Atomistic Simulations of Defect Production in Monolayer and Bulk Hexagonal Boron Nitride under Low- and High-Fluence Ion Irradiation

Round 1

Reviewer 1 Report

Hexagonal boron nitride is one typical 2D materials and has attracted significant attentions in the past few years. Study on the defect product in hBN is helpful to understand the relationship between structures and properties. Ghaderzadeh et al. systematically simulated the formation and evolution of defects in monolayer and bulk hBN, which will guide the experiments to synthesize the specified structured BN samples. Based on the discussion, the paper can be accepted after major revision and several key issues need to be addressed as follows:

1. Bilayer 2D materials are drawing efforts due to the presence of unique structures. Can the author offer the defects simulation in the bilayer hBN system?
2. Although this work mainly involved the theoretical simulations, the author should provide a few experimental results to verify the simulation. Or maybe several references should be cited.
3. Graphene and hBN share very similar crystal lattices, discussion about the defects creation under different energy should be provided to demonstrate the unique features of this work.

Comments for author File: Comments.pdf

Author Response

Referee 1:

1. Bilayer 2D materials are drawing efforts due to the presence of unique structures. Can the author offer the defects simulation in the bilayer hBN system?

Authors: 

Following the suggestions of the Referee, we carried out the simulations for the bilayer h-BN. The results are presented in Fig. 9 in the revised manuscript (a new figure added), and the corresponding discussion is on pages 10-11:

“In order to understand how the production of defects in the top layers is affected by the presence of the underlaying layers, we carried out ion irradiation simulations for bilayer h-BN and compared the results to those for the multi-layer system. A high fluence of 5 × 1014 ions/cm2 and Argon ions. The results are presented in Fig. 9. Although the density of single-vacancies in the top-most layer (green color) is slightly affected by reducing the h-BN layers to two, the second layer (blue color) has undergone a more noticeable change and the induced single vacancies are clearly increased in the studied energy regime, as compared to the multilayer system. This is due to the lack of any material underneath the second layer in the bilayer target, whose atoms have therefore more freedom to escape from the system and leave vacancies behind. At the same time, the density of double and complex vacancies, although being small, are also overall increased in the bilayer system. Therefore, one can conclude that in a free-standing bilayer h-BN more vacancies are produced than in the multilayer system under the studied irradiation fluence and incident energy regime. For supported materials, this effect will likely be diminished by the substrate, as the substrate will play the role of the third layer. However, for lighter ions (e.g. He) and higher energies, the presence of substrate can increase the number of produced defects, as shown previously for other 2D materials [42].”

Referee 1:

2. Although this work mainly involved the theoretical simulations, the author should provide a few experimental results to verify the simulation. Or maybe several references should be cited.

Authors:

We fully agree with the Referee that a comparison of the theoretical results to the experimental data should always be done. However, there is not much experimental data for the types of ions and energy range we study. A comparison was made in a paper by Fisher et al., [doi:10.1126/sciadv.abe7138], as already discussed in the manuscript. To illustrate the lack of systematic studies, we added the following sentence to the manuscript (introduction):

“The response of mono-layer h-BN on metal substrates to heavy-ion irradiation has been studied for a narrow range of ion energies (low-energy limit [26,27]), along with the ions in MeV range [28,29] or in high charge states [30], but the systematic experimental studies of the response of single and few-layer h-BN to ion irradiation are scarce, and the comprehensive picture of the behavior of this system under ion bombardment cannot be drawn based solely on the experimental data. We note that in a wider context, understanding the response of h-BN to irradiation is also important for the use of this material in various radiation-related applications, such as neutron and particle detectors and scintillators [9,28,31].”

Referee 1:

3. Graphene and hBN share very similar crystal lattices, discussion about the defects creation under different energy should be provided to demonstrate the unique features of this work.

Authors:

The similarities in defect production of graphene and h-BN are discussed on page 5 of the revised manuscript:

”Overall, such abehavior with a clear maximum on defect production probability vs. ion energy curve is typical for 2D materials [46], e.g., graphene [47], which has a very similar atomic structure.”

 

Reviewer 2 Report

The authors used MD and DFT to investigate the mechanisms oof vacancy creation in mono and few-layer hBN. The manuscript was well present. Here, I only have one question that needs authors to clarify well before publication in Nanomaterials. What are the defect formation energies obtained from MD and DFT without irradiation? The comparison may prove the MD potentials are reliable. 

Author Response

Referee 2.

What are the defect formation energies obtained from MD and DFT without irradiation? The comparison may prove the MD potentials are reliable.

Authors:

In fact, a detailed comparison of defect formation energies obtained by DFT and MD has been already carried out in Ref. 35 in the revised manuscript, as also mentioned on page 2 of the revised manuscript:

“The potential has been carefully benchmarked against the results of density-functional theory (DFT) calculations of defect formation energies in h-BN.”

Reviewer 3 Report

This is a rather solid article, which contains a detailed description of atomistic modeling of the formation of defects in a monolayer and bulk h-BN and, of course, is suitable for publication after clarifying some insufficiently well described fundamental concepts in the introduction.

1. In particular, and what do the authors understand for simple vacancies of boron and nitrogen? For example, in the case of alkali halide crystals there are two types of Frenkel defects – neutral (F and H centers) and charged (bare halogen vacancies and interstitials) [see  recent discussion, E. Kotomin, et al, J. Phys. Soc. Jpn. 63, 2602 (1994). https://doi.org/10.1143/JPSJ.63.2602  Kuzovkov et al, Low Temperature Physics 42, 588 (2016); https://doi.org/10.1063/1.4959018 ) In simple oxides (like MgO) oxygen vacancies have three charge states [A. I. Popov et al, Phys. Status Solidi B 195, 61 (1996). https://doi.org/10.1002/pssb.2221950107 and Mg- vacancies  also  have three charge states (Chen, Y., & Abraham, M. M. (1990). Trapped-hole centers in alkaline-earth oxides. Journal of Physics and Chemistry of Solids, 51(7), 747-764.) Note , that different charge states  of vacancies were also found in  h-BN and c-BN, see for example:

Toledo et al, https://doi.org/10.1088/1361-6463/abc37c

Fanciulli https://doi.org/10.1080/01418639708241100

 and Atobe et al  https://doi.org/10.1143/JJAP.32.2102

2. In the Introduction the following new applications, such as neutron and particle detectors and scintillators, are not mentioned at all. See

Lopes, J.M.J.   2021    Progress in Crystal Growth and Characterization of Materials 67(2),10052.   

Simos et al,   https://doi.org/10.1016/j.nimb.2020.06.018

Doan et al https://doi.org/10.1016/j.nima.2015.02.045

3. First paragraph and the first 7 references are far-fetched, do not help in any way for further reading and are recommended to be removed.
4. Please provide discussion: What charge states and what vacancies were considered simultaneously, what interactions between them were taken into account? How can two identical vacancies form nearby? Isn't there a Coulomb repulsion between them?? How was elastic interaction taken into account and what are the radii of spontaneous recombination for defects  with different charge?
5. Please check reference 12.

Author Response

Referee 3.

1. In particular, and what do the authors understand for simple vacancies of boron and nitrogen? For example, in the case of alkali halide crystals there are two types of Frenkel defects – neutral (F and H centers) and charged (bare halogen vacancies and interstitials) [see recent discussion, E. Kotomin, et al, J. Phys. Soc. Jpn. 63, 2602 (1994). https://doi.org/10.1143/JPSJ.63.2602 Kuzovkov et al, Low Temperature Physics 42, 588 (2016); https://doi.org/10.1063/1.4959018 ) In simple oxides (like MgO) oxygen vacancies have three charge states [A. I. Popov et al, Phys. Status Solidi B 195, 61 (1996). https://doi.org/10.1002/pssb.2221950107 and Mg- vacancies  also  have three charge states (Chen, Y., & Abraham, M. M. (1990). Trapped-hole centers in alkaline-earth oxides. Journal of Physics and Chemistry of Solids, 51(7), 747-764.) Note , that different charge states  of vacancies were also found in  h-BN and c-BN, see for example:

Toledo et al, https://doi.org/10.1088/1361-6463/abc37c

Fanciulli https://doi.org/10.1080/01418639708241100

 and Atobe et al  https://doi.org/10.1143/JJAP.32.2102

Authors:

We fully agree with the Referee that defects in h-BN and other semiconducting/insulating materials may exist in different charge states, which affects their formation energy when the system is in the thermodynamic equilibrium. Our group has in fact published many papers where this issue (also in h-BN) has been addressed. However, this is not relevant to the simulations of effects of irradiation, as the system is not under equilibrium conditions. Moreover, defect charge states cannot fundamentally be accounted for in the analytical potential molecular dynamics.

Referee:

In the Introduction the following new applications, such as neutron and particle detectors and scintillators, are not mentioned at all. See

Lopes, J.M.J.   2021    Progress in Crystal Growth and Characterization of Materials 67(2),10052.  

Simos et al,   https://doi.org/10.1016/j.nimb.2020.06.018

Doan et al https://doi.org/10.1016/j.nima.2015.02.045

Authors:

These irradiation-related issues are mentioned in the revised manuscript and all three papers are cited, page 2 in the revised manuscript:

“We note that in a wider context, understanding the response of h-BN to irradiation is also important for the use of this material in various radiation-related applications, such as neutron and particle detectors and scintillators [9,28,31].”

Referee:

1. First paragraph and the first 7 references are far-fetched, do not help in any way for further reading and are recommended to be removed.

Authors:

The goal of this paragraph was to emphasize the importance of defects (and thus irradiation as a means to produce them) for quantum mechanical applications such as single photon emission and sensing (h-BN is just only one of them). Thus we would like to keep this paragraph, and potentially attract attention of a larger readership.

Referee:

2. Please provide discussion: What charge states and what vacancies were considered simultaneously, what interactions between them were taken into account? How can two identical vacancies form nearby? Isn't there a Coulomb repulsion between them?? How was elastic interaction taken into account and what are the radii of spontaneous recombination for defects with different charge?

Authors:

As mentioned above, the issue of charge states of the defects is not directly relevant to defect production, and moreover, it cannot be accounted for in analytical potential molecular dynamics simulations. The clustering of vacancies and defect recombination is automatically taken into account in molecular dynamics simulations.

Referee:

    Please check reference 12.

Authors:

The reference appears to be correct: the journal “Science Advances” does not have page numbers, but codes consisting of letters and numbers are used.

 

Round 2

Reviewer 2 Report

The authors well answered my comments and I consider it can be accepted for publication in Nanomaterials.

Author Response

We than the Reviewer for reading the revised manuscript and our response to the original reports.

Reviewer 3 Report

I am absolutely not satisfied with the authors' answers.
I know and agree that "defect charge states cannot fundamentally be accounted for in the analytical potential molecular dynamics." Unfortunately, the authors are silent about this problem in introduction and thus mislead those who are not familiar with the possibilities and critical shortcomings of molecular dynamics. What works well in metals is no longer able to correctly describe binary oxides and nitrides, where the simultaneous formation of several distinct pairs of Frenkel defects coexists. Deliberately keeping silent about this and thus deliberately narrowing the understanding of the problem, which directs other scientists in a false circle, does not allow me to accept this text as a professional work. I would like the authors should honestly say that reality is much more complicated and MD is not able to correctly describe the situation and they consider what they can, but this may be far from reality

Author Response

We thank the Referee for reading the revised manuscript and our response to his/her comments provided at the first round of refereeing. Based on his/her latest remark, we better understand what he/she meant. Following the Referee’s suggestion, we added a paragraph about the limitations of empirical potential molecular dynamics when the method is applied to the simulations of irradiation effects in non-metallic materials.

 

The paragraph is given below. We note that in the original report, the Referee wrote about the account for the charge states of the defects in the molecular dynamics (MD) simulation. We stress once more that there are two different problems:

 

1. Assessment of the concentration of defects under equilibrium conditions in semiconductors/insulators;

 

2. Assessment of the concentration of defects produced by energetic particles, e.g., ions.

 

As for the first problem, defect concentration defined by their formation energies indeed depends on the charge state of the defect, that is the position of the Fermi level in the system. Formation energy of defects can even be affected by the presence of defects of other types through charge transfer from one type of defects to another. Note that formation energies normally differ by no more than a few eVs.

 

As for the second, the types of defects produced by the impact of the ion and their concentration are defined by the kinetics, that is energy transfer from the energetic ion to the target atoms. Thus, the concept of the charge state of the defect is not relevant to defect production. Note also that here the relevant energy range is tens, even hundreds of eVs.

 

In a wider context, the account for electronic degrees of freedom in the defect production process is definitely very important, but this is a different issue. Indeed, depending on the charge state of the ion or ion energy, electronic effects may dominate over the ballistic mechanism of energy transfer and defect production. For example, highly charged ions can give rise to Coulomb explosion, or at high ion energies, the energy deposition can be mostly into the electronic excitations, which may or may not eventually give rise to the formation of defects. However, in our work we consider single charged ions and the energy range when ballistic energy transfer dominates. Thus we believe that the simulations describe the physical processes governing defect production at least qualitatively correct.

 

We would also like to note that analytical potential MD has been widely used for the simulations of irradiation effects in semiconductors, and dozens if not hundreds of papers have been published. Just to mention a few:

 

Diamond: Journal of Applied Physics 117, 245901 (2015); Phys. Rev. B 49, 3030 (1994).

GaN: Phys. Rev. B 86, 104114 (2012); J. Phys. D: Appl. Phys. 50 505110 (2017); Journal of Applied Physics 112, 043517 (2012).

SiC: Journal of Nuclear Materials 289, 57 2001; Journal of Applied Physics 126, 125902 (2019);

Silicon: Applied Surface Science 416, 86 (2017).

 

Many other examples can be found in a recent review article: Journal of Nuclear Materials 520 (2019) 273.

 

Moreover, even binary-collision TRIM simulations, which can be referred to as an oversimplified version of MD, give frequently the results, which are in a good agreement with the experimental data.

 

Section 2 “Computational details” has been changed to account for that:

 

We stress that in the analytical potential MD, ions can be treated only as neutral atoms. The neglect of charge transfer during the collisions and also electronic excitations certainly affect the outcomes of ion impacts in semiconductors and insulators, that is the types of the produced defects and their concentrations. However, for the range of ion energies we consider, the ballistic energy transfer governs defect production, so that the results should be at least qualitatively correct, as demonstrated previously for a wide range of non-metallic materials, see, e.g., [Journal of Nuclear Materials 520 (2019) 273] for an overview. We also note that even DFT-based Born-Oppenheimer MD cannot describe correctly the evolution of the electronic subsystem during ion impacts, and the Ehrenfest dynamics combined with time-dependent DFT should be used, which is computationally too expensive for systematic studies of effects of ion irradiation on a material. We refer the readers to Ref. [Journal of Nuclear Materials 520 (2019) 273] for an overview of the methods used in the simulations of irradiation effects in solids and a discussion of their accuracy and applicability.

Round 3

Reviewer 3 Report

ACCEPT