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Bi(1 ML)-(2×1)
Surface Science 402–404 (1998) 641–644
Ab-initio density functional calculations for Si(001)/Bi(1 ML)-(2×1) S.C.A. Gay *, S.J. Jenkins, G.P. Srivastava Physics Department, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK Received 17 July 1997; accepted for publication 19 September 1997
Abstract We present calculations for atomic geometry, electronic states and bonding for a monolayer (1 ML) of Bi on the Si(001) surface using a first-principles pseudopotential method. The (2×1) surface reconstruction is due to formation of symmetric Bi dimers of ˚ at a height of 1.76 A ˚ above the Si substrate. This geometry is compared with that obtained recently for length 3.06 A Si(001)/Sb(1 ML)-(2×1). Our results show the surface to be semiconducting with covalent bonding between the adatoms and substrate. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Bismuth; Chemisorption; Density functional calculations; Semiconductor surfaces; Silicon; Surface relaxation and reconstruction
1. Introduction The study of adsorbate-covered semiconductor surfaces is presently of great interest. In particular, it is important to investigate the structural and electronic properties of X/Si(001) ( X=As, Sb and Bi) systems, due to the surfactant property of these group V elements in the epitaxial growth of Ge on Si(001) [1]. It is generally thought that only one monolayer of surfactant is required in order to achieve the epitaxial growth. Whereas deposition of a monolayer of As or Sb gives rise to a (2×1) reconstruction of the Si(001) surface, recent experiments suggest that a monolayer coverage of Bi leads to a more complicated (2×n) reconstruc* Corresponding author. Fax: (+44) 1392 264 111; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 97 ) 0 09 2 4 -2
tion pattern with 5≤n≤13 [2]. The basic reconstruction mechanism of such structures is Bi–Bi dimer formation, with a (2×n) unit cell containing n−1 dimers (i.e. with one missing dimer per (2×n) cell ). Prior to investigating Bi/Si(001)-(2×n), it is desirable to study in detail the Si(001)/Bi(1 ML)(2×1) system in order to understand characteristic features of Bi–Bi dimers and the bonding between the Bi overlayer and the Si substrate. The (2×1) cell is also of interest when comparing the Bi–Bi dimer to previous results obtained for the Sb–Sb dimer in the Si(001)/Sb(1 ML)-(2×1) system [3]. In this paper, we use the pseudopotential method, within the local density approximation, to study the atomic geometry, electronic states and bonding for a monolayer deposition of Bi on Si(001) in the (2×1) reconstruction, and compare the results with those for the Sb overlayer.
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S.C.A. Gay et al. / Surface Science 402–404 (1998) 641–644
2. Method The ab-initio results presented in this paper were obtained using the density functional theory within the local density approximation. Electron correlation was taken into account using the Ceperley and Alder correlation scheme as parametrised by Perdew and Zunger [4]. The electron–ion interaction was considered in the form of the norm conserving pseudopotentials listed by Bachelet et al. [5]. A plane wave basis was used for expanding the wave functions. On the (001) surface, a (2×1) periodicity, consistent with Bi–Bi dimer formation, was considered. An artificial periodic boundary condition was imposed in the direction perpendicular to the surface by using a supercell of length equivalent to 12 atomic layers of bulk Si (at our theoretical ˚ ). The supercell bulk Si lattice parameter of 5.42 A contained a slab of eight atomic layers of Si capped on one side with one monolayer of Bi. On the opposite side of the slab, two Si layers were frozen into their bulk positions, and the back surface was passivated with two H atoms per Si atom. All the remaining Si atoms, the Bi atoms and the passivating H atoms were allowed to relax into their minimum energy positions using a conjugate gradient method [6 ]. The surface geometry and band structure were obtained using an 8-Ryd kinetic energy cutoff for the plane wave basis. Convergence tests up to a cutoff of 12 Ryd confirmed that this yields satisfactory structural parameters. Band structures obtained at 8 Ryd, though not fully converged, do contain all the qualitative features of a fully converged high cutoff band structure. Brillouin zone sampling was performed using four special kpoints within the irreducible segment of the Brillouin zone.
structed (2×1) surface is shown in Fig. 1. The ˚, Bi–Bi dimer bond length is calculated to be 3.06 A ˚ which is in good agreement with a figure of 3.12 A estimated from Pauling’s covalent radius for Bi. ˚ compared to The Bi–Si bond length is 2.62 A ˚ 2.63 A for the sum of the covalent tetrahedral radii ˚ of Si and Bi. The dimer is at a height of 1.76 A above the substrate. Examination of the total charge density reveals a very strong bond between the Bi and Si atoms, much stronger than the Bi–Bi bond (see Fig. 2). This implies that the Bi atoms are firmly bonded to the substrate and that the Bi–Bi bond is relatively easy to split in comparison. The Bi atoms are found to bond covalently to each other and to the topmost Si atoms of the substrate, in agreement with the experimental work of Koval et al. [7]. The electronic band structure obtained for the surface is shown in Fig. 3. There is a surface state below the Si bulk valence band that is fully occupied and is identified as the s bond between the Bi atoms in the dimer pair. Fig. 3 also shows a surface state in the vicinity of J9 ∞ localised on the first Si layer at around 9 eV below the valence band maximum. On examination of the partial charge density arising from this band, the state is found to be pps-like with a rather small amplitude, and localised in the top Si layer. There are a
3. Results The (1×1) reconstruction of the system is metallic and therefore unstable in terms of electronic occupancy of the bonding orbitals. Stability is achieved by dimerisation of the Bi atoms, thus forming a semiconducting (2×1) reconstructed surface. The equilibrium geometry of this recon-
Fig. 1. Side view of Si(001)/Bi(1 ML)-(2×1) equilibrium geometry.
S.C.A. Gay et al. / Surface Science 402–404 (1998) 641–644
643
(a)
Fig. 3. Electronic band structure for the Si(001)/Bi(1 ML)(2×1) system. The shaded region is the bulk (2×1) projected band structure for Si, the thick lines show occupied surface bands and the thin line shows the lowest unoccupied surface band.
(b)
Fig. 2. Total valence charge density (a) on plane cutting vertically through the Bi–Bi dimer and (b) on plane cutting obliquely through the Bi dimer so as to include the Bi–Si bond.
further two fully occupied surface bands situated a little below the bulk valence band maximum and an unoccupied surface state a little above the bulk conduction band minimum. This means that the fundamental gap is clear of surface states, in agreement with the experimental results of Gavioli et al. [8].
The two highest energy occupied surface states are localised on the Bi–Bi dimer, as may be seen in the partial charge density plots of Fig. 4. The highest energy occupied surface band is the pbonding (ungerade-like) state formed by the p z orbitals from each Bi atom interacting with each other. The lower of the two corresponds to an occupied p-antibonding (gerade-like) state. A similar state is observed for the CNC dimer on the (001) surface of diamond [9], where it is unoccupied. However, in this system, the antibonding state is occupied due to the extra electron per Bi atom, resulting in a considerable energy drop for this orbital due to the electron–electron exchangecorrelation interactions. This drop is large enough to make the energy of the gerade-like bond (p ) g lower than that of the ungerade-like bond (p ). A u similar situation is obtained for the Si(001)/Sb(1 ML)-(2×1) system [3]. Note that there is some interaction between the overlayer ungerade-like p orbital and the substrate p u z orbital. Though one might ordinarily expect the p bondu
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S.C.A. Gay et al. / Surface Science 402–404 (1998) 641–644
cant contribution to the dimer bond strength. This explains why the Bi–Bi dimer bond length is well described by the Pauling covalent radius of Bi. Overall, the structural, bonding and electronic features for the Bi overlayer are very similar to those for the Sb overlayer in the (2×1) reconstruction on the Si(001) surface [3].
4. Conclusions
(a)
We have presented a fully relaxed geometry for the Si(001)/Bi(1 ML)-(2×1) system. We have also obtained the bonding and electronic band structure for this system, and found it to be very similar to Si(001)/Sb(1 ML)-(2×1). The Bi–Bi dimer bond is found to be weak in comparison to the bonding of the Bi adsorbate with the Si substrate. Despite having three components to it (s, p and p ), the g u Bi–Bi bond is found to be essentially s-like. This is because any contribution gained from the p u bond is largely cancelled out by the p antibond, g resulting in the strength of the bond coming mostly from the s bond. The system is semiconducting with the fundamental Si band gap fully cleared of surface states.
Acknowledgements S.C.A.G. and S.J.J. are grateful to the EPSRC for financial support. The computational work has been supported by the EPSRC ( UK ) through the CSI scheme.
(b)
Fig. 4. Electronic charge density plotted at the K 9 point for (a) highest surface band (above the bulk valence band ) and showing the p -bonding nature of this surface state and (b) second u highest surface band (above the bulk valence band ), showing the p -anti-bonding nature of this surface state. g
ing orbital to make a contribution to the dimer bond strength, any such contribution is largely cancelled out by the p antibonding contribution. g Thus, it is the s bond that makes the most signifi-
References [1] M. Katayama, T. Nakayama, M. Aono, C.F. McConville, Phys. Rev. B 54 (1996) 8600. [2] T. Hanada, M. Kawai, Surf. Sci. 24 (1991) 137. [3] S.J. Jenkins, G.P. Srivastava, Surf. Sci. 352 (1996) 411. [4] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [5] G.B. Bachelet, D.R. Hamann, M. Schlu¨ter, Phys. Rev. B 26 (1982) 4199. [6 ] A. Umerski, G.P. Srivastava, Phys. Rev. B 51 (1995) 2334. [7] I.F. Koval, P.V. Melnik, N.G. Nakhodkin, M.Y. Pyatnitsky, T.V. Afanasieva, Surf. Sci. 333 (1995) 585. [8] L. Gavioli, M. Betti, C. Mariani, Surf. Sci. 377 (1997) 215. [9] P. Kru¨ger, J. Pollmann, Phys. Rev. Lett. 74 (1994) 1155.
Ab-initio density functional calculations for Si(001)/Bi(1 ML)-(2×1) S.C.A. Gay *, S.J. Jenkins, G.P. Srivastava Physics Department, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK Received 17 July 1997; accepted for publication 19 September 1997
Abstract We present calculations for atomic geometry, electronic states and bonding for a monolayer (1 ML) of Bi on the Si(001) surface using a first-principles pseudopotential method. The (2×1) surface reconstruction is due to formation of symmetric Bi dimers of ˚ at a height of 1.76 A ˚ above the Si substrate. This geometry is compared with that obtained recently for length 3.06 A Si(001)/Sb(1 ML)-(2×1). Our results show the surface to be semiconducting with covalent bonding between the adatoms and substrate. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Bismuth; Chemisorption; Density functional calculations; Semiconductor surfaces; Silicon; Surface relaxation and reconstruction
1. Introduction The study of adsorbate-covered semiconductor surfaces is presently of great interest. In particular, it is important to investigate the structural and electronic properties of X/Si(001) ( X=As, Sb and Bi) systems, due to the surfactant property of these group V elements in the epitaxial growth of Ge on Si(001) [1]. It is generally thought that only one monolayer of surfactant is required in order to achieve the epitaxial growth. Whereas deposition of a monolayer of As or Sb gives rise to a (2×1) reconstruction of the Si(001) surface, recent experiments suggest that a monolayer coverage of Bi leads to a more complicated (2×n) reconstruc* Corresponding author. Fax: (+44) 1392 264 111; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 97 ) 0 09 2 4 -2
tion pattern with 5≤n≤13 [2]. The basic reconstruction mechanism of such structures is Bi–Bi dimer formation, with a (2×n) unit cell containing n−1 dimers (i.e. with one missing dimer per (2×n) cell ). Prior to investigating Bi/Si(001)-(2×n), it is desirable to study in detail the Si(001)/Bi(1 ML)(2×1) system in order to understand characteristic features of Bi–Bi dimers and the bonding between the Bi overlayer and the Si substrate. The (2×1) cell is also of interest when comparing the Bi–Bi dimer to previous results obtained for the Sb–Sb dimer in the Si(001)/Sb(1 ML)-(2×1) system [3]. In this paper, we use the pseudopotential method, within the local density approximation, to study the atomic geometry, electronic states and bonding for a monolayer deposition of Bi on Si(001) in the (2×1) reconstruction, and compare the results with those for the Sb overlayer.
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S.C.A. Gay et al. / Surface Science 402–404 (1998) 641–644
2. Method The ab-initio results presented in this paper were obtained using the density functional theory within the local density approximation. Electron correlation was taken into account using the Ceperley and Alder correlation scheme as parametrised by Perdew and Zunger [4]. The electron–ion interaction was considered in the form of the norm conserving pseudopotentials listed by Bachelet et al. [5]. A plane wave basis was used for expanding the wave functions. On the (001) surface, a (2×1) periodicity, consistent with Bi–Bi dimer formation, was considered. An artificial periodic boundary condition was imposed in the direction perpendicular to the surface by using a supercell of length equivalent to 12 atomic layers of bulk Si (at our theoretical ˚ ). The supercell bulk Si lattice parameter of 5.42 A contained a slab of eight atomic layers of Si capped on one side with one monolayer of Bi. On the opposite side of the slab, two Si layers were frozen into their bulk positions, and the back surface was passivated with two H atoms per Si atom. All the remaining Si atoms, the Bi atoms and the passivating H atoms were allowed to relax into their minimum energy positions using a conjugate gradient method [6 ]. The surface geometry and band structure were obtained using an 8-Ryd kinetic energy cutoff for the plane wave basis. Convergence tests up to a cutoff of 12 Ryd confirmed that this yields satisfactory structural parameters. Band structures obtained at 8 Ryd, though not fully converged, do contain all the qualitative features of a fully converged high cutoff band structure. Brillouin zone sampling was performed using four special kpoints within the irreducible segment of the Brillouin zone.
structed (2×1) surface is shown in Fig. 1. The ˚, Bi–Bi dimer bond length is calculated to be 3.06 A ˚ which is in good agreement with a figure of 3.12 A estimated from Pauling’s covalent radius for Bi. ˚ compared to The Bi–Si bond length is 2.62 A ˚ 2.63 A for the sum of the covalent tetrahedral radii ˚ of Si and Bi. The dimer is at a height of 1.76 A above the substrate. Examination of the total charge density reveals a very strong bond between the Bi and Si atoms, much stronger than the Bi–Bi bond (see Fig. 2). This implies that the Bi atoms are firmly bonded to the substrate and that the Bi–Bi bond is relatively easy to split in comparison. The Bi atoms are found to bond covalently to each other and to the topmost Si atoms of the substrate, in agreement with the experimental work of Koval et al. [7]. The electronic band structure obtained for the surface is shown in Fig. 3. There is a surface state below the Si bulk valence band that is fully occupied and is identified as the s bond between the Bi atoms in the dimer pair. Fig. 3 also shows a surface state in the vicinity of J9 ∞ localised on the first Si layer at around 9 eV below the valence band maximum. On examination of the partial charge density arising from this band, the state is found to be pps-like with a rather small amplitude, and localised in the top Si layer. There are a
3. Results The (1×1) reconstruction of the system is metallic and therefore unstable in terms of electronic occupancy of the bonding orbitals. Stability is achieved by dimerisation of the Bi atoms, thus forming a semiconducting (2×1) reconstructed surface. The equilibrium geometry of this recon-
Fig. 1. Side view of Si(001)/Bi(1 ML)-(2×1) equilibrium geometry.
S.C.A. Gay et al. / Surface Science 402–404 (1998) 641–644
643
(a)
Fig. 3. Electronic band structure for the Si(001)/Bi(1 ML)(2×1) system. The shaded region is the bulk (2×1) projected band structure for Si, the thick lines show occupied surface bands and the thin line shows the lowest unoccupied surface band.
(b)
Fig. 2. Total valence charge density (a) on plane cutting vertically through the Bi–Bi dimer and (b) on plane cutting obliquely through the Bi dimer so as to include the Bi–Si bond.
further two fully occupied surface bands situated a little below the bulk valence band maximum and an unoccupied surface state a little above the bulk conduction band minimum. This means that the fundamental gap is clear of surface states, in agreement with the experimental results of Gavioli et al. [8].
The two highest energy occupied surface states are localised on the Bi–Bi dimer, as may be seen in the partial charge density plots of Fig. 4. The highest energy occupied surface band is the pbonding (ungerade-like) state formed by the p z orbitals from each Bi atom interacting with each other. The lower of the two corresponds to an occupied p-antibonding (gerade-like) state. A similar state is observed for the CNC dimer on the (001) surface of diamond [9], where it is unoccupied. However, in this system, the antibonding state is occupied due to the extra electron per Bi atom, resulting in a considerable energy drop for this orbital due to the electron–electron exchangecorrelation interactions. This drop is large enough to make the energy of the gerade-like bond (p ) g lower than that of the ungerade-like bond (p ). A u similar situation is obtained for the Si(001)/Sb(1 ML)-(2×1) system [3]. Note that there is some interaction between the overlayer ungerade-like p orbital and the substrate p u z orbital. Though one might ordinarily expect the p bondu
644
S.C.A. Gay et al. / Surface Science 402–404 (1998) 641–644
cant contribution to the dimer bond strength. This explains why the Bi–Bi dimer bond length is well described by the Pauling covalent radius of Bi. Overall, the structural, bonding and electronic features for the Bi overlayer are very similar to those for the Sb overlayer in the (2×1) reconstruction on the Si(001) surface [3].
4. Conclusions
(a)
We have presented a fully relaxed geometry for the Si(001)/Bi(1 ML)-(2×1) system. We have also obtained the bonding and electronic band structure for this system, and found it to be very similar to Si(001)/Sb(1 ML)-(2×1). The Bi–Bi dimer bond is found to be weak in comparison to the bonding of the Bi adsorbate with the Si substrate. Despite having three components to it (s, p and p ), the g u Bi–Bi bond is found to be essentially s-like. This is because any contribution gained from the p u bond is largely cancelled out by the p antibond, g resulting in the strength of the bond coming mostly from the s bond. The system is semiconducting with the fundamental Si band gap fully cleared of surface states.
Acknowledgements S.C.A.G. and S.J.J. are grateful to the EPSRC for financial support. The computational work has been supported by the EPSRC ( UK ) through the CSI scheme.
(b)
Fig. 4. Electronic charge density plotted at the K 9 point for (a) highest surface band (above the bulk valence band ) and showing the p -bonding nature of this surface state and (b) second u highest surface band (above the bulk valence band ), showing the p -anti-bonding nature of this surface state. g
ing orbital to make a contribution to the dimer bond strength, any such contribution is largely cancelled out by the p antibonding contribution. g Thus, it is the s bond that makes the most signifi-
References [1] M. Katayama, T. Nakayama, M. Aono, C.F. McConville, Phys. Rev. B 54 (1996) 8600. [2] T. Hanada, M. Kawai, Surf. Sci. 24 (1991) 137. [3] S.J. Jenkins, G.P. Srivastava, Surf. Sci. 352 (1996) 411. [4] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [5] G.B. Bachelet, D.R. Hamann, M. Schlu¨ter, Phys. Rev. B 26 (1982) 4199. [6 ] A. Umerski, G.P. Srivastava, Phys. Rev. B 51 (1995) 2334. [7] I.F. Koval, P.V. Melnik, N.G. Nakhodkin, M.Y. Pyatnitsky, T.V. Afanasieva, Surf. Sci. 333 (1995) 585. [8] L. Gavioli, M. Betti, C. Mariani, Surf. Sci. 377 (1997) 215. [9] P. Kru¨ger, J. Pollmann, Phys. Rev. Lett. 74 (1994) 1155.