appear darker because of a smaller DOS. The stacking structures discussed are schematically depicted in Fig. 6a. The corresponding regions of different stacking that belong to a moire´ type superstructure due to rotational misorientation of two adjacent graphite layers are illustrated in Fig. 6b. In this case the deformation force that leads to the misorientation influences the interlayer van der Waals bondings but leaves the intralayer bondings totally unaffected. However, in the present study we find strong evidence for a close relation between the appearance of a superstructure and intralayer deformation forces. In order to give an idea of the possible in-plane deforming strain, we will try in the following to present a crude estimation of the bending force that affects the superstructured sheet in Fig. 5. Regarding image (c) we suppose that the folded part of the island that shows a superstructure is pinned by the folding edge at point A and an in-plane bending force F affects the island at point B because of the influence of the apparent surface distortion near B. F is pointing perpendicular to the longitudinal extension of the folded sheet toward the lower right corner of the image. The superstructure is terminated on the folded sheet at the location, where the boundary line propagates underneath the island, presumably inducing a strong basal dislocation ribbon that compensates for the shearing stress. Applying simple mechanical considerations, starting with Hooke’s rule, one finds that the value of F is given by F=
Eb3h 4L3
tan h,
(3)
where E is the elasticity modulus of graphite (E=121.9×109 N m−2)1, b is the mean width of 1 E was calculated according to the equation E=2G(1+m). The shear modulus G=45.5×109 N m−2 and Poisson’s ratio m=0.34 have been taken from Ref. [26 ], where these values were derived in conjugation with anisotropic elasticity theory.
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Fig. 6. (a) Schematic representation of the atomic positions in different stacking sequences of graphite. A cut through three adjacent planes is shown. An abc atomic plane arrangement belongs to rhombohedral graphite, whereas an aba stacking belongs to hexagonal graphite. (b) Projection of two adjacent planes (solid and dashed hexagons, respectively) on the (0001) plane. The layers are ˚ . Dashed circles indicate regions rotationally misoriented by an angle of 3.8° to give a moire´-type pattern with a periodicity of 37 A ˚ 2. (c) Projection of a part of a basal of different stacking. 876 atoms of each plane are shown corresponding to an area of 41×48 A plane dislocation network near a twist boundary on the (0001) plane. The underlying dashed layer is undistorted. Again a ˚ 2 section of the adjacent layers are shown. The dislocation lines between regions of different stacking are indicated by dashed 41×48 A grey lines. Note that the in plane direction of the atomic orientation is similar in all stacking regions. Schema (a) represents a cut through the basal plane along the thick black line in (c).
˚ ), h is the the superstructured region (b=230 A ˚ ), L is the length of height of the island (h=7 A the bent region (from A to B in Fig. 5c: L= ˚ ). tan h stands for the slope of the bent 2200 A graphite sheet due to F at point B. The angle h reflects the difference in the atomic orientation of the folded island near point A relative to the atomic orientation at point B ( Fig. 5c). Hence, h can be calculated from the periodicity of the ˚, superstructure near point A, which is D=50±2 A using Eq. (1). According to these considerations the deformation force affecting the graphite sheet with the superstructure in Fig. 5 was estimated to be about F#2×10−10 N. The maximum stress s in the most strongly deformed part of the folded island near point A ( Fig. 5c) that results from this
bending force can be calculated according to s=
6FL b2h
,
(4)
and one obtains s#700 MPa. For comparison, the shearing stress necessary to induce dislocation motion, measured with an STM, is clearly below this value (5–200 MPa [26 ]). Interestingly, macroscopic indentation experiments indicate that stress on the order of about 1 GPa damages the surface of graphite [27], which is confirmed by the present investigation (cf. Fig. 5). In particular the observed force is considerably larger than the macroscopic average critically resolved shearing stress for the basal plane of annealed HOPG which amounts to
T.M. Bernhardt et al. / Surface Science 408 (1998) 86–94
only 0.6 MPa [28]. Therefore it seems not unreasonable to assume that shearing forces on the estimated order of magnitude applied to graphite in the direction of the basal plane can result not only in a bending of a graphite layer but can also introduce basal dislocations. It has been recognized for a long time that shearing stress due to twist boundaries generates regular dislocation networks consisting of an array of contracted and extended nodes [29,30]. In these cases transmission electron microscopic investigations reveal triangular-shaped network patterns. Such patterns could also be observed with an STM [26 ] and the image contrast was as well attributed to regions of different stacking. Besides, the STM observation of a tip induced transformation of such a triangular dislocation network superstructure into a three-fold superlattice has been reported recently [12]. Hence, it is reasonable to assume that the presence of a network of dislocations is the reason for the appearance of the described superstructures observed on the stressed graphite islands. This model has been proposed by Garbarz et al. [6 ] and is detailed in Fig. 6c. Furthermore, in a dislocation network near a twist boundary the atomic positions in the hexagonal dislocation segments are slightly shifted (by d/2) to give the different stacking, but there exists no rotational misorientation between the atomic orientation of adjacent layers, as can be seen from Fig. 6c. This could be a possible explanation for the superstructures observed by Beebe and co-workers [16,17], where indeed no rotation angle between the atomic orientation in a superstructured area and the underlying second topmost graphite layer has been identified. However, because of the oxidative etching procedure employed in their experiments to uncover parts of the second graphite layer, a distortion of the topmost graphite monolayer could be suggested that presumably induced an intralayer deformation which was identified in the present work to be a possible reason for the appearance of a superstructure. Unfortunately no high quality atomic resolution image of the superstructures in the strained regions has been achieved up to now because of the lability of the bent graphite sheets and their tendency to
93
break off. The investigation of the orientation of the superlattice with respect to the atomic lattice and the evaluation of exact atomic position would be a good test for the identification of dislocations. We are going to proceed in this direction and we furthermore intend to use our new manipulation method to investigate other possible dislocation networks and the conceivable transformation of a rotational moire´ misorientation into a dislocation network with increasing shearing stress.
5. Conclusions We introduced a new method for surface modification on HOPG at room temperature. This method has been applied to the investigation of superperiodic features on this surface. It appears that several different factors can lead to the formation of superperiodic patterns on graphite. In this paper we present and discuss a new unusual form of superstructure which is characterized by a spatially varying lattice constant. Previous reports on superstructures have revealed only patterns with constant periodicity. The tip-induced manipulation of weakly bound graphite islands leads to the direct observation of formation and subsequent destruction of such a superstructure and these experimental results point toward the importance of intralayer strain as a possible reason for the appearance of superperiodic features.
Acknowledgements Financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie is gratefully acknowledged.
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[4] M. Kuwabara, D.R. Clarke, D.A. Smith, Appl. Phys. Lett. 56 (1990) 2396. [5] J.E. Buckley, J.L. Wragg, H.W. White, A. Bruckdorfer, D.L. Worcester, J. Vac. Sci. Technol. B 9 (1991) 1079. [6 ] J. Garbarz, E. Lacaze, G. Faivre, S. Gauthier, M. Schott, Philos. Mag. A 65 (1992) 853. [7] P.I. Oden, T. Thundat, L.A. Nagahara, S.M. Lindsay, G.B. Adams, O.F. Sankey, Surf. Sci. 254 (1991) L454. [8] X. Yang, C. Bromm, U. Geyer, G. von Minnigerode, Ann. Phys. 1 (1992) 3. [9] J. Xhie, K. Sattler, M. Ge, N. Venkateswaran, Phys. Rev. B 47 (1993) 15835. [10] P.W. de Bont, P.M.L.O. Scholte, M.H.J. Hottenhuis, G.M.P. von Kempen, J.W. Kerssemakers, F. Tuinstra, Appl. Surf. Sci. 74 (1994) 73. [11] Z.Y. Rong, P. Kuiper, Phys. Rev. B 48 (1993) 17427. [12] P.J. Ouseph, Phys. Rev. B 53 (1996) 9610. [13] G. Oster, Endeavour 27 (1968) 60. [14] K. Kobayashi, Phys. Rev. B 53 (1996) 11091. [15] K. Kobayashi, Phys. Rev. B 54 (1996) 17029. [16 ] D.L. Patrick, T.P. Beebe Jr., Surf. Sci. 297 (1993) L119. [17] V.J. Cee, D.L. Patrick, T.P. Beebe Jr., Surf. Sci. 329 (1995) 141.
[18] K. Besocke, Surf. Sci. 181 (1987) 145. [19] J.J. Metois, J.C. Heyraud, Y. Takeda, Thin Solid Films 51 (1978) 105. [20] J.D. Bernal, Proc. R. Soc. London, Ser. A 106 (1924) 749. [21] D. Toma´nek, S.G. Louie, H.J. Mamin, D.W. Abraham, R.E. Thomson, E. Ganz, J. Clarke, Phys. Rev B 35 (1987) 7790. [22] H.J. Mamin, E. Ganz, D.W. Abraham, R.E. Thomson, J. Clarke, Phys. Rev. B 34 (1986) 9015. [23] S. Gwo, C.K. Shih, Phys. Rev. B 47 (1993) 13059. [24] J.M. Soler, A.M. Baro, N. Garcia, H. Rohrer, Phys. Rev. Lett. 57 (1986) 444. [25] J.-C. Charlier, J.-P. Michenaud, Ph. Lambin, Phys. Rev. B 46 (1992) 4540. [26 ] S.R. Snyder, W.W. Gerberich, H.S. White, Phys. Rev. B 47 (1993) 10823. [27] J. Skinner, N. Gane, D. Tabor, Nature, Phys. Sci. 232 (1971) 195. [28] D.E. Soule, C.W. Nezbeda, J. Appl. Phys. 39 (1968) 5122. [29] G.K. Williamson, Proc. R. Soc. London, Ser. A 257 (1960) 457. [30] S. Amelinckx, P. Delavignette, M. Heerschap, in: P.L. Walker, Jr. ( Ed.), Chemistry and Physics of Carbon, Dekker, New York, 1965.
Formation of superperiodic patterns on highly oriented pyrolytic graphite by manipulation of nanosized graphite sheets with the STM tip T.M. Bernhardt, B. Kaiser *, K. Rademann Walther-Nernst-Institut fu¨r Physikalische und Theoretische Chemie der Humboldt-Universita¨t zu Berlin, Bunsenstraße 1, 10117 Berlin, Germany Received 13 November 1997; accepted for publication 11 February 1998
Abstract Scanning tunneling microscopy investigations of superperiodic lattices on graphite (0001) are reported. The origin of these superperiodic features is still uncertain. In this investigation particular attention is paid to unusual superstructures with a spatially varying periodicity, because this sort of superstructures refers to the presence of in plane bending forces which affect the topmost graphite layer. We use the tip of the scanning tunneling microscope to manipulate single weakly bound nanometer-sized sheets on the graphite surface in order to directly induce intralayer strain and interlayer mismatch. By this means it has been possible to fold a graphite sheet onto a step or a boundary region and thus create superstructures with hexagonal symmetry. The observed lattice ˚ . The giant pattern vanished as the topmost layer was forced constants in the stressed area varied continuously between 50 and 80 A to break up. These observations also point to the important role of intralayer strain in the formation of the observed superstructures on graphite surfaces and are discussed in terms of the rotational moire´ pattern hypothesis and a dislocation network model. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Graphite; Scanning tunneling microscopy; Surface structure
1. Introduction The (0001) basal plane of graphite is one of the most often investigated substrates in scanning tunneling microscopy, mainly because of its versatility as a weakly interacting substrate for molecular imaging and deposition experiments. On this surface regular superlattices with periodicities on the ˚ ngstrøms can be order of tens or hundreds of A observed occasionally. Several authors have conducted closer investigations of these superperiodic * Corresponding author. Fax: (+49) 30 20935559; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 98 ) 0 01 5 2 -6
patterns [1–12] and their major findings are: (1) The superstructures appear as giant hexagonal lattices superimposed on the atomic lattice of graphite, (2) the periodicities of the observed giant lattices show a large variety of values ranging from ˚ [7], (3) the vertical amplitudes of 7.4 [3] to 440 A the superstructures are considerably larger than ˚ the atomic corrugation of graphite (up to 15 A [4,8]), (4) the superlattices can extend over thou˚ ngstrøms and they are usually termisands of A nated by sharp boundaries [10]. It has been noted [3,4] that these hexagonal superperiodic structures strongly resemble rotational moire´ patterns. Moire´ patterns are generally
T.M. Bernhardt et al. / Surface Science 408 (1998) 86–94
known as interference structures of two periodic lattices which are slightly rotated against each other [13]. Proposed explanations for the generation of such moire´ type structures on a graphite surface are as follows. (1) Double tip effects, i.e. the giant lattices are due to a superposition of atomic images taken by two minitips tunneling simultaneously on differently oriented graphite grains [3]. (2) Rotational misorientation, which means that the topmost graphite layer is rotated by a defined angle with respect to the underlying bulk atomic orientation. The influence of the sublayers may result in a periodic modulation of the surface density of states which appears as an electronic superlattice with a periodicity dependent on the rotation angle of the graphite layers [4,8–11]. (3) Finally, recent theoretical calculations show that the nanoscale patterns observed with the STM could also be due to lattice imperfections which are buried deep in subsurfaces [14,15]. However, a complete understanding of the mechanisms that lead to the formation of such moire´ type superstructures has not yet been achieved. Instead there are several recent observations by Beebe and co-workers [16,17] which are in marked contradiction with the most widely accepted rotational misorientation moire´ pattern hypothesis. This shows the need for further investigations of the formation mechanisms of superperiodic patterns. In the present paper we focus our attention on superstructures on highly oriented pyrolytic graphite (HOPG) with a non-constant periodicity in order to obtain a deeper insight into other possible formation mechanisms. This is the first report on the observation of such unusual superperiodic patterns. In particular we describe a possibility for the carefully directed generation of these superstructures by manipulation of nanosized graphite sheets with the tip of the STM.
2. Experimental A commercial ‘‘beetle-type’’ STM (Besocke Delta Phi, Ju¨lich and Omicron, Taunusstein,
87
Germany; [18]) operating at room temperature in an UHV environment (4×10−11 mbar) was used to image the HOPG substrates. The graphite samples (ZYH grade from Advanced Ceramics, Cleveland, USA) were prepared by cleaving with adhesive tape in air and subsequent heating to 600°C for several hours in ultrahigh vacuum [19]. The STM is operated in the constant current mode. Typical tunneling parameters for imaging are 50–1000 mV and 0.2–1 nA, and typical scan rates are 5–8 Hz. The STM images shown have been electronically differentiated to enhance vertical resolution and to compensate for a possible tilt of the whole surface area. They therefore represent the surface as it appears when illuminated from the left.
3. Results Superperiodic lattices on the (0001) basal plane of graphite have been detected generally in the vicinity of grain boundaries or steps. Fig. 1 shows a superstructured region between two boundary
˚ 2 STM image of a superperiodic pattern on Fig. 1. 787×787 A HOPG. Tunneling parameters: 480 mV, 0.6 nA. The superstructured region is terminated by sharp boundaries on the left and ˚ on the right. The distance between the boundary lines is 440 A and this feature extends over a length of more than 1 mm.
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lines. Similar features have been observed quite often during our investigation of different HOPG samples with the STM and this is in agreement with observations by other authors. The superperiodic structure is superimposed on the atomic lattice of graphite which appears in a STM image commonly as a lattice with three-fold symmetry, where only every second atom of the uppermost graphite layer is visible. The observation of half the carbon atoms of a graphite (0001) plane has been attributed to the abab-type stacking of hexagonal graphite [20]. Therefore only every second carbon atom of the (0001) plane has a direct neighbor in the underlying graphite layer (a sites). The b site carbon atoms are located above the center of the atomic hexagonal rings of the second graphite layer. Theoretical investigations indicate that the local density of states (DOS), which determines the measured tunneling current, is larger at the b sites than at the a sites, i.e. only b site carbon atoms are visible in the STM image [21]. In Fig. 2 an atom-resolved view of the center of the superstructured region in Fig. 1 is shown. The three-fold symmetry of both the atomic and the
˚ 2 STM image of the centre region of the Fig. 2. 104×104 A superperiodic pattern in Fig. 1. Tunneling parameters: 210 mV, 0.6 nA. The atomic corrugation of graphite as well as the super˚ are visible. The orientastructure with a periodicity of 40±1 A tion angle w of the superperiodic lattice relative to the atomic lattice is measured from this image to be 28±1°.
superperiodic lattice is clearly visible. The periodic˚, ity D of the observed superstructure is 40±1 A whereas the spacing d of the atomic corrugation ˚ . If one applies of graphite is known to be 2.46 A the hypothesis that in this case a moire´ type pattern is observed which is caused by rotation of the topmost graphite layer, then the relative rotation angle h is given by D=
d 2 sin(h/2)
,
(1)
and one finds that the atomic lattices of the two uppermost graphite layers must be rotated against each other by an angle of h=3.5±1° [4]. This implies, that the orientation angle w of the superstructure in comparison with the atomic lattice of the graphite top layer amounts to h w=30°− #28°, 2
(2)
which is in good agreement with the experimental observation (cf. Fig. 2). A quite different appearance of a superstructured region is shown in Fig. 3. This stable superlattice deviates from previously reported superperiodic features in the way that its periodicity changes spatially, i.e. the spacing between the bright maxima of the superstructure increases from the lower left to the upper right corner of the image. In order to demonstrate this further, a line scan between the arrow markers in Fig. 3 is drawn in Fig. 4a. The corresponding spacings D between adjacent corrugation maxima of the superstructure are shown in Fig. 4b. It can be seen that D ˚ over a distance increases by approximately 40 A ˚ . If one again applies the moire´ rotation of 1500 A hypothesis and assumes that the superstructure in Fig. 3 is caused by rotation of a graphite layer with respect to the underlying bulk, then as a consequence of the varying lattice spacing D the relative rotation angle h must also change with distance. Fig. 4c shows h as a function of the distance, calculated according to Eq. (1). This implies that in the region where this superstructure appears the graphite layer (probably the uppermost) is not only rotated, but also bent in the lateral plane. Hence, an intralayer bending or
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˚ 2 STM image of a superstructure with nonFig. 3. 2480×2480 A constant periodicity. Tunneling parameters: 60 mV, 0.6 nA. The superstructure appears on a graphite sheet, one monolayer in height, which is pinned in a valley between a strong surface distortion on the left and a multiatomic step on the right hand side. A line scan between the arrow markers is shown in Fig. 4.
shearing strain has to be assumed which could possibly originate from the distorted graphite surface on the left side of the superstructured region in Fig. 3. In order to investigate further the role of intralayer strain as well as interlayer mismatch in the formation mechanism of superstructures on graphite surfaces, we tried to manipulate nanometersized graphite sheets consisting of only one or a few graphite monolayers (such as that shown in Fig. 5a) with the STM tip. For this purpose we located the tip over quite stepped and structured regions on the graphite substrate and searched for appropriate graphite flakes. In this first step the tunneling voltage was held at about 800–1000 mV (current, 1 nA) in order to minimize tip–sample interaction. It is known that the tip–sample interaction on graphite increases drastically if the tunneling voltage is below 500 mV (current, 1 nA) [22–24]. In a second step we use this effect to influence the surface topography by scanning over weakly bound graphite sheets with decreased tunneling voltage, i.e. small tip–sample distance through the lowered tunneling resistance.
Fig. 4. (a) Height profile along the line defined by the two arrow markers in Fig. 3. (b) Values of the spacing D between adjacent corrugation maxima in (a). (c) Moire´ rotational misorientation angle h between two successive graphite layers necessary to produce the observed superstructure calculated form D and Eq. (1). Lines in (b) and (c) are drawn to guide the eye.
Surprisingly, the generally observed reaction of these sheets on the tip-induced force was folding. Folding of parts of a graphite sheet occurred quite easily, when the height of a sheet was one to three monolayers, whilst we were not able to fold for ˚ height (six monolayers). example islands of 20 A During the whole procedure the sampling feedback had not been interrupted. The surface structure was manipulated during the normal scanning process. The folding direction could be influenced to a certain extent by variation of the scan direction. Fig. 5 shows a sequence of images of a nanosized graphite sheet two monolayers in height. Each image was acquired with a tunneling voltage of 370 mV (current, 1 nA). Image (a) represents the first scan of this region. Initially no surface modification can be observed. However, apparently during tip repositioning for the next scan, a folding has occurred. From image (b), a slightly enlarged
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Fig. 5. Manipulation of a weakly bound nanosized graphite sheet with the STM tip. The sequence of images shows the influence of the tip on the structure of the sheet and the formation of a superstructure. Tunnelling parameters: 370 mV, 1 nA. (a) ˚ 2 STM image. (b) 2480×2480 A ˚ 2 STM image. A folding of a part of the sheet appeared apparently during repositioning 4960×4960 A ˚ 2 STM image of the whole folded area. The apparent pinning points of the folded sheet are of the tip for this scan. (c) 2480×2480 A ˚ 2 magnification of image (c). The inset shows line scans between the arrow markers AA and BB, denoted A and B. (d) 1550×1550 A ˚ 2 STM image. New scan of the area. Arrows demonstrating the giant lattice and the non constant periodicity. (e) 1550×1550 A ˚ 2 STM image showing the broken sheet. indicate the scan line during which the folded part of the sheet breaks off. (f ) 1550×1550 A The superstructure has totally disappeared.
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view, it can be seen that the end of the sheet has been folded toward the lower left corner on top of the boundary line propagating diagonally from the lower left to the upper right corner of the images. A superperiodic pattern is clearly visible on that part of the folded sheet which is positioned to the right of the boundary line. Image (c) is the result of a new scan, showing the whole folded part of the graphite sheet. The periodicity of the observed superstructure becomes larger with increasing distance from the folding edge and the boundary line. As stated above, this is an indication of a bending force that influences this part of the folded sheet. The resultant intralayer strain decreases with increasing lattice constant from the upper right part in the vicinity of the folding edge (marked by the arrow A) to the lower left end, where the sheet is pinned to a distortion of the graphite surface (arrow B). A magnification of image (c) is shown in image (d ) together with two line scans across the superstructure illustrating the ˚ ). varying lattice periodicity (D between 50 and 80 A The presence of intralayer strain and its strong relation to the observed superstructure finally becomes evident, when during one of the subsequent scans, exactly at the scan line marked with two arrows in image (e), the stressed layer breaks up and immediately, apparently as a result of the relaxation of the folded sheet, the superstructure vanishes. In the following image (f ) the whole rupture propagating along the boundary line is visible and no superperiodic pattern can be identified, either on the island which has been detached from the original sheet or on the remaining part of the sheet which is still in contact with the folding edge.
4. Discussion The purpose of the following discussion is to clarify the atomic origin of the observed superstructures and to show that, dependent on the presence of bending or shearing forces, different mechanisms can lead to the formation of superstructures. It is now widely accepted that the image contrast in superstructured regions observed with the STM on graphite is due to areas of different stacking sequences which result in a different local
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DOS [9,11]. The measured asymmetry between a and b sites in the different parts of a superstructure [11] and tight-binding DOS calculations for different graphite modifications [25] lead to the following assignment. The bright areas of the hexagonal superstructure correspond to regions of aab-type stacking, whereas aba- and abc-stacked regions appear darker because of a smaller DOS. The stacking structures discussed are schematically depicted in Fig. 6a. The corresponding regions of different stacking that belong to a moire´ type superstructure due to rotational misorientation of two adjacent graphite layers are illustrated in Fig. 6b. In this case the deformation force that leads to the misorientation influences the interlayer van der Waals bondings but leaves the intralayer bondings totally unaffected. However, in the present study we find strong evidence for a close relation between the appearance of a superstructure and intralayer deformation forces. In order to give an idea of the possible in-plane deforming strain, we will try in the following to present a crude estimation of the bending force that affects the superstructured sheet in Fig. 5. Regarding image (c) we suppose that the folded part of the island that shows a superstructure is pinned by the folding edge at point A and an in-plane bending force F affects the island at point B because of the influence of the apparent surface distortion near B. F is pointing perpendicular to the longitudinal extension of the folded sheet toward the lower right corner of the image. The superstructure is terminated on the folded sheet at the location, where the boundary line propagates underneath the island, presumably inducing a strong basal dislocation ribbon that compensates for the shearing stress. Applying simple mechanical considerations, starting with Hooke’s rule, one finds that the value of F is given by F=
Eb3h 4L3
tan h,
(3)
where E is the elasticity modulus of graphite (E=121.9×109 N m−2)1, b is the mean width of 1 E was calculated according to the equation E=2G(1+m). The shear modulus G=45.5×109 N m−2 and Poisson’s ratio m=0.34 have been taken from Ref. [26 ], where these values were derived in conjugation with anisotropic elasticity theory.
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Fig. 6. (a) Schematic representation of the atomic positions in different stacking sequences of graphite. A cut through three adjacent planes is shown. An abc atomic plane arrangement belongs to rhombohedral graphite, whereas an aba stacking belongs to hexagonal graphite. (b) Projection of two adjacent planes (solid and dashed hexagons, respectively) on the (0001) plane. The layers are ˚ . Dashed circles indicate regions rotationally misoriented by an angle of 3.8° to give a moire´-type pattern with a periodicity of 37 A ˚ 2. (c) Projection of a part of a basal of different stacking. 876 atoms of each plane are shown corresponding to an area of 41×48 A plane dislocation network near a twist boundary on the (0001) plane. The underlying dashed layer is undistorted. Again a ˚ 2 section of the adjacent layers are shown. The dislocation lines between regions of different stacking are indicated by dashed 41×48 A grey lines. Note that the in plane direction of the atomic orientation is similar in all stacking regions. Schema (a) represents a cut through the basal plane along the thick black line in (c).
˚ ), h is the the superstructured region (b=230 A ˚ ), L is the length of height of the island (h=7 A the bent region (from A to B in Fig. 5c: L= ˚ ). tan h stands for the slope of the bent 2200 A graphite sheet due to F at point B. The angle h reflects the difference in the atomic orientation of the folded island near point A relative to the atomic orientation at point B ( Fig. 5c). Hence, h can be calculated from the periodicity of the ˚, superstructure near point A, which is D=50±2 A using Eq. (1). According to these considerations the deformation force affecting the graphite sheet with the superstructure in Fig. 5 was estimated to be about F#2×10−10 N. The maximum stress s in the most strongly deformed part of the folded island near point A ( Fig. 5c) that results from this
bending force can be calculated according to s=
6FL b2h
,
(4)
and one obtains s#700 MPa. For comparison, the shearing stress necessary to induce dislocation motion, measured with an STM, is clearly below this value (5–200 MPa [26 ]). Interestingly, macroscopic indentation experiments indicate that stress on the order of about 1 GPa damages the surface of graphite [27], which is confirmed by the present investigation (cf. Fig. 5). In particular the observed force is considerably larger than the macroscopic average critically resolved shearing stress for the basal plane of annealed HOPG which amounts to
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only 0.6 MPa [28]. Therefore it seems not unreasonable to assume that shearing forces on the estimated order of magnitude applied to graphite in the direction of the basal plane can result not only in a bending of a graphite layer but can also introduce basal dislocations. It has been recognized for a long time that shearing stress due to twist boundaries generates regular dislocation networks consisting of an array of contracted and extended nodes [29,30]. In these cases transmission electron microscopic investigations reveal triangular-shaped network patterns. Such patterns could also be observed with an STM [26 ] and the image contrast was as well attributed to regions of different stacking. Besides, the STM observation of a tip induced transformation of such a triangular dislocation network superstructure into a three-fold superlattice has been reported recently [12]. Hence, it is reasonable to assume that the presence of a network of dislocations is the reason for the appearance of the described superstructures observed on the stressed graphite islands. This model has been proposed by Garbarz et al. [6 ] and is detailed in Fig. 6c. Furthermore, in a dislocation network near a twist boundary the atomic positions in the hexagonal dislocation segments are slightly shifted (by d/2) to give the different stacking, but there exists no rotational misorientation between the atomic orientation of adjacent layers, as can be seen from Fig. 6c. This could be a possible explanation for the superstructures observed by Beebe and co-workers [16,17], where indeed no rotation angle between the atomic orientation in a superstructured area and the underlying second topmost graphite layer has been identified. However, because of the oxidative etching procedure employed in their experiments to uncover parts of the second graphite layer, a distortion of the topmost graphite monolayer could be suggested that presumably induced an intralayer deformation which was identified in the present work to be a possible reason for the appearance of a superstructure. Unfortunately no high quality atomic resolution image of the superstructures in the strained regions has been achieved up to now because of the lability of the bent graphite sheets and their tendency to
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break off. The investigation of the orientation of the superlattice with respect to the atomic lattice and the evaluation of exact atomic position would be a good test for the identification of dislocations. We are going to proceed in this direction and we furthermore intend to use our new manipulation method to investigate other possible dislocation networks and the conceivable transformation of a rotational moire´ misorientation into a dislocation network with increasing shearing stress.
5. Conclusions We introduced a new method for surface modification on HOPG at room temperature. This method has been applied to the investigation of superperiodic features on this surface. It appears that several different factors can lead to the formation of superperiodic patterns on graphite. In this paper we present and discuss a new unusual form of superstructure which is characterized by a spatially varying lattice constant. Previous reports on superstructures have revealed only patterns with constant periodicity. The tip-induced manipulation of weakly bound graphite islands leads to the direct observation of formation and subsequent destruction of such a superstructure and these experimental results point toward the importance of intralayer strain as a possible reason for the appearance of superperiodic features.
Acknowledgements Financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie is gratefully acknowledged.
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