Despite the complexity of the surface reconstructions now known, certain simple assumptions remain. The most obvious of these is that the reconstruction is always treated as taking place on the stable diamond structure bulk material. However, as described previously, Si is known to also exist at ambient pressure in the metastable low-symmetry crystal structure BC8.
The departures from ideal tetrahedral bonding in BC8 silicon also make it an important prototype crystal for understanding the effects of short range disorder on the properties of amorphous Si. It is therefore important to study the surface of such a structure since features common to amorphous silicon may exist.
Band structure calculations suggest that BC8 Si is semimetallic, as calculated in Chapter 3, however, integration of the BC8 Si bond charge yields exactly 2.0 electrons (see the discussion on bond charge integration in Chapter 3) per bond with a maximum of charge density between the two atoms indicating that its cohesion is dominated by covalent bonding despite its semimetallic transport properties. This suggests that a covalently bonded model of the surface is an appropriate description. The reconstructive pressure-induced transitions which lead to BC8 Si formation occur with large volume discontinuities and do not preserve single crystals. This has so far precluded examination of the BC8 Si surface by conventional experimental methods and makes computer simulations essential.
In what follows, the notation used (for example, (001) surface, reconstruction, etc.) refers to the 16 atom simple cubic representation of the BC8 structure as opposed to the 8 atom body centred description of the unit cell.
The BC8 unit cell has two double layers perpendicular to the (001) direction. This gives two distinct possible terminations of the crystal normal to this direction. As pointed out by Biswas et al , (001) possesses a natural cleavage plane which breaks the least number of bonds (all B-bonds), 17.5% more broken bonds per unit area than the Si-I (111) cleavage plane, but half as many as the alternate BC8 (001) truncation discussed below. Structurally, the resulting surface (which is hereafter referred to as system-I) consists of B bonds lying in the plane linking dimers of threefold coordinated atoms. This surface is shown in Figure 6.2 and does not include atoms labeled v and w. Each atom in the dimer has an A and B bond extending into the bulk and a dangling B-bond. This is similar in nature to the dimers formed on 2 1 reconstruction of the Si-I (111) surface. The supercell representing system-I involves 32 silicon atoms.
Figure 6.2: The 1 1 reconstruction of the Si-BC8 (001) surface showing dimerization of the adatoms. The numbers in the circles gives the height of the atoms in units of a/10 ( is the BC8 unit cell parameter). The figure illustrates systems-I (without the adatoms), III and IV. The letters a to p are used to label the atoms. Adatoms v and w show the position of the dimer reconstruction of the surface and the dashed lines indicate the bonds formed by the adatoms.
The other possible (001) termination of the BC8 crystal is a cut leaving each of the four resulting surface atoms having two dangling bonds. This surface (referred to as system-II) is shown in Figure 6.3 and it contains two surface dimer bonds O - D and I - F. Each atom in a dimer has only one B-bond directed into the bulk. A simple counting of broken bonds suggests that this surface will be considerably less favorable than that of system-I. This supercell also contains 32 atoms.
Figure 6.3: This figure illustrates the reconstruction undergone by system-II. The notation is similar to that of the previous figure and the dashed lines illustrate the bonds formed by the four 5-fold coordinated atoms on the layer below the surface.
Both systems-I and II are allowed to relax from their intial starting configurations which is that of the terminated bulk crystal by allowing the atoms to move using a conjugate gradients algorithm. This represents the two simplest forms of surface reconstructions possible on the (001) plane of BC8 silicon.
After relaxation of system I, the surface dimers b-g and i-p (see Figure 6.2 which describes the notation) reduce in length from the unrelaxed bulk value of 2.36Å to 2.28Å. The charge density within the bond is integrated by the method given in Chapter 3. The charge associated with a surface dimer increases to 2.2 electrons with the remaining 1.8 electrons localised in non-bonding orbitals directed into the vacuum. The A and B bonds from each surface atom extending into the bulk contain a charge of 2.0 electrons. The length of each bond increases, although most notably the A bonds o-b and p-a become the longest at 2.60Å. These changes in bond lengths are associated with a tilt of the dimer from initially lying parallel to the surface. Atoms b and p are displaced upwards by 0.13Å such that the dimers tilt at 3.3 to the plane of the surface. The total surface energy of system-I (after ionic relaxation) is found to be 0.1057eV/Å .
For system-II it is found that substantial structural relaxation occurs in the top surface layer and that the resulting surface energy is only 0.0047 eV/Å higher than that of system-I. With two dangling bonds per surface atom, system II relaxes in a somewhat different manner as shown in Figure 6.3. The surface atoms D, F, I and O relax in such a way as to reduce the second nearest neighbour distance to atoms on the lower plane. Atoms A, G, L and N become five fold coordinated, where the dangling bonds are partially saturated in order to create the fifth bond, that is, charge goes out of the dangling bond to create a new covalent bond. These extra bonds fall into two distinct categories. Bonds A-F and G-D are slightly shorter at 2.61Å than bonds L-O and N-I at 2.64Å. In both cases the atoms of each bond have moved together from the unrelaxed second nearest neighbour distance of 3.39Å. Although the two fifth neighbour bondlengths only differ by approximately 1% the charge differs by 15% with 2.0 electrons in the short bond and 1.7 electrons in the long bond. The two surface dimers in the unit cell I-F and D-O reduce in length from the bulk B bond length to 2.25Å. Although the dimer remains in the plane of the surface, the dipole formed by the movement of charge from the dangling bond causes the dimers to rotate by an angle of 22.9 from the bulk position about the center of the bond in a direction such that the fifth nearest neighbour (the new donated bond) distance is shortened.