From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Wed, 6 Apr 2011 15:49:18 +0000 (+0200)
Subject: added reply to refs + changes to text
X-Git-Url: https://hackdaworld.org/gitweb/?a=commitdiff_plain;h=df1216b4231b3c8aac63e813549d5beb88119aeb;p=lectures%2Flatex.git

added reply to refs + changes to text
---

diff --git a/posic/publications/defect_combos.tex b/posic/publications/defect_combos.tex
index 307e18a..2238374 100644
--- a/posic/publications/defect_combos.tex
+++ b/posic/publications/defect_combos.tex
@@ -16,7 +16,6 @@
 
 \begin{document}
 
-%\title{Mobility of Carbon in Silicon -- a first-principles study}
 \title{First-principles study of defects in carbon implanted silicon}
 \author{F. Zirkelbach}
 \author{B. Stritzker}
@@ -78,14 +77,17 @@ The first-principles DFT calculations were performed with the plane-wave based V
 The Kohn-Sham equations were solved using the generalized-gradient exchange-correlation (XC) functional approximation proposed by Perdew and Wang\cite{perdew86,perdew92}.
 The electron-ion interaction was described by norm-conserving ultra-soft pseudopotentials\cite{hamann79} as implemented in VASP\cite{vanderbilt90}.
 Throughout this work an energy cut-off of \unit[300]{eV} was used to expand the wave functions into the plane-wave basis.
-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 was proven 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.
 The ions and cell shape were allowed to change in order to realize a constant pressure simulation.
+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.
 Ionic relaxation was realized by the conjugate gradient algorithm.
 Spin polarization has been fully accounted for.
 
 Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.
+While not guaranteed to find the true minimum energy path the method turns out to identify reasonable pathways for the investigated structures.
 The defect formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ is defined by choosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation.
+In the same way defect formation energies are determined in the articles used for comparison.
 The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations.
 Accordingly, energetically favorable configurations show binding energies below zero while non-interacting isolated defects result in a binding energy of zero.
 
@@ -594,8 +596,284 @@ Prof. Kai Nordlund is greatly acknowledged for useful comments on the present ma
 
 % --------------------------------- references -------------------
 
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 \end{document}
 
diff --git a/posic/publications/defect_combos_reply01.txt b/posic/publications/defect_combos_reply01.txt
new file mode 100644
index 0000000..72ab194
--- /dev/null
+++ b/posic/publications/defect_combos_reply01.txt
@@ -0,0 +1,74 @@
+Summary of changes
+------------------
+
+
+
+
+Response to recommendations
+---------------------------
+
+Ref 1:
+
+a)
+
+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 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.
+
+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.
+
+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.
+
+XXXX.....
+
+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.
+
+The respective citation and an explanation is added.
+
+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.
+
+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.
+
+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.
+
+Hint on the fact that there is no guarantee to identify the true minimum energy path added into methodology section.
+
+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.
+
+Explanation added to methodology section.
+
+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.
+
+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.
+
+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.
+
+
+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.
+
+However, the choice of the k point mesh is always a tradeoff concerning accuracy and computational effort. 
+
+Citation and explanation added.
+