Long-Range Surface Reconstruction: Si110-16  2 A. A. Stekolnikov, J. Furthmu ¨ller, and F. Bechstedt Institut fu ¨r Festko ¨rpertheorie und -optik, Friedrich-Schiller-Universita ¨t, 07743 Jena, Germany (Received 14 April 2004; published 22 September 2004) A variety of reconstruction models is studied for the Si110-16  2 surface using first-principles calculations. Assuming appropriate rebonding of edge atoms and surface chains buckled in antiphase, we show that steps along the   112 direction yielding a trench indeed lower the surface energy. We explain the long-range surface reconstruction and develop a geometry model based on steps, adatoms, tetramers, and interstitials. The model is able to explain the stripes of paired pentagons seen obviously in empty-state scanning tunneling microscopy images. DOI: 10.1103/PhysRevLett.93.136104 PACS numbers: 68.35.Bs, 68.35.Md, 68.37.Ef, 73.20.At Low-index surfaces of group-IV semiconductors such as Si111-7  7 or Ge111c2  8 show long-range reconstructions. This tendency is also observable in the (110) case. Nonvicinal, clean, and well-annealed Si(110) surfaces exhibit a 16  2 reconstruction [1], the atomic structure of which is still unknown. In recent years important structural details have been obtained from scanning tunneling microscopy (STM) experiments [1–5]. They clearly showed that the bond rotation and bond contraction relaxation accompanied with zigzag chains along the   110 direction, i.e., the mechanism on the 1101  1 surfaces of III–V semicon- ductors, does not occur in the Si(110) case. Rather, STM studies [1–5] suggested that a 16  2 reconstructed Si(110) surface consists of equally spaced and alternately raised (up-stripes) and lowered (down-stripes) stripes parallel to the   112 direction which are separated by atomic steps with height a 0 =2  2 p (a 0 is the bulk lattice constant). The STM images of the stripes are less clear and consequently led to different local pictures and atomic structures [1,4,5]. This concerns the contradictory results obtained for filled-state and empty-state images, the clarity of the images, as well as the spot arrangements. In any case, the stripes consist of zigzag pattern with a repetition distance of  6 p a 0 [5]. The stripes are stacks of paired elements whose shape is interpreted differently by the various authors: octets [6], pentagons [4], or even arrangements of centered stretched hexagons [5]. Based on the different numbers of observed spots, several atomic geometries have been proposed to interpret the Si110-16  2 surface including different reconstruc- tion elements, e.g., adatoms, dimers, missing rows, and tetramers with interstitial atoms [1,4,5,7,8]. However, there are no total-energy calculations for the resulting structures, only for isolated structural elements and smaller unit cells [9–12]. In order to understand the atomic geometry and the bonding of the Si110-16  2 surface, one has to study the energetic preference and the structure of the step configuration observed by STM. Until now there has been no idea why steps may occur on a flat, nonvicinal low-index surface and how they contribute to the stabili- zation of the 16  2 translational symmetry. First- principles calculations exist only for the Ge110-16  2 surface [13]. They suggest a higher surface energy when steps are introduced, in contrast to the experimental observations of images in form of stripes on lower and higher terraces also for germanium [14]. In this Letter we present results of a systematic study of the 16  2 reconstruction of the Si(110) surface based on ab initio calculations. Whole 16  2 unit cells with nomi- nally 64 atoms in one atomic layer are investigated. The total-energy calculations are performed within the den- sity functional theory in the local density approximation. The electron-electron interaction is described by the Ceperley-Alder functional. The interaction of the elec- trons with the atomic cores is treated by non- normconserving ab initio ultrasoft pseudopotentials [15]. An energy cutoff of 130 eV is used. Explicitly we use the VASP code [16]. In the bulk case, our calculation yields a cubic lattice constant of a 0  5:398  A and an indirect fundamental energy gap of E g  0:46 eV. The surfaces are modeled by repeated slabs. Each 16  2 slab consists of seven atomic layers and nine layers of vacuum. The bottom sides of the slabs are passivated by hydrogen atoms and kept frozen during the surface optimization. The topmost five layers of each slab are allowed to relax. Two k points are used in the irreducible part of the Brillouin zone. The surface geometry is de- termined allowing to relax the atomic positions until the Hellmann-Feynman forces are less than 10 meV=  A. The eigenvalues and eigenfunctions of the Kohn-Sham equa- tion [17] are used to calculate the STM images within the Tersoff-Hamann approach [18] assuming a constant- height mode. In order to get an idea about the convergence of the total-energy and force calculations using the 16  2 oblique Bravais lattice, we have first studied the ideal, relaxed Si(110) surface. The bond-rotation relaxation with all chains buckled in one direction gives rise to an energy gain of 0.44 eV per 1  1 unit cell (see Table I). VOLUME 93, NUMBER 13 PHYSICAL REVIEW LETTERS week ending 24 SEPTEMBER 2004 136104-1 0031-9007= 04=93(13)=136104(4)$22.50  2004 The American Physical Society 136104-1