This section will concentrate on the further stabilization of system-I by means of the addition of adatoms and will investigate the effect of symmetric and antisymmetric dimer bond tilting on surface energy. The next thing considered is a 1 1 adatom reconstruction of the Si-BC8(001) surface. Atoms v and w are placed close to the surface (see Figure 6.2) such that a dimer is formed bonding to each of the dangling bonds on atoms g, i, b and p thus reducing the number of dangling bonds to 2 per unit cell. The initial configuration is set such that the five bonds created by the adatoms are approximately equal in length and the adatoms are placed at the same height above the cleavage plane. On relaxation of this (from now on known as system-III), the dimer tilts from being parallel to the surface to an angle of 6.5 . A three dimensional representation of the charge density of the 2 1 symmetric dimer is shown in Figure 6.5 where four symmetrically tilted dimers are illustrated. The bond length of the dimer relaxes to a length of 2.31Å. This bond length is shorter than either of the bulk bondlengths. This is probably due to -bonding between the atoms of the dimer. The bonds formed from the dimer to atoms i,b,g and p relax to approximately equal lengths (2.45 Å, 2.39Å, 2.34Å and 2.46Å, respectively). The valence charge in the dimer is found to be 2.3 electrons while the dimer-to-bulk bonds contain approximately 2.1 electrons. A contour plot of the electronic charge density in a slice through the surface dimer is shown in Figure 6.4. The charge in the dimer being larger than that of a single covalent bond also suggests -bonding in the dimer. The surface energy of system-III is found to be 0.0796eVÅ which is lower in energy than that of any other previously reported silicon surface. To check that no further relaxation takes place between dimers in neighbouring cells, a 2 1 symmetric dimer configuration was examined. The surface energy and dimer tilt angle of the corresponding 2 1 configuration was found to be identical to the 1 1 case which indicates that the symmetric dimer configuration is completely described in system-III.
Figure 6.4: Charge density plot in the plane defined by the surface dimer atoms v-w and atom g. the dimer bond charge density is clearly higher than that of the w-g bond.
Figure 6.5: Three dimensional valence charge density of the (001) surface with the symmetric dimer configuration of silicon in the BC8 structure. The figure shows an isosurface of the charge density where the symmetrically tilted dimers can clearly be seen. This figure gives evidence that, although BC8 Si is semimetallic, the bonds are covalent in nature. Note the slightly larger bonds on the dimers illustrating they contain more electronic charge than that of the single covalent bonds found in the bulk.
The 2 1 dimer configuration was set up in a symmetric formation. It is possible that this is only a local minimum energy configuration, being metastable with respect to an antisymmetric dimer configuration. To investigate this point further, the 2 1 antisymmetric-tilt reconstruction of BC8 Si is also considered. This configuration is referred to as system-IV. In this case the calculation is begun by tilting alternate dimer bonds in opposite directions and then allowing the configuration to relax. It is found that this corresponds to a metastable situation in which the antisymmetric configuration is preserved. However, the angle that each dimer forms to the surface differs greatly. One dimer forms an an angle to the surface of only 3 where atom v is 0.11Å below the level of atom w. Using the same notation to label the atoms in the cell containing the other dimer, atom v is 0.44Å above the level of atom w therefore tilting in the opposite direction at an angle of 11 to the plane of the surface. Similar to that of the symmetric case the dimer bondlengths both reduce in length, in this case to 2.26Å each containing a charge, slightly greater than that of a single bond, of 2.3 electrons. Quite surprisingly, this antisymmetric dimer configuration is found to be the least favorable of any of the surfaces considered here, having a surface energy of 0.1460eV/Å .