-Summary of changes
-------------------
+Dear Editor,
+thank you for the feedback to our submission. We included most of the
+suggestions of the referees and believe that they were very helpful to
+improve the quality of our manuscript.
+Please find below the summary of changes and a detailed response to
+the recommendations of the referees.
+Sincerely,
-Response to recommendations
----------------------------
+Frank Zirkelbach
-Ref 1:
-a)
+------------------ Summary of changes ------------------
+
+ - = line removed
+ + = line added
+
+Change 1)
+#########
+
+-Sampling of the Brillouin zone was restricted to the $\Gamma$-point.
+
++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}.
+
+Change 2)
+#########
+
++Formation energies and structures are reasonably converged with
+ respect to the system size.
+
+Change 3)
+#########
+
++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 4)
+#########
+
++While not guaranteed to find the true minimum energy path, the method
+ turns out to identify reasonable pathways for the investigated
+ structures.
+
+Change 5)
+#########
+
++This corresponds to the definition utilized in another study on C
+ defects in Si\cite{dal_pino93} that we compare our results to.
+
+Change 6)
+#########
+
+-Accordingly, energetically favorable configurations show binding
+ energies below zero while non-interacting isolated defects result in a
+ binding energy of zero.
+
++Accordingly, energetically favorable configurations result in binding
+ energies below zero while unfavorable configurations show positive
+ values for the binding energy.
-Chosing 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 interaction strength, i.e. the absolute value of the binding
+ energy, approaches zero for increasingly non-interacting isolated
+ defects.
-The convergence of the formation energies of single defects with respect to the size of the supercell is ensured. For this reason, they are reffered to as single isolated defects.
+Change 7)
+#########
-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 correspond to the energetics of two isolated defects. This is indicated by 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 in the text already in the early beginning of section III B.
+-\includegraphics[width=\columnwidth]{c_sub_si110.ps}
-Nevertheless, the focus is on closely neighbored, interacting defects (for which an interaction with their own image is, therefore, supposed to be neglectable small, too). At no time, our aime was to investigate single isolated defect structures and their properties by increasing the separation distance of two defects belonging to a a defect combination.
++\includegraphics[width=\columnwidth]{c_sub_si110_data.ps}
-XXXX.....
+-\caption{Binding energies of combinations of a C$_{\text{s}}$ and a
+ Si$_{\text{i}}$ DB with respect to the separation distance. The
+ binding energies of the defect pairs are well approximated by a
+ Lennard-Jones 6-12 potential, which is used for curve fitting.}
+
++\caption{Binding energies of combinations of a C$_{\text{s}}$ and a
+ Si$_{\text{i}}$ DB with respect to the separation distance.}
+
+-The interaction of the defects is well approximated by a
+ Lennard-Jones 6-12 potential, which was used for curve fitting.
+
+-The binding energy quickly drops to zero.
+
+-The Lennard-Jones fit estimates almost zero interaction already at
+ \unit[0.6]{nm}, indicating a low interaction capture radius of the
+ defect pair.
+
++As can be seen, the interaction strength, i.e. the absolute value of
+ the binding energy, quickly drops to zero with increasing separation
+ distance.
+
++Almost zero interaction may be assumed already at distances about
+ \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the
+ defect pair.
+
+
+
+--------------- Response to recommendations ----------------
+
+Ref 1:
+
+a)
+
+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)
b)
-For large supercells the k-point constituting the avareage point over the Brillouine zone approaches the Gamma point. Indeed k-point convergence was observed for the Gamma point already for a 32 atom supercell in 'PRB 47 (1993) 12554' by comparing it to defect calculations considering the Baldereschi point. Again, the reason for chosing Gamma point only calculations is to reduce computational efforts.
+For sufficiently large supercells the Brillouin zone is accurately
+sampled with the Gamma point. Indeed k-point convergence was observed
+for the Gamma point already for a 32 atom supercell in 'PRB 47 (1993)
+12554' by comparing it to defect calculations considering the
+Baldereschi point. Again, the reason for choosing Gamma point only
+calculations is to reduce computational efforts.
-The respective citation and an explanation is added.
+The respective citation and an explanation is added. (-> Change 1)
c1)
-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 the 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, 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.
+Constant volume calculations were not performed and, thus, we cannot
+provide concrete differences.
-The fact of the small change in volume was added to the methodology section.
+The fact that there are only small changes in volume is added to the
+methodology section. (-> Change 3)
c2)
-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.
+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.
-Hint on the fact that there is no guarantee to identify the true minimum energy path added into methodology section.
+For clarity we added a statement, however, that of course the true
+minimum energy path may still be missed. (-> Change 4)
d)
-We defined the formation energy in the same way as it was done in the articles we compare our resluts to. They used SiC as a reference particle reservoir. Using the same reservoir, we can directly compare the defect formation energies.
+With respect to the definition of the formation energy we follow the
+work of Dal Pino et. al. (PRB 47 (1993) 12554). They used SiC as a
+reference particle reservoir. Using the same reservoir, we can
+directly compare the defect formation energies.
-Explanation added to methodology section.
+Explanation added to methodology section. (-> Change 5)
e)
-The results are given in chapter III section A (Separated defects in silicon). The formation energy is 3.63 eV (Table I), which fits quite well to experimental estimates. A very good agreement is achieved with another theoretical investigation, which is stated in Table I.
+The results are given in chapter III section A (Separated defects in
+silicon). The formation energy is 3.63 eV (Table I), which fits quite
+well to experimental estimates. A very good agreement is achieved with
+another theoretical investigation, which is stated in Table I.
f)
-There is no model we propose that would demand a Lennard-Jones-like interaction of the defect pair. However, the LJ fit quite well indicates the decrease of the interaction with increasing distance. Although there is a positive value at ~0.45 nm (indeed there is no zero value!), this does not mean that the interaction dropped to zero. Indeed the absolute value of the binding energy is higher than that of the slightly lower separations (though negative) indicating an energetically unfavorable configuration (due to the interaction, which, thus, is not zero at all).
-
-The referee is right, however, that LJ is not adequate for describing this kind of interaction behaviour since it does not account for possible positive values to the right of the minimum. However, after mirroring the positive values of the binding energies with respect to the x axis, the LJ fit would still describe very well the interaction characteristics. Thus, the LJ fit should be thought of an envelope describing the interaction strength.
+There is no model we propose that would demand a Lennard-Jones-like
+interaction of the defect pair. However, the LJ fit quite well
+indicates the decrease of the interaction with increasing distance.
+Although there is a positive value at ~0.45 nm (indeed there is no
+zero value!), this does not mean that the interaction dropped to zero.
+Indeed the absolute value of the binding energy is higher than that of
+the slightly lower separations (though oppositely signed) indicating
+an energetically unfavorable configuration (due to the interaction,
+which, thus, is not zero at all). This is now clarified in the revised
+manuscript (-> Change 6 / Change 7)
+
+Furthermore, the referee is right that LJ is not adequate for
+describing this kind of interaction behavior since it does not account
+for possible positive values located to the right of the minimum.
+Thus, the LJ Fit and the respective statements are omitted in the
+revised manuscript. (-> Change 7)
beginning and final remark)
-Although differences of 0.2 eV in DFT calculations would generally be acknowledged to be insignificant when comparing results to experimental or other ab initio data, we consider these differences to be not at all insignificant when comparing the results of a systematic study among each other. This is commonly done as can be seen in the cited literature given in the section investigating defects and their energy of formation, which very often yield a difference in energy that is less than 0.2 eV.
+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.
+
+Cutting the discussion in each section down to 10-20 lines as proposed
+by the referee would stringently result in the loss of valuable
+information and details that are of particular interest giving new
+insights to the physics of carbon defect structures and diffusion
+processes in silicon.
+
+Therefore we did not follow the suggestion of the referee to remove
+statements that are based on energy differences that are smaller than
+0.2 eV. However, we revised the manuscript according to the remaining
+recommendations. In order to shorten the paper at least somewhat we
+omitted the LJ Fit.
Ref 2:
-(see Ref 1 b))
-
-For the specific case of C defects in Si, a theoretical study (PRB 47 (1993) 12554) showed that convergence by less than 0.02 eV with respect to k points is already achieved for a 32 atom supercell sampling the Brillouine zone at the Gamma point.
+For the specific case of C defects in Si, a theoretical study (PRB 47
+(1993) 12554) showed that convergence by less than 0.02 eV with
+respect to the k point mesh is already achieved for a 32 atom
+supercell sampling the Brillouin zone at the Gamma point.
-However, the choice of the k point mesh is always a tradeoff concerning accuracy and computational effort.
+Of course, the choice of the k point mesh constitutes a tradeoff
+concerning accuracy and computational effort.
-Citation and explanation added.
+As proposed by the referee, the respective citation and explanation is
+added into the methodology section. (-> Change 1)
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