The Di-Carbon Defect

All atoms of an 87 atom cluster C Si H containing two substitutional C atoms between which a Si is sited, were allowed to relax. This corresponds to the B-form of the di-carbon defect shown in Fig. 3. The Si moved away from the bond centered site, with the carbon atoms moving slightly from their substitutional sites until the equilibrium structure was obtained. The bonding in the equilibrium structure is given in Table 1. The C-Si -C angle is 126 showing that the Si has moved well-away from a bond centered site. This leads to a great splitting in the two gap Kohn-Sham levels and is consistent with the large donor-acceptor level difference.

The local vibrational modes of this defect are given in Table . It is clear that the B-form must give rise to six local modes - two of which are A modes due to asymmetric and symmetric stretch of the C-Si . These modes must be of high frequency, simply because the reduced coordination of Si must result in stronger C-Si bonds. The remaining four modes involve predominantly the motion of the C atoms together with their Si neighbors. If the Si was at the bond centered site, these would correspond to two degenerate E modes in a defect, but are split into four with the lower C symmetry resulting from the displacement of Si .

We find six modes above the Raman peak, ranging from 543 to 838 cm . The C-Si stretch modes occur at 838 and 715 cm and these shift by 22 and 23 cm with pure C, but pronounced shifts occur in the mixed isotope case. The shifts of these modes in the mixed case reflect the fact that the two carbon atoms are almost equivalent in this configuration. The magnitude of these modes, and the fact that they exhibit mixed splitting clearly rules them out as being responsible for the modes observed by PL.

The next four modes involve mainly the C atoms and their back bonded neighbors, with little motion of Si . The 649 and 552 cm modes are decoupled with one carbon moving along [011] in each mode. However, these modes are of B symmetry, and therefore would not be detected by PL. The final two local modes are of A symmetry, occurring at 582 and 543 cm , and represent vibrations in which each C atom moves independently against its Si neighbors, but not including Si . These modes shift by 14 and 5 cm with pure C, but the additional modes in the mixed isotopic case are all within 2 cm of the pure modes. Therefore these modes are essentially decoupled, and are in excellent agreement with the those found by PL. This gives two A modes at 579 and 543 cm with shifts 15 and 10 cm for pure C. No further vibrational modes are observed experimentally, which raises the question as to why the highest two calculated A modes are not detected. Now, PL does not necessarily detect all A modes of a defect, for example in the C defect, discussed above, the A mode at 921 cm is not detected as a replica of the 856 meV zero phonon line. However, IR studies on the di-carbon defect have also failed to find any local modes. A possible explanation as to why these higher modes are not detected is that they have very short lifetimes. The energy of these modes 0.1 eV, is comparable to the activation barrier for the conversion from the B-form to the A-form (0.16 eV). Since the configuration energy curves must have zero gradient at the barrier height, it suggests that the curves cannot be described by a harmonic potential much beyond 0.1 eV. We therefore suggest that anharmonic effects are considerable, leading to particularly large three phonon scattering processes which have very short lifetimes.

Investigations were also made into the A-form of the defect, shown in Fig. 2, the equilibrium bond lengths are given in Table 1. The energy differences between the two forms in the neutral charge state was found to be 0.35 eV, the A-form being lower, - a figure very much greater than the experimental difference of about 0.04 eV. It seems that accurate energy differences require a very much larger cluster as the strain fields of the two defects are very different. Although there is an offset of around 0.3 eV between our results and experiment, it is interesting to investigate the trends in energy difference between the two configurations with charge state. The A-form was found to be lower in energy by 0.43 and 0.50 eV for both positive and negative charge states respectively. These results are in good qualitative agreement with experiment, showing that when charged, the relative stability of the A-form over the B-form increases by 0.08 and 0.15 eV, compared to the experimental values of 0.04 and 0.06 eV for the positive and negative charge states respectively. These results are given in Table 4, along with the experimental values [14] and the previous theoretical calculations [9, 12].