> 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.
+two manuscripts in a single comprehensive manuscript. Also, according
+to the referee's suggestions, some points were clarified and explained
+in more detail.
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.
+Some arguments here were already put forward in our previous reply and
+are repeated for the sake of clarity. We would be glad to comment at
+length on further upcoming, more detailed questions.
Sincerely,
--------------- 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
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
+> 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
formation energies of single defects with respect to the size of the
supercell is assumed.
+A respective statement was added (Change 3).
+
> 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
> 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.
+The calculations criticized by the referee did not aim at the
+properties of isolated, non-intertacting defects, but rather at the
+defect-defect interaction. Single defects were modeled in separate
+simulation runs. However, we did 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. Combinations of defects with similar distances were
+already successfully modeled in a supercell containing 216 atoms as
+described in PRB 66, 195214 (2002).
+
+An explanation of the binding energy and the relation to the
+interaction of defects was added (Change 8).
> 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.
+In experiment, substrate swelling is observed for high-dose carbon
+implantation into silicon. Indeed, for a single defect, the change in
+volume is less than 0.2% in simulation. Due to this, results of single
+defects within an isothermal-isobaric simulation are not expected to
+differ drastically to results of constant volume simulations. Based on
+the experimentally observed change in volume for high-dose carbon
+implantations, however, the respective relaxation is allowed for in
+simulation for both, single defect calulations as well as the high
+carbon concentration simulations.
+
+A respective statement was added to the methodology section
+(Change 4).
> 4. What method do they use to determine migration paths? How can
> they convince us that the calculations cover all possible
> 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)
+The constrained relaxation technique is used to determine migration
+pathways. The method is specified and a reference is now given in the
+methodology section. The method not necessarily unveils the lowest
+energy migration path. The supposed saddle point structure needs to be
+attested by investigating the vibrational modes. However, reasonable
+results are obtained for the specific system. In fact, so far, the
+best quantitative agreement with experimental findings has been
+achieved concerning the interstitial carbon mobility (PRB 82, 094110
+(2010)) utilizing the constrained relaxation technique. Thus, obtained
+migration paths are assumed to be valid without investigating the
+vibrational modes of every single supposed saddle point configuration.
+
+For clarity we added a statement that, of course, the true minimum
+energy path may still be missed (Change 7).
> 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
+
+Indeed, discrepancies exist. However, both methods predict the C-Si
+100 DB configuration to be the ground-state structure. 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.
+
+This is discussed in full detail in section V in the combined
+manuscript.
+
> 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.
+
+See below for hopefully convincing arguments.
+
> 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
> 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)).
+There is not necessarily a correlation of the cohesive and migration
+energies. One can always add a constant to the cohesive energies of
+respective structures. It is the difference in the cohesive energies
+of structures within the migration path, which determines the
+migration barrier.
+
+In fact, cohesive energies are most often well described by the
+classical potentials since these are most often used to fit the
+potential parameters.
+
+The overestimated migration barrier, however, is due to the short
+range character of the potential, which drops the interaction to
+zero within the first and next neighbor distance using a special
+cut-off function as explained in PRB 76, 224103 (2007). The
+overestimated barrier and slightly different pathway (however,
+starting and final configuration/orientation agree) is indeed
+demonstrated for the carbon interstitial within the present study.
+Since the reason of overestimation is inherent to the short range
+potential, migration pathways among other configurations are
+likewise overestimated.
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).
+Thus, increased temperatures result in an increased probability of
+transition. Obviously, this enables the structural transformation
+into energetically less stable structures of substitutional carbon and
+interstitial silicon that are observed in the high temperature
+simulations. Being in nice agreement with experimental findings, these
+results suggest the usage of increased temperatures to constitute a
+necessary condition to deviate the system out of the ground state as
+it is the case in the ion beam synthesis process.
+
+A respective statement and a more detailed comparison with experiment
+was added to the combined version of the manuscript (Change 22).
+
+Again, we would like to repeat the arguments that legitimate the usage
+of increased temperatures although cohesive and formational energies
+are not ovrestimated in the same way than the migration barriers.
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
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.
+Indeed, the cut-off effect increases if the system is driven away from
+the equilibrium, such as it is the case in IBS. Since this is to some
+extent cured by increasing the simulation temperature, the work-around
+is particularly helpful for short range potentials.
-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 ----------------
+Since the new manuscript is a combination of manuscripts BC11912 and
+BA11443, the following summary of changes mainly contains the
+construction of the new manuscript by text blocks of previous
+manuscripts. Please let me know if a more detailed summary of changes
+is required.
+The title of the new manuscript is that of BC11912. Thus, stated
+changes apply to this manuscript.
---------------- Summary of changes ----------------
+Description:
++ = line added
+- = line removed
+
+Change 1: added/merged parts of 'Abstract' of BA11443
+
+ from: These aime to clarify ...
+ until: Finally, results of the ...
+
+Change 2: added/merged parts of 'Introduction' of BA11443
+
+ from: A lot of theoretical work has been done ...
+ until: However, investigations are, first of all, ...
+
+ from: By first-principles atomistic simulations ...
+ until: Furthermore, highly accurate quantum-mechanical ...
+
+Change 3: convergence of BZ sampling and size of the supercell
+
+-Sampling of the Brillouin zone was restricted to the $\Gamma$-point.
+-The defect structures and the migration paths have been modeled in
+ cubic supercells containing 216 Si atoms.
++To reduce the computational effort sampling of the Brillouin zone was
+ restricted to the $\Gamma$-point, which has been shown to yield
+ reliable results\cite{dal_pino93}.
++The defect structures and the migration paths were modelled in cubic
+ supercells with a side length of \unit[1.6]{nm} containing $216$ Si
+ atoms.
++Formation energies and structures are reasonably converged with
+ respect to the system size.
+
+Change 4: only small changes in volume
+
++The observed changes in volume were less than \unit[0.2]{\%} of the
+ volume indicating a rather low dependence of the results on the
+ ensemble choice.
+
+Change 5: name algorithm used for structural relaxation
+ in DFT calculations
+
++Ionic relaxation was realized by the conjugate gradient algorithm.
+
+Change 6: name reason for reservoir choice
+
++This corresponds to the definition utilized in another study on C
+ defects in Si\cite{dal_pino93} that we compare our results to.
+
+Change 7: CRT not necessarily predicts the minimum energy path
+
++While not guaranteed to find the true minimum energy path, the method
+ turns out to identify reasonable pathways for the investigated
+ structures.
+
+Change 8: added definition and explanation of the binding energy to
+ the 'Methodology' section
+
+ from: The binding energy of a defect pair ...
+ until: The interaction strength, i.e. the ...
+
+Change 9: removed 'Results' section
+
+Change 10: added 'Comparison of classical potential and
+ first-principles methods' section
+
++In a first step, quantum-mechanical calculations of defects in Si and
+ respective diffusion processes are compared to classical potential
+ simulations as well as to results from literature.
++Shortcomings of the analytical potential approach are revealed and
+ its applicability is discussed.
+
+Change 11: comprehensive Table including all defects and methods
+
+Change 12: added text on unstable hexagonal Si defect for classical
+ potentials - necessary due to combination of manuscripts!
+
+ from: The hexagonal configuration ...
+ until: While not completely rendering impossible ...
+
+Change 13: added configurations that require spin polarized
+ calculations
+
+ from: Instead of giving an explicit value ...
+ until: No other configuration, within ...
+
+Change 14: 'Carbon mobility' section of BC11912 mapped to 'Mobility of
+ carbon defects' section
+
+Change 15: added 'Quantum-mechanical investigations of defect
+ combinations and related diffusion processes' section
+ corresponding to 'Results' section of BA11443
+
+Change 16: added 'Mobility of silicon defects" section from III A of
+ BA11443
+
+Change 17: added 'Summary' section from 'Discussion' section of
+ BA11443
+
+Change 18: relocate 'Excursus: Competition of C_i and C_s-Si_i' section
+ of BC11912
+
+Change 19: section 'Classical potential calculations on the SiC
+ precipitation in Si' and respective glue text added
+
+ from: The MD technique is used to gain ...
+ until: The approach is follwed and, ...
+
+ content corresponds to 'Results' section of BC11912
+
+Change 20: 'Summary of classical potential calculations' section added
+ containing parts of 'Discussion and summary' section of BC11912
+
+Change 21: 'Conclusions' section added containing parts of the
+ 'Discussion' section of BA11443 and the 'Discussion and
+ summary' section of BC11912
+
+Change 22: more detailed comparison to experiment added
+ starting from: Moreover, results of the MD simulations ...
+Change 23: 'Summary' section added containing parts of the 'Summary'
+ section of BA11443 and the 'Discussion and summary' section
+ of BC11912
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