Electronic and Structural Properties of Si 46 : A Novel Solid of Silicon Fullerenes
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Figure 1: Dodecahedral Si20 fullerene.
55 Mat. Res. Soc. Symp. Proc. Vol. 358 01995 Materials Research Society
Figure 2: Geometry of Na 2 Ba.6 Si 46 . There are two dodecahedral Si 2o fullerenes per unit
cell forming bcc lattice with 90* rotation of the center Si 20 . Additional Si atoms (smallest hatched spheres) and Ba atoms (large open spheres) occupy the interstitial sites of the bcc lattice. Na atoms (smaller open spheres) occupy the Si20 center site. In the middle of 1980s, on the other hand, we proposed the twenty-atom dodecahedral-cage cluster of group-IV elements (C20 , Si20 , and Ge 20) (Fig.1) [8] and reported [9] the electronic structure of Si20 obtained using the local-density approximation (LDA) in the density-functional theory [10]. This dodecahedral cluster is now known as the smallest possible fullerene unit consisting of twelve pentagons and no hexagons. In the present work, we report the electronic and geometrical properties of the Si lattice consisting mainly of Si 20 fullerenes (Si46 ), and its metal-doped fulleride (Na 2 Ba 6Si4e). GEOMETRIES In Fig.2, the geometry of the metal-doped fulleride Na2Ba 6 Si46 is shown. In this Si network, Si20 fullerenes form the body-centered cubic (bcc) lattice with 90* rotation of the center Si20 , giving the simple-cubic (sc) unit cell. In addition, three more Si atoms occupy the distorted-tetrahedral interstitial sites fo the bcc lattice. Due to the bonds between these interstitial-site atoms and Si20 fullerenes as well as between Si20 fullerenes, all 46 Si atoms are tetrahedrally coordinated. We have optimized the geometry of the Si46 lattice through the total-energy electronic-structure calculation in the LDA. We used the normconserving pseudopotentials with plane-wave basis set (8 and 16 Ryd cut-off energy for the geometry optimization and the electronic-structure calculation, respectively), and the geometrical parameters have been optimized using the conjugategradient procedure [11]. At the optimized geometry, the lattice constant is found to be 10.19 A, or just about 1 nm. The average bond length and angle are 2.366 A and 109.4', respectively. The cohesive energy per atom in Si46 is found to be only 0.09 eV smaller than that of the diamond Si lattice. These geometrical parameters are very similar to the observed values in Na and Ba codoped Si4 6 : 10.26 A, 2.383 A, and 109.4' [12], which are used for the electronic-structure calculation for Na 2 Ba 6 Si46.
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Energy (eV) Figure 3: Electronic density of states of (a) Si46 and (b) Na 2Ba6Si 46. ELECTRONIC STRUCTURE The calculated electronic DOS of the Si 46 lattice is shown in Fig.3(a). There are several remarkable points to be noted compared with the diamond lattice. First of all, there appears a new gap within the valence band in addition to the fundamental gap between the valence band and the conduction band. This fundamental gap is also considerably wider than that of the diamond lattice. Their
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