3 Combined ab initio and classical potential simulation study on the
4 silicon carbide precipitation in silicon
5 by F. Zirkelbach, B. Stritzker, K. Nordlund, et al.
10 Thank you very much for informing us about the status of our
15 i) requests a clarification of the relation of the present
16 manuscript to a previous submission of ours (BA11443)
17 ii) has reservations about the methodology used in the present work
18 iii) suggests to possibly combine some account of the present
19 work with the previous submission BA11443.
21 What concerns (ii), the classical potential molecular dynamics used in
22 the present work certainly has limitations. Precisely in order to
23 quantify these limitations, a comparison is made with ab initio
24 calculations as well as earlier first-principles work (BA11443).
25 Despite the shortcomings of classical potential simulations, they
26 nevertheless provide valuable insight in the physical mechanism of
27 silicon carbide precipitation on length and time scales which are not
28 accessible to more accurate ab initio techniques. A detailed response
29 to the referee's concerns is given below.
31 Concerning (i) and (iii), the ab initio work BA11443 is a
32 self-contained and comprehensive manuscript, which already now has an
33 appreciable length. It is a first-principles study on defects in
34 carbon-implanted silicon. In contrast, the present study mainly
35 applies classical potentials to model the SiC precipitation in Si on
36 large time and length scales. While the material is the same, the
37 methodologies applied and the questions addressed in the present work
38 and in BA11443 largely differ. For this reason, and because both
39 manuscripts already contain a substantial amount of information, we
40 believe it is not in the interest of the readers to combine the two
41 manuscripts. Perhaps it would be good idea to make BA11443 available
42 to the referee of the present work?
44 Please find below a reply to the comments of the referee, which we
45 hope will satisfactorily answer his concerns on the suitability of our
46 work for publication in the Physical Review B.
54 Response to the comments of the referee
55 ---------------------------------------
57 > It follows on naturally from a previous paper on the carbon
58 > interstitial in silicon (their ref 42), but does not appear to be a
59 > "serial publication". However, it also refers to an (as yet)
60 > unpublished study (ref 60) of the same topic as the present paper
61 > with almost the same authors, using ab initio MD. Perhaps the
62 > authors could comment on how these two papers differ, and whether
63 > ref 60 improves on the results of the present paper in such a way
64 > that makes present paper superfluous.
66 Manuscript BA11443 (Ref. 60) entitled 'First-principles study of
67 defects in carbon-implanted silicon' investigates single native and C
68 point defects as well as their combinations in Si exclusively by first
69 principles calculations. In that, it constitutes a self-contained,
70 rather substantial study.
72 The present work studies the limitations of classical potentials by
73 means of comparison with first-principles results (and has virtually
74 no overlap with the results of BA11443). Based on this comparison, an
75 approach is proposed that allows to overcome some of the limitations
76 of the classical potentials as well as the general problem inherent to
77 MD describing phase transitions made up of a multiple of infrequent
78 transition events. This enables us to simulate the phase transition of
79 the Si structure during C insertion.
81 Although conclusions on the SiC precipitation in Si were already
82 derived in the DFT study BA11443 based on calculatiuons for single
83 defects and some selected combinations, the classical potential MD
84 simulations allow the investigation of far larger and, thus, much more
85 complex systems on a larger time scale, reinforcing conclusions
86 concerning the SiC precipitation in Si.
88 There are no contradictions or improvements to the present study in
89 BA11443 that would make either manuscript obsolete.
91 > I have some serious reservations about the methodology employed in
92 > this paper, for reasons that are discussed at length in it. I am not
93 > convinced that the measures they take to circumvent the problems in
94 > the method do not introduce further uncertainties, and I would need
95 > a bit more convincing that the results are actually valid. Actually,
96 > the proof I would need is probably within the simulations of ref 60,
97 > hence my question above! The problems I refer to are the huge
98 > over-estimate of the C interstitial migration energy (a process
99 > which is at the heart of the simulations) using the potential used
100 > in the paper, probably due to the short cut-off of the interactions.
101 > The authors' circumvention of this is to do the simulations at much
102 > heightened temperatures. However, this only gives a good model of
103 > the system if all cohesive and migration energies are over-estimated
104 > by a similar factor, which is demonstrably untrue in this case,
105 > where the C_s formation energy is actually underestimated. There are
106 > long discussions of these points in the paper, which leads me to the
107 > conclusion that the EA potential used is unreliable in these
108 > simulations, possibly unless backed up by some ab initio work, which
109 > the authors have done in ref 60.
111 There is not necessarily a correlation of cohesive energies or defect
112 formation energies with activation energies for migration. Cohesive
113 energies are most often well described by the classical potentials
114 since these are most often used to fit the potential parameters. The
115 overestimated barriers, however, are due to the short range character
116 of these potentials, which drop the interaction to zero within the
117 first and next neighbor distance using a special cut-off function.
118 Since the total binding energy is 'accommodated' within this short
119 distance, which according to the universal energy relation would
120 usually correspond to a much larger distance, unphysical high forces
121 between two neighbored atoms arise. This is explained in detail in the
122 study of Mattoni et. al. (Phys. Rev. B 76, 224103 (2007)).
124 Since most of the defect structures show atomic distances below the
125 critical distance, for which the cut-off function is taking effect,
126 the respective formation energies are quite well described, too (at
127 least they are not necessarily overestimated in the same way).
129 While the properties of some structures near the equilibrium position
130 are well described, the above mentioned effects increase for
131 non-equilibrium structures and dynamics. Thus, for instance, it is not
132 surprising that short range potentials show overestimated melting
133 temperatures. This is not only true for the EA but also (to an even
134 larger extent) for Tersoff potentials, one of the most widely used
135 classical potentials for the Si/C system. The fact that the melting
136 temperature is drastically overestimated although the cohesive
137 energies are nicely reproduced indicates that there is no reason why
138 the cohesive and formational energies should be overestimated to the
139 same extent in order to legitimate the increase in temperature to
140 appropriately consider the overestimated barrier heights for
143 Indeed, a structural transformation with increasing temperature is
144 observed, which can be very well explained and correlated to
145 experimental findings.
147 The underestimated energy of formation of substitutional C for the EA
148 potential does not pose a problem in the present context. Since we
149 deal with a perfect Si crystal and the number of particles is
150 conserved, the creation of substitutional C is accompanied by the
151 creation of a Si interstitial. The formation energies of the
152 different structures of an additional C atom incorporated into
153 otherwise perfect Si shows the same ground state, i.e. the C-Si 100 DB
154 structure, for classical potential as well as ab initio calculations.
156 The arguments discussed above are now explained in more detail in the
157 revised version of our work. (-> Change 1, Change 2)
159 > Therefore, I do not feel that this paper can stand alone - either
160 > its conclusions are contradicted by those of ref 60 (in which case
161 > there's no need to publish this paper), or supported by them (in
162 > which case ref 60 supercedes this paper, and some brief account of
163 > this work could be included in it).
165 As mentioned above, there are no conclusions in Ref. 60 that
166 contradict to the results of the present manuscript. Indeed, the
167 results of Ref. 60 are important for the present study and, therefore,
168 supporting this work. However, the different approaches, i.e. modeling
169 thousands of C atoms incorporated into a large Si host matrix by
170 molecular dynamics simulations on a large time scale vs accurate
171 investigations of the structure of single and double defects in Si and
172 some selected diffusion processes, suggests the separate publication
187 +Thus, the underestimated energy of formation of C$_{\text{s}}$ within
188 the EA calculation does not pose a serious limitation in the present
191 +Since C is introduced into a perfect Si crystal and the number of
192 particles is conserved in simulation, the creation of C$_{\text{s}}$
193 is accompanied by the creation of Si$_{\text{i}}$, which is
194 energetically less favorable than the ground state, i.e. the
195 C$_{\text{i}}$ \hkl<1 0 0> DB configuration, for both, the EA and ab
201 -The cut-off function of the short range potential limits the
202 interaction to nearest neighbors, which results in overestimated and
203 unphysical high forces between neighbored atoms.
205 +The cut-off function of the short range potential limits the
206 interaction to nearest neighbors.
208 +Since the total binding energy is, thus, accommodated within this
209 short distance, which according to the universal energy relation would
210 usually correspond to a much larger distance, unphysical high forces
211 between two neighbored atoms arise.
213 +While cohesive and formational energies are often well described,
214 these effects increase for non-equilibrium structures and dynamics.
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