Structure and energetics of Ga-rich GaAs(001) surfaces - Institut fÃ¼r ...

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K. Seino et al. / Surface Science 507–510 (2002) 406–410 407 calculated in order to identify the most favourable adsorption sites and to study the diffusion characteristics. Based on these data possible configurations for a (4 6) reconstructed GaAs surface are probed. 2. Computational method Fig. 1. Top and side view of the relaxed GaAs(0 0 1)fð4 2Þ surface. Light (dark) balls represent Ga (As) atoms. The notation of the atoms corresponds to Table 1. GaAs(0 0 1)(4 2) surfaces [9,10] indicates that either the surface has many defects or that structuralmodels different from the f structure need to be considered. Under certain preparation conditions the STM images of the Ga-rich GaAs(4 2) surface show additionalcorrugations [11–13]. Xue and co-workers [1,11] interprete these corrugations as clusters consisting of 6–8 Ga atoms. According to their studies these Ga clusters are responsible for the observation of the (4 6) surface reconstruction. A more recent study by Kruse et al., on the other hand, associates the corrugations seen in similar STM images to surface excess charge localized in Ga dangling bonds of the GaAs(4 2) surface [12]. As or Ga adatoms could be another explanation for STM observations: fourfold coordinated Ga adatoms in the trenches of the (4 2) surface are seemingly observed in X-ray diffraction experiments [7]. We perform first-principles total-energy calculations in order to contribute to a better understanding of the Ga-rich GaAs(0 0 1) surface. The potential-energy surface (PES) for Ga and As adsorbed on the GaAs(0 0 1)fð4 2Þ geometry is The calculations are based on a real-space finite-difference implementation [14] of the densityfunctionaltheory in local-density approximation (DFT-LDA). Nonlocal norm-conserving pseudopotentials [15] are used for the description of the electron-ion interaction. Ga 3d electrons are partially taken into account by means of a nonlinear core correction to the exchange and correlation energy. The spacing of the finest grid used to represent the electronic wave functions and charge density was determined through a series of bulk calculations. We find that structural and electronic properties are converged for a spacing corresponding to 4% of the bulk lattice constant. The calculations were performed using the theoretical equilibrium lattice constants of 5.57 A for GaAs. Integrations in the surface Brillouin zone are performed over four special k points in its irreducible part. We modelthe surfaces by using periodic supercells containing material slabs which are about 12 A thick. They are separated by 12 A of vacuum. The dangling bonds at the bottom layer are saturated with fractionally charged pseudohydrogens. The atoms in the lowest bilayer are kept frozen in their idealbulk positions. In order to map the PES the [0 0 1] coordinate of the respective adatom is allowed to relax, while its lateral position is fixed. 3. Results and discussion In Fig. 2 the calculated phase diagram for the GaAs(0 0 1) surface is shown. Extreme and moderately As-rich surfaces are characterized by cð4 4Þ and b2ð2 4Þ reconstructions, respectively [6]. For a very narrow range of surface preparation conditions the a2ð2 4Þ surface [3] may be observed. Under Ga-rich conditions the fð4 2Þ structure due to Lee et al. [4] forms (cf. Fig. 1).
408 K. Seino et al. / Surface Science 507–510 (2002) 406–410 Table 1 Calculated atomic coordinates (in A, normalized to the experimentallattice constant) of the GaAs(0 0 1)fð4 2Þ surface x y z First layer Ga(1) 7.943 2.770 2.882 As(2) 5.745 2.054 3.797 Ga(3) 4.423 0.002 3.375 Ga(4) 4.335 3.991 3.276 As(5) 1.982 3.996 3.043 As(6) 2.049 0.006 3.072 Second layer Ga(7) 2.013 1.990 1.603 Ga(8) 5.829 1.270 1.288 Fig. 2. Relative formation energy per (1 1) unit cell for GaAs surface reconstructions vs. the Ga chemicalpotential. Dashed lines mark the approximate anion- and cation-rich limits of the thermodynamically allowed range of Dl(Ga). Structural details of the calculated f modelare given in Table 1. They are in excellent agreement with the X-ray diffraction data by Paget and coworkers [7]. Another X-ray diffraction study [8] suggests a slightly modified f structure, with additionalGa adatoms. The most favourable sites for the adsorption of single Ga or As atoms are given by the global minima of the respective PES. The calculated PES for Ga and As adsorption on top of the (4 2) reconstructed GaAs(0 0 1) surface is shown in Fig. 3. We find the adsorption behaviour for ad-cations to be very different from that of adsorbed anions. The preferred bonding position for single Ga adatoms (AC in Fig. 3) is located in the trenches, Third layer As(9) 3.904 2.000 0.012 As(10) 7.982 1.977 0.198 As(11) 0.022 1.974 0.198 The notation of the atoms corresponds to Fig. 1. fourfold coordinated between the doubly occupied dangling bonds of the first layer As atoms (see Ref. [9] for a discussion of the surface electronic properties of GaAs(0 0 1)fð4 2Þ). That position seems to agree with a recent X-ray analysis [7], which was interpreted to indicate that about 19% of the AC positions are occupied by Ga adatoms. However, even at extreme Ga-rich surface preparation conditions we find the adsorption of additionalGa atoms in AC position to increase the surface energy per (1 1) surface unit cell by 0.1 eV. It does therefore not constitute an equilibrium surface structure. Fig. 3 shows also the PES as experienced by As adatoms on top of the GaAs(0 0 1)fð4 2Þ surface. In this case the most favourable adsorption position (denoted AA) allows a threefold coordination of the As adatom with three empty Ga dangling bonds. However, occupation of the AA site Fig. 3. Potential-energy surface for the adsorption of As (left panel) and Ga (right panel) on the Ga-rich GaAs(0 0 1)fð4 2Þ surface. The contour spacing is 0.15 eV. Light regions indicate low-energy adsorption positions.
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