Atomic and electronic structure of the Si(0 0 1)2 1 K surface

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1 Surface Science 561 (2004) Atomic and electronic structure of the Si(0 0 1)2 1 K surface H.Q. Shi, M.W. Radny, P.V. Smith * School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, 2308 Australia Received 13 January 2004; accepted for publication 11 May 2004 Available online 5 June 2004 Abstract The plane-wave pseudopotential density functional theory method has been used to study the Si(0 0 1)2 1 K adsorption system for 0.5 and 1.0 monolayer coverage. The minimum energy atomic configuration for 0.5 monolayer coverage was found to correspond to the potassium atom in each 2 1 surface unit cell occupying the valley bridge site. A double-layer model was determined to be the optimised geometry of the Si(0 0 1)2 1 K chemisorption system for 1.0 monolayer coverage. The geometry of this double-layer model was found to be in good agreement with the current experimental data. A detailed analysis of the electronic structure of this double-layer model has also been performed. The overall dispersion of the occupied and unoccupied surface state bands has been shown to be in excellent agreement with the angle-resolved and inverse photoemission data. The nature and dispersion of the surface states of the doublelayer model in the vicinity of the energy gap provide evidence of strong interactions, both between the two inequivalent potassium atoms in each 2 1 surface unit cell, and between these adatoms and the underlying substrate. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Silicon; Alkali metals; Chemisorption; Density functional calculations; Surface structure, morphology, roughness, and topography; Surface electronic phenomena (work function, surface potential, surface states, etc.) 1. Introduction In the last few years there has been a rapid increase in our ability to engineer structures with reduced dimensionality on an atomic scale. This has led to the investigation of real systems that approximate idealised systems such as onedimensional (1D) quantum wells or two-dimensional (2D) atomic layers. Systems resulting from the chemisorption of alkali elements on metallic * Corresponding author. Tel.: ; fax: address: phpvs@alinga.newcastle.edu.au (P.V. Smith). and/or semiconducting surfaces are some of the candidates that are now being seriously considered in this context [1]. In this paper we report theoretical calculations of the atomic and electronic structure which results from the formation of 2D arrays of potassium atoms on the Si(0 0 1)2 1 surface. The chemisorption of alkali elements, and especially potassium (K), on metallic and semiconducting surfaces has attracted a great deal of attention [2 22]. The generally preferred model for K adsorption on the Si(0 0 1)2 1 surface at 0.5 monolayer (ML) coverage was the Levine model which had been originally proposed for Cs in 1973 [2 4]. In this model, the adatoms were assumed to chemisorb at the pedestal sites along the hills of /$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi: /j.susc

2 216 H.Q. Shi et al. / Surface Science 561 (2004) Fig. 1. Top and side views of the DL model of the Si(0 0 1)2 1 K chemisorption system for 1.0 ML coverage. The 2 1 surface unit cell is indicated by the dashed lines. The pedestal site A, bridge site B, valley bridge site C, cave site D, and dangling bond sites E and F, are indicated. the dimer rows (the A site in Fig. 1). Some experiments, however, suggested other sites. These included the cave site D [7], and the dangling bond sites E and F [8]. Morikawa et al. [9] and Kobayashi et al. [18], using a first-principles molecular-dynamics method [10], proposed that the valley bridge site C is the most stable site for the Si(0 0 l)2 1 K chemisorption system at 0.5 ML. A first-principles total-energy cluster calculation based on density functional theory (DFT) performed by Ye et al. [11], and a self-consistentfield Hartree Fock (SCF-HF) intermediate neglect of differential overlap (INDO) slab calculation by Ramirez [12], on the other hand, indicated the cave site D as the most stable site. For the saturation coverage of 1.0 ML, Abukawa and Kono [13] proposed, based on X-ray photoelectron diffraction (XPD) patterns, a double-layer (DL) model in which the potassium atoms sit at each pedestal site A and each valley bridge site C. This model was supported by thermal-desorption [14], reflection high-energy electron-diffraction (RHEED) [15], ion scattering [16], and synchrotron radiation angle-resolved photoelectron spectroscopy (SR-ARPES) [17] experiments. Total energy calculations by Kobayashi et al. [18] and Morikawa et al. [9,19] also supported the DL model. Despite all of this theoretical and experimental work, however, some of the features of the surface electronic structure induced by this double-layer of K adatoms on the Si(0 0 1)2 1 surface still remain unresolved. The valence band electronic structure for the DL model determined by Kobayashi et al. [18], Morikawa et al. [19], Ishida and Terakura [20] and Kr uger and Pollmann [21] has been shown to be in good agreement with the experimental data. The inverse photoemission data for the unoccupied electronic surface states obtained by Johansson and Reihl [22], however, reveals some interesting and somewhat surprising features. The lowest unoccupied surface state band in the C J 0 direction of the surface Brillouin zone (SBZ) (parallel to the dimer rows) exhibits a paraboliclike dispersion. This was attributed by Johansson and Reihl to a metallic overlayer behaviour of the K atoms on the Si(0 0 1)2 1 surface in this direction. The dispersion of the empty surface state bands in the C J direction (perpendicular to the dimer rows) is also parabolic, but shows a continuation of this free-electron like dispersion into the second surface Brillouin zone with negligible energy gap at the SBZ boundary. This indicates that the dispersion of the empty surface states in the C J direction may not follow the 2 1 periodicity of the Si(0 0 1) substrate. One possible

3 H.Q. Shi et al. / Surface Science 561 (2004) explanation for this unexpected behaviour, suggested by Johansson and Reihl [22], is that the chemisorbed K atoms form an overlayer with an essentially 1 1 periodicity. In this paper we report the results of accurate first principles DFT calculations of the atomic and electronic structure of the Si(0 0 1)2 1 K chemisorption system at 0.5 and 1.0 ML coverage. These results predict C site chemisorption for 0.5 ML coverage, and a double-layer model configuration involving both A and C site chemisorption for 1.0 ML coverage. The calculated electronic structure, and associated surface states, for the DL model are shown to be in excellent agreement with the current experimental data. Detailed analysis of this surface electronic structure shows that there is significant interaction between the Si substrate and the K overlayer, and between the K adatoms within the overlayer, and leads to a new understanding and reinterpretation of the nature of the electronic states of this DL chemisorption system in the vicinity of the Fermi energy. 2. Method and procedure All of the calculations have been carried out using the ab initio total energy and molecular dynamics program VASP [23 25]. This program is based on the density functional theory method and employs a plane wave basis set and periodic unit cells. The local density approximation (LDA) has been used for exchange and correlation and ultrasoft Vanderbilt pseudopotentials employed to represent the silicon, potassium and hydrogen atoms. The Kohn Sham equations were solved using plane waves with kinetic energies up to 12 Ry and 4 special k points in the irreducible part of the SBZ of the Si(0 0 1)2 1 cell. To represent the surface we have used a periodic slab model. Two separate slabs were employed in the calculations. One slab consisted of 8 silicon layers with hydrogen atoms below the bottom silicon atoms to saturate the bulk dangling bonds. In this case, the optimised geometries were determined by allowing all of the atoms in the top four layers, plus the chemisorbed potassium atoms, to relax. The second slab was comprised of 10 silicon layers with potassium atoms on both surfaces. Optimisation calculations for this slab were performed with only the two middle layers kept fixed. In each case, the lowest energy structure was found by minimising the forces using the Hellmann Feynman theorem, and a sufficient vacuum region was employed to ensure that no interactions occurred between the top and bottom surfaces. The surface geometries obtained from these two slabs were virtually identical to one another. The electronic surface states were identified by calculating the function q nk ðzþ. This latter quantity is defined by Z q nk ðzþ ¼ jw nk ðx; y; zþj 2 dxdy; SUC where x and y lie in the surface plane, z is out of the surface, and the integration is performed over the surface unit cell (SUC). This function gives the z dependence of the modulus of the wave function squared averaged over the SUC. States for which the envelope of the q nk ðzþ function exhibited clear exponential decay into the bulk were taken to be surface states. 3. Results 3.1. Atomic structure Initial calculations were performed for the Si(0 0 1)2 1 K chemisorption system at 0.5 ML coverage (i.e. one potassium atom per 2 1 SUC). The optimised geometries corresponding to the chemisorption of the potassium at the A, B, C, D, E and F sites were determined using the VASP plane-wave pseudopotential DFT code. We found the most energetically favourable site is the C (valley-bridge) site, in agreement with the firstprinciples calculations of Morikawa et al. [9] and Kobayashi et al. [18]. Lindsay et al. [8] found that the best fit to their SEXAFS data at 0.5 ML coverage resulted from the potassium atoms occupying the E or F dangling bond sites. Our calculations, however, have found these two sites to be unstable at 0.5 ML coverage. Starting the calculations with the potassium atoms positioned at the E sites resulted in the adsorbate atoms

4 218 H.Q. Shi et al. / Surface Science 561 (2004) Table 1 Energies of the Si(0 0 1)2 1 K system at 0.5 ML coverage corresponding to chemisorption at the A, B, C and D sites Site Energy (ev) A 0.35 B 0.91 C 0.00 D 0.40 The energies are per 2 1 SUC and are defined relative to that for C site chemisorption. moving to the C sites, while positioning the potassium atoms at the F sites, resulted in them moving to the D sites. The relative energies of the A, B, C and D site optimised geometries are presented in Table 1. We observe that the total energy for Levine s model (A site) is predicted by our calculations to be 0.35 ev per 2 1 SUC higher than that corresponding to C site chemisorption. The B site and D site configurations are even less energetically favourable with energies that are 0.91 and 0.40 ev higher, respectively, than that for the energetically favourable C site. The Si Si dimers of our C site 0.5 ML minimum energy configuration were found to be completely symmetrical with a bond length of 2.40 A. This is in good agreement with the calculations of Morikawa et al. [9] who found the Si Si dimers to have 1.9 buckle, and a bond length of 2.39 A. The Si K bond length for our optimised C site geometry was 3.46 A. This is smaller than the values of 3.53 and 3.60 A predicted by Morikawa et al. [9], but larger than the values of A that have been determined for the Si K bond length of the Si(0 0 1)2 1 K system at 0.5 ML coverage from EXAFS measurements [8,26,27]. Geometry optimization calculations were also performed for the Si(0 0 1)2 1 K chemisorption system at 1.0 ML coverage. The DL model structure, in which the two potassium atoms in each SUC sit at the pedestal and valley bridge sites, was found to be the most stable (see Fig. 1). This is consistent with the XPD results of Abukawa and Kono [13], and the theoretical calculations of Morikawa et al. [9], both of which supported the DL model based on the potassium atoms occupying the pedestal and valley bridge sites at 1.0 ML coverage. The calculated atomic relaxations and bond lengths of the various atoms of interest are presented in Table 2. The geometry predicted by our VASP calculations for the DL model is seen to be in very good agreement with the RHEED Table 2 Optimised geometry of the Si(0 0 1)2 1 K chemisorption system obtained from the VASP calculations at 1.0 ML coverage, compared with experiment and other theoretical calculations Geometry Present calculation Experiment Theory [15] [13] [9] z KðAÞ ± * z KðCÞ ± * z ± * z ± * z KðAÞ z KðCÞ ± ± z KðAÞ z ± z KðCÞ z ± Dz 1 )0.08 )0.2 )0.01 Dz 2 ) z Sið3aÞ z Sið3bÞ z Sið4aÞ z Sið4bÞ d Sið1aÞ d Sið1bÞ * d KðAÞ d Sið1aÞ * d KðCÞ d Sið1aÞ * The labelling is the same as in Fig. 1. The asterisks denote values calculated from the data of Morikawa et al. [9]. The z denote values normal to the surface, relative to the (invariant) fifth silicon layer. The Dz represent the vertical displacements with respect to the ideal bulk silicon layers, and the d denote the various bond lengths of interest. All of the values are given in Angstroms.

5 H.Q. Shi et al. / Surface Science 561 (2004) and XPD data (see Table 2). The vertical distance between the two potassium atoms in each 2 1 SUC, z KðAÞ z KðCÞ, is predicted by our calculations to be 1.11 A. This is in excellent agreement with the RHEED and XPD values of 1.25 ± 0.10 and 1.1 ± 0.1 A, respectively, and the first-principles molecular dynamics result of Morikawa et al. of 1.11 A [9]. Generally, our calculated results are closer to the experimental measurements than those of Morikawa et al. This includes the vertical distances between the upper and lower potassium atoms and the fifth silicon layer, z KðAÞ and z KðCÞ, the vertical distance between the first silicon layer and the fifth silicon layer, z 1, and the vertical distances between the upper and lower potassium atoms and the first silicon layer, z KðAÞ z 1 and z KðCÞ z 1. The Si Si dimer was predicted by our calculation to be completely symmetrical. This is in agreement with the experimental RHEED results [15], as well as with the theoretical predictions of Morikawa et al. [9] and Kr uger and Pollmann [21]. Our calculated dimer length of 2.51 A is very similar to the values of 2.54 and 2.56 A determined by Morikawa et al. [19] and Kr uger and Pollmann [21], respectively. Our theoretically predicted relaxation of the first layer (dimer) silicon atoms of )0.08 A is somewhat smaller than the RHEED result of )0.2 A, but larger than the value of )0.01 A obtained by Morikawa et al. [9]. Our calculated bond length between the upper potassium atom (at the A site) and its nearest neighbour silicon atoms is 3.18 A, and the calculated bond length between the lower potassium atom (at the C site) and its nearest neighbour silicon atoms is 3.38 A. To our knowledge, an experimental measurement of the K Si bond lengths for the Si(0 0 1)2 1 K DL model has not yet been made. Our calculated Si K bond lengths seem reasonable, however, as they fall mid-way between the larger values of 3.36 and 3.47 A derived from the calculations of Morikawa et al. [9], and the considerably smaller values of 3.08 and 3.01 A obtained by Kr uger and Pollmann [21] Electronic structure Electronic structure calculations have been carried out for our minimum energy Si(0 0 1)2 1 K DL model structure at 1.0 ML coverage. The resulting eigen-energies in the vicinity of the energy gap have been determined for 120 k-points along the C J K J 0 C symmetry directions of the SBZ. The corresponding energy bands are plotted in Fig. 2a. In order to identify the electronic surface states, the function q nk ðzþ has been calculated at 30 k-points along these symmetry directions for all of the bands within a few electron volts (ev) of the Fermi energy. The identified surface states are (a) (b) S 1 S 2 S' 1 Fig. 2. The electronic structure for the DL model of the Si(0 0 1)2 1 K chemisorption system at 1.0 ML coverage. (a) The empty ellipses represent the surface states determined from the VASP calculations. The grey shaded lines (green shaded lines in the online colour figure) indicate the occupied surface state bands determined by Abukawa et al. [17], and the filled ellipses and rectangles indicate the unoccupied surface states obtained by Johansson and Reihl [22]. The labelling of the occupied surface states as S 1,S 0 1 and S 2 is that of Abukawa et al. [17]. (b) The character of the different surface states as indicated by the different symbols (see text). E F E F

6 220 H.Q. Shi et al. / Surface Science 561 (2004) indicated by the empty symbols in Fig. 2a. The SR-ARPES data for the occupied surface states obtained by Abukawa et al. [17] and the IPES data for the unoccupied surface states obtained by Johansson and Reihl [22] for the Si(0 0 1)2 1 K system at 1.0 ML coverage in the vicinity of the Fermi energy are also indicated in Fig. 2a. This data is indicated by the grey shaded lines (green shaded lines in the online colour figure) (occupied states) and filled ellipses and rectangles (unoccupied states), with these latter symbols representing strong and weak peaks, respectively. The ARPES data [17] has been shifted down by 0.16 ev relative to the Fermi energy to match the values predicted by the VASP calculations close to the C point. The IPES data has been left unchanged in Fig. 2a. No experimental data is available for the unoccupied surface states for the J K and K J 0 symmetry directions. As can be seen from Fig. 2a, the agreement between the theoretical results and the experimental data is very good for both the occupied and unoccupied states. Our calculations accurately reproduce the behaviour of the three occupied surface state bands S 1,S 0 1 and S 2 observed in the SR-ARPES experiments [17]. This includes the splitting of the S 1 and S 0 1 surface state bands along the C J, J K and J 0 C symmetry directions of the SBZ, and the downward dispersion of the S 2 band along the C J 0 symmetric direction. The lowerlying valence band surface states found in the ARPES data are also seen to be predicted by our theoretical calculations. Our calculations predict the S 1 and S 0 1 surface state bands to have a splitting of 0.15 ev at the K point of the SBZ, with these two bands gradually merging along the K J 0 symmetric direction. This is consistent with the calculations of both Morikawa et al. [19] and Kr uger and Pollmann [21]. The experimental SR- ARPES data, however, determined these two bands to be essentially degenerate both at the K point and along the K J 0 symmetric direction [17]. The IPES experiments of Johannson and Reihl [22] have evidenced an unoccupied surface state band that disperses upward along the C J and C J 0 symmetric directions of the SBZ. This surface state band is indicated in Fig. 2a by the filled ellipses. The theoretical calculations are observed to accurately reproduce this unoccupied surface state band with the predicted dispersions being in excellent agreement with the IPES data. The IPES experiments also determined an unoccupied surface state along the C J symmetry direction that dispersed strongly upwards from the J point to the C point. Our theoretical calculations also predict a surface state near the J point with an upward dispersion along the J C symmetry direction. The weak unoccupied surface states determined by the IPES measurements denoted by the filled rectangles in Fig. 2a are not reproduced by the VASP calculations. In order to understand the nature of the occupied and unoccupied surface states of the Si(0 0 1)2 1 K chemisorption system at 1.0 ML coverage, we have calculated the three-dimensional (3D) charge/probability density distributions for all of the theoretically predicted surface states. The varying character of these electronic surface states is indicated by the use of different symbols in Fig. 2b. The occupied electronic surface states denoted by the triangles and squares in Fig. 2b represent the silicon dangling bond surface states. These states correspond to the S 2 and S 1 states of Ishida and Terakura [20], and Morikawa et al. [19] (note this labelling of the states is different to the labelling of Abukawa et al. [17] that is included in Fig. 2a). 3D charge density plots for these surface states at the K point of the SBZ are presented in Fig. 3a and b, together with the corresponding q nk ðzþ. The band denoted by the squares represents the p silicon dangling bond surface state (Fig. 3a), while the band denoted by the triangles corresponds to the p Si dangling bond surface state (Fig. 3b). Analysis of the composition of these occupied p and p molecular orbitals shows contributions from the K atomic orbitals. Such contributions are indeed clearly seen in the 3D charge density plots for the p and p surface states bands at the J point of the SBZ presented in Fig. 3c and d, respectively. It is clear that the molecular orbitals for the states shown in Fig. 3a and c can be regarded as combinations of the p Si dangling bond orbitals and contributions from the lower and upper potassium atoms, respectively. Similarly, the molecular orbitals for the states shown in

7 H.Q. Shi et al. / Surface Science 561 (2004) Fig. 3. Side and top views of the 3D charge density distribution, and the corresponding q nk ðzþ function, for the valence band surface states of the Si(0 0 1)2 1 K system at 1.0 ML coverage indicated in Fig. 2b by the squares (a and c) and triangles (b and d) for the K and J symmetry points of the SBZ, respectively. The charge density isosurface value was e/ A 3 for (a) and (b), and e/ A 3 for (c) and (d). In this figure, and all subsequent figures, the larger and smaller filled circles represent the potassium and silicon atoms, respectively, and the silicon dimer is centred within the 2 1 SUC, as shown in the top view. The positions of the top layer silicon atoms and the hydrogen atoms at the bottom of the slab are at z 0 and )10.26 A, respectively. Fig. 3b and d can be regarded as combinations of the p Si dangling bond orbitals and contributions from the upper and lower potassium atoms, respectively. Despite this mixing of the potassium and Si dangling bond orbitals, the overall trend in the dispersion of these occupied surface states is found to closely follow the dispersion of the p and p dangling bond surface states of the clean, K- induced, reconstructed Si(0 0 1)2 1 surface, as illustrated in Fig. 4. As can be seen from this figure, the only significant change in the dispersion of these surface states is observed for the p states in the vicinity of the C and J 0 symmetry points, and for the p states in the vicinity of the J and J 0 symmetry points of the SBZ. Interestingly, these changes have been found to be mainly due to contributions from the lower K adatoms, with the upper K adatoms having little effect on the dispersion of the occupied surface state bands. Entirely analogous results have been observed for the Si(0 0 1)2 1 Rb chemisorption system at 1.0 ML coverage [28]. Kr uger and Pollmann [21] also determined two dominant occupied surface state bands close to the Fermi energy which they labeled as D and D.In agreement with the above discussion, these were shown to be hybrid states formed by the interaction of the silicon dangling bonds and the valence electrons of the potassium atoms. Kr uger and Pollmann found that these states were quite localized along the J K and K J 0 symmetry directions of the SBZ but became resonant with

8 222 H.Q. Shi et al. / Surface Science 561 (2004) Fig. 4. Electronic structure of the substrate of the Si(0 0 1)2 1 K system for 1.0 ML coverage in the vicinity of the Fermi energy. The continuous lines indicate the energy bands for the reconstructed clean Si(0 0 1) substrate while the squares and triangles denote the occupied p and p surface states, respectively, for the Si(0 0 1)2 1 K system at monolayer coverage. The energy bands of the substrate have been shifted upward to match the calculated Si(0 0 1)2 1 K results at the C point of the SBZ. the bulk states along the C J and J 0 C symmetry directions, with the D state becoming a very broad resonance near C that could not be clearly identified from the local density of states (LDOS). Our results are in general agreement with these conclusions although we find the upper surface state at C to still be quite localized, while the lower (p dangling bond) surface state is shifted downwards and becomes a weak surface resonance due to interaction of the lower K adatoms with the substrate. The occupied electronic surface states denoted by the empty diamonds and asterisks in Fig. 2b represent the silicon dimer r bond surface states, and states involving predominantly the first and third silicon back bond states, respectively. 3D charge density plots for the silicon dimer r bond surface state at the J 0 point of the SBZ, together with the corresponding q nk ðzþ, are shown in Fig. 5a. Corresponding plots for the first silicon back bond surface state at the J point of the SBZ are presented in Fig. 5b. Comparison with the corresponding surface states of the clean surface shows that the energy and dispersion of these two occupied surface states are little affected by the presence of the K adatoms on the surface. Analogous states, labelled as D i and B 1, were also found by Kr uger and Pollmann [21] along the C J 0 symmetry directions of the SBZ. These authors were unable to unambiguously identify their D i surface state band as the S 2 surface band determined by Abukawa and Kono [17]. Our calculated dispersion for the surface states represented by the empty diamonds in Fig. 2b, however, is in excellent agreement with these experimentally determined surface states (see Fig. 2a). In addition to the occupied states, our calculations have also identified a number of unoccupied electronic surface states. These are indicated in Fig. 2b by the right and left arrows, crosses and solid diamonds. While the low-lying unoccupied surface states result predominantly from the presence of the K adatoms, they are best described as combinations of the K atomic orbitals and Si dimer dangling bond orbitals. The states indicated by the right arrows in Fig. 2b are made up predominantly of orbitals from the upper potassium atoms and the p silicon dimer dangling bond orbitals. 3D probability density plots for this unoccupied surface state at the J point of the SBZ, together with the corresponding q nk ðzþ, are shown in Fig. 6a. A detailed analysis of these surface states shows that they can also contain a small contribution from the orbitals of the lower K adatoms. This contribution, however, is clearly only seen in the vicinity of the C point and decreases rapidly along the C J symmetry direction of the SBZ to become negligible along the J K symmetry direction. The contribution from the silicon dimer dangling bond orbitals to the lowest unoccupied surface states is also significant in the vicinity of the C point of the SBZ but decreases steadily along the C J K and C J 0 symmetry directions, to become negligible along the K J 0 symmetric direction. In this region of the SBZ the lowest unoccupied surface states have been represented in Fig. 2b by crosses. These states, while having no contribution from the Si dimer bonds, have significant contributions from the upper potassium and subsurface silicon atoms (Fig. 7a). 3D probability density plots for the unoccupied surface state at the J point of the SBZ represented by the left arrows in Fig. 2b, are shown in Fig. 6b. These

9 H.Q. Shi et al. / Surface Science 561 (2004) Fig. 5. Side and top views of the 3D charge density distribution, and the corresponding q nk ðzþ function, for the valence band surface states of the Si(0 0 1)2 1 K system at 1.0 ML coverage indicated in Fig. 2b by (a) the empty diamonds at the J 0 point and (b) the asterisks at the J point of the SBZ. The charge density isosurface value was e/ A 3. unoccupied surface states are combinations of orbitals from the lower and upper potassium adatoms, and the p silicon dimer dangling bond orbitals. In contrast to the surface states denoted by the right arrows in Fig. 2b, however, these states are made up of comparable orbital contributions from both the upper and lower K adatoms along both the C J and J K symmetry directions of the SBZ. The final unoccupied surface states that we have identified are denoted in Fig. 2b by the solid diamonds. These are combinations of the atomic orbitals of the lower potassium atoms and the antibonding r dimer bond molecular orbitals. 3D probability density plots for this surface state band for a wavevector along the J K symmetry direction of the SBZ are given in Fig. 7b. The orbital composition and dispersion of this unoccupied surface state band along the C J K J 0 C symmetry directions of the SBZ are virtually identical to those predicted for the Si(0 0 1)2 1 Rb chemisorption system at monolayer coverage [28]. As already highlighted, the predicted dispersion of the theoretically determined low-lying unoccupied surface states is in excellent agreement with the parabolic-like dispersion of the IPES surface states obtained along the C J and C J 0 symmetric directions by Johansson and Reihl [22]. Moreover, our theoretical calculations predict, in agreement with the experimental IPES data, a continuation of the parabolic, free-electron-like dispersion along the C J symmetry direction of the SBZ into the second surface Brillion zone with no energy gap at the SBZ boundary (J point). As stated earlier, this

10 224 H.Q. Shi et al. / Surface Science 561 (2004) Fig. 6. Side and top views of the 3D probability density distribution, and the corresponding q nk ðzþ function, for the unoccupied surface states of the Si(0 0 1)2 1 K system at 1.0 ML coverage indicated in Fig. 2b by (a) the right arrows at the J point and (b) the left arrows at the J point of the SBZ. The probability density isosurface value was A 3. suggests that the dispersion of these empty surface states may not follow the 2 1 periodicity of the substrate in the direction perpendicular to the dimer rows. Johansson and Reihl [22] suggested that this could be explained by assuming that the positions of the potassium atoms within the overlayer closely approximated a 1 1 periodicity, and that there were much stronger interactions between the potassium atoms within the overlayer than between the K adatoms and the substrate. Our results suggest some modifications to the above interpretation. First of all, a 1 1 periodicity for the overlayer requires the two potassium adatoms to be chemisorbed at equivalent positions in the 2 1 SUC. Our calculations, and those of Morikawa et al. [9], however, predict a minimum energy atomic configuration for monolayer coverage in which the two K atoms in each 2 1 SUC are chemisorbed at the non-equivalent A and C sites of a reconstructed Si(0 0 1)2 1 surface with a relative vertical displacement of 1.1 A. Similar results have been obtained from experiment [13,15]. Secondly, our analysis shows that the lowlying unoccupied surface states indicated by the right arrows in Fig. 2b are composed predominantly of orbitals from the upper K adatom, while the band indicated by the left arrows consists of orbitals from both the upper and lower K adatoms. The observed degeneracy of these two bands at the J point of the SBZ suggests that these unoccupied surface state bands are independent and non-interacting, and may represent two distinct modes resulting primarily from interaction between the K adatoms within the overlayer (left arrows), and between the adatoms and the substrate (right arrows). As can be seen from Fig. 2b,

11 H.Q. Shi et al. / Surface Science 561 (2004) Fig. 7. Side and top views of the 3D probability density distribution, and the corresponding q nk ðzþ function, for the conduction band surface states of the Si(0 0 1)2 1 K system at 1.0 ML coverage indicated in Fig. 2b by (a) the crosses at the K point and (b) the solid diamonds for a wavevector along the J K symmetry direction of the SBZ. The probability density isosurface values were A 3 (a) and A 3 (b). the band denoted by the left arrows exhibits parabolic-like behaviour. Moreover, the dispersion of this band remains essentially unaltered along both the C J and J K symmetry directions of the SBZ from that calculated for the isolated K overlayer. It is thus clear that this band describes interactions between the adatoms within the overlayer and is not affected by interactions with the Si substrate. The unoccupied surface state band denoted by the right arrows, on the other hand, describes mainly interactions between the upper chemisorbed K adatoms and the Si substrate. This interaction is strong enough to reduce the dispersion of this band by approximately 50% along the C J and C J 0 symmetry directions relative to that of the isolated K overlayer, and results in a fairly flat, strongly localized, band along the J K symmetry direction of the SBZ (see Fig. 2b). As discussed earlier, evidence for a significant interaction between the substrate and the overlayer can also be identified in the occupied part of the surface electronic band structure. In that case, however, the interaction is mediated by the lower K adatom chemisorbed at the C site of the 2 1SUC. 4. Concluding remarks The Si(0 0 1)2 1 K chemisorption system has been studied for both 0.5 and 1.0 ML coverage using the VASP plane-wave pseudopotential DFT code. The valley-bridge site has been found to be the preferred chemisorption site for 0.5 ML coverage. For 1.0 ML coverage, the DL model in which

12 226 H.Q. Shi et al. / Surface Science 561 (2004) the potassium atoms chemisorb at the pedestal and valley-bridge sites, has been confirmed to be the minimum energy structure. The predicted geometry for this DL model has been found to be in good agreement with the experimental results of Abukawa and Kono [13] and Makita et al. [15]. The electronic structure for the DL model has also been calculated using the VASP program. By carefully analysing the nature of the wave functions in the vicinity of the Fermi energy, we have been able to identify the electronic surface states along the various symmetry directions of the SBZ. The overall dispersion of the surface-state bands has been shown to be in excellent agreement with both the SR-ARPES data of Abukawa et al. [17] and the IPES data of Johansson and Reihl [22]. Detailed analysis of the occupied and unoccupied surface states close to the Fermi energy suggests that there is relatively strong interaction both between the potassium atoms chemisorbed at the pedestal and valley-bridge sites, and between these potassium atoms and the substrate. References [1] M. Milun, P. Pervan, D.P. Woodruff, Rep. Prog. Phys. 65 (2002) 99. [2] J.D. Levine, Surf. Sci. 34 (1973) 90. [3] T. Aruga, H. Tochihara, Y. Murata, Phys. Rev. Lett. 53 (1984) 372. [4] G.S. Glander, M.B. Webb, Bull. Am. Phys. Soc. 33 (1988) 570; G.S. Glander, M.B. Webb, Surf. Sci. 222 (1989) 64; G.S. Glander, M.B. Webb, Surf. Sci. 224 (1990) 60. [5] R. Holtom, P.M. Gundry, Surf. Sci. 63 (1977) 263. [6] I.P. Batra, J.M. Nicholls, B. Reihl, J. Vac. Sci. Technol. A 5 (1987) 898. [7] E.G. Michel, P. Pervan, G.R. Castro, R. Miranda, K. Wandelt, Phys. Rev. B 45 (1992) [8] R. Lindsay, H. D urr, P.L. Wincott, I. Colera, B.C. Cowie, G. Thornton, Phys. Rev. B 51 (1995) [9] Y. Morikawa, K. Kobayashi, K. Terakura, S. Bl ugel, Phys. Rev. B 44 (1991) [10] R. Car, M. Parrinello, Phys. Rev. Lett. 55 (1985) [11] L. Ye, A.J. Freeman, B. Delley, Phys. Rev. B 39 (1989) [12] R. Ramirez, Phys. Rev. B 40 (1989) [13] T. Abukawa, S. Kono, Phys. Rev. B 37 (1988) [14] S. Tanaka, N. Takagi, N. Minami, M. Nishijima, Phys. Rev. B 42 (1990) [15] T. Makita, S. Kohmoto, A. Ichimiya, Surf. Sci. 242 (1991) 65. [16] A.J. Smith, W.R. Graham, E.W. Plummer, Surf. Sci. 243 (1991) L37. [17] T. Abukawa et al., Surf. Sci. 261 (1992) 217. [18] K. Kobayashi, Y. Morikawa, K. Terakura, S. Bl ugel, Phys. Rev. B 45 (1992) [19] Y. Morikawa, K. Kobayashi, K. Terakura, Surf. Sci. 283 (1993) 377. [20] H. Ishida, K. Terakura, Phys. Rev. B 40 (1989) [21] P. Kr uger, J. Pollmann, Appl. Phys. A 59 (1994) 487. [22] L.S.O. Johansson, B. Reihl, Phys. Rev. Lett. 67 (1991) [23] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558; G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) [24] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [25] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) [26] T. Kendelewicz, P. Soukiassian, R.S. List, J.C. Woicik, P. Pianetta, I. Lindau, W.E. Spicer, Phys. Rev. B 37 (1988) [27] P. Soukiassian, L. Spiess, K.M. Schirm, P.S. Mangat, J.A. Kubby, S.P. Tang, A.J. Freeman, J. Vac. Sci. Technol. B 11 (1993) [28] H.Q. Shi, M.W. Radny, P.V. Smith, Phys. Rev. B, submitted for publication.