First-principles investigations of low-coverage Ca-induced reconstructions on the Si(001) surface

Surface Science 605 (2011) 101–106

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Surface Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u s c

First-principles investigations of low-coverage Ca-induced reconstructions on the Si(001) surface A.Z. AlZahrani a,⁎, G.P. Srivastava b a b

Department of Physics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK

a r t i c l e

i n f o

Article history: Received 29 July 2010 Accepted 1 October 2010 Available online 8 October 2010 Keywords: Metal adsorption Si(001) surface Density functional theory STM Relative stability

a b s t r a c t Using the pseudopotential method and the local density approximation of density functional theory we have investigated the stability, atomic geometry, and electronic states for low-coverage Ca adsorbates on the Si (001) surface within the (2 × n) reconstructions with n = 2, 3, 4, 5. Our total energy calculations suggest that the (2 × 4) phase represents the most energetically stable structure with the Ca coverage of 0.375 ML. Within this structural model, each Ca atom is found to form a bridge with the inner two Si–Si dimers. The inner Si–Si dimers become elongated and symmetric (untilted). The band structure calculation indicates that the system is semiconducting with a small band gap. Significant amount of charge transfer from the Ca atoms to neighbouring Si atoms has been concluded by analysing the electronic charge density and simulation of scanning tunnelling microscopy images. The highest occupied and lowest unoccupied electronic states are found to arise from the inner and outer Si–Si dimer components, respectively. © 2010 Elsevier B.V. All rights reserved.

1. Introduction In the past few decades, studies of elemental adsorption on semiconductor surfaces have been carried out intensively both experimentally and theoretically for the understanding of metal semiconductor interfaces and their potential applications. Of potential technological importance and of scientific interest is the physics of metal adsorbed Si(111) and Si(001) surfaces. While the former surface structures have been widely investigated [1–12], studies of the latter have been inconclusive yet. However, although the adsorption of alkali metals (AMs) on Si(001) surfaces has attracted a lot of interest for several years [13–19], alkaline-earth metals (AEMs) have received little attention. The change in the behaviour of Ba atoms on the Si(001) surface has been experimentally studied, using Auger electron spectroscopy (AES) and low-energy electron diffraction (LEED), as a function of the substrate temperature and Ba coverage [20,21]. Urano et al. [21] have reported that, with less than a monolayer (ML), Ba induces (2 × 1), (2 × 3), and (2 × 4) reconstructions on Si(001). Kim et al. [22] have reported that the adsorption of Ba on the Si(001)(2 × 1) surface at about 870 °C leads to two well-ordered phases, (2 × 3) and (2 × 1), both of which have semiconducting nature. Similar reconstructions, (2 × 2) and (2 × 3) have been also reported for the adsorption of Mg atoms on the Si(001) surface using scanning tunnelling microscopy (STM) [23–25]. Kawashima et al. [24] have presented LEED and AES

⁎ Corresponding author. E-mail address: [email protected] (A.Z. AlZahrani). 0039-6028/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2010.10.006

results for the surface structures of the Mg/Si(001) system during the process of thermal desorption. They have observed that as the Mg coverage decreases different structural phases appeared in the order (1 × 1), (2 × 3), (2 × 2) and another (2 × 3) which correspond to the Mg coverages of 1, 1/3, 1/4, and 1/6 ML, respectively. Hutchison et al. [25] have discussed three different adsorption geometries for Mg in its low-coverage regime using data obtained by STM. They have found that the most preferable geometry consists of a single Mg atom adsorbed on a cave site. Shaltaf et al. [26] have performed firstprinciples calculations for the adsorption of Mg on the Si(001) surface with different Mg coverages. They concluded that for both 1/4 and 1/ 2 ML coverages the most favorable site for the Mg adsorption is the cave site between two Si–Si dimers. They also determined that preferable configurations for 1/4 ML coverage is a (2 × 2) reconstruction while the (2 × 1) reconstruction corresponds to the 1/2 ML. The adsorption of Sr atoms on the Si(001) surface has also been studied using the ultra-high vacuum STM, LEED, and AES [27]. In their study, Bakhtizin et al. [27] have proposed a structural model of (2 × 3) with Sr coverage of 1/3 ML. Moreover, it has been reported [28] that at low Sr coverages, (1 × 2) and (1 × 5) reconstructions will be also induced whereas (1 × 3) appears when Sr coverage reaches 1 ML. However, among various AEM adsorbates on Si(001), Ca has received much less work. Very recently, Cui and Nogami [29] have experimentally studied the growth of Ca atoms on the Si(001) surface using the STM and LEED techniques. It is well known that the roomtemperature reconstruction of Si(001) is (2 × 1) structure. Cui and Nogami first heated the Si(001)(2 × 1) up to 1150 °C to remove the oxide layer, then annealed at 950 °C, and then reduced the temperature to the range 500–800 °C for deposition of Ca. Depending

A.Z. AlZahrani, G.P. Srivastava / Surface Science 605 (2011) 101–106

upon Ca coverages and growth temperatures, different reconstructions of the surface are observed. These reconstructions are results of interaction between Ca adatoms and the surface atoms. It has been reported that a coverage of 0.15 ML of Ca atoms induces (2 × n) phases of surface reconstruction with (n = 3, 4, 5). Increasing the coverage to 0.65 ML results in a (2 × 6) phase. However, a (1 × 3) phase has also been observed at approximately 1 ML coverage of the metallic element. The STM images of these structures are found to be highly bias dependent and thus no firm atomic models have been assigned. To the best of our knowledge, there is no theoretical investigation of the Ca/Si(001) system. Consideration of highly complex interactions between the adsorbate Ca atoms and the Si(001) atoms is beyond the scope of most present-day theoretical investigations. In this paper, we present results of first-principles calculations, based on the planewave pseudopotential method and the density functional scheme, of the atomic geometry and electronic properties of the most stable low-coverage Ca-adsorbed (2 × n) reconstructions on Si(001). We further discuss the relative stabilities of these reconstructions as a function of the Ca coverage. 2. Computational method Our calculations were performed in the framework of the density functional theory [30] within the local density approximation (LDA) using the Ceperley–Alder correlation [31] as parametrised by Perdew and Zunger [32]. Electron–ion interactions were treated by using norm-conserving, ab initio, fully separable pseudopotentials [33,34] in the framework of Bachelet, Hamann and Schlüter scheme [35]. The single-particle Kohn-Sham [36] wave functions were expanded in a plane wave basis set with a kinetic energy cutoff of 12 Ryd. Surface calculations were performed by adopting the repeated slab method [37], with a supercell containing 10 silicon layers, the Ca adatom layer, and a vacuum region equivalent to 4.0 times the bulk lattice constant. Each Si atom at the back surface is saturated with two hydrogen atoms. Throughout the surface calculations we have used our theoretical equilibrium lattice constant for the bulk Si of 5.43 Å. The equilibrium atomic positions were determined by relaxing all atoms except the bottom layer of Si atoms which was kept fixed. The Hellmann–Feynman forces on ions were calculated and minimised to obtain the relaxed atomic geometry. Atoms were relaxed until forces converged to within 5 meV/Å. The electronic charge density was calculated by using a n × 2 × 1 k-points Monkhorst–Pack set [38] for all (2 × n) reconstructions. Calculation of energy barriers and reaction paths will involve a great deal of computational work, and is beyond the resources available to us. The main focus of our paper is the investigation of relative stabilities of the various reconstructions for different Ca coverages, the corresponding equilibrium atomic geometries and electronic states, with a view to supporting experimental STM observations. 3. Results and discussion On the basis of STM observations obtained in Ref. [29] we have studied the adsorption of Ca atoms on the Si(001) surface for the low coverages of 0.25, 0.34, 0.375, and 0.4 ML. These coverages correspond to (2 × 2), (2 × 3), (2 × 4), and (2 × 5) reconstructions, respectively. In all these models, the asymmetric first-layer Si dimers are characteristic of the clean Si (001)(2 × 1) surface and the Si substrate (subsurface layer) has the bulk-terminated structure. For each reconstruction we have chosen various adsorption sites resulting in 20 different structures divided into three main categories. In one of these categories, the Ca atoms are located just above the Si–Si dimers. In the other two categories, the Ca atoms are located between two adjacent Si–Si dimers, forming either bridge and/or valley cave sites. Our total energy calculations indicate that, for all of these reconstructions, the

bridge site represents the preferable adsorption site for Ca atoms on the Si(001) surface. A similar conclusion was reached in Ref. [39] for the adsorption of Yb on Si(001). Figure 1 shows the change of the energy as the system evolves from (2 × 2) to (2 × 5) as compared with the 0.5 ML coverage forming the Ca/Si(001)(2 × 1) structure. The reference structure (Ca/Si(001)(2 × 1)) is not considered as a genuine phase, but is used for comparing the relative stabilities of the various structures considered in this work. In order to compare the total energies of the various reconstructions containing different numbers of Ca atoms, we calculated the total energy of an isolated Ca atom in a unit cell equivalent to each reconstructed (2 × n) unit cell. In order to explain our procedure let us consider the (2 × 4) reconstruction with three Ca adatoms within a unit cell. We consider another unit cell which is four times expansion of the (2 × 1) cell, thus containing four Ca atoms. These two versions of the (2 × 4) unit cells are obviously non-stoichiometric with respect to Ca coverage. The energy gain of Ca/Si(001)(2 × 4) reconstruction is, thus, calculated as: Energy gain = Total energy of expanded ð2 × 4Þ cell −total energy of the original ð2 × 4Þ cell −total energy of an isolated Ca atom:

Similar considerations are made for other reconstructions. A slightly different version of this procedure will be employed in the discussion of the relative stabilities of the various reconstructions, with different Ca coverages, in another section later on. Using our procedure we find that the (2 × 4) structure is the most stable. However, the (2 × 3) and (2 × 5) structures are only slightly less stable than the (2 × 4) structure, by approximately 0.05 eV/(1 × 1) and 0.1 eV/(1 × 1), respectively. The closeness in the energy stabilities of the (2 × 3), (2 × 4) and (2 × 5) structures is supportive of the experimental STM images obtained by Cui and Nogami [29]. Indeed, in Ref. [29] the STM images are found to be highly bias dependent, and the empty-state images have been interpreted as a combination of these three structures. Cui and Nogami have also reached a similar conclusion regarding the mixed (2 × n), with n = 3–5, from an analysis of the filled-state STM images in the Ca coverage range 1/6 to 1/5 ML. We believe that a comparison of theoretically calculated and experimentally measured (from angle-resolved photoemission experiments) occupied-state dispersion curves would provide additional, and valuable, input in establishing the exact identity of the equilibrium (2 × n) structure.

0.4

Energy gain, eV/(1x1)

102

0.25 ML

0.3

0.40 ML

0.2 0.34 ML

0.1

0

0.375 ML

0.50 ML

1

2

3

4

5

Ca/Si(001)-(2xn) reconstructions Fig. 1. Surface formation energy per (1 × 1) unit cell corresponding to different Ca/Si (001)(2 × n) reconstructions. The energy gain is calculated with respect to Ca/Si(001) (2 × 1) surface with Ca coverage of 0.5 ML.

A.Z. AlZahrani, G.P. Srivastava / Surface Science 605 (2011) 101–106

3.1. Structural properties Figure 2 shows a top and side view of the optimized geometry for the Ca/Si(001)(2 × 4) structure. We have two classes of Si–Si dimers: inner and outer. The inner Si–Si dimer retains the symmetric feature while the outer is asymmetric. The bond lengths of the inner and outer dimers are approximately 2.47 and 2.37 Å, respectively. The calculated inner and outer bond lengths are larger than that obtained for the clean Si(001) surface of 2.34 Å. However, it is clearly noticed that the bond length of the inner Si–Si dimer is much larger than that of the outer Si–Si dimer, suggesting that the inner dimer is weaker than the outer dimer. These changes in the Si–Si dimers are also observed in the case of the adsorption of Yb on the Si(001) surface [39]. The amount of tilt (0.11 Å) in the outer dimer is significantly reduced compared to that on the clean Si(001)(2× 1) surface. It is found that the average Ca–Si distance is 3.20 Å, which is much larger than the sum of their atomic radii, indicating that Ca atoms do not form a strong bond with the Si atoms. Moreover, Ca atoms are found to locate at approximately 2.16 Å above the uppermost surface layer, and the Si–Ca–Si bond angle is about 77.7°. These findings are quite similar to our previous results of Ca adsorption on the Si(111) surface [12]. Furthermore, the lateral distance between neighbouring Ca atoms along the metal row is found to be 3.9 Å which is quite larger than the double of its covalent radius (1.74 Å), suggesting very weak adatom–adatom interaction. The Si–Si back bonds have length 2.34 Å, equivalent to the bulk bond length. These parameters along with other reconstruction parameters are summarized in Table 1.

103

Table 1 The total energies of the studied reconstructions with respect to the 0.5 ML: Ca/Si(001) (2 × 1). The bond lengths are measured in Angstroms (Å). Configuration

(2 × 1)

(2 × 2)

(2 × 3)

(2 × 4)

(2 × 5)

Total energy (eV/1 × 1) (Si–Si)outer dimer (Si–Si)inner dimer (Si–Si)back bond (Ca–Si)average

0.0 2.45 2.45 2.37 3.20

0.30 2.36 2.36 2.34 3.20

0.15 2.36 2.52 2.34 3.20

0.10 2.37 2.47 2.34 3.20

0.20 2.35 2.50 2.35 3.20

and becomes less dispersive along the ΓJ′ (normal to the Si–Si dimers) direction. It is clearly noted that this state is located close to the Fermi level at one edge (J) of the Brillouin zone and lies at approximately 0.2 eV below the Fermi level at the other edge (J′) of the Brillouin zone. The LUMO state, on the other hand, is quite flat along both directions. An inspection of the orbital nature of the HOMO and LUMO has been performed by examining the partial charge density at the Γ point. Figure 4(a) shows that the HOMO state is derived from the πlike orbital at the inner Si–Si dimers. The LUMO state, shown in Fig. 4(b), originates from the π* (antibonding) orbital on the outer Si–Si dimers. The lower panel of Fig. 3 compares the density of states for the Ca/Si (001)(2 × 4) surface with the clean Si(001)(2× 1) surface. From this we observe that the effect of the Ca adsorbate is to develop a shoulder at around EF − 0.75 eV and to reduce the small peak at around EF − 4 eV. The adsorbate covered surface is characterised by a clear peak at around EF + 0.5 eV, a shoulder at around EF + 2.5 eV, and a small peak at around J’

3.2. Electronic properties

Γ

J

2 1.5 1

Energy (eV)

The electronic surface band structure, along the high-symmetry directions, for the Ca/Si(001)(2 × 4) configuration is shown in the upper panel of Fig. 3. It is clearly shown that the highest occupied molecular orbital (HOMO) occurs at the J point of the surface Brillouin zone whereas the lowest unoccupied molecular orbital (LUMO) occurs at the Γ point, suggesting an indirect band gap of approximately 0.1 eV. Furthermore, the calculations reveal that the configuration has a semiconducting surface with a direct LDA band gap of 0.25 eV which is slightly smaller than the band gap of the clean Si (001)(2 × 1) surface. We have also found that the HOMO state shows much dispersion along the ΓJ (parallel to the Si–Si dimers) direction

0.5 EF −0.5 −1 −1.5 −2

2.47

2.37

2.37

2.47 3.2

125

2.14

2.16

2.34

(b)

DOS (arb. unit)

0.11

J’

150

(a)

2.16

Γ

J

Clean surface Ca adsorbed (2x4) surface

100 75 50 25

Ca atoms Surface Si atoms Sub−surface Si atoms Fig. 2. (a) Top and (b) side views of the optimized structure of the Ca/Si(001)(2 × 4) surface with the key structural parameters in Å.

0 −12−11−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 EF 1

2

3

4

5

Energy (eV) Fig. 3. (Upper panel) Surface electronic band structure, along the high-symmetry directions, of the Ca/Si(001)(2 × 4) reconstruction. The surface Brillouin zone is indicated. (Lower panel) Electronic density of states (DOS) for the (2 × 4) surface and the clean Si(001)(2 × 1) surface.

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(a)

(a) Charge density (e/a.u3)

0.08

Inner Si−Si dimer Outer Si−Si dimer

0.06

0.04

0.02 Si

Distance along the (outer) inner Si−Si dimer

(Si) Si

0.06

(b) (b)

Charge density (e/a.u3)

0.05 0.04 0.03 0.02 0.01 0 Si

Distance along the Ca−Si bond

Ca

Fig. 5. Total charge density for the Ca/Si(001)(2 × 4) reconstruction along (a) an inner and an outer Si–Si dimer and (b) the Ca–Si bond. The inset shows the distribution of the total charge density in a horizontal plane containing the Ca adatom, an inner Si dimer, and an outer Si–Si dimer. Fig. 4. Partial charge density of the (a) HOMO and (b) LUMO at the zone centre, Γ point. The plots in (a) and (b) are in vertical planes containing a symmetric inner Si–Si dimer and a tilted outer Si–Si dimer, respectively.

EF + 4.5 eV. These results are due to the fact that the adsorbed Ca atoms interact with the surface and partially saturate the dangling bonds of the surface Si dimer atoms, as explained later. The interaction between Ca atoms and Si surface atoms is mainly due to the bonding of Ca 4 s and 3p states of the Si dimer atoms. The peak at EF + 0.5 eV is mainly contributed by Si 3p and Ca 4 s states. We hasten to mention that the peak positions above EF are subject to an appropriate shift relevant to band gap corrections required for the DFT results presented in this work. In Fig. 5(a), we have shown the total charge density along inner and outer Si–Si dimers. The adsorption of Ca atoms has weakened the inner Si–Si dimer, the maximum charge density in which is quite smaller than the outer Si–Si dimer. To determine the nature of the Si–Ca bonding, we have also plotted the total charge density along a line joining one Ca atom with a surface Si atom. Figure 5(b) shows that the charge is entirely localised around the Si site, suggesting that the Si–Ca bond has a large amount of ionic character. For more clarity, we have shown in the inset a contour map of the total charge density on a horizontal plane containing a Ca adatom, an inner S–Si dimer, and outer Si–Si dimers. From this plot we clearly observe charge accumulation around the Si surface atoms and a significant amount of charge loss around the Ca adatom. These observations imply, in direct support of the line charge plots, that the Si–Si and Si–Ca bonds have, respectively, covalent and largely ionic characters.

Following the Tersoff–Hamann scheme [40], we further examine our simulated STM image in the constant-height mode. In this scheme the tunnelling current is derived from the local density of states close to the Fermi energy EF, i.e. an integrated local density of states from EF to EF + VB, where VB is the bias voltage. In our simulation we considered ±2.0 eV for the bias voltage VB. Both the filled and empty images shown in Fig. 6 are plotted at the horizontal plane just above the Ca atoms on the relaxed surface. The filled-state image, panel (a), shows brighter protrusions around both components of the symmetric inner Si–Si dimers. This is due to the significantly large electronic charge transfer from the Ca 4 s orbitals to the Si atoms which turns the inner dimers symmetric. We note that the huge amount of charge transfer from Ca atoms to neighbouring Si atoms is also observed in the case of Ca adsorption on the Si(111) surface [12]. Less bright protrusions are also observed at the asymmetric outer Si–Si dimers. These features are consistent with the experimental STM images for the filled states obtained by Cui and Nogami [29] for very low Ca coverages which show that the reconstructed areas have rows of protrusions running parallel to adjacent Si dimer rows with different concentrations between the inner and outer dimers. Panel (b), showing the empty-state image, indicates that the lower components of the outer Si–Si dimers have much brighter protrusions. This means that not all of the dangling bonds of the outer Si–Si dimers are fully saturated by the valence electrons transferred from the Ca atoms. This can be appreciated from the following simple-minded picture. The three Ca atoms can donate six 4 s electrons to the (2 × 4) surface atoms. Since this surface unit cell contains eight first-layer Si atoms (all with dangling bonds in the asymmetric dimer configuration), it is obvious that all these dangling bonds cannot be completely saturated

A.Z. AlZahrani, G.P. Srivastava / Surface Science 605 (2011) 101–106

(a)

105

(b) 0.00000 0.00039 0.00078 0.00117 0.00156 0.00194 0.00233 0.00272 0.00311 0.00350 0.00389 0.00428 0.00467 0.00506 0.00544 0.00583 0.00622 0.00661 0.00700 0.00740

Fig. 6. Simulated STM images of the (a) filled and (b) empty states of the Ca/Si(001)(2 × 4) reconstruction with voltage bias of ±2.0 eV with respect to the Fermi level. Black circles indicate the sites of the Ca adatoms. The scale of charge density, measured in 103 e/a.u3, is shown on the right hand side.

by the Ca adsorption on the (2 × 4) structure. However, these Ca atoms donate four 4 s electrons to the inner Si dimers (two electrons to both) and two 4 s electrons to the outer Si dimers (one electron to both), as is clearly seen from Fig. 2(a).

difference between the (2 × 3), (2 × 4) and (2 × 5) structures is also consistent with the analysis of STM images presented by Cui and Nogami [29], in that these three structures are likely to be coexistence in the low Ca coverage regime.

3.3. Relative stabilities of reconstructions 4. Summary and conclusion

ΔEn = En −Eref −ΔNCa ðμCa bulk −μCa Þ = Eð2 × nÞ−nEð2 × 1Þ−ΔNCa ðμCa bulk −ΔμCa Þ;

ð1Þ

where En is the total energy of the (2 × n) reconstruction, Eref is taken as the total energy of the Ca/Si(001)–(2 × 1) surface, and μCa bulk is taken as the total energy of bulk fcc Ca crystal. In our study we have aimed to investigate the properties of Cainduced Si(100) structures in a low-coverage limit (i.e. less than or equal 0.4 ML). Therefore Ca/Si(100)(2 × 1) with 0.5 ML coverage is out of our coverage limit. However, as seen both in Figs. 1 and 7, (2 × 1) represents a stable structure for Ca/Si(100) but at a Ca coverage larger than our target coverage limit. This has been a good reason for us to consider the (2 × 1) as a reference structure to compare the relative stabilities of the reconstructions studied here. Figure 7 shows the results for the surface energy per (1 × 1) unit cell as a function of the physically meaningful range of the Ca chemical potential ΔμCa. For the Ca-rich region, (2 × 2) reconstruction represents the energetically most favorable structure for the Ca/Si(001) surface. For medium-rich Ca, both (2 × 2) and (2 × 5) reconstructions are likely to represent the stable configurations, with a slight preference for the (2 × 4) phase. In Ca very-poor condition, (2 × 4) is the most stable structure among the others. These results thus indicate that the (2 × 4) structure is the overall stable structure for the Ca/Si(001) surface in the low-coverage regime. The low-energy

In this work, we have presented an ab initio study of the structural and electronic properties of the low-coverage Ca-induced Si(001) surface. Our calculations suggest that the (2 × 2) and (2 × 4) are the energetically most preferable structure for Ca/Si(001) in the Ca highand low-coverage limits, respectively. Using the chemical potential analysis, we have concluded that (2 × 3), (2 × 4) and (2 × 5) structures are likely to be co-existent, supporting the analysis of the STM images obtained by Cui and Nogami [29].

0.2

Surface energy, (eV)

We have examined the relative thermodynamic stability for these reconstructions as a function of chemical potential. Since the Ca coverage is not the same for these reconstructions, the surface formation energy of a (2 × n) reconstruction can be written as

2x1 2x2 2x3 2x4 2x5

0.1

0

-0.1

-0.2 -1

-0.75

-0.5

-0.25

0

0.25

0.5

Chemical Potential of Ca, (eV) Fig. 7. The surface formation energy of the studied reconstructions per (1 × 1) unit cell as a function of the Ca chemical potential.

106

A.Z. AlZahrani, G.P. Srivastava / Surface Science 605 (2011) 101–106

Our relaxed geometry of the Ca/Si(001)(2 × 4) surface indicates two types of Si–Si dimers; inner and outer. It is found that the inner dimers are symmetric with bond lengths larger than the asymmetric outer dimers. The surface electronic band structure indicates that the system is semiconducting with a direct LDA band gap of 0.25 eV which is much smaller than the bulk Si band gap. Similar to Ca/Si(111), Ca atoms transfer a significant amount of their charges to the neighbouring Si atoms, inferring that the Ca–Si bond is of ionic type. Our simulated STM for the filled (empty) states show that the bright protrusions are mainly due to the inner Si–Si (the lower components of the outer Si–Si) dimers. The HOMO and LUMO states are found to originate from the symmetric inner and asymmetric outer Si–Si dimers, respectively. Acknowledgement The calculations reported here were performed using the University of Exeter's SGI Altix ICE 8200 supercomputer. Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10.1016/j.susc.2010.10.006. References [1] J.D. O'Mahony, J.F. McGilp, C.F.J. Flipse, P. Weightman, F.M. Leibsle, Phys. Rev. B 49 (1994) 2527. [2] S. Hasegawa, M. Maruyama, Y. Hirata, D. Abe, H. Nakashima, Surf. Sci. 405 (1998) L503. [3] A.A. Saranin, V.G. Lifshits, K.V. Ignatovich, H. Bethge, R. Kayser, H. Goldbach, A. Klust, J. Wollschläger, M. Henzler, Surf. Sci. 448 (2000) 87. [4] A. Baski, S. Erwin, M. Turner, K. Tones, J. Dickinson, J. Carlisle, Surf. Sci. 476 (2001) 22. [5] T. Sekiguchi, F. Shimokoshi, T. Nagao, S. Hasegawa, Surf. Sci. 493 (2001) 148.

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