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Atomic geometry, electronic states and possible hydrogen passivation of the InP(1 1 1)A surface
Applied Surface Science 252 (2006) 7678–7683 www.elsevier.com/locate/apsusc
Atomic geometry, electronic states and possible hydrogen passivation of the InP(1 1 1)A surface K. Chuasiripattana *, G.P. Srivastava School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom Available online 9 May 2006
Abstract We present a first-principles theoretical study of the atomic geometry and electronics states of the InP(1 1 1)A surface under In- and P-rich conditions. The In-rich surface, characterised by an In vacancy per unit (2 2) cell, obeys the electron counting rule (ECR) and pffiffiffiis semiconducting. pffiffiffi Under P-rich conditions we have considered two surface reconstructions: (2 2) with 3/4 monolayer pffiffiffi (ML) pffiffiffi P coverage and ( 3 3) with 1 ML coverage. In complete agreement withpaffiffirecent ffi pffiffiffiexperimental work by Li et al., it is found that the ( 3 3) reconstruction is more stable than the (2 2) reconstruction. However, the ( 3 3) reconstruction has a metallic band structure and thus does not satisfy the ECR. The stability of this reconstruction is explained to arise from a competition between the ECR and a significant elastic deformation in the surface region. We confirm the suggestion by Li et al. that this surface can be passivated both chemically as well as electronically with 1/4 ML coverage of hydrogen. # 2006 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface electronic phenomena; Electron counting rule; Surface passivation; InP(1 1 1)
1. Introduction III–V(1 1 1) compound semiconductor surfaces, e.g. GaAs(1 1 1) and InP(1 1 1), are very important components in wireless communications and optoelectronics industry. It is suggested that the reconstruction of III–V surfaces would follow the electron counting rule (ECR) [1] by having all the dangling bonds of the electropositive surface atoms (III) unoccupied and all those of electronegative surface atoms (V) occupied. The gallium-terminated or GaAs(1 1 1)A surface is characterized by (2 2) reconstruction with one Ga vacancy in each unit cell (known as Ga vacancy model) [2,3] and satisfies the electron counting rule. The arsenic-terminated or GaAs(1 1 1)B surface is characterized pffiffiffiffiffi pffiffiffiffiffi by several reconstructions, e.g. (2 2), ( 19 19) and (1 1). The GaAs(1 1 1)B-(2 2) surface has one As trimer on top of a complete layer of As atoms in every unit cell [2]. Other III– V(1 1 1) surfaces, e.g. InP(1 1 1), are not well studied but believed to have the same reconstructions as GaAs(1 1 1). Recently, Li et al. [4] have reported the atomic structure of the InP(1 1 1)A (i.e. indium-terminated surface) by using
* Corresponding author. Tel: +44 1392 264198; fax: +44 1392 264111. E-mail address: [email protected] (K. Chuasiripattana). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.03.087
scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), and X-ray photoelectron spectroscopy (XPS). reconstructions were observed: (2 2) and pffiffiffi pTwo ffiffiffi ( 3 3). The InP(1 1 1)A- ð2 2Þ surface was prepared in the In-rich condition and is characterized by one In atom missing in every unit pffiffiffi cell, pffiffiand ffi thus is the vacancy model. On the other hand, the ( 3 3) surface was observed in the P-rich condition. From their STM observations, Li et al. proposed that the surface has 1 monolayer (ML) of phosphorus coverage in the form of a trimer in every unit cell. This reconstruction has never been observed before on any III–V(1 1 1) surface. For this P coverage and reconstruction, the electron counting rule is disobeyed and the surface should exhibit metallic behaviour. However, from a first-principles study, Kaxiras et al. [5] proposed that in the As-rich condition the GaAs(1 1 1)A(2 2) reconstruction should be observed. This structure satisfies the electron counting rule by having one As trimer per unit cell amounting to As coverage of 0.75 ML. This might suggest that the P-rich InP(1 1 1)A should also exhibit the (2 2) reconstruction for P coverage of 0.75 ML. In this work, we present a first-principles theoretical study of the atomic geometry and electronic states of the InP(1 1 1)A surface with the three structures discussed above. In order to avoid any possible confusion, we will label the In-rich vacancy model as InP(1 1 1)A-(2 2)-vac, P-rich Kaxiras model as
K. Chuasiripattana, G.P. Srivastava / Applied Surface Science 252 (2006) 7678–7683
InP(1 1 1)A-(2p and the P-rich Li model as ffiffiffi 2)-Kaxiras, pffiffiffi InP(1 1 1)A-( 3 3 ). We explain why the InP(1 1 1)Apffiffiffi pffiffiffi ( 3 3) model, which disobeys the ECR, is observed in STM and LEED studies and is more stable than the InP(1 1 1)A-(2 2)-Kaxiras model. We also propose a possible pffiffiffi pffiffiffi passivation mechanism of the InP(1 1 1)A( 3 3) reconstruction by a sub-monolayer coverage of hydrogen. 2. Method Our calculations were performed in the framework of the density functional theory, within the local density approximation (LDA) [6]. The electron–ion interaction was treated by using norm-conserving, ab initio, fully separable pseudopotentials [7]. The single-particle Kohn–Sham wave functions were expanded in a plane wave basis set with a kinetic energy cutoff 12 Ry. The resulting bulk equilibrium lattice constant of ˚ . Surface calculations are performed by adopting InP is 5.85 A the repeated slab model with a supercell containing pffiffifour ffi pbiffiffiffi layer of InP for the (2 2) reconstruction. For the ( 3 3) reconstruction, the supercell contained four bi-layer of InP and one layer of phosphorus trimer covered. A layer of pseudohydrogen with fractionally valency of 0.75 e was applied to saturate the anion bonds at the bottom layer of the pffiffiffi dangling pffiffiffi slab. As the ( 3 3) unit cell has a fractional number of
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electrons, pffiffiffi pwe ffiffiffi modelled this reconstruction by using a (2 3 2 3) unit cell. Both supercells also have a vacuum region equivalent pffiffiffi to twice pffiffiffi the bulk lattice constant. For both the (2 2) and (2 3 2 3) cells we generated an equivalent set of special k-points, corresponding to 12 points in the irreducible part of the (1 1) surface Brillouin zone. The bottom bi-layer of InP was kept fixed and all other atoms were relaxed to their equilibrium geometry. A dipole correction scheme was applied to eliminate the presence of the microscopic electric field extending over the supercell. 3. Results and discussions 3.1. InP(1 1 1)A-(2 2)-vac The relaxed atomic geometry of the InP(1 1 1)A-(2 2)vac model is shown in Fig. 1. The key relaxed structural parameters are tabulated in Table 1. Some of the P atoms in the top bilayer are three-fold coordinated (e.g. P1) and some are four-fold coordinated (e.g. P1a). The topmost In atoms move inward along the [1 1 1] direction with respect to their bulk ˚ and form sp2-like hybridised bonds with positions, by 0.57 A three neighbouring P atoms. The P1atoms move towards the In ˚ , forming p3-like hybridisation. In vacancy site by 0:33 A the top two layers, there is a bimodal distribution of the In–P bond length. The bond length between In1and the three-fold
Fig. 1. The III–V(1 1 1)-(2 2)-vac reconstruction: (a) top view with the shaded area indicating the (2 2) unit cell; (b) a side view in the AA0 plane; (c) electronic band structure. Table 1 pffiffiffi pffiffiffi Structural parameters for InP(1 1 1)A-(2 2)-vac, InP(1 1 1)A-( 3 3) and InP(1 1 1)A-(2 2)-Kaxiras models d (P–P)tri
d (In–Ptri)
dz (Ptri–(In1)
(2 2)-vac
d1 (In–P)
d2 (In–P)
dz (In–P)
2.51 (In1–P1) 2.59 (In1a–P1a)
2.63 (In2–P1) 2.63 (In2–P1a)
0.28 (In1–P1) 0.33 (In1a–P1a)
pffiffiffi pffiffiffi ( 3 3)
2.20
2.66
2.47
2.54 (In1–P1) 2.58 (In1–P1a)
2.49 (In2–P1) 2.61 (In2a–P1a)
1.16 (In1–P1) 0.73 (In1–P1a)
(2 2)-Kaxiras
2.23
2.63
2.42
2.57 (In1–P1) 2.49 (In1a–P1)
2.54 (In2–P1)
1.10 (In1–P1) 0.49 (In1a–P1)
˚. d: the bond length; Ptri: trimer; dz: the coordinate difference along [1 1 1]; unit: A
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pffiffiffi pffiffiffi pffiffiffi pffiffiffi pffiffiffi pffiffiffi Fig. 2. The InP(1 1 1)A- ð 3 3ÞR30 surface: (a) top view with ð 3 3ÞR30 and ð2 3 2 3ÞR30 unit cells indicated; (b) a side view.
˚ , approximately 1.2% coordinated P atoms (P1) is 2.51 A ˚ . The smaller than the theoretical bulk InP bond length of 2.54 A bond length between In1a and the four-fold coordinated P atoms ˚ , approximately 3.2% larger than the bulk bond (P1a) is 2.59 A length. The bond length between the In2 and P1, and between ˚ , approximately 3.5% larger than the bulk In2 and P1a, is 2.63 A bond length. The coordinate differences along [1 1 1] between ˚ . This In1 and P1, In1a and P1a are, respectively, 0.28 and 0.33 A shows that the In1a atoms are located slightly higher than In1. The band structure calculation shown in Fig. 1 c suggests that this surface is semiconducting. There are no electronic surface states lying within the minimum of the InP bulk valenceconduction gap. The highest occupied state originates from the dangling bond at the P1atom and is localised towards the In vacancy. The lowest unocupied state is localised at the dangling bonds of the In1a atoms and has the pz character. pffiffiffi pffiffiffi 3.2. InP(1 1 1)A-( 3 3) pffiffiffi pffiffiffi The InP(1 1 1)A-( 3 3) reconstruction is shown in Fig. 2 and in Table 1. The P–P bond length in the P-trimer is ˚ , almost identical to twice the atomic radius for P of 2.20 A ˚ 2.22 A. The bond length between In1and P-trimer atoms is ˚ , which is bigger than the InP bulk bond length of 2.54 A ˚ 2.66 A by approximately 4.7%. The P-trimer is adsorbed at the height of ˚ above the In layer. There are two types of P atoms in the 2.47 A third layer, denoted as P1and P1a. The P1 atoms are situated in the
middle right below the P-trimers while the P1a atoms are situated below but beside the P-trimers. The bond length between In1 and ˚ , 1.6% shorter than that between In1 and P1a of P1 is 2.54 A ˚ 2.58 A. The adsorption of P-trimers leads to the bond length of ˚ between In2 and P1 which is shorter than 2.61 A ˚ between 2.49 A In2a and P1a of 4.6%. The coordinate difference along [1 1 1] ˚ , bigger than 0.73 A ˚ between In1 and between In1 and P1 is 1.16 A P1a, indicating the adsorption of P-trimers has pushed the P1 ˚ . The electronic band structure in Fig. 3 atoms down by 0.43 A pffiffiffi pffiffiffi shows that InP(1 1 1)A- ð 3 3Þ is a metallic surface. The metallicity of this surface is more clearly shown in Fig. 3 b. The Fermi energy level cuts through both the largely occupied bands indicated as V1 and a largely unoccupied band (C1). The partial charge density plot in Fig. 4 a at the G point in the horizontal plane containing the phosphorus trimers shows the s orbital character of the phosphorus atoms. The plot in Fig. 4 b in the aa0 plane shows the pzorbital character of the phosphorus-trimer atoms. We conclude that the metallicity of this surface comes from the partially filled bands originating from the P-trimer atoms and has an overall spz character. pffiffiffi pffiffiffi 3.3. Stability of the InP(1 1 1)A-( 3 3) surface In view of the fact that Kaxiras et al. [5] predicted the GaAs(1 1 1)A-(2 2)-Kaxiras surface to be a stable configuration, and that experimental observations by Li petffiffiffi al.p[4] ffiffiffi suggest a stable configuration for the InP(1 1 1)A-( 3 3)
pffiffiffi pffiffiffi Fig. 3. (a) Surface electronic band structure for the InP(1 1 1)A-( 3 3) surface; (b) details near the Fermi energy level.
K. Chuasiripattana, G.P. Srivastava / Applied Surface Science 252 (2006) 7678–7683
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pffiffiffi pffiffiffi Fig. 4. Partial charge density plot of the InP(1 1 1)A-( 3 3) surface at the G point: (a) a combination of the three partially filled states in the horizontal plane containing P trimers; (b) a combination of the three partially filled states in the aa0 vertical plane containing one P atom. Units: 103 e/bohr3.
surface, we investigated pffiffiffi pffiffiffi the relative stability of the (2 2)Kaxiras and ( 3 3) models for InP(1 1 1)A. The (2 2)Kaxiras model is shown in Fig. 5. We calculated the formation energy of the two reconstructions as a function of the chemical potential of phosphorus. The surface formation energy (DEi ) can be expressed as DEi ¼ Ei Eideal DnP DmPp ffiffiffiDnPp mffiffiPffi bulk , where Ei is the total energy of the InP(1 1 1)A-( 3 3) or the InP(1 1 1)A-(2 2)-Kaxiras model, Eideal the total energy of the InP(1 1 1)A ideal surface (viz. the InP(1 1 1)A-(2 2) reconstruction without In vacancy), DnP the difference in the number of P atoms between the two models, and DmP is the chemical potential of phosphorus relative to the bulk phosphorus chemical potential. The bulk phosphorus chemical potential (mPbulk ) is calculated from the total energy of the orthorhombic phase of phosphorus. The results pffiffiffi pin ffiffiffi Fig. 6 indicate that in the P-rich condition, the ( 3 3) reconstruction is more stable than the (2 2)-Kaxiras reconstruction for the whole range of DmP . This clearly explains that the (2 2)-Kaxiras reconstruction is unlikely to be observed for the InP(1 1 1)A surface. The P–P bond length in the ˚ phosphorus trimer in the Kaxiras pffiffiffi model pffiffiffi is 2.23 A, which is ˚ bigger than 2.20 A for the ( 3 3) model by 1.4%. The bond length between In1 and a phosphorus trimer atom in the
˚ , which is shorter than 2.66 A ˚ for the Kaxiras is 2.63 A pffiffiffi pmodel ffiffiffi ( 3 3) model by 1.1%. The height of the P trimer in the model is [1 1 1] direction with respect to In1 inpthe ffiffiffi the pffiffiKaxiras ffi ˚ , smaller than 2.47 A ˚ for the ( 3 3) model by 2%. 2.42 A In the Kaxiras model, the bond length between the In1 and the ˚ phosphorus (P1) atoms in p the ffiffiffi layer pffiffiffi below is 2.57 A which is ˚ larger than 2.54 A for the ( 3 3) model by 1.2%. The bond ˚ which is shorter than that length between In1a and P1 is 2.49 A between In1 and P1 by 3.1%. The bond length between In2 and ˚ P1 in the Kaxiras model is 2.54 pffiffiA ffi , similar pffiffiffi to the InP bulk bond length. In contrast, in the ( 3 3) model there are two different bond lengths, namely In2–P1 and In2a–P1a, both of which are different from the InP bulk bond length. The coordinate diffrence along the [1 1 1] direction, viz. dz (In1– ˚ ˚ P1), in the pffiffiKaxiras ffi pffiffiffi model is 1.10 A which is smaller than 1.16 A for the ( 3 3) model by 5.2%. More significantly, dz (In1a– ˚ P1) in the Kaxiras model is 0.49 pffiffiffi A which pffiffiffi is 33% smaller than dz ˚ (In1–P1a) of 0.73 A in the ( 3 3) model. On the chemical level, p one ffiffiffi obvious pffiffiffi diffrence between these two models is that in the ( 3 3) model every second-layer In atom is four-fold coordinated, whereas in the Kaxiras model one out of four In atoms in the second layerp isffiffiffileftpuncovered ffiffiffi and three-fold coordinated. Moreover, the ( 3 3) model
Fig. 5. The (2 2) InP(1 1 1)A-Kaxiras reconstruction: (a) top view; (b) a side view.
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K. Chuasiripattana, G.P. Srivastava / Applied Surface Science 252 (2006) 7678–7683
Fig. 6. Relative formation energy per (1 1) unit cell with respect to the InP(1 1 1)A ideal surface as a function of DmðPÞ. Dashed lines indicate the thermodynamically allowed range DHf DmðPÞ 0.
also contains 33% more P–P bonds when compared to the Kaxiras model. Since P–P bonds are quite strong, with energies of 5 eV [9], Li et al. suggested that under the metal organic vapour phase epitaxy (MOVPE) phosphorus rich growth conditions, pffiffiffi pffiffiffi the higher packing density of P trimers in the ( 3 3) reconstruction should be favoured over the (2 2)Kaxiras reconstruction. pffiffiffi pffiffiffi Thus we believe that the stability of the InP(1 1 1)A-( 3 3) model over the (2 2)-Kaxiras model comes from two sources in favour of the former: (i) a significant elastic deformation and (ii) ability to accommodate a larger number of strong P–P bonds. pffiffiffi pffiffiffi 3.4. Passivation of InP(1 1 1)A-( 3 3) There is a strong possibility pffiffiffi that pffiffiffi the seemingly clean MOVPE-grown InP(1 1 1)A-( 3 3) surface observed by Li et al. is covered by a small dosage of hydrogen present in the growth chamber. It should be pointed out that hydrogen may
influence the experimentally observed surface structures. Such a situation has already been clarified experimentally for the clean MOVPE-grown InP(0 0 1) surfaces [10,11]. Theoretical work [12] has subsequently proved the stability of the (2 1) reconstruction of hydrogen covered InP(0 0 1). With this possibility pffiffiffi pffiffiffi in mind, Li et al. [4] proposed that the InP(1 1 1)A( 3 3) surface mightpffiffipossibly ffi pffiffiffi be covered by three H atoms onto every four ( 3 3) unit cells. Li et al. [4] further that with this amount of hydrogen coverage pffiffiffisuggested pffiffiffi the ( 3 3) reconstruction should obey the ECR and make the InP(1 1 1)A pffiffiffi surface pffiffiffi semiconducting. We modelled the InP(1 1 1)A-( 3 3) covered with 1/4 ML coverage of H. However, there is a huge number of possible structures with pffiffiffi p ffiffiffi three H atoms adsorbed in every four ( 3 3) unit cells, since there are twelve P atoms out of the four P trimers for the three H atoms to sit on. We have considered some of the possible structures, as shown in Fig. 7. Our calculations clearly indicate that for each of these adsorption geometries, the
pffiffiffi pffiffiffi Fig. 7. Possible positioning of hydrogen atoms to achieve passivation of the InP(1 1 1)A-( 3 3) surface.
K. Chuasiripattana, G.P. Srivastava / Applied Surface Science 252 (2006) 7678–7683
surface becomes semiconducting and the ECR is fully observed. Thus we p can ffiffiffi confirm pffiffiffi that the H modified structure is possible on the ( 3 3) surface and the surface is both chemically as well as electronically passivated.
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pffiffiffi pffiffiffi forward by Li et al. that the ( 3 3) surface can be fully passivated by 1/4 ML coverage of hydrogen, which is readily available in a MOVPE chamber. References
4. Summary and conclusion In this work, we have presented the atomic geometry and electronic states of the InP(1 1 1)A surface in In- and P-rich conditions. In the In-rich condition we studied the well known (2 2) reconstruction with an In vacancy. In the P-rich condition we considered two reconstructions: the (2 2) reconstruction proposed p byffiffiffi Kaxiras et al. with 3/4 ML pffiffiffi coverage of P and the ( 3 3) reconstruction proposed by pffiffiffiLi et pffiffiffial. with 1 ML coverage of P. It is found that the ( 3 3) reconstruction is more stable than the (2 2)Kaxiras reconstruction, thus supporting the LEED and STM observations by Li et al. Although this reconstruction violates the ECR, it is stabilised by the development of an elastic deformation and accommodation of a larger number of P–P bonds in the surface region. We also confirm the suggestion put
[1] M.D. Pashley, Phys. Rev. B 40 (1989) 10481. [2] D.K. Biegelsen, R.D. Bringans, J.E. Northrup, L.E. Swartz, Phys, Rev. Lett. 65 (1990) 452. [3] A. Ohtake, J. Nakamura, T. Komura, T. Hanada, T. Yao, Hi, M. Kuramochi, Ozeki, Phys. Rev. B 64 (2001) 45318. [4] C.H. Li, Y. Sun, D.C. Law, S.B. Visbeck, R.F. Hicks, Phys. Rev. B 68 (2003) 85320. [5] E. Kaxiras, Y. Bar-Yam, J.D. Joannopoulos, K.C. Pandey, Phys. Rev. B 35 (1987) 9625. [6] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [7] X. Gonze, R. Stumpf, M. Scheffler, Phys. Rev. B 44 (1991) 8503. [9] J.A. Dean, Lange’s Handbook of Chemistry, 15th ed., McGraw Hill, New York, 1999. [10] L. Li, B.K. Han, Q. Fu, R.F. Hicks, Phys, Rev. Lett. 82 (1999) 1879. [11] Q. Fu, E. Negro, G. Chen, D.C. Law, C.H. Li, R.F. Hichs, K. Raghavachari, Phys. Rev. B 65 (2002) 75318. [12] W.G. Schmidt, P.H. Hahn, F. Bechstedt, N. Esser, P. Vogt, A. Wange, W. Richter, Phys. Rev. Lett. 90 (2003) 126101.
Atomic geometry, electronic states and possible hydrogen passivation of the InP(1 1 1)A surface K. Chuasiripattana *, G.P. Srivastava School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom Available online 9 May 2006
Abstract We present a first-principles theoretical study of the atomic geometry and electronics states of the InP(1 1 1)A surface under In- and P-rich conditions. The In-rich surface, characterised by an In vacancy per unit (2 2) cell, obeys the electron counting rule (ECR) and pffiffiffiis semiconducting. pffiffiffi Under P-rich conditions we have considered two surface reconstructions: (2 2) with 3/4 monolayer pffiffiffi (ML) pffiffiffi P coverage and ( 3 3) with 1 ML coverage. In complete agreement withpaffiffirecent ffi pffiffiffiexperimental work by Li et al., it is found that the ( 3 3) reconstruction is more stable than the (2 2) reconstruction. However, the ( 3 3) reconstruction has a metallic band structure and thus does not satisfy the ECR. The stability of this reconstruction is explained to arise from a competition between the ECR and a significant elastic deformation in the surface region. We confirm the suggestion by Li et al. that this surface can be passivated both chemically as well as electronically with 1/4 ML coverage of hydrogen. # 2006 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface electronic phenomena; Electron counting rule; Surface passivation; InP(1 1 1)
1. Introduction III–V(1 1 1) compound semiconductor surfaces, e.g. GaAs(1 1 1) and InP(1 1 1), are very important components in wireless communications and optoelectronics industry. It is suggested that the reconstruction of III–V surfaces would follow the electron counting rule (ECR) [1] by having all the dangling bonds of the electropositive surface atoms (III) unoccupied and all those of electronegative surface atoms (V) occupied. The gallium-terminated or GaAs(1 1 1)A surface is characterized by (2 2) reconstruction with one Ga vacancy in each unit cell (known as Ga vacancy model) [2,3] and satisfies the electron counting rule. The arsenic-terminated or GaAs(1 1 1)B surface is characterized pffiffiffiffiffi pffiffiffiffiffi by several reconstructions, e.g. (2 2), ( 19 19) and (1 1). The GaAs(1 1 1)B-(2 2) surface has one As trimer on top of a complete layer of As atoms in every unit cell [2]. Other III– V(1 1 1) surfaces, e.g. InP(1 1 1), are not well studied but believed to have the same reconstructions as GaAs(1 1 1). Recently, Li et al. [4] have reported the atomic structure of the InP(1 1 1)A (i.e. indium-terminated surface) by using
* Corresponding author. Tel: +44 1392 264198; fax: +44 1392 264111. E-mail address: [email protected] (K. Chuasiripattana). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.03.087
scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), and X-ray photoelectron spectroscopy (XPS). reconstructions were observed: (2 2) and pffiffiffi pTwo ffiffiffi ( 3 3). The InP(1 1 1)A- ð2 2Þ surface was prepared in the In-rich condition and is characterized by one In atom missing in every unit pffiffiffi cell, pffiffiand ffi thus is the vacancy model. On the other hand, the ( 3 3) surface was observed in the P-rich condition. From their STM observations, Li et al. proposed that the surface has 1 monolayer (ML) of phosphorus coverage in the form of a trimer in every unit cell. This reconstruction has never been observed before on any III–V(1 1 1) surface. For this P coverage and reconstruction, the electron counting rule is disobeyed and the surface should exhibit metallic behaviour. However, from a first-principles study, Kaxiras et al. [5] proposed that in the As-rich condition the GaAs(1 1 1)A(2 2) reconstruction should be observed. This structure satisfies the electron counting rule by having one As trimer per unit cell amounting to As coverage of 0.75 ML. This might suggest that the P-rich InP(1 1 1)A should also exhibit the (2 2) reconstruction for P coverage of 0.75 ML. In this work, we present a first-principles theoretical study of the atomic geometry and electronic states of the InP(1 1 1)A surface with the three structures discussed above. In order to avoid any possible confusion, we will label the In-rich vacancy model as InP(1 1 1)A-(2 2)-vac, P-rich Kaxiras model as
K. Chuasiripattana, G.P. Srivastava / Applied Surface Science 252 (2006) 7678–7683
InP(1 1 1)A-(2p and the P-rich Li model as ffiffiffi 2)-Kaxiras, pffiffiffi InP(1 1 1)A-( 3 3 ). We explain why the InP(1 1 1)Apffiffiffi pffiffiffi ( 3 3) model, which disobeys the ECR, is observed in STM and LEED studies and is more stable than the InP(1 1 1)A-(2 2)-Kaxiras model. We also propose a possible pffiffiffi pffiffiffi passivation mechanism of the InP(1 1 1)A( 3 3) reconstruction by a sub-monolayer coverage of hydrogen. 2. Method Our calculations were performed in the framework of the density functional theory, within the local density approximation (LDA) [6]. The electron–ion interaction was treated by using norm-conserving, ab initio, fully separable pseudopotentials [7]. The single-particle Kohn–Sham wave functions were expanded in a plane wave basis set with a kinetic energy cutoff 12 Ry. The resulting bulk equilibrium lattice constant of ˚ . Surface calculations are performed by adopting InP is 5.85 A the repeated slab model with a supercell containing pffiffifour ffi pbiffiffiffi layer of InP for the (2 2) reconstruction. For the ( 3 3) reconstruction, the supercell contained four bi-layer of InP and one layer of phosphorus trimer covered. A layer of pseudohydrogen with fractionally valency of 0.75 e was applied to saturate the anion bonds at the bottom layer of the pffiffiffi dangling pffiffiffi slab. As the ( 3 3) unit cell has a fractional number of
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electrons, pffiffiffi pwe ffiffiffi modelled this reconstruction by using a (2 3 2 3) unit cell. Both supercells also have a vacuum region equivalent pffiffiffi to twice pffiffiffi the bulk lattice constant. For both the (2 2) and (2 3 2 3) cells we generated an equivalent set of special k-points, corresponding to 12 points in the irreducible part of the (1 1) surface Brillouin zone. The bottom bi-layer of InP was kept fixed and all other atoms were relaxed to their equilibrium geometry. A dipole correction scheme was applied to eliminate the presence of the microscopic electric field extending over the supercell. 3. Results and discussions 3.1. InP(1 1 1)A-(2 2)-vac The relaxed atomic geometry of the InP(1 1 1)A-(2 2)vac model is shown in Fig. 1. The key relaxed structural parameters are tabulated in Table 1. Some of the P atoms in the top bilayer are three-fold coordinated (e.g. P1) and some are four-fold coordinated (e.g. P1a). The topmost In atoms move inward along the [1 1 1] direction with respect to their bulk ˚ and form sp2-like hybridised bonds with positions, by 0.57 A three neighbouring P atoms. The P1atoms move towards the In ˚ , forming p3-like hybridisation. In vacancy site by 0:33 A the top two layers, there is a bimodal distribution of the In–P bond length. The bond length between In1and the three-fold
Fig. 1. The III–V(1 1 1)-(2 2)-vac reconstruction: (a) top view with the shaded area indicating the (2 2) unit cell; (b) a side view in the AA0 plane; (c) electronic band structure. Table 1 pffiffiffi pffiffiffi Structural parameters for InP(1 1 1)A-(2 2)-vac, InP(1 1 1)A-( 3 3) and InP(1 1 1)A-(2 2)-Kaxiras models d (P–P)tri
d (In–Ptri)
dz (Ptri–(In1)
(2 2)-vac
d1 (In–P)
d2 (In–P)
dz (In–P)
2.51 (In1–P1) 2.59 (In1a–P1a)
2.63 (In2–P1) 2.63 (In2–P1a)
0.28 (In1–P1) 0.33 (In1a–P1a)
pffiffiffi pffiffiffi ( 3 3)
2.20
2.66
2.47
2.54 (In1–P1) 2.58 (In1–P1a)
2.49 (In2–P1) 2.61 (In2a–P1a)
1.16 (In1–P1) 0.73 (In1–P1a)
(2 2)-Kaxiras
2.23
2.63
2.42
2.57 (In1–P1) 2.49 (In1a–P1)
2.54 (In2–P1)
1.10 (In1–P1) 0.49 (In1a–P1)
˚. d: the bond length; Ptri: trimer; dz: the coordinate difference along [1 1 1]; unit: A
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pffiffiffi pffiffiffi pffiffiffi pffiffiffi pffiffiffi pffiffiffi Fig. 2. The InP(1 1 1)A- ð 3 3ÞR30 surface: (a) top view with ð 3 3ÞR30 and ð2 3 2 3ÞR30 unit cells indicated; (b) a side view.
˚ , approximately 1.2% coordinated P atoms (P1) is 2.51 A ˚ . The smaller than the theoretical bulk InP bond length of 2.54 A bond length between In1a and the four-fold coordinated P atoms ˚ , approximately 3.2% larger than the bulk bond (P1a) is 2.59 A length. The bond length between the In2 and P1, and between ˚ , approximately 3.5% larger than the bulk In2 and P1a, is 2.63 A bond length. The coordinate differences along [1 1 1] between ˚ . This In1 and P1, In1a and P1a are, respectively, 0.28 and 0.33 A shows that the In1a atoms are located slightly higher than In1. The band structure calculation shown in Fig. 1 c suggests that this surface is semiconducting. There are no electronic surface states lying within the minimum of the InP bulk valenceconduction gap. The highest occupied state originates from the dangling bond at the P1atom and is localised towards the In vacancy. The lowest unocupied state is localised at the dangling bonds of the In1a atoms and has the pz character. pffiffiffi pffiffiffi 3.2. InP(1 1 1)A-( 3 3) pffiffiffi pffiffiffi The InP(1 1 1)A-( 3 3) reconstruction is shown in Fig. 2 and in Table 1. The P–P bond length in the P-trimer is ˚ , almost identical to twice the atomic radius for P of 2.20 A ˚ 2.22 A. The bond length between In1and P-trimer atoms is ˚ , which is bigger than the InP bulk bond length of 2.54 A ˚ 2.66 A by approximately 4.7%. The P-trimer is adsorbed at the height of ˚ above the In layer. There are two types of P atoms in the 2.47 A third layer, denoted as P1and P1a. The P1 atoms are situated in the
middle right below the P-trimers while the P1a atoms are situated below but beside the P-trimers. The bond length between In1 and ˚ , 1.6% shorter than that between In1 and P1a of P1 is 2.54 A ˚ 2.58 A. The adsorption of P-trimers leads to the bond length of ˚ between In2 and P1 which is shorter than 2.61 A ˚ between 2.49 A In2a and P1a of 4.6%. The coordinate difference along [1 1 1] ˚ , bigger than 0.73 A ˚ between In1 and between In1 and P1 is 1.16 A P1a, indicating the adsorption of P-trimers has pushed the P1 ˚ . The electronic band structure in Fig. 3 atoms down by 0.43 A pffiffiffi pffiffiffi shows that InP(1 1 1)A- ð 3 3Þ is a metallic surface. The metallicity of this surface is more clearly shown in Fig. 3 b. The Fermi energy level cuts through both the largely occupied bands indicated as V1 and a largely unoccupied band (C1). The partial charge density plot in Fig. 4 a at the G point in the horizontal plane containing the phosphorus trimers shows the s orbital character of the phosphorus atoms. The plot in Fig. 4 b in the aa0 plane shows the pzorbital character of the phosphorus-trimer atoms. We conclude that the metallicity of this surface comes from the partially filled bands originating from the P-trimer atoms and has an overall spz character. pffiffiffi pffiffiffi 3.3. Stability of the InP(1 1 1)A-( 3 3) surface In view of the fact that Kaxiras et al. [5] predicted the GaAs(1 1 1)A-(2 2)-Kaxiras surface to be a stable configuration, and that experimental observations by Li petffiffiffi al.p[4] ffiffiffi suggest a stable configuration for the InP(1 1 1)A-( 3 3)
pffiffiffi pffiffiffi Fig. 3. (a) Surface electronic band structure for the InP(1 1 1)A-( 3 3) surface; (b) details near the Fermi energy level.
K. Chuasiripattana, G.P. Srivastava / Applied Surface Science 252 (2006) 7678–7683
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pffiffiffi pffiffiffi Fig. 4. Partial charge density plot of the InP(1 1 1)A-( 3 3) surface at the G point: (a) a combination of the three partially filled states in the horizontal plane containing P trimers; (b) a combination of the three partially filled states in the aa0 vertical plane containing one P atom. Units: 103 e/bohr3.
surface, we investigated pffiffiffi pffiffiffi the relative stability of the (2 2)Kaxiras and ( 3 3) models for InP(1 1 1)A. The (2 2)Kaxiras model is shown in Fig. 5. We calculated the formation energy of the two reconstructions as a function of the chemical potential of phosphorus. The surface formation energy (DEi ) can be expressed as DEi ¼ Ei Eideal DnP DmPp ffiffiffiDnPp mffiffiPffi bulk , where Ei is the total energy of the InP(1 1 1)A-( 3 3) or the InP(1 1 1)A-(2 2)-Kaxiras model, Eideal the total energy of the InP(1 1 1)A ideal surface (viz. the InP(1 1 1)A-(2 2) reconstruction without In vacancy), DnP the difference in the number of P atoms between the two models, and DmP is the chemical potential of phosphorus relative to the bulk phosphorus chemical potential. The bulk phosphorus chemical potential (mPbulk ) is calculated from the total energy of the orthorhombic phase of phosphorus. The results pffiffiffi pin ffiffiffi Fig. 6 indicate that in the P-rich condition, the ( 3 3) reconstruction is more stable than the (2 2)-Kaxiras reconstruction for the whole range of DmP . This clearly explains that the (2 2)-Kaxiras reconstruction is unlikely to be observed for the InP(1 1 1)A surface. The P–P bond length in the ˚ phosphorus trimer in the Kaxiras pffiffiffi model pffiffiffi is 2.23 A, which is ˚ bigger than 2.20 A for the ( 3 3) model by 1.4%. The bond length between In1 and a phosphorus trimer atom in the
˚ , which is shorter than 2.66 A ˚ for the Kaxiras is 2.63 A pffiffiffi pmodel ffiffiffi ( 3 3) model by 1.1%. The height of the P trimer in the model is [1 1 1] direction with respect to In1 inpthe ffiffiffi the pffiffiKaxiras ffi ˚ , smaller than 2.47 A ˚ for the ( 3 3) model by 2%. 2.42 A In the Kaxiras model, the bond length between the In1 and the ˚ phosphorus (P1) atoms in p the ffiffiffi layer pffiffiffi below is 2.57 A which is ˚ larger than 2.54 A for the ( 3 3) model by 1.2%. The bond ˚ which is shorter than that length between In1a and P1 is 2.49 A between In1 and P1 by 3.1%. The bond length between In2 and ˚ P1 in the Kaxiras model is 2.54 pffiffiA ffi , similar pffiffiffi to the InP bulk bond length. In contrast, in the ( 3 3) model there are two different bond lengths, namely In2–P1 and In2a–P1a, both of which are different from the InP bulk bond length. The coordinate diffrence along the [1 1 1] direction, viz. dz (In1– ˚ ˚ P1), in the pffiffiKaxiras ffi pffiffiffi model is 1.10 A which is smaller than 1.16 A for the ( 3 3) model by 5.2%. More significantly, dz (In1a– ˚ P1) in the Kaxiras model is 0.49 pffiffiffi A which pffiffiffi is 33% smaller than dz ˚ (In1–P1a) of 0.73 A in the ( 3 3) model. On the chemical level, p one ffiffiffi obvious pffiffiffi diffrence between these two models is that in the ( 3 3) model every second-layer In atom is four-fold coordinated, whereas in the Kaxiras model one out of four In atoms in the second layerp isffiffiffileftpuncovered ffiffiffi and three-fold coordinated. Moreover, the ( 3 3) model
Fig. 5. The (2 2) InP(1 1 1)A-Kaxiras reconstruction: (a) top view; (b) a side view.
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Fig. 6. Relative formation energy per (1 1) unit cell with respect to the InP(1 1 1)A ideal surface as a function of DmðPÞ. Dashed lines indicate the thermodynamically allowed range DHf DmðPÞ 0.
also contains 33% more P–P bonds when compared to the Kaxiras model. Since P–P bonds are quite strong, with energies of 5 eV [9], Li et al. suggested that under the metal organic vapour phase epitaxy (MOVPE) phosphorus rich growth conditions, pffiffiffi pffiffiffi the higher packing density of P trimers in the ( 3 3) reconstruction should be favoured over the (2 2)Kaxiras reconstruction. pffiffiffi pffiffiffi Thus we believe that the stability of the InP(1 1 1)A-( 3 3) model over the (2 2)-Kaxiras model comes from two sources in favour of the former: (i) a significant elastic deformation and (ii) ability to accommodate a larger number of strong P–P bonds. pffiffiffi pffiffiffi 3.4. Passivation of InP(1 1 1)A-( 3 3) There is a strong possibility pffiffiffi that pffiffiffi the seemingly clean MOVPE-grown InP(1 1 1)A-( 3 3) surface observed by Li et al. is covered by a small dosage of hydrogen present in the growth chamber. It should be pointed out that hydrogen may
influence the experimentally observed surface structures. Such a situation has already been clarified experimentally for the clean MOVPE-grown InP(0 0 1) surfaces [10,11]. Theoretical work [12] has subsequently proved the stability of the (2 1) reconstruction of hydrogen covered InP(0 0 1). With this possibility pffiffiffi pffiffiffi in mind, Li et al. [4] proposed that the InP(1 1 1)A( 3 3) surface mightpffiffipossibly ffi pffiffiffi be covered by three H atoms onto every four ( 3 3) unit cells. Li et al. [4] further that with this amount of hydrogen coverage pffiffiffisuggested pffiffiffi the ( 3 3) reconstruction should obey the ECR and make the InP(1 1 1)A pffiffiffi surface pffiffiffi semiconducting. We modelled the InP(1 1 1)A-( 3 3) covered with 1/4 ML coverage of H. However, there is a huge number of possible structures with pffiffiffi p ffiffiffi three H atoms adsorbed in every four ( 3 3) unit cells, since there are twelve P atoms out of the four P trimers for the three H atoms to sit on. We have considered some of the possible structures, as shown in Fig. 7. Our calculations clearly indicate that for each of these adsorption geometries, the
pffiffiffi pffiffiffi Fig. 7. Possible positioning of hydrogen atoms to achieve passivation of the InP(1 1 1)A-( 3 3) surface.
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surface becomes semiconducting and the ECR is fully observed. Thus we p can ffiffiffi confirm pffiffiffi that the H modified structure is possible on the ( 3 3) surface and the surface is both chemically as well as electronically passivated.
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pffiffiffi pffiffiffi forward by Li et al. that the ( 3 3) surface can be fully passivated by 1/4 ML coverage of hydrogen, which is readily available in a MOVPE chamber. References
4. Summary and conclusion In this work, we have presented the atomic geometry and electronic states of the InP(1 1 1)A surface in In- and P-rich conditions. In the In-rich condition we studied the well known (2 2) reconstruction with an In vacancy. In the P-rich condition we considered two reconstructions: the (2 2) reconstruction proposed p byffiffiffi Kaxiras et al. with 3/4 ML pffiffiffi coverage of P and the ( 3 3) reconstruction proposed by pffiffiffiLi et pffiffiffial. with 1 ML coverage of P. It is found that the ( 3 3) reconstruction is more stable than the (2 2)Kaxiras reconstruction, thus supporting the LEED and STM observations by Li et al. Although this reconstruction violates the ECR, it is stabilised by the development of an elastic deformation and accommodation of a larger number of P–P bonds in the surface region. We also confirm the suggestion put
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