Review Reports

Round 1

Reviewer 1 Report

I carefully read the manuscript by J. Yang et al.. The manuscript concern a theoretical study about the effects of Cu(II) and Cu(0) valence states on the resistive switching in HfO2 based junction.  In my opinion, the manuscript is interesting and provides an advancement in understanding the topic. This reviewer has no particular technical remark. However, I have some suggestions that should improve the impact of this article, in particular:

The introduction should stress the practical technological advantages of this type of RRAM.  For example, the simple architecture of the devices, such as the cross-bar configuration or similar (see for example, Nature Electronics (2018), 1, 33–343), the possibility to regenerate the devices (see for example Advanced  Materials (2012),  24, 1197-1201), and so on. This literature, or similar, should be cited in the introduction.

In the conclusions, the authors should add a sentence better explaining how this work can help fabricate better RRAM devices.

Once addressed the issues listed above, I expect the manuscript to be suitable for publication in Inorganics.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

In this manuscript, the authors examine electronic states and migration behaviors of a Cu dopant in HfO₂ from first principles to understand the switching mechanism of resistive random access memory. They pay special attention to the charge state of Cu dopant.

The manuscript may contain results worth publication regarding the charge state dependence of electronic states and migration behaviors of Cu dopants. However, their analyses have a few serious problems as described below. Therefore, the manuscript should not be published in the present form regardless of the journal in which the manuscript is published. 

Firstly, it is well known that the charge state stability of defects and impurities (dopants) depend on the Fermi level. A standard method to examine this via first-principles calculations has been established, and there are many papers on the defect/impurity analyses using the method (for example, npj Comput. Mater. 3, 12 (2017) and Phys. Rev. Appl. 9, 054036 (2018)). Section 3.1 should be completely revised after performing analyses using the above standard method or another relevant approach.

Second, the migration barrier of Cu(2+), 5.12 eV, is too high. This value suggest that Cu(2+) is practically immobile unless a very large bias voltage is applied to. This result cannot explain the operation of RRAM. Although to clarify the reason for the too-high migration barrier may be difficult, at least the authors should discuss this issue in their manuscript. I speculate that 1) the small supercell size used in their calculation may involve artifacts due to the interaction between Cu(2+) ions in the adjacent cells, or 2) Cu(2+) ions are really immobile in perfect crystal of HfO₂, and some kinds of structural imperfection such as vacancy and grain boundary are essential for Cu(2+) migration.

Finally, the authors seem to neglect the possible charge state difference between the migrating Cu and Cu in the conductive filament. The former is usually considered to be ionized (and thus can respond to the applied electric fields) and the latter neutral. Consequently, their discussion seems out of point.

Besides the above crucial issues, there are several careless and/or insufficient descriptions as follows.

1. They write that Fig. 3 shows the isosurface of the partial charge density of the impurity energy, but they do not write details about “impurity energy”. It is desirable to write the values of impurity energy (measured from e.g. the valence band maximum).
2. In the caption of Table 4, “Figure 7” should be “Figure 5.” In addition, the unit of the values in Table 4 is missing (probably angstrom).
3. From Table 4, I notice the displacement of atom No. 4 in the case of Cu(0), 2.28, is exceptionally large. If this value is correct, it is desirable to discuss the reason for this exceptionally large value.
4. References 6 and 7 are the same. And references 16 and 20 are the same.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Judging from the authors’ reply, I do not think the authors understand my comments correctly. In consequence, their revisions responding to my major comments are not relevant (for details, see the comments below). Therefore, I cannot recommend the publication of this manuscript.

First, they write in the revised manuscript that they calculated the defect formation energies using eq. (5), if I understand correctly. However, this must be wrong, because the quantity calculated via eq. (5) depends on the value of the Fermi level, which is a variable. That is, we can tune the Fermi level by dopants, defects and/or heterostructure formation. On the other hand, in their reply, they write “we consider again our method, and believe our methods is able to calculate the formation energies.” If the authors believe these two are consistent, they should describe persuasive argument at least in their response to the reviewer comments.

In addition, I note that the paper cited in “3.1 Valence Determination”, ref. [20], is a work on silicon nonvolatile memory, and the operation mechanism of this device is quite different from RRAM discussed in the present manuscript.

Second, they admitted that the energy barrier for Cu(2+) migration is very high, but does not include any meaningful discussion on this. The sentence “it (= the high energy barrier and the fact that Cu(2+) is practically immobile) won’t affect adding Cu irons, by which it can help to change other factors and form the charging channels” suggests they have not considered this seriously.

For Q3, I point out that the conductive filaments grow from the interface between the electrode and insulator (in the case of the present work, HfO₂). Then charge transfer between the filament and electrode can change the charge state of Cu in the filament.

Author Response

Please see detail response in attached file.

Author Response File: Author Response.docx

Round 3

Reviewer 2 Report

It is a pity that the most crucial point has not been improved in the second revised manuscript. Now the authors and I have reached agreement on the formula of the defect formation energy, and the fact that the formation energies of charged depend on the Fermi level. In addition, I note that the excerpt that they included in their second reply, “EF…which is typically considered to range between the VBM and CBM…” is important.

Then I cannot understand why the authors remain Table 2 and the paragraph discussing the stability of defects unchanged. It is obvious from the references (such as Phys. Rev. B 75, 104112 (2007) and npj Comput. Mater. 3, 12 (2017), both referred to in the authors’ reply) that the stability should be discussed based on the plots of Fermi level vs. formation energy. 

I am afraid that the authors may misunderstand something seriously, or may deliberately avoid the above point. 

Author Response

See detail in attached file.

Author Response File: Author Response.docx