Defect
Previous theoretical modelling studies
[8, 9, 10, 11] has found that the ground state
configuration is the [100] C-Si split-interstitial, with 
symmetry, as illustrated in Fig. 1. We therefore take this structure
as the starting point, and relaxed all atoms of the 72 atom cluster
containing the defect shown in Fig. 1 in various charge states.
Details of the structure found for C 
are given in Table 1. and
compare favorably with a previous ab initio calculation
[11]. For the neutral defect, the C atom made strong bonds
with the Si atom, labeled Si 
, along the [100] axis and
slightly weaker bonds with its neighboring Si atoms, labeled Si 
,
along [011]. Nevertheless, the C atom pulls in the Si neighbors
along this direction leaving the Si -Si bonds along [011] slightly
stretched at 2.352 Å. The Si -C-Si and Si -C-Si bond
angles are 137 
and 125 .
There are two high frequency modes at 922.2 ( 
) and 866.9 ( 
)
cm 
, which decrease by 27.6 and 27.8 cm respectively with
C. These frequencies are in fair agreement with the
experimental results (Table 
) of 921 and 930 cm -
although the ordering of the modes is given incorrectly. The
calculated isotope shifts are in very good agreement with the
experimental results, with a decrease of 28.8 and 25.8 cm for
the and the modes respectively. These results are similar
to those of [9], where again, the ordering of the LVMs were
given incorrectly.
The separation of the two vibrational modes is much greater than
experiment and is very sensitive to the C-Si bond lengths
[24]. If the length of the C-Si bond is reduced by 2% then
the modes become 926 cm ( ) and 950 cm ( ) and
the ordering is now in agreement with experiment. In fact, the 1%
difference in the experimental frequencies suggests that the C-Si bond
lengths can differ by no more than 0.03% [25].
We then investigated the structure of the negatively charged defect.
Adding an electron and relaxing all the atoms of the cluster, without
any restriction, causes the three C-Si bond lengths to become almost
equal: the C-Si and C-Si bonds becoming 1.788 and 1.805 (2)
Å respectively. The Si -C-Si bond angle decreased slightly
to 136.0 , and the Si -Si bond length decreased slightly
to 2.238 Å . The resulting vibrational modes have now crossed over
with an ordering in agreement with experiment. The mode has
decreased to 840.98 cm with a corresponding increase of the
mode to 901.78 cm . So, once again the near degeneracy of
these modes seems to arise from an equality in the three Si-C bonds.
In this case, if
the C bond angles were 120 , the C atom and its three Si
neighbors would then make a molecule with a 
axis along
[011]. This would then automatically give a two-fold degenerate E
vibrational mode [24]. This symmetry would, however, also
imply that the infra-red intensities of the two modes are equal which
is contrary to experiment. The effective charges for the highest two
local modes of the fully relaxed neutral defect were then calculated
from the change in the cluster dipole moment with the atoms displaced
according to the normal coordinates. The effective charges were found
to be 
=0.44|e| and 
=0.34|e|. The IR
intensity ratio of the local modes is given by
, and results in a ratio in the range
1.5-1.7:1, in reasonable agreement with the experimental ratio of 2:1
with the mode being the more intense in agreement with
observation. For the negatively charge defect, we find the intensity
ratio to be in the range 1.4-1.5:1. Thus although the symmetry of the
core of the defect is almost trigonal and the two LVMs transform as
E, the departure from symmetry is sufficient to lead to quite
distinct induced dipole moments.
We now discuss the electronic structure of the defect. Although the
energy levels are only given approximately by the theory, we use them
along with the pseudo-wavefunctions for a qualitative analysis of the
zero phonon transition. The Kohn Sham eigenvalues indicated that there
are at two, possibly three defect related levels in the band gap.
The highest
occupied state has 
symmetry, and in agreement with EPR
[4] it corresponds to a non-bonding p- orbital on carbon
(Fig. 4b). This lies above an 
level whose wave-function,
Fig. 4a, has little amplitude on C, and is mainly localized over the
Si atoms neighboring C atoms. The first unoccupied state shown in
Fig. 4c has 
symmetry, and is diffusely localized over the three
Si neighbors of C, predominantly on Si but with little amplitude
on carbon. Again, this is in agreement with the EPR data on the
ionized donor and acceptor states [5]. The level above the
level has symmetry, and is delocalized and probably part
of the conduction band. The 856 meV zero phonon line transition might
be either due to an electron in the upper state recombining with
a hole trapped in the state associated with the non-bonding
p-orbital on C, or, alternatively a electron in the upper
state recombining with a hole in the lower state. Most workers
have considered it to be the former process, involving the state
localized on carbon [26]. This seems to us as unlikely
because the PL has no fine structure, and the zero phonon line is
unaffected by substitution of C [27]. This implies
that the bonding of carbon is unchanged as a result of the
transition. If the C atom relaxed as a consequence of a hole occupying
the C-related state - as indicated by the calculations - then an
isotope shift would be expected. We therefore suggest that the
observed PL involves the latter transition, which involves the
diffusely localized states. This would imply that the dipole for the
PL transition is at right angles to the p-orbital on the carbon
atom.
The energies for migration/reorientation of the defect were also
calculated for the trajectories considered by Capaz et al using
a relaxation procedure with constraints. In contradiction to this
work, we find that both the 
and bond centered saddle points
have almost equivalent barrier heights, with an energy of 1.10 eV.
We therefore conclude that both are viable paths for the
migration/rotation of C . The 1.10 eV barrier is in fair
agreement with the experimental results of between 0.73-0.87 eV for
both migration and re-orientation.
In summary, the calculations yield a structure which has approximately
equal C-Si bonds and gives two almost degenerate modes around 920
cm . The near degeneracy in modes being attributed to an
approximate trigonal symmetry. However, the deviation from this
symmetry cause the two modes to have different absorption
strengths. The migration energy of the defect is low with the C atom
being either two- or four-fold coordinated at the saddle point.