Re: BC11912 Combined ab initio and classical potential simulation study on the silicon carbide precipitation in silicon by F. Zirkelbach, B. Stritzker, K. Nordlund, et al. and Re: BA11443 First-principles study of defects in carbon-implanted silicon by F. Zirkelbach, B. Stritzker, J. K. N. Lindner, et al. Dear Dr. Dahal, thank you for the feedback to our submission. > We look forward to receiving such a comprehensive manuscript. When you > resubmit, please include a summary of the changes made, and a detailed > 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. 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. Sincerely, Frank Zirkelbach --------------- 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 > accept the authors argument that they should be two papers ­ they > address the same issues, using the same methods. If they were to > be split into two papers, it would be one for the VASP > calculations, and one for the MD ­ this is not how I suggest you > do it, though. We now combined the two manuscripts to a single comprehensive one. > do it, though. First, though, the following issues should be > addressed (some are simply pasted from my previous reviews, where > I feel that the authors have ignored them, or not responded > adequately). > > 1. I feel that the authors are a bit too convinced by their own > calculations. They do not state the error bars that would be > expected for calculations like this +/- 0.2 eV would be a very > optimistic estimate, I suggest. That being so, many of their > conclusions on which structure or migration routes are most > likely start to look rather less certain. In literature, very often, differences less than 0.2 eV are obtained in DFT studies and respective conclusions are derived. For instance, differences in the energy of formation ranging from 0.05 - 0.12 eV are considered significant enough to conclude on the energetically most favorable intrinsic defect configurations in Si (PRB 68, 235205 (2003); PRL 83, 2351 (1999)). This is due to the fact that existing errors are most probably of the systematic rather than the random type. The error in the estimate of the cohesive energy is canceled out since it is likewise wrong in the defect as in the bulk configuration, which are substracted in the expression of the defect formation energy. Even if the defect formation energy is overestimated due to a too small size of the supercell resulting in a non-zero interaction of the defect with its images, this is likewise true for other defects. Although the actual value might be wrong, observed differences in energy, thus, allow to draw conlcusions on the stability of defect configurations. This is also valid for diffusion barriers, which are given by differences in energy of different structures. In fact, differences of 0.2 eV in DFT calculations are considered insignificant when being compared to experimental results or data of 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 > properties are known to converge very slowly with supercell size. Of course, choosing a supercell containing 216 atoms constitutes a tradeoff. It is considered the optimal choice with respect to computational efficiency and accuracy. We would like to point out that, both, single defects as well as combinations of two defects were investigated in such supercells in successive calculations. For single defects, the size of the supercell should be sufficient. This is shown in PRB 58, 1318 (1998) predicting convergence of the vacancy in silicon - the defect assumed to be most critical due to the flatness of the total energy surface as a function of the ionic coordinates - for supercells containing more than 128 atomic sites, where the defect formation energy is already well estimated using smaller supercells of 64 atomic sites. Thus, convergence of the formation energies of single defects with respect to the size of the supercell is assumed. > 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 > spacings from a whole array of real and image defects ­ how does > 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. > 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. > 4. What method do they use to determine migration paths? How can > they convince us that the calculations cover all possible > migrations paths ­ that is, the paths they calculate are really > the lowest energy ones? This is a major issue ­ there are a > 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) > 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 > 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. > 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 > over-estimated by a similar factor, which is demonstratably > untrue in this case. For this reason, despite the reputation and > previous work with Tersoff (and similar) potentials, the results > 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)). 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). 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 surprising that short range potentials show overestimated melting temperatures. This is not only true for the EA but also (to an even larger extent) for Tersoff potentials, one of the most widely used classical potentials for the Si/C system. The fact that the melting temperature is drastically overestimated although the cohesive energies are nicely reproduced indicates that there is no reason why the cohesive and formational energies should be overestimated to the same extent in order to legitimate the increase in temperature to 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. 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 ----------------