------------------ Summary of changes ------------------
- - = line removed + = line added
+ - = line removed
+ + = line added
-Change 1) #########
+Change 1)
+#########
-Sampling of the Brillouin zone was restricted to the $\Gamma$-point.
restricted to the $\Gamma$-point, which has been shown to yield
reliable results\cite{dal_pino93}.
-Change 2) #########
+Change 2)
+#########
+Formation energies and structures are reasonably converged with
respect to the system size.
-Change 3) #########
+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) #########
+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) #########
+Change 5)
+#########
-+In the same way defect formation energies are determined in the
- articles used for comparison.
++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) #########
+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.
+
++The interaction strength, i.e. the absolute value of the binding
+ energy, approaches zero for increasingly non-interacting isolated
+ defects.
+
+Change 7)
+#########
+
+-\includegraphics[width=\columnwidth]{c_sub_si110.ps}
+
++\includegraphics[width=\columnwidth]{c_sub_si110_data.ps}
-\caption{Binding energies of combinations of a C$_{\text{s}}$ and a
Si$_{\text{i}}$ DB with respect to the separation distance. The
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 strength of the defect pairs are well approximated by a
- Lennard-Jones 6-12 potential, which is used for curve fitting.}
+ 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 interaction of the defects is well approximated by a
- Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting.
-
-+Unable to model possible positive values of the binding energy, i.e.
- unfavorable configurations, located to the right of the minimum, the
- LJ fit should rather be thought of an envelope describing the
- interaction strength, i.e. the absolute value of the binding energy.
+-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.
-+The LJ fit estimates almost zero interaction already at
- \unit[0.6]{nm}, indicating a low interaction capture radius of the
++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.
a)
-Chosing a 216 atom supercell constitutes a tradeoff, of course.
+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 reffered to as single isolated defects.
+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
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 in the text
-already in the early beginning of section III B.
+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 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
+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
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. (-> Change 1)
migration, for which the activation energy perfectly matches
experimental data.
-A hint that there is no guarantee to identify the true minimum energy
-path is added into the methodology section. (-> Change 4)
+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. (-> 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
+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.
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).
+which, thus, is not zero at all). This is now clarified in the revised
+manuscript (-> Change 6 / Change 7)
-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 located 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.
-
-This is now clarified in the text and figure caption. (-> Change 6)
+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)
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, of which some is cited
+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
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:
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 Brillouine zone at the Gamma point.
+supercell sampling the Brillouin zone at the Gamma point.
Of course, the choice of the k point mesh constitutes a tradeoff
concerning accuracy and computational effort.
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