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+
+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 your's 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 accusation that we did ignore or not adequatley answered them.
+However, we did comment on every single issue and a more adequate
+answer is hindered if the referee does not specify the respective
+points of criticism. Thus, some responses are identical to these
+included of our previous answer.
+
+Sincerely,
+
+Frank Zirkelbach
+
+
+--------------- Response to recommendations ----------------
+
+> 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 into 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.
+
+Although differences of 0.2 eV in DFT calculations would generally be
+acknowledged to be insignificant when being compared to experimental
+results or data of other ab initio studies, these differences are
+considered to be reliable when comparing results, i.e. differences in
+energy, of a systematic study among each other. This is commonly done
+as can be seen in a great deal of literature, some of which is cited
+in the section of the present manuscript that investigates defect
+structures and formation energies. Very often differences less than
+0.2 eV are obtained and conclusions on the stability of a particular
+structure are derived.
+
+> 2. Why is 216 atoms a large enough supercell many defect
+> properties are known to converge very slowly with supercell size.
+> 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.
+
+Choosing a 216 atom supercell constitutes a tradeoff, of course.
+However, it is considered the optimal choice with respect to both,
+computing time and accuracy of the results.
+
+The convergence of the formation energies of single defects with
+respect to the size of the supercell is ensured. For this reason, they
+are referred to as single isolated defects.
+
+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 distance 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. This is stated now more
+clearly in section II of the revised manuscript. (-> Change 6)
+
+Nevertheless, the focus is on closely neighbored, interacting defects
+(for which an interaction with their own image is, therefore, supposed
+to be negligible, too). At no time, our aim was to investigate single
+isolated defect structures and their properties by increasing the
+separation distance of two defects belonging to a a defect
+combination.
+
+A note is added to let the reader know that convergence with respect
+to the system size is ensured. (-> Change 2)
+
+> 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.
+
+Constant volume calculations were not performed and, thus, we cannot
+provide concrete differences.
+
+The fact that there are only small changes in volume is added to the
+methodology section. (-> Change 3)
+
+> 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.
+
+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. (Phys. Rev. B 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)
+
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