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 related to 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 very much for informing us about the status of our manuscript. The referee i) has reservations about the methodology used in the present work ii) requests a clarification of the relation of the present manuscript to a previous submission of ours (BA11443) iii) suggests to possibly combine some account of the present work with the previous submission BA11443. What concerns (i), the classical potential molecular dynamics used in the present work certainly has limitations. Precisely in order to quantify these limitations, a comparison is made with ab initio calculations as well as earlier first-principles work (BA11443). Despite the shortcomings of classical potential simulations, they nevertheless provide valuable insight in the physical mechanism of silicon carbide precipitation on length and time scales which are not accessible to more accurate ab initio techniques. A detailed response to the referee's concerns is given below. Concerning (ii) and (iii), the ab initio work BA11443 is a self-contained and comprehensive manuscript, which already now has an appreciable length. It is a first-principles study on defects in carbon-implanted silicon. In contrast, the present study mainly applies classical potentials to model the SiC precipitation in Si on large time and length scales. While the material is the same, the methodologies applied and the questions addressed in the present work and in BA11443 largely differ. For this reason, and because both manuscripts already contain a substantial amount of information, we believe it is not in the interest of the readers to combine the two manuscripts. Perhaps it would be good idea to make BA11443 available to the referee of the present work? Please find below a reply to the comments of the referee, which we hope will satisfactorily answer his concerns on the suitability of our work for publication in the Physical Review B. Sincerely, Frank Zirkelbach Response to the comments of the referee --------------------------------------- > It follows on naturally from a previous paper on the carbon > interstitial in silicon (their ref 42), but does not appear to be a > "serial publication". However, it also refers to an (as yet) > unpublished study (ref 60) of the same topic as the present paper > with almost the same authors, using ab initio MD. Perhaps the > authors could comment on how these two papers differ, and whether > ref 60 improves on the results of the present paper in such a way > that makes present paper superfluous. Manuscript BA11443 (Ref. 60) entitled 'First-principles study of defects in carbon-implanted silicon' investigates single native and C point defects as well as their combinations in Si exclusively by first principles calculations. In that, it constitutes a self-contained, rather substantial study. The present work studies the limitations of classical potentials by means of comparison with first-principles results (and has virtually no overlap with the results of BA11443). Based on this comparison, an approach is proposed that allows to overcome some of the limitations of the classical potentials as well as the general problem inherent to MD describing phase transitions made up of a multiple of infrequent transition events. This enables us to simulate the phase transition of the Si structure during C insertion. Although conclusions on the SiC precipitation in Si were already derived in the DFT study BA11443 based on calculatiuons for single defects and some selected combinations, the classical potential MD simulations allow the investigation of far larger and, thus, much more complex systems on a larger time scale, reinforcing conclusions concerning the SiC precipitation in Si. There are no contradictions or improvements to the present study in BA11443 that would make either manuscript obsolete. > I have some serious reservations about the methodology employed in > this paper, for reasons that are discussed at length in it. 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. Actually, > the proof I would need is probably within the simulations of ref 60, > hence my question above! The problems I refer to are 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, probably due to the short cut-off of the interactions. > 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 demonstrably untrue in this case, > where the C_s formation energy is actually underestimated. There are > long discussions of these points in the paper, which leads me to the > conclusion that the EA potential used is unreliable in these > simulations, possibly unless backed up by some ab initio work, which > the authors have done in ref 60. 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. (Phys. Rev. B 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) > Therefore, I do not feel that this paper can stand alone - either > its conclusions are contradicted by those of ref 60 (in which case > there's no need to publish this paper), or supported by them (in > which case ref 60 supercedes this paper, and some brief account of > this work could be included in it). As mentioned above, there are no conclusions in Ref. 60 that contradict to the results of the present manuscript. Indeed, the results of Ref. 60 are important for the present study and, therefore, supporting this work. However, the different approaches, i.e. modeling thousands of C atoms incorporated into a large Si host matrix by molecular dynamics simulations on a large time scale vs accurate investigations of the structure of single and double defects in Si and some selected diffusion processes, suggests the separate publication of the results. Summary of changes ------------------ - = line removed + = line added Change 1 -------- + +Thus, the underestimated energy of formation of C$_{\text{s}}$ within the EA calculation does not pose a serious limitation in the present context. +Since C is introduced into a perfect Si crystal and the number of particles is conserved in simulation, the creation of C$_{\text{s}}$ is accompanied by the creation of Si$_{\text{i}}$, which is energetically less favorable than the ground state, i.e. the C$_{\text{i}}$ \hkl<1 0 0> DB configuration, for both, the EA and ab initio treatment. Change 2 -------- -The cut-off function of the short range potential limits the interaction to nearest neighbors, which results in overestimated and unphysical high forces between neighbored atoms. +The cut-off function of the short range potential limits the interaction to nearest neighbors. +Since the total binding energy is, thus, 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. +While cohesive and formational energies are often well described, these effects increase for non-equilibrium structures and dynamics.