Ab Initio Molecular Dynamics Study of Al, Ga and Si Adsorption on the Si(001) Surface
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(Actual configurations will be shown later in Fig. 1.) We found that the 2x2 orthogonal dimer configuration is least stable for both Al and Si, and the 2x2 parallel dimer and the 2x4 configurations are most stable for Al and Si, respectively. This is consistent with the experimental and theoretical results[2-5,7,9-10], and the results for the Al adsorption agree well with other theoretical results[l I]. To understand more deeply the, difference of the stable structures, we calculated the LDOS of each surface atom for these optimized configurations. We newly developed a method of calculating the LDOS of each atom for the plane wave basis. MODEL AND METHOD The present calculation is based on the local density approximation in the density functional theory and on the norm-conserving pseudopotential. The pseudopotentials we used for Al, Ga and Si are obtained following the prescription by Bachelet, Hamann and Schluter[15], and are transformed into a separable form as suggested by Kleinman and Bylander[16]. The d part is treated as a local potential. We adopt a repeating-slab geometry and a plane wave basis. The unit cell consists of a substrate of 10 Si-layers and a vacuum region of the same thickness. The cut-off energy of the plane-wave basis is 9.0 Ry. We use 8 k points in the two dimensional irreducible Brillouin zone for the 2x2 configurations and 2 k points for the 2x4 configuration. We adopt the steepest-descent type algorithm for the electronic degree of freedom as proposed by Williams and Soler[ 17], and ordinary molecular dynamics for the ionic motion. In the process of structure optimization, the Si atoms in the two center layers of each Si slab are fixed at the bulk positions. SFor all optimized structures, we calculate densities of states of each surface atom. Generally, the tetrahedron method[1 8,19] is used to calculate DOS p,( ) at an energy level E. NT
Here, i and v denote a tetrahedron and a band, respectively, and NT is the number of tetrahedra. fi, 1 ( e ) is a function of e, and depends on the energy eigen values at four comer k points of the i-th tetrahedron and the tetrahedron volume. We define LDOS of an atom denoted by E as, NT
P$ where w (i, v ,) tetrahedron.
)
(2)
Vi= l
is a weight factor which is the contribution of the $ -th atom to the i-th
w(i,
V
fij
f I Fj(
a•
)
dr
(3)
Here, n(ij) means that the j-th corner k-point of the i-th tetrahedron corresponds to the n-th kis a region for the $ -th atom allocated in a similar point in the irreducible Brillouin zone. 0 way as the Wigner-Seitz cell.
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RESULTS AND DISCUSSION Al adsorption We optimized three kinds of configurations for the case of 0 = 1/2 as described : 1) 2x2 orthogonal dimer configuration (Fig.I a); 2) 2x2 parallel dimer configuration (Fig. I c); 3) 2x4 (dense) orthogonal dimer configuration (Fig.I b). Adsorbed Al atoms form symmetric dimers in all cases. In the 2x2 configurations, the substrate Si-dimers become symmetric and their bond length expands due to the termination of the dangling bonds. In the case of t
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