Cover Letter/Response Letter
Paper Number: 357
Article title: Electronic properties of two-dimensional zinc oxide in hexagonal, (4,4)-tetragonal, and
(4,8)-tetragonal structures by using Hybrid Functional calculation
Author : Chumpol Supatutkul, Sittichain Pramchu, Yongyut Laosiritaworn, Atchara Punya
Jaroenjittichai
Corresponding author: Atchara Punya Jaroenjittichai
Corresponding author’s email address: [email protected]
Dear Editor and Reviewer,
Thank you very much for your comments, which the authors find very useful. We have made
some changes, which are highlighted in yellow in the revised manuscript, as well as responses to the
reviewer’s comment as the following in this cover letter.
Reviewer’s comments
Please revise or respond to the following reviewer comments and reupload a revised version within 2
weeks. The authors employed hybrid-density functional calculations to study the electronic properties
of two-dimensional ZnO. This work would be suitable to be published after the following issues are
addressed:
(1) Why did the authors use 40% of exact exchange for the Hatree-Fock mixing parameter? The
reason stated in the sentence "the electrons in the Zn 3d orbital is less likely to be localized" is hard to
understand and should be incorrect.
Response: In this work, the 40% HF mixing ratio was chosen by calibrating the calculated band gaps
of the bulk ZnO in both wurtzite and zincblend with the recent experimental values. We found that
40% (or 0.4) of HF exchange yield band gaps close to experimental values for both wurtzite and
zincblende ZnO. We also feel thankful to the reviewer for pointing out that the sentence ‘the
electrons in the Zn 3d orbital is less likely to be localized’ is incorrect, which has been revised. Note
that one of the reasons in introducing the HSE method was to treat materials with localized electrons.
Therefore we have modified by adding some more details and remove ambiguous points to enhance
the accessibilities with explanations highlighted below;
“The 40% of exact exchange were used in HSE calculations because the electrons in the Zn 3d orbital
is less likely to be localized” is changed to “The mixing parameter for the HSE functional in our work
was set to 0.4 (40% of HF exchange), resulting from calibration of wurtzite and zincblende ZnO band
gaps to match the experimental values [9, 10], i.e. see Table 1.”
(2) The authors calculated the band gaps of two-dimensional ZnO, however, have not identified
whether they are direct or indirect.
Response: In order to provide a clearer picture of band gaps, we have constructed the energy band
structures of our three 2D-ZnO sheets. Thus, we have replaced the two energy band structures of
wurtzite and zincblend of bulk ZnO by the three energy band structures of 2D ZnO as showed below;
b)
a)
c)
Figure 2. The band structures of 2D ZnO monolayer in (a) hexagonal, (b) (4,8)-tetragonal and (c)
(4,4)-tetragonal structures.
Therefore, the old explanations were rearranged and added some details to make this point become
more elucidated (i.e. in section 3 on paragraph 2 of the manuscript) as highlighted below;
“Next, the electronic band structures of 2D ZnO sheets were calculated. The band structures
shows that both hexagonal and (4,8)-tetragonal monolayers have direct band gap at Γ but the (4,4)tetragonal monolayer has indirect band gap at X-Γ as shown in Figure 2. The band gaps obtained
from using HSE hybrid calculations are 4.20 eV and 4.59 eV for hexagonal and (4,8)-tetragonal
sheets respectively, which is wider than that of the bulk ZnO (3.37 eV and 3.22 eV for wurtzite and
zincblende). Nevertheless, the (4,4)-tetragonal structure has a direct band gap of 5.00 eV and indirect
band gap of 3.06 eV. Note that, only the band gap of the hexagonal monolayer is availably measured
and has been reported recently at 4.48 eV [12], whereas other 2D structures have not been
synthesized yet.”
(3) [Page 4] The sentence "In term of structural stability, the hexagonal ZnO has more energetically
favorable than both of (4,4)- and (4,8)-tetragonal ZnO for about 5.10 eV and 3.15 eV" is very hard to
understand and unclear what is the meaning of those 5.10 eV and 3.15 eV. Are they total energy per
formula unit of ZnO, or heat of formation ? The following sentence is also inaccurate because 5.10 eV
and 3.15 eV are not small different values at all.
Response: The total energy differences of 5.10 eV and 3.15 eV are not the energy per formula unit.
They are the difference of total energy from the corresponding 2D ZnO supercell (which consists of
16 Zn atoms and 16 O atoms). So, the energy differences per formula unit are 318 meV and 197 meV
for (4,4)-tetragonal and (4,8)-tetragonal structures respectively, considering the total energy of
hexagonal structures as a reference.
Therefore, we have corrected the energy differences and added more clarified explanation to replace
the ambiguous sentences in the manuscript as highlighted below:
“In term of structural stability, the hexagonal ZnO has more energetically favorable than both of
(4,4)- and (4,8)-tetragonal ZnO for about 5.10 eV and 3.15 eV…” is replaced by “For the stability of
the structures, we found that the hexagonal ZnO is the most stable structure. The (4 ,4 )- and (4 ,8 )tetragonal ZnO have total energy per formula of 3 1 8 meV and 1 9 7 meV higher than that of the
hexagonal one, respectively”
(4) The conclusion also has to be revised because of the above issue.
Response: The conclusion and abstract have been corrected in according to the changes made in the
revised manuscripts.
(5) The minor English grammatical errors should be corrected. For example, in the abstract, "the
calculation results" should be replaced by "the calculated results" In Methods "which mixes the exact
non-local exchange of Hartree-Fork (HF) theory"; "theory"should be replaced by "potential" because
we cannot mix theory with potential.
Response: The English grammatical errors are also revised and corrected.
Yours sincerely,
Chumpol Supatutkul , Sittichain Pramchu, Yongyut Laosiritaworn, Atchara Punya Jaroenjittichai