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Atomic geometry and electronic states on GaAs(1 1 1)A–Se(23×23 )
Surface Science 566–568 (2004) 909–915 www.elsevier.com/locate/susc
Atomic geometry and electronic pffiffiffi pstates ffiffiffi on GaAs(1 1 1)A–Se(2 3 2 3) K. Chuasiripattana a, R.H. Miwa b, G.P. Srivastava b
a,*
a School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK Faculdade de Fısica, Universidade Federal de Uberl^andia, Caixa Postal 593, CEP 38400-902 Uberl^andia, MG, Brazil
Available online 20 June 2004
Abstract In this work we have performedpaffiffiffi theoretical study of the atomic geometry and scanning tunelling microscopy pffiffiffi simulation of the GaAs(1 1 1)A–Se(2 3 2 3) surface. The calculated geometry with Se trimers on H3 sites agrees well with results reported recently from STM and RHEED experiments. Simulated STM images, corresponding to orbital localisation near the fundamental gap, support the experimental observations of bright spots on Se trimers. 2004 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface electronic phenomena (work function, surface potential, surface states, etc.); Chemisorption; Gallium arsenide; Chalcogens
1. Introduction III–V semiconductor surfaces, in particular GaAs surfaces, have been the subject of intense experimental and theoretical studies over the past decade, due to their important role in the development of new optoelectronic nanodevices. GaAs(1 1 1) surfaces are known to exhibit a (2 · 2) reconstruction. The Ga-terminated, or GaAs(1 1 1)A, surface is characterised by a Ga vacancy. The As-terminated, or GaAs(1 1 1)B, surface is characterised by an As trimer per unit surface cell. Deposition of Group-V elements such as As, Sb and Bi on the GaAs(1 1 1)B surface also forms well ordered reconstructions [1–4]. Theoretical investi-
*
Corresponding author. Tel.: +44-1392-264080; fax: +441392-264111. E-mail address: [email protected] (G.P. Srivastava).
gations [5,6] of such systems have provided support to experimental work. Recently Ohtake and co-workers [7], using reflection high energy electron diffraction (RHEED) and scanning tunnelling microscopy (STM), have provided a detailed study of the Ga-vacancy model for the clean GaAs(1 1 1)A-(2 · 2) surface. Ohtake and co-workers [8,9] have also recently examined in detail the adsorption process and the atomic geometry of the Se-covered GaAs(1 1 1)A surface. Using STM RHEED experiments, they propffiffiand ffi p ffiffiffi posed a (2 3 2 3) surface reconstruction for a Se-coverage of 0.5 monolayer (ML) coverage, with two Se-trimers per unit cell adsorbed on the H3 sites. The occupied states STM images clearly show bright spots, forming hexagonal rings, which are associated to the Se-trimers [9]. In this work we report results of a theoretical study of the atomic geometry, electronic structure and STM simulations of the Se-covered
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.06.137
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K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
pffiffiffi pffiffiffi GaAs(1 1 1)A–Se(2 3 2 3) surface. To our knowledge, there are no previous reports of any ab initio studies of this structure. We have considered the adsorption of Se-trimers on H3 sites pffiffiffi of GaAs(1 1 1)A, forming a well ordered (2 3 pffiffiffi 2 3) surface reconstruction. Our calculated equilibrium geometry agrees well with the recent experimental results obtained experimentally by Ohtake and co-workers. The electronic orbital localisation, near the fundamental band gap, has been depicted and our simulated STM images support Ohtake’s experimental interpretation based upon bright spots on the Se-trimers.
2. Method Our calculations were performed in the framework of the density functional theory, within the local density approximation (LDA) using the Ceperley–Alder correlation as parametrised by Perdew and Zunger (see, e.g. [10]). The electron–ion interaction was treated by using norm-conserving, ab initio, fully separable pseudopotentials [11]. The wave functions were expanded in a plane wave basis set with a kinetic energy cutoff of 12 Ry. The resulting bulk equilibrium lattice constant is 5.62 Surface calculations were performed by A. adopting the repeated slab method [10], with a supercell containing three bi-layers of GaAs, the Se layer, and a vacuum region equivalent to twice the bulk lattice constant. A layer of fractionally charged hydrogen atoms was used to saturate the cation dangling bonds at the bottom layer of the slab, and a dipole correction scheme [12] was applied to eliminate the presence of the microscopic electric field extending over the supercell. The electronic charge density was calculated using a set of four special k-points in the irreducible part of the surface Brillouin zone.
3. Results and discussions 3.1. GaAs(1 1 1)A-(2 2) surface Before presenting results for the GaAspffiffiffi pffiffiour ffi (1 1 1)A–Se(2 3 2 3) surface, we will briefly
discuss the key structural and electronic features of the clean GaAs(1 1 1)A-(2 · 2) surface. Fig. 1 and Table 1 show details of the equilibrium atomic geometry of this surface. We note that some of the As atoms in the top bilayer are three-fold coordinated and some are four-fold coordinated. These are labelled As1 and As2, respectively, in the figure. The topmost Ga adatoms move inward along the [1 1 1] direction by with respect to their bulk positions, 0.62 A forming sp2 -like hybridised bonds with three neighbouring As atoms. These As atoms move forming towards the vacancy site by 0.31 A, pyramidal p3 -like hybridisation. There is bimodal distribution of Ga–As bond lengths on the surface. The bond length between the topmost Ga adatoms (Ga1) and the three-fold coordinated As approximately adatoms (As1), dGa1–As1 ¼ 2:40 A 1% smaller than the theoretical bulk GaAs bond This is smaller than the bond length of 2.43 A. length between the topmost Ga adatoms (Ga1) and the four-fold coordinated As adatoms (As2), (1.5% larger than the bulk dGa1–As2 ¼ 2:48 A value). While the bimodal bond length distribution is verified in the RHEED analysis by Ohtake et al., their determined value of dGa1–As2 ¼ 2:56 A is much too large compared to our results. However, it is pleasing to note that from firstprinciples calculations Ohtake et al. obtained and dGa1–As2 ¼ 2:49 A in exceldGa1–As1 ¼ 2:44 A lent agreement with our results. We obtained a vertical distance between As1 and As2 of 0.03 A, which is in quite good agreement with the experimental results presented by Ohtake et al. of However, while our results suggest that 0.02 A. the four-fold coordinated As2 lies higher than the three-fold coordinates As1, this cannot be verified by RHEED analysis due to significant error margin involved in the procedure. Our calculations suggest that the GaAs(1 1 1)(2 · 2) surface is semiconducting, with the HOMO–LUMO gap (LDA) values of approximately 0.2 and 1.8 eV at the C and M points of the surface Brillouin zone. These values are very similar to those presented in Ref. [13]. In accordance with the so-called electron counting rule (ECR) [14], the three Ga dangling bonds become fully empty and the three As dangling bonds be-
K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
A
(a)
911
B
As 3
Ga
3
2
1 1
1 4
3 2
3 1
1
2
1 d 1
3
d = 3.42
B
A (b)
AA
2
3
(c)
2
1
1
3 4
BB
1
3
1
2
3
Fig. 1. Atomic geometry of the GaAs(1 1 1)A-(2 · 2) surface. The As and Ga atoms are shown with filled and open circles, respectively. In the top bilayer As atoms are four-fold and three-fold coordinated in the AA and BB planes, respectively. The (2 · 2) surface unit is shown by the shaded region in (a). Atoms referred to as As1, As2, Ga1 and Ga2 in the text are indicated in panels (b) and (c) for the atomic planes AA and BB, respectively.
Table 1 pffiffiffi pffiffiffi Charactristic structural parameters for the GaAs(1 1 1)A-(2 · 2) and GaAs(1 1 1)A–Se(2 3 2 3) surfaces d(Ga–As)
Buckling in As layer
Vertical height of surface Ga atoms
Bulk GaAs
2.43
GaAs(1 1 1)A Present Expt. (Ref. [7]) Theo. (Ref. [7])
2.40, 2.48 2.40, 2.56 2.44, 2.49
0.03 0.02 0.17
)0.62
Se/GaAs(1 1 1)A Present Expt. (Ref. [7])
2.43, 2.48 2.26, 2.55
0.1 0.32
)0.57 )0.22
Buckling in Ga layer
d(Ga–Se)
d(Se–Se)
z(Se)–z(Ga)
0.14 0.12
2.63 2.05
2.44 2.68
2.44 2.68
0.0
z denotes the coordinate along [1 1 1]. Unit: A.
come fully occupied. As seen in Fig. 2 the HOMO is localised along the As dangling bond (towards the nearest Ga vacancy), and LUMO originates from the pz dangling bond at the surface Ga atoms.
pffiffiffi pffiffiffi 3.2. GaAs(1 1 1)A–Se(2 3 2 3) surface For the GaAs(1 1 1)A surface covered by Setrimers we considered the structural model recently proposed by Ohtake and co-workers [8],
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K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
Fig. 2. Partial charge density plots for GaAs(1 1 1)A-(2 · 2) in the AA plane shown in Fig. 1: (a) highest occupied state, and (b) lowest unoccupied state.
viz: (i) Se coverage of 0.5 ML, (ii) formation of Se-trimers pffiffiffi pffiffiffiadsorbed on the H3 sites, and (iii) (2 3 2 3) surface reconstruction. Fig. 3 shows the proposed structural model and details of the calculated equilibrium geometry. This structural model is consistent with the electron counting rule (ECR) [14]. Each surface unit cell is characterised by nine As dangling bonds (due to the formation three Ga vacancies) and three Ga dangling bonds. Ohtake et al. proposed that all As dangling bonds can be fully saturated due to the availability of 18 excess electrons from the two Se trimers and 94 4 electrons from the three Ga dangling bonds. The adsorption of Se results in some gallium atoms on
the top clean surface layer to become four-fold coordinated. The surface Ga atoms lying in the AA plane remain three-fold coordinated. The adsorption of Se does not alter the three- and fourfold coordinations of As atoms in the top bilayer. The calculated Se–Se bond-length is 2.44 A, larger than bulk Se bond length which is 0.1 A [15]. The RHEED analysis of Ohtake (2.34 A) for et al. suggests a much too large value of 2.68 A the Se–Se bond length. The Ga adatoms bonded with the Se-trimers are displaced upward by with respect to the GaAs(1 1 1)A 0.08 ± 0.03 A clean surface. Our results indicate a Ga–Se bond which is approxlength (dGa1–Se ) of 2.63 ± 0.05 A, A B
As Ga Se
B A
pffiffiffi pffiffiffi Fig. 3. Atomic geometry of the GaAs(1 1 1)A–Se(2 3 2 3) surface. The atomic labelling referred to as As1, As2, Ga1 and Ga2 in the text is the same as in Fig. 1.
K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
2
Energy (eV)
imately 9% bigger than the sum of Ga and Se On the other hand, the covalent radii (2.42 A). RHEED analysis by Ohtake et al. suggests the which is approxiGa–Se bond length of 2.05 A, mately 15% smaller than the sum of the covalent radii. There are further differences between our results and the values obtained from the RHEED analysis by Ohtake and co-workers. For example, for the vertical the experimental value of 1.92 A distance between Ga1 and Se atoms is much Simishorter than the calculated result of 2.60 A. for the larly, the experimental value of 0.32 A vertical distance between As2 and As1 atoms is We much larger than our calculated value of 0.1 A. is an believe that a huge displacement of 0.32 A overestimation, since none of the As atoms is directly bonded to the Se trimers. We note that the in the As layer on the Se vertical buckling of 0.1 A covered surface is significantly larger than its value on the clean surface. Adsorption of Se of 0.03 A renders two different heights for surface Ga atoms. It is pleasing to note that our calculated vertical distance between the three-fold and four-fold coordinated gallium atoms (viz. Ga2 and Ga1, in excellent agreement with respectively) is 0.14 A, The the experimentally deduced value of 0.12 A. difference between the bimodal distribution of Ga– As bond lengths in the top surface bilayer has reduced from 2.5% for the clean surface to 1.5% for the covered surface. Compared to the clean surface, the bond length between the topmost Ga
913
1.5 c1
1 0.5
v1
0 - 0.5
M
Γ
K
pffiffiffi pffiffiffi Fig. 4. Electronic states on the GaAs(1 1 1)A–Se(2 3 2 3) surface.
adatoms (Ga1) and the three-fold coordinated As adatoms (As1) has increased to dGa1–As1 ¼ 2:43 A (almost equal to the bulk value) due to Se adsorption, and the bond length between the topmost Ga adatoms (Ga1) and the four-fold coordinated As adatoms (As2) remains unchanged This is understandable, as in at dGa1–As2 ¼ 2:48 A. the AA plane there is no effect on the Ga–As bond length from the adsorption of selenium. pffiffiffi pAs ffiffiffi seen in Fig. 4, the GaAs(1 1 1)A–Se(2 3 2 3) surface is semiconducting with a small band gap of approximately 0.2 eV (within the LDA). The adsorption of Se trimers saturates the Ga dangling bonds and pushes its energy inside the bulk region. As seen in Fig. 5(a), the highest
pffiffiffi pffiffiffi Fig. 5. Partial charge density plots for the GaAs(1 1 1)A–Se(2 3 2 3) surface at the C-point: (a) the highest occupied state v1 plotted in a horizontal plane through the Se trimers, (b) the lowest unoccupied state c1 plotted in the BB vertical plane, (c) the lowest unoccupied state c1 plotted in a horizontal plane through the top As layer. (For a colour version of the figure see the online paper.)
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K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
above the topmost Se-trimers. Fig. 6 at 5 A exhibits the STM image for an energy interval of 2.5 eV below the calculated Fermi level. The formation of hexagonal rings has been clearly verified, confirming the experimental STM interpretation by Othake et al. Similarly, for an energy interval of 1 eV above the Fermi level, the hexagonal rings have also been observed for empty states STM images.
4. Conclusions Fig. p6.ffiffiffi Theoretical STM image of the GaAs(1 1 1)A– pffiffiffi Se(2 3 2 3) surface for an energy interval of 2.5 eV below the calculated Fermi level.
occupied state, v1 , arises from a combination of px and py orbitals from Se atoms. Fig. 5(b) and (c) clearly indicate that the lowest unoccupied state, c1 , is localised on the As atoms facing the Ga vacancy. In particular, it can be noticed that one of three As atoms facing the vacancy (but furthest from the Se trimer) has emptied its dangling bond, while the other two As atoms contribute less to the c1 state and with p-orbitals not directly pointing towards the vacancy. Our results, thus, provide a generalised view of the ECR for this system comprised of three elements with different electronegativities: charge transfer from the dangling bonds on Ga (the least electronegative species) to As dangling bonds (species with intermediate electronegativity), and some charge transfer from three-fold coordinated As atoms to Se (the most electronegative species). This should be considered as a slight modification of the original proposal put forward by Ohtake et al. For a further investigation of electronic states we performed a simulation of the pffiffiffi STM pffiffiffiimage of the Se-covered GaAs(1 1 1)A-(2 3 2 3) surface within the Tersoff–Hamann approach [16]. In this approach the tunneling current is proportional to the local density of states (at the ‘‘tip’’ position) integrated over different energy intervals for occupied or unoccupied states. We have summed the filled/empty orbitals and projected the calculated density of states over a constant-height plane
The present ab initio work has presented details of the atomic geometry and electronic states forpffiffithe GaAs(1 1 1)A–Se surface based on the ffi p ffiffiffi (2 3 2 3) reconstruction proposed by Ohtake et al. using the STM and RHEED techniques. While our work has confirmed details of many of the key structural parameters deduced by RHEED analysis, there are some notable differences. The GaAs(1 1 1)A–Se surface exhibits a small band gap, similar to the clean GaAs(1 1 1)A surface. The HOMO on the GaAs(1 1 1)A–Se surface results from the px , py orbitals on the Se trimers. Our theoretically simulated STM images confirm the formation of experimentally observed hexagonal rings for both occupied and unoccupied states.
Acknowledgements R.H. Miwa acknowledges financial support from the Brazilian agencies CNPq, FAPEMIG. This work was partially developed at CENAPAD/ CO-MG and CENAPAD/SP. References [1] D.K. Biegelsen, R.D. Bringans, J.E. Northrup, L.E. Swartz, Phys. Rev. Lett. 62 (1990) 452. [2] C. Setzer, J. Platen, H. Bludau, M. Gierer, O. Over, K. Jacobi, Surf. Sci. 402–404 (1998) 782. [3] C. McGinley, A.A. Cafolla, B. Murphy, D. Teehan, P. Moriarty, Appl. Surf. Sci. 152 (1999) 169. [4] P. Moriarty, P.H. Beton, D.A. Woolf, Phys. Rev. B 51 (1995) 7950. [5] R.H. Miwa, G.P. Srivastava, Phys. Rev. B 64 (2001) 192328.
K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915 [6] R.H. Miwa, G.P. Srivastava, Phys. Rev. B 63 (2001) 125341. [7] A. Ohtake, J. Nakamura, T. Komura, T. Hanada, T. Yao, H. Kuramochi, M. Ozeki, Phys. Rev. B 64 (2001) 045318. [8] A. Othake, T. Komura, T. Hanada, S. Miwa, T. Yasuda, K. Arai, T. Yao, Phys. Rev. B 59 (1999) 8032. [9] A. Othake, T. Komura, T. Hanada, S. Miwa, T. Yasuda, T. Yao, Appl. Surf. Sci. 162–163 (2000) 419. [10] G.P. Srivastava, Theoretical Modelling of Semiconductor Surfaces, World Scientific, Singapore, 1999.
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[11] X. Gonze, R. Stumpf, M. Scheffler, Phys. Rev. B 44 (1991) 8503. [12] J. Neugebauer, M. Scheffler, Phys. Rev. B 46 (1992) 16067. [13] E. Kaxiras, Y. Bar-Yam, J.D. Joannopolous, K.C. Pandey, Phys. Rev. B 35 (1987) 16067. [14] M.D. Pashley, Phys. Rev. B 40 (1989) 10481. [15] See D.R. Lide (Ed.), CRC Handbook of Chemsitry and Physics, CRC Press, Inc., Boca Raton, 1994. [16] J. Tersoff, D.J. Hamann, Phys. Rev. B 31 (1985) 805.
Atomic geometry and electronic pffiffiffi pstates ffiffiffi on GaAs(1 1 1)A–Se(2 3 2 3) K. Chuasiripattana a, R.H. Miwa b, G.P. Srivastava b
a,*
a School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK Faculdade de Fısica, Universidade Federal de Uberl^andia, Caixa Postal 593, CEP 38400-902 Uberl^andia, MG, Brazil
Available online 20 June 2004
Abstract In this work we have performedpaffiffiffi theoretical study of the atomic geometry and scanning tunelling microscopy pffiffiffi simulation of the GaAs(1 1 1)A–Se(2 3 2 3) surface. The calculated geometry with Se trimers on H3 sites agrees well with results reported recently from STM and RHEED experiments. Simulated STM images, corresponding to orbital localisation near the fundamental gap, support the experimental observations of bright spots on Se trimers. 2004 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface electronic phenomena (work function, surface potential, surface states, etc.); Chemisorption; Gallium arsenide; Chalcogens
1. Introduction III–V semiconductor surfaces, in particular GaAs surfaces, have been the subject of intense experimental and theoretical studies over the past decade, due to their important role in the development of new optoelectronic nanodevices. GaAs(1 1 1) surfaces are known to exhibit a (2 · 2) reconstruction. The Ga-terminated, or GaAs(1 1 1)A, surface is characterised by a Ga vacancy. The As-terminated, or GaAs(1 1 1)B, surface is characterised by an As trimer per unit surface cell. Deposition of Group-V elements such as As, Sb and Bi on the GaAs(1 1 1)B surface also forms well ordered reconstructions [1–4]. Theoretical investi-
*
Corresponding author. Tel.: +44-1392-264080; fax: +441392-264111. E-mail address: [email protected] (G.P. Srivastava).
gations [5,6] of such systems have provided support to experimental work. Recently Ohtake and co-workers [7], using reflection high energy electron diffraction (RHEED) and scanning tunnelling microscopy (STM), have provided a detailed study of the Ga-vacancy model for the clean GaAs(1 1 1)A-(2 · 2) surface. Ohtake and co-workers [8,9] have also recently examined in detail the adsorption process and the atomic geometry of the Se-covered GaAs(1 1 1)A surface. Using STM RHEED experiments, they propffiffiand ffi p ffiffiffi posed a (2 3 2 3) surface reconstruction for a Se-coverage of 0.5 monolayer (ML) coverage, with two Se-trimers per unit cell adsorbed on the H3 sites. The occupied states STM images clearly show bright spots, forming hexagonal rings, which are associated to the Se-trimers [9]. In this work we report results of a theoretical study of the atomic geometry, electronic structure and STM simulations of the Se-covered
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.06.137
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K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
pffiffiffi pffiffiffi GaAs(1 1 1)A–Se(2 3 2 3) surface. To our knowledge, there are no previous reports of any ab initio studies of this structure. We have considered the adsorption of Se-trimers on H3 sites pffiffiffi of GaAs(1 1 1)A, forming a well ordered (2 3 pffiffiffi 2 3) surface reconstruction. Our calculated equilibrium geometry agrees well with the recent experimental results obtained experimentally by Ohtake and co-workers. The electronic orbital localisation, near the fundamental band gap, has been depicted and our simulated STM images support Ohtake’s experimental interpretation based upon bright spots on the Se-trimers.
2. Method Our calculations were performed in the framework of the density functional theory, within the local density approximation (LDA) using the Ceperley–Alder correlation as parametrised by Perdew and Zunger (see, e.g. [10]). The electron–ion interaction was treated by using norm-conserving, ab initio, fully separable pseudopotentials [11]. The wave functions were expanded in a plane wave basis set with a kinetic energy cutoff of 12 Ry. The resulting bulk equilibrium lattice constant is 5.62 Surface calculations were performed by A. adopting the repeated slab method [10], with a supercell containing three bi-layers of GaAs, the Se layer, and a vacuum region equivalent to twice the bulk lattice constant. A layer of fractionally charged hydrogen atoms was used to saturate the cation dangling bonds at the bottom layer of the slab, and a dipole correction scheme [12] was applied to eliminate the presence of the microscopic electric field extending over the supercell. The electronic charge density was calculated using a set of four special k-points in the irreducible part of the surface Brillouin zone.
3. Results and discussions 3.1. GaAs(1 1 1)A-(2 2) surface Before presenting results for the GaAspffiffiffi pffiffiour ffi (1 1 1)A–Se(2 3 2 3) surface, we will briefly
discuss the key structural and electronic features of the clean GaAs(1 1 1)A-(2 · 2) surface. Fig. 1 and Table 1 show details of the equilibrium atomic geometry of this surface. We note that some of the As atoms in the top bilayer are three-fold coordinated and some are four-fold coordinated. These are labelled As1 and As2, respectively, in the figure. The topmost Ga adatoms move inward along the [1 1 1] direction by with respect to their bulk positions, 0.62 A forming sp2 -like hybridised bonds with three neighbouring As atoms. These As atoms move forming towards the vacancy site by 0.31 A, pyramidal p3 -like hybridisation. There is bimodal distribution of Ga–As bond lengths on the surface. The bond length between the topmost Ga adatoms (Ga1) and the three-fold coordinated As approximately adatoms (As1), dGa1–As1 ¼ 2:40 A 1% smaller than the theoretical bulk GaAs bond This is smaller than the bond length of 2.43 A. length between the topmost Ga adatoms (Ga1) and the four-fold coordinated As adatoms (As2), (1.5% larger than the bulk dGa1–As2 ¼ 2:48 A value). While the bimodal bond length distribution is verified in the RHEED analysis by Ohtake et al., their determined value of dGa1–As2 ¼ 2:56 A is much too large compared to our results. However, it is pleasing to note that from firstprinciples calculations Ohtake et al. obtained and dGa1–As2 ¼ 2:49 A in exceldGa1–As1 ¼ 2:44 A lent agreement with our results. We obtained a vertical distance between As1 and As2 of 0.03 A, which is in quite good agreement with the experimental results presented by Ohtake et al. of However, while our results suggest that 0.02 A. the four-fold coordinated As2 lies higher than the three-fold coordinates As1, this cannot be verified by RHEED analysis due to significant error margin involved in the procedure. Our calculations suggest that the GaAs(1 1 1)(2 · 2) surface is semiconducting, with the HOMO–LUMO gap (LDA) values of approximately 0.2 and 1.8 eV at the C and M points of the surface Brillouin zone. These values are very similar to those presented in Ref. [13]. In accordance with the so-called electron counting rule (ECR) [14], the three Ga dangling bonds become fully empty and the three As dangling bonds be-
K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
A
(a)
911
B
As 3
Ga
3
2
1 1
1 4
3 2
3 1
1
2
1 d 1
3
d = 3.42
B
A (b)
AA
2
3
(c)
2
1
1
3 4
BB
1
3
1
2
3
Fig. 1. Atomic geometry of the GaAs(1 1 1)A-(2 · 2) surface. The As and Ga atoms are shown with filled and open circles, respectively. In the top bilayer As atoms are four-fold and three-fold coordinated in the AA and BB planes, respectively. The (2 · 2) surface unit is shown by the shaded region in (a). Atoms referred to as As1, As2, Ga1 and Ga2 in the text are indicated in panels (b) and (c) for the atomic planes AA and BB, respectively.
Table 1 pffiffiffi pffiffiffi Charactristic structural parameters for the GaAs(1 1 1)A-(2 · 2) and GaAs(1 1 1)A–Se(2 3 2 3) surfaces d(Ga–As)
Buckling in As layer
Vertical height of surface Ga atoms
Bulk GaAs
2.43
GaAs(1 1 1)A Present Expt. (Ref. [7]) Theo. (Ref. [7])
2.40, 2.48 2.40, 2.56 2.44, 2.49
0.03 0.02 0.17
)0.62
Se/GaAs(1 1 1)A Present Expt. (Ref. [7])
2.43, 2.48 2.26, 2.55
0.1 0.32
)0.57 )0.22
Buckling in Ga layer
d(Ga–Se)
d(Se–Se)
z(Se)–z(Ga)
0.14 0.12
2.63 2.05
2.44 2.68
2.44 2.68
0.0
z denotes the coordinate along [1 1 1]. Unit: A.
come fully occupied. As seen in Fig. 2 the HOMO is localised along the As dangling bond (towards the nearest Ga vacancy), and LUMO originates from the pz dangling bond at the surface Ga atoms.
pffiffiffi pffiffiffi 3.2. GaAs(1 1 1)A–Se(2 3 2 3) surface For the GaAs(1 1 1)A surface covered by Setrimers we considered the structural model recently proposed by Ohtake and co-workers [8],
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K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
Fig. 2. Partial charge density plots for GaAs(1 1 1)A-(2 · 2) in the AA plane shown in Fig. 1: (a) highest occupied state, and (b) lowest unoccupied state.
viz: (i) Se coverage of 0.5 ML, (ii) formation of Se-trimers pffiffiffi pffiffiffiadsorbed on the H3 sites, and (iii) (2 3 2 3) surface reconstruction. Fig. 3 shows the proposed structural model and details of the calculated equilibrium geometry. This structural model is consistent with the electron counting rule (ECR) [14]. Each surface unit cell is characterised by nine As dangling bonds (due to the formation three Ga vacancies) and three Ga dangling bonds. Ohtake et al. proposed that all As dangling bonds can be fully saturated due to the availability of 18 excess electrons from the two Se trimers and 94 4 electrons from the three Ga dangling bonds. The adsorption of Se results in some gallium atoms on
the top clean surface layer to become four-fold coordinated. The surface Ga atoms lying in the AA plane remain three-fold coordinated. The adsorption of Se does not alter the three- and fourfold coordinations of As atoms in the top bilayer. The calculated Se–Se bond-length is 2.44 A, larger than bulk Se bond length which is 0.1 A [15]. The RHEED analysis of Ohtake (2.34 A) for et al. suggests a much too large value of 2.68 A the Se–Se bond length. The Ga adatoms bonded with the Se-trimers are displaced upward by with respect to the GaAs(1 1 1)A 0.08 ± 0.03 A clean surface. Our results indicate a Ga–Se bond which is approxlength (dGa1–Se ) of 2.63 ± 0.05 A, A B
As Ga Se
B A
pffiffiffi pffiffiffi Fig. 3. Atomic geometry of the GaAs(1 1 1)A–Se(2 3 2 3) surface. The atomic labelling referred to as As1, As2, Ga1 and Ga2 in the text is the same as in Fig. 1.
K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915
2
Energy (eV)
imately 9% bigger than the sum of Ga and Se On the other hand, the covalent radii (2.42 A). RHEED analysis by Ohtake et al. suggests the which is approxiGa–Se bond length of 2.05 A, mately 15% smaller than the sum of the covalent radii. There are further differences between our results and the values obtained from the RHEED analysis by Ohtake and co-workers. For example, for the vertical the experimental value of 1.92 A distance between Ga1 and Se atoms is much Simishorter than the calculated result of 2.60 A. for the larly, the experimental value of 0.32 A vertical distance between As2 and As1 atoms is We much larger than our calculated value of 0.1 A. is an believe that a huge displacement of 0.32 A overestimation, since none of the As atoms is directly bonded to the Se trimers. We note that the in the As layer on the Se vertical buckling of 0.1 A covered surface is significantly larger than its value on the clean surface. Adsorption of Se of 0.03 A renders two different heights for surface Ga atoms. It is pleasing to note that our calculated vertical distance between the three-fold and four-fold coordinated gallium atoms (viz. Ga2 and Ga1, in excellent agreement with respectively) is 0.14 A, The the experimentally deduced value of 0.12 A. difference between the bimodal distribution of Ga– As bond lengths in the top surface bilayer has reduced from 2.5% for the clean surface to 1.5% for the covered surface. Compared to the clean surface, the bond length between the topmost Ga
913
1.5 c1
1 0.5
v1
0 - 0.5
M
Γ
K
pffiffiffi pffiffiffi Fig. 4. Electronic states on the GaAs(1 1 1)A–Se(2 3 2 3) surface.
adatoms (Ga1) and the three-fold coordinated As adatoms (As1) has increased to dGa1–As1 ¼ 2:43 A (almost equal to the bulk value) due to Se adsorption, and the bond length between the topmost Ga adatoms (Ga1) and the four-fold coordinated As adatoms (As2) remains unchanged This is understandable, as in at dGa1–As2 ¼ 2:48 A. the AA plane there is no effect on the Ga–As bond length from the adsorption of selenium. pffiffiffi pAs ffiffiffi seen in Fig. 4, the GaAs(1 1 1)A–Se(2 3 2 3) surface is semiconducting with a small band gap of approximately 0.2 eV (within the LDA). The adsorption of Se trimers saturates the Ga dangling bonds and pushes its energy inside the bulk region. As seen in Fig. 5(a), the highest
pffiffiffi pffiffiffi Fig. 5. Partial charge density plots for the GaAs(1 1 1)A–Se(2 3 2 3) surface at the C-point: (a) the highest occupied state v1 plotted in a horizontal plane through the Se trimers, (b) the lowest unoccupied state c1 plotted in the BB vertical plane, (c) the lowest unoccupied state c1 plotted in a horizontal plane through the top As layer. (For a colour version of the figure see the online paper.)
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above the topmost Se-trimers. Fig. 6 at 5 A exhibits the STM image for an energy interval of 2.5 eV below the calculated Fermi level. The formation of hexagonal rings has been clearly verified, confirming the experimental STM interpretation by Othake et al. Similarly, for an energy interval of 1 eV above the Fermi level, the hexagonal rings have also been observed for empty states STM images.
4. Conclusions Fig. p6.ffiffiffi Theoretical STM image of the GaAs(1 1 1)A– pffiffiffi Se(2 3 2 3) surface for an energy interval of 2.5 eV below the calculated Fermi level.
occupied state, v1 , arises from a combination of px and py orbitals from Se atoms. Fig. 5(b) and (c) clearly indicate that the lowest unoccupied state, c1 , is localised on the As atoms facing the Ga vacancy. In particular, it can be noticed that one of three As atoms facing the vacancy (but furthest from the Se trimer) has emptied its dangling bond, while the other two As atoms contribute less to the c1 state and with p-orbitals not directly pointing towards the vacancy. Our results, thus, provide a generalised view of the ECR for this system comprised of three elements with different electronegativities: charge transfer from the dangling bonds on Ga (the least electronegative species) to As dangling bonds (species with intermediate electronegativity), and some charge transfer from three-fold coordinated As atoms to Se (the most electronegative species). This should be considered as a slight modification of the original proposal put forward by Ohtake et al. For a further investigation of electronic states we performed a simulation of the pffiffiffi STM pffiffiffiimage of the Se-covered GaAs(1 1 1)A-(2 3 2 3) surface within the Tersoff–Hamann approach [16]. In this approach the tunneling current is proportional to the local density of states (at the ‘‘tip’’ position) integrated over different energy intervals for occupied or unoccupied states. We have summed the filled/empty orbitals and projected the calculated density of states over a constant-height plane
The present ab initio work has presented details of the atomic geometry and electronic states forpffiffithe GaAs(1 1 1)A–Se surface based on the ffi p ffiffiffi (2 3 2 3) reconstruction proposed by Ohtake et al. using the STM and RHEED techniques. While our work has confirmed details of many of the key structural parameters deduced by RHEED analysis, there are some notable differences. The GaAs(1 1 1)A–Se surface exhibits a small band gap, similar to the clean GaAs(1 1 1)A surface. The HOMO on the GaAs(1 1 1)A–Se surface results from the px , py orbitals on the Se trimers. Our theoretically simulated STM images confirm the formation of experimentally observed hexagonal rings for both occupied and unoccupied states.
Acknowledgements R.H. Miwa acknowledges financial support from the Brazilian agencies CNPq, FAPEMIG. This work was partially developed at CENAPAD/ CO-MG and CENAPAD/SP. References [1] D.K. Biegelsen, R.D. Bringans, J.E. Northrup, L.E. Swartz, Phys. Rev. Lett. 62 (1990) 452. [2] C. Setzer, J. Platen, H. Bludau, M. Gierer, O. Over, K. Jacobi, Surf. Sci. 402–404 (1998) 782. [3] C. McGinley, A.A. Cafolla, B. Murphy, D. Teehan, P. Moriarty, Appl. Surf. Sci. 152 (1999) 169. [4] P. Moriarty, P.H. Beton, D.A. Woolf, Phys. Rev. B 51 (1995) 7950. [5] R.H. Miwa, G.P. Srivastava, Phys. Rev. B 64 (2001) 192328.
K. Chuasiripattana et al. / Surface Science 566–568 (2004) 909–915 [6] R.H. Miwa, G.P. Srivastava, Phys. Rev. B 63 (2001) 125341. [7] A. Ohtake, J. Nakamura, T. Komura, T. Hanada, T. Yao, H. Kuramochi, M. Ozeki, Phys. Rev. B 64 (2001) 045318. [8] A. Othake, T. Komura, T. Hanada, S. Miwa, T. Yasuda, K. Arai, T. Yao, Phys. Rev. B 59 (1999) 8032. [9] A. Othake, T. Komura, T. Hanada, S. Miwa, T. Yasuda, T. Yao, Appl. Surf. Sci. 162–163 (2000) 419. [10] G.P. Srivastava, Theoretical Modelling of Semiconductor Surfaces, World Scientific, Singapore, 1999.
915
[11] X. Gonze, R. Stumpf, M. Scheffler, Phys. Rev. B 44 (1991) 8503. [12] J. Neugebauer, M. Scheffler, Phys. Rev. B 46 (1992) 16067. [13] E. Kaxiras, Y. Bar-Yam, J.D. Joannopolous, K.C. Pandey, Phys. Rev. B 35 (1987) 16067. [14] M.D. Pashley, Phys. Rev. B 40 (1989) 10481. [15] See D.R. Lide (Ed.), CRC Handbook of Chemsitry and Physics, CRC Press, Inc., Boca Raton, 1994. [16] J. Tersoff, D.J. Hamann, Phys. Rev. B 31 (1985) 805.