Ab Initio MD Study of the Mechanism of Carbonization of Si(001) Surfaces with Methane at High Temperatures

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study utilizes ab initio metadynamics to simulate the carbonization of {001} Si using Chemical Vapor Deposition (CVD) at 1423 K. The complete reaction mechanism, including the initial formation of SiC crystals, is revealed. The theoretical model incorporates the presence of surficial native oxide. The mechanism is detailed with all intermediate products and transition states (TS) identified, and the free-energy surface (FES) of the reaction chain is determined. Carbonization begins with alkylated surface products and proceeds through sequential dehydrogenation steps. Carbon integrates into the volume near the crystal surface only when no covalent interactions with hydrogen remain. Native oxide does not hinder carbonization, as oxygen atoms exhibit surface mobility at high temperatures. Hypervalency of carbon atoms is observed in TS structures. The activation free energy for the rate-determining step is calculated to be 166 kJ/mol. Some improvements should be addressed.

The significance and highlights of this article need to be further highlighted, such as the use of initially formed SiC: ACS Applied Nano Materials 7 (13), 15078–15085

The accuracy of computational simulation needs further verification.

More description is needed for Figure 1, such as atomic type, color of bond etc.

The obtained transition states (TS) identified, and the free-energy surface (FES) of the reaction chain should be compared with other reports.

Comments on the Quality of English Language

 The English could be improved to more clearly express the research.

Author Response

Dear Reviewer,

We sincerely appreciate your comments and recommendations, which we believe will greatly enhance the scientific quality of the manuscript. Below, you will find our point-by-point responses. All revisions in the updated manuscript are highlighted in green.

Sincerely yours,

Stefan K. Kolev

Reviewer #1:

Comment #1: The significance and highlights of this article need to be further highlighted, such as the use of initially formed SiC: ACS Applied Nano Materials 7 (13), 15078–15085

Reply: We added this work (https://doi.org/10.1021/acsanm.4c01803) to the reference list and referenced it in the Introduction section. We have further highlighted the significance of our research through additional text in the Abstract and Introduction sections.

The added text is highlighted in green in the Introduction section (page 2).

… Recently, single-atomic-layer SiC has been experimentally prepared and characterized [17]. Huang et al. [18] have employed molecular dynamics to reveal the mechanism of thermo-mechanical coupling, governing the thermal conductivity in two-dimensional SiC, thus improving the understanding of the processes governing these characteristics. …

Additional text is highlighted in green in the Abstract (page 1).

… This work sheds light on the advantage of practical use of Si(001) substrates for the synthesis of silicon carbide and Si-O-C glasses by direct carbonization via chemical vapor deposition. We also aim to enable more methodical design of future synthetic routes and better-informed decisions for experimental investigations…

Additional text is highlighted in green in the Introduction section (page 3).

… Our model also considers the presence of native oxide, as it is well known that traces of oxygen are very often observed, regardless of the methods for the reduction/removal of native oxides from the surface of Si wafers. To our knowledge regarding theoretical research, the only previous study, which accounts for oxygen passivation of silicon, is also ours [20]. …

Additional text is highlighted in green in the Introduction section (page 3).

… Our work demonstrates the advantage of using Si(001) substrates for synthesizing SiC and Si-O-C glasses by direct carbonization via CVD processes. Our results contributed to the detailed understanding of the studied processes at an atomic scale. This knowledge will help to make a more systematic design of future synthetic routes. …

Comment #2: The accuracy of computational simulation needs further verification.

Reply: The Perdew-Burke-Ernzerhof is one of the most widely examined, benchmarked, and used DFT functionals. It is well known that, compared to most other DFT functionals, PBE is more broadly based on physics and is less dependent on statistical correlations and intuition. This functional is perhaps the most widely used in the time-demanding ab initio molecular dynamics. The basis set of choice (DZVP-MOLOPT-SR-GTH) is rather modern and optimized specifically for solid-state material science and gas phase calculations. The weak interactions are accounted for using the latest version of the DFT + D correction: DFT + D3. A recent study has been carried out to check the accuracy of the combination of PBE, a large basis set, and D3 correction (https://doi.org/10.1002/jcc.24866). The study involved the very robust: ISO34, ISOL22, NHTBH38/08, and BHPERI datasets of experimentally determined reaction energetics (including barriers). The MAE for PBE is only 1.6 kcal/mol – a value well within the chemical accuracy, expected from a theoretical method. It is to be noted that PBE outperforms even the widely used hybrid-GGA functional B3LYP.

Additional text has been highlighted in green in the section Methods (page 3).

… A recent study has concluded that the accuracy of the combination of PBE, D3, and a large basis set is relatively high for reaction energetics, including barriers. The MAE was found to be only 6.7 kJ/mol [28], outperforming even the highly popular hybrid-GGA functional B3LYP. …

Comment #3: More description is needed for Figure 1, such as atomic type, color of bond, etc.

Reply:  The caption of Figure 1 has been corrected and now includes information about the colors that designate the atomic types and the bonds they participate in. We have also explicitly mentioned details regarding standard omitting some atomic spheres (for visual clarity).

The added text is in the Results and Discussion section (page 4):

… From now onward, the Si atoms are given in beige, hydrogen atoms are white, oxygen atoms are red, and carbon atoms are gray. For clarity, not all atoms are presented as spheres. Each point where two sticks intersect represents a position of an atom. Each half-side of a bond is shown in the same color as the corresponding atom. …

Comment #4: The obtained transition states (TS) identified, and the free-energy surface (FES) of the reaction chain should be compared with other reports.

Reply: To our knowledge all previous studies stop after the very first step of the process - initial surface alkylation. Thus, no free-energy surfaces are available in these studies, even for the initial step. For this reason, we added a short comparison with our previous theoretical research. It includes the full mechanism of high-temperature carbonization of Si wafers with methane, via the CVD process of Si(111) wafer at a temperature of 1423 K. We had already compared the activation energy of the rate-determining reaction with the corresponding values of multiple experimental CVD processes for SiC growth. To our knowledge, we have modeled the process with the lowest free energy barrier compared to the reported ones in the literature. Moreover, we now have initial experimental data, confirming these conclusions. We are preparing to publish a paper with experimental results supporting this theoretical one.

The additional text is highlighted in green in the Results and Discussion section (page 8).

… The rate-determining reaction in the CVD carbonization of Si(111) wafer (from our previous theoretical research [20]) has a similar value – 173 kJ/mol. All reactions appear to have comparable activation energies. …

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses by theoretical methods the formation of SiC on Si(100)  using methane as a reactant. This study is similar to the one already published for Si(111) by the same authors.

I think the manuscript deserves publication on Coatings after the authors will have considered the following comments and modified the paper accordingly.

1) References from 1 to 15 in the bibliography are clearly related to computational methods and not to the properties of SiC mentioned in the introduction. References to computational  methods are welcome and necessary but reference numbering must be revised and corrected in the entire paper.

E.g., also  ref 17 at line 66 and ref. 18 at line 73 clearly correspond to ref. 19 and 20 respectively in the present bibliography.

2) The red balls are oxygen atom. Please specify what are the red bonds (without red balls) in the figures.

3) Apparently the entire simulation considers reactions taking place at one site. What does it happen at neighbouring sites? Please clarify whether the  activation barriers reported in table I are correct only in the low coverage limit (i.e. when no SiC forms at neighbour sites) and how they change when also neigghbour sites react with methane. This is clearly relevant to attain a full SiC layer.

Author Response

Dear Reviewer,

We sincerely appreciate your comments and recommendations, which we believe will greatly enhance the scientific quality of the manuscript. Below, you will find our point-by-point responses. All revisions in the updated manuscript are highlighted in green.

Sincerely yours,

Stefan K. Kolev

Reviewer #2:

Comment #1: References from 1 to 15 in the bibliography are clearly related to computational methods and not to the properties of SiC mentioned in the introduction. References to computational  methods are welcome and necessary but reference numbering must be revised and corrected in the entire paper.

E.g., also  ref 17 at line 66 and ref. 18 at line 73 clearly correspond to ref. 19 and 20 respectively in the present bibliography.

Reply: All missing references have been added to the manuscript (see List of References). The numbering of the references has also been corrected.

Comment #2: The red balls are oxygen atom. Please specify what are the red bonds (without red balls) in the figures.

Reply: The red sticks designate bonds to oxygen atoms. For clarity, not every atom is presented as a sphere, but only those critical for the modelled reactions. In other words, the point where two red sticks meet is the position of an oxygen atom.

A clarifying text is added to the caption of Figure 1 (page 4). The text is highlighted in green.

… For clarity, not all atoms are presented as spheres. Each point where two sticks intersect represents a position of an atom. Each half-side of a bond is shown in the same color as the corresponding atom. …

A clarifying text is added to the caption of Figure 2 (page 6). The text is highlighted in green.

… For clarity, not all atoms are presented as spheres. Each point where two sticks intersect represents a position of an atom. Each half-side of a bond is shown in the same color as the corresponding atom. …

A clarifying text is added to the caption of Figure 3 (page 7). The text is highlighted in green.

… For clarity, not all atoms are presented as spheres. Each point where two sticks intersect represents a position of an atom. Each half-side of a bond is shown in the same color as the corresponding atom. …

Comment #3: Apparently the entire simulation considers reactions taking place at one site. What does it happen at neighbouring sites? Please clarify whether the  activation barriers reported in table I are correct only in the low coverage limit (i.e. when no SiC forms at neighbour sites) and how they change when also neigghbour sites react with methane. This is clearly relevant to attain a full SiC layer.

Reply: In the initial structure, all Si sites are equivalent, hence the exact site of the first reaction is irrelevant. We must emphasize that a thorough investigation of the influence of an already integrated carbon atom on the reactivity of neighboring sites would require a vast amount of time and computational resources. The minor expected changes in energy barrier will depend on the following factors: 1) the number of integrated carbon atoms; 2) topology of the already formed SiC structure; 3) distance to each reactive site, and 4) orientation of each reactive site. All these factors are supposed to vary in wide ranges. Thus, such a multidimensional problem is hard to address. In future research, we plan to investigate the impact of already integrated carbon atoms on the carbonization process, but only for a limited number of cases. Either way, such an investigation essentially doubles the number of simulations.

One can expect that the free energy barrier mainly depends on the free valence of each Si atom (i.e., the maximal possible valence minus the actual valence, which is not an integer number). Therefore, it would be rather dependent on the radically reconstructed crystalline structure, which is an effect that occurs due to the high reaction temperature. Another critical factor is the covalent effect in the methane molecule and the surface carbon species, after forming at least one covalent Si–C bond. Therefore, the already integrated carbon atoms have a much smaller impact on the reaction barriers than the main factors of reaction energetics.

Moreover, the use of dynamics (previously available for such processes only in our research) enables appropriate accounting for the entropy, hence the free energy of the process. All previous theoretical studies, regarding the SiC synthesis (other than our previous one), use static calculations in which the deviation in the free energy is close to arbitrary, due to the severe qualitative limitations of static calculations, regarding the recovery of entropy. We emphasize the less-approximate paradigm of the employed computational methods, hence the higher qualitative accuracy in reaction energetics.  

Reviewer 3 Report

Comments and Suggestions for Authors

see attachment

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

We sincerely appreciate your comments and recommendations, which we believe will greatly enhance the scientific quality of the manuscript. Below, you will find our point-by-point responses. All revisions in the updated manuscript are highlighted in green.

Sincerely yours,

Stefan K. Kolev

Reviewer #3:

Comment #1: However, the application of molecular dynamics – here within the BornOppenheimer approach (BOMD) is already problematic. It sounds nice to overcome the simulation time problem of “standard” molecular dynamics by application of the so called “metadynamics” I view critically. (For a discussion of this problem see e.g. Nat.Comm. 15 (2024) 240, as an example for a recent paper.) But this may be viewed as a personal opinion and should not hinter the publication of such paper.

Reply: In ab initio molecular dynamics, the Born-Oppenheimer approximation means that the electronic density follows the nuclei. However, the electronic shells and the valence interactions are still modelled at the DFT level. Metadynamics can use bias/collective variables (CVs) only for energy increase to overcome a reaction barrier. The metadynamics accelerates the standard dynamics, so the chances of a chemical process do not remain purely statistical, and the simulation can be accomplished in a feasible amount of time. The evolution of the reaction and the energy profile remain unbiased/natural. Additionally, metadynamics does not prohibit parallel/conjunctive processes. A wrong choice of CVs would not result in the correct product. An unexpected/undesired reaction will occur if the barrier is lower than for the guided process.

Comment #2: Fig. 1 is not really conclusive, explanation is missing.

Reply: The caption for Figure 1 has been expanded. The colors of atoms and bonds have been explained. Each crossing of at least two bonds coincides with an atomic position, even if the sphere of an atom has been omitted for clarity.

The additional text is highlighted in green in Fig. 1 (Results and Discussion section, page 4).

… From now onward, the Si atoms are given in beige, hydrogen atoms are white, oxygen atoms are red, and carbon atoms are gray. For clarity, not all atoms are presented as spheres. Each point where two sticks intersect represents a position of an atom. Each half-side of a bond is shown in the same color as the corresponding atom. …

Comment #3: What is meant with “present native oxide”?

In connection with this: What is meant with “ oxidized (001) Si slab” From where comes the oxygen?

How this is considered in the simulations.

“The presence of native oxide does not prohibit the synthesis of SiC.” – See above, this “native oxide is mentioned at several places in the paper, but its consideration in the simulations – cautiously formulated – not explained.

Reply: The surface of silicon is rarely clean. If it is exposed to air, it is passivated by oxygen in fractions of a second. In general, the formed oxide is labelled as “native oxide”. Usually, this oxide has a variable composition and is designated as SiO_(2-x). Its presence is a major factor in material/ heteromaterial synthesis. Oxygen is difficult to remove and may remain as an impurity in the SiC phase or form a buffer layer of Si-C-O glass mixed with SiC particles. Often, carbonization is carried out regardless of the presence of native oxide on the wafer’s surface. To our knowledge, the only previous theoretical model, which accounts for the native oxide, is also ours (https://doi.org/10.1016/j.matchemphys.2024.129180). The oxygen atoms are introduced in the model in the way to saturate the dangling bonds of Si atoms on the surface. This approach causes minimal structural alterations. Some additional details regarding the modelling of the native oxide were added to the manuscript.

The added text is highlighted in green in Results and Discussion section (page 4):

… In particular, each two neighboring silicon atoms, which would have a free valence in the pristine slab surface, are now bound covalently to an oxygen atom. …

Comment #4: The term “free electrons“ is not appropriate.

Reply: The term “free electrons” has been substituted with “dangling bonds” everywhere in the manuscript.

Changes to the text have been highlighted in green in the Results and Discussion section (page 4).

Comment #5: “The first reaction step has the prevalent rate.” This is a meaningless statement!

Reply: The sentences: “The first reaction step has the prevalent rate. The activation FE of the following three dehydrogenations are similar and approximately three times higher.” have been moved to the end of the Results and Discussion section. The word “prevalent” has been changed to “highest”.

The modified and transferred text has been highlighted in green in Results and Discussion section (page 9):

… The first reaction step has the highest rate. The activation FE of the following three dehydrogenations is similar and approximately three times higher. …

Comment #6: “Reconstruction of the slab surface at this temperature results in the loss of lattice parameters.” What is the “loss of lattice parameters”?

Reply: The term “lattice parameters” in the sentence “Reconstruction of the slab surface at this temperature results in the loss of lattice parameters, characteristic for Si(001) surface orientation.” has been used in its standard, scientific meaning: “the quantities specifying a unit cell or the unit of the periodicity of the atomic arrangement”. However, we understand the possibility of misleading the reader and have replaced the sentence with:

... Reconstruction of the slab surface at this temperature results in the loss of local lattice symmetry characteristic for Si(001) surface orientation. ...

Comment #7: “The initializing reaction step has the prevalent rate.” See above.

Reply: The term “prevalent” has been substituted with “highest”.

The changes in the text are highlighted in green in the Conclusions section (page 9).

Comment #8: “In conclusion, hydrogen atoms play a significant role in the carbonization process.” This is nonsense.

Reply: The quantum-mechanical model of the CVD process of silicon carbonization revealed that without a total loss of hydrogen no carbonization occurs (see Results and Discussion section), Figure 2 (page 6) and text (page 9). However, we understand the possibility of misleading the reader and have replaced the sentence with:

... In conclusion, removing hydrogen atoms from the attacking C species is crucial for the carbonization. ...

Comment #9: - “The proposed process is economically and ecologically attractive.” This is a hollow phrase in such a basic study.

Reply: Due to the very low free energy barrier of the rate-determining reaction, the modelled CVD process is expected also to have very low temperature requirements. However, we understand the ambiguity of the expression and removed it from the revised version of the manuscript.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made efforts to make corrections and the current manuscript version is acceptable.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have improved their manuscript and considered my hints appropiately.

The "problem" with the native oxide is now properly described in the text. Though the clarity could still be improved in fig. 1, I can recommend the publication in its present form, leaving the fig. 1 as an optional point.