Re: BC11912
Combined ab initio and classical potential simulation study on the
silicon carbide precipitation in silicon
by F. Zirkelbach, B. Stritzker, K. Nordlund, et al.
and
Re: BA11443
First-principles study of defects in carbon-implanted silicon
by F. Zirkelbach, B. Stritzker, J. K. N. Lindner, et al.
Dear Dr. Dahal,
thank you for the feedback to our submission.
> We look forward to receiving such a comprehensive manuscript. When you
> resubmit, please include a summary of the changes made, and a detailed
> response to all recommendations and criticisms.
We decided to follow yours and the referee's suggestion to merge the
two manuscripts into a single comprehensive manuscript.
Please find below the summary of changes and a detailed response to
the recommendations of the referee.
Most of the criticism is pasted from the previous review justified by
the statement that we did ignore or not adequatley respond to it.
However, we commented on every single issue and a more adequate
answer is hindered if the referee does not specify the respective
points of criticism. Thus, some part of the response might be
identical to our previous one.
Sincerely,
Frank Zirkelbach
--------------- Response to recommendations ----------------
TODO: add changes applied due to criticism ...
> I am not happy with these two papers for a multitude of reasons,
> and I recommend that the authors rewrite them as a single longer
> paper, to eliminate the criticism of serial publication. I do not
> accept the authors argument that they should be two papers they
> address the same issues, using the same methods. If they were to
> be split into two papers, it would be one for the VASP
> calculations, and one for the MD this is not how I suggest you
> do it, though.
We now combined the two manuscripts to a single comprehensive one.
> do it, though. First, though, the following issues should be
> addressed (some are simply pasted from my previous reviews, where
> I feel that the authors have ignored them, or not responded
> adequately).
>
> 1. I feel that the authors are a bit too convinced by their own
> calculations. They do not state the error bars that would be
> expected for calculations like this +/- 0.2 eV would be a very
> optimistic estimate, I suggest. That being so, many of their
> conclusions on which structure or migration routes are most
> likely start to look rather less certain.
In literature, very often, differences less than 0.2 eV are obtained
in DFT studies and respective conclusions are derived. For instance,
differences in the energy of formation ranging from 0.05 - 0.12 eV are
considered significant enough to conclude on the energetically most
favorable intrinsic defect configurations in Si (PRB 68, 235205
(2003); PRL 83, 2351 (1999)). This is due to the fact that existing
errors are most probably of the systematic rather than the random
type. The error in the estimate of the cohesive energy is canceled out
since it is likewise wrong in the defect as in the bulk configuration,
which are substracted in the expression of the defect formation
energy. Even if the defect formation energy is overestimated due to a
too small size of the supercell resulting in a non-zero interaction of
the defect with its images, this is likewise true for other defects.
Although the actual value might be wrong, observed differences in
energy, thus, allow to draw conlcusions on the stability of defect
configurations. This is also valid for diffusion barriers, which are
given by differences in energy of different structures.
In fact, differences of 0.2 eV in DFT calculations are considered
insignificant when being compared to experimental results or data of
other ab initio studies. However, the observed differences in energy
within our systematic DFT study are considered reliable.
> 2. Why is 216 atoms a large enough supercell many defect
> properties are known to converge very slowly with supercell size.
Of course, choosing a supercell containing 216 atoms constitutes a
tradeoff. It is considered the optimal choice with respect to
computational efficiency and accuracy.
We would like to point out that, both, single defects as well as
combinations of two defects were investigated in such supercells in
successive calculations.
For single defects, the size of the supercell should be sufficient.
This is shown in PRB 58, 1318 (1998) predicting convergence of the
vacancy in silicon - the defect assumed to be most critical due to
the flatness of the total energy surface as a function of the ionic
coordinates - for supercells containing more than 128 atomic sites,
where the defect formation energy is already well estimated using
smaller supercells of 64 atomic sites. Thus, convergence of the
formation energies of single defects with respect to the size of the
supercell is assumed.
> They appear to be separating defects by as large a distance as
> can be accommodated in the supercell to approximate the isolated
> defects, but then they are only separated by a few lattice
> spacings from a whole array of real and image defects how does
> that compare with taking the energies of each defect in a
> supercell.
Again, we would like to point out that it is not our purpose to
separate defects by a large distance in order to approximate the
situation of isolated defects. However, we find that for increasing
defect distances, configurations appear, which converge to the
energetics of two isolated defects. This is indicated by the (absolute
value of the) binding energy, which is approaching zero with
increasing distance. From this, we conclude a decrease in interaction,
which is already observable for defect separation distances accessible
in our simulations.
Nevertheless, the focus is on closely neighbored, interacting defects
(for which an interaction with their own image is, therefore, supposed
to be negligible, too). In fact, combinations of defects exhibiting
equivalent distances were successfully modeled in a supercell
containing 216 atoms in PRB 66, 195214 (2002). At no time, our aim was
to investigate single isolated defect structures and their properties
by a structure with increased separation distance of the two defects.
> 3. Constant pressure solves some problems, but creates others
> is it really a sensible model of implantation? What differences
> are seen for constant volume calculations (on a few simple
> examples, say)?
In experiment substrate swelling is observed for high-dose carbon
implantation into silicon. Indeed, using the NpT ensemble for
calculations of a single (double) C defect in Si is questionable.
However, only small changes in volume were observed and, thus, it is
assumed that there is no fundamental difference between calculations
in the canonical and isothermal-isobaric ensemble.
> 4. What method do they use to determine migration paths? How can
> they convince us that the calculations cover all possible
> migrations paths that is, the paths they calculate are really
> the lowest energy ones? This is a major issue there are a
> number of methods used in the literature to address it are the
> authors aware of them? Have they used one of them?
A slightly modified version of the constrained conjugate gradient
relaxation method is used. It is named in the very beginning of the
second part of chapter II and a reference is given. Although, in
general, the method not necessarily unveils the lowest energy
migration path it gives reasonable results for the specific system.
This can be seen for the resulting pathway of C interstitial DB
migration, for which the activation energy perfectly matches
experimental data.
For clarity we added a statement, however, that of course the true
minimum energy path may still be missed. (-> Change 4)
> 5. I have some serious reservations about the methodology
> employed in the MD calculations. The values given for the basic
> stabilities and migration energies in some cases disagree
> radically with those calculated by VASP, which I would argue
> (despite 4 above) to be the more reliable values. The main
> problems is the huge over-estimate of the C interstitial
> migration energy (a process which is at the heart of the
> simulations) using the potential used in the paper. I am not
> convinced that the measures they take to circumvent the problems
> in the method do not introduce further uncertainties, and I would
> need a bit more convincing that the results are actually valid.
> The authors' circumvention of this is to do the simulations at
> much heightened temperatures. However, this only gives a good
> model of the system if all cohesive and migration energies are
> over-estimated by a similar factor, which is demonstratably
> untrue in this case. For this reason, despite the reputation and
> previous work with Tersoff (and similar) potentials, the results
> need a critical scrutiny, which I am not very convinced by in
> this case.
TODO: add idea that elevated temperatures are considered necessary to
deviate the system out of equilibrium, as assumed to be the case in IBS
you can always add constant to energy.
formation energies are not overestimated
just the migration barriers are
to increase probability of transitions, temperature is increased
occupation of energetically more unfavorable states likewise increased
indeed, sub conf, which is slightly higher than c-si DB, is increased
comparing with experimental findings that suggest c sub for higher
temperatures gives rise to the conclusion that the increased
temperatures are needed to deviate the system out of the ground state!
There is not necessarily a correlation of cohesive energies or defect
formation energies with activation energies for migration. Cohesive
energies are most often well described by the classical potentials
since these are most often used to fit the potential parameters. The
overestimated barriers, however, are due to the short range character
of these potentials, which drop the interaction to zero within the
first and next neighbor distance using a special cut-off function.
Since the total binding energy is 'accommodated' within this short
distance, which according to the universal energy relation would
usually correspond to a much larger distance, unphysical high forces
between two neighbored atoms arise. This is explained in detail in the
study of Mattoni et. al. (PRB 76, 224103 (2007)).
Since most of the defect structures show atomic distances below the
critical distance, for which the cut-off function is taking effect,
the respective formation energies are quite well described, too (at
least they are not necessarily overestimated in the same way).
While the properties of some structures near the equilibrium position
are well described, the above mentioned effects increase for
non-equilibrium structures and dynamics. Thus, for instance, it is not
surprising that short range potentials show overestimated melting
temperatures. This is not only true for the EA but also (to an even
larger extent) for Tersoff potentials, one of the most widely used
classical potentials for the Si/C system. The fact that the melting
temperature is drastically overestimated although the cohesive
energies are nicely reproduced indicates that there is no reason why
the cohesive and formational energies should be overestimated to the
same extent in order to legitimate the increase in temperature to
appropriately consider the overestimated barrier heights for
diffusion.
Indeed, a structural transformation with increasing temperature is
observed, which can be very well explained and correlated to
experimental findings.
The underestimated energy of formation of substitutional C for the EA
potential does not pose a problem in the present context. Since we
deal with a perfect Si crystal and the number of particles is
conserved, the creation of substitutional C is accompanied by the
creation of a Si interstitial. The formation energies of the
different structures of an additional C atom incorporated into
otherwise perfect Si shows the same ground state, i.e. the C-Si 100 DB
structure, for classical potential as well as ab initio calculations.
The arguments discussed above are now explained in more detail in the
revised version of our work. (-> Change 1, Change 2)
--------------- Summary of changes ----------------