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##

Generation of a damaged region in diamond

In a previous publication [112], we searched for the minimum
energy (the "displacement energy" *E*_{d}) required to permanently
remove a carbon atom from its initial diamond lattice site for various
displacement directions. We found that for a "random" direction,
defined as an ``off-axis'' direction, 7^{o} off the <100> axis in
the *xy* plane and 5^{o} perpendicular to it [113], *E*_{d} =52
eV, in agreement with results of previous calculations and with the
average of the displacement energies experimentally found for
different directions in the diamond crystal[112,114].
To create a heavily damaged region in diamond we have energetically
displaced bulk atoms with a momentum which corresponds to an initial
kinetic energy of 416 eV (i.e 8 times *E*_{d}). These calculations
required the use of the relatively large sample
unit cells), so that the effects due to the damage were contained in
less than 1/3 of the total volume of the sample. Although the
calculations were carried out at 0K, the introduction of kinetic
energy to some atoms has led to the local heating of the sample, as
will be described in the next section. The Berendsen's energy
dissipation process [115] described above was thus applied, to
rapidly quench the configuration around the defects and return the
crystal back to
0 K within about 2.5 ps after one bombarding
event. Up to 12 carbon atoms (each with an energy of 416 eV) were
knocked, one at a time, into the same volume from slightly different
directions along ``off-axis'' orientations, so that the damage regions
created by all recoiling atoms overlapped, and the largest component
of the initial velocity of the 12 atoms displaced was *x*.

To check the generality of our results, we have displaced in a similar
manner 12 different atoms at different ``off-axis'' directions, also
at T= 0 K. The similarity of the structural configurations of the
damage obtained for the two cases, and their behavior under
post-bombardment annealing, as deduced from statistical analysis,
proved that the general nature of the heavily damaged region is
independent of the details of the damaging process. We selected an
initial kinetic energy of 416 eV imparted to 12 atoms because under
these conditions we obtain a heavily damaged region inside an intact
diamond matrix. Higher energies would require larger samples to
minimize boundary effects, at the cost of computation time. Much lower
energies would produce a too small damaged region to yield
statistically meaningful results.

We also created sample with a much lower density of defects. This was
obtained by the energetic displacement of just one atom, with an
initial kinetic energy of 416 eV. Exactly the same boundary conditions
an energy dissipationas those above, were applied in this case. By
comparing the results obtained with the heavily damaged and the
slightly damaged samples, we could study the role play by the defect
density on the post annealing structure.

** Next:** Annealing of the damage
** Up:** General description and justification
** Previous:** Comparison with ab initio
*David Saada*

*2000-06-22*