> response to all recommendations and criticisms.
We decided to follow yours and the referee's suggestion to merge the
-two manuscripts in 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,
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)?
-Differences are supposed to be negligible small since only small
-changes in volume are detected. However, in experiment, substrate
-swelling is observed. Thus, to allow for full relaxation, simulations
-were performed in the NpT ensemble. However, for the above-mentioned
-reason, no fundamental differences are expected for single defect
-configurations in the canonical and isothermal-isobaric ensemble with
-respect to energy.
+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.
+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
> authors aware of them? Have they used one of them?
The constrained relaxation technique is used to determine migration
-pathways. The method is named and a reference is given in the
+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
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.
+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
> in the method do not introduce further uncertainties, and I would
> need a bit more convincing that the results are actually valid.
-We hope to be able to convince by responding to the following
-statement of the referee.
+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
> this case.
There is not necessarily a correlation of the cohesive and migration
-energies. You can always add a constant to the cohesive energies of
+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.
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.
+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
appropriately consider the overestimated barrier heights for
diffusion.
-Indeed the cut-off effect increases if the system is deviated from
-equilibrium. Thus, to mimic IBS, a process far from equilibrium,
-increased temperatures are exceptionally necessary if short range
-potentials are utilized.
+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.
--------------- 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.
+
+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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