New Method to Recover Activation Energy: Application to Copper Oxidation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Objective of the manuscript is not clearly stated.

2. What is the novelty of the work? and the applications are not highlighted.

3. Provide more figures to make easy to the readers to understand. 

4. Overall the manuscript requires improvement in the presentation. 

5. Clearly state how this new proposed method for calculating the activation energy improves upon existing methods.

6.How this new methodology does make novel contributions in the field of metal-oxide study. Is this method applicable to any type of metal and metal-oxide layers?

7.Show comparison, particularly by graphical presentation in what ways this new method for calculating activation energy of CuO metal layers improves accuracy to traditional techniques.

8.Provide structural characterization such as SEM, TEM, XPS, etc., to claim the accuracy of the new methodology.

 

Author Response

Comments 1: Objective of the manuscript is not clearly stated.

Response 1: We improve the introduction in order to state the objective of the manuscript and we add in the text:

- Page 2, (lines 40-44):

“The objective is the calculation of the activation energy, from successive annealings of the same initial sample, at ambient air pressure and at controlled temperature. The classical methods used to calculate the activation energy from experiments are directly based on the fitting of the oxidation rate using measurement of thicknesses, as a function of the inverse of temperature, assuming a given oxidation law.”

 

- Page 2, (lines 67-70):

“To achieve these goals, we consider the activation energy as the solution of an inverse problem instead of simply the result of a fitting of experimental data. Such inverse problem resolution necessitates more numerical evaluations than a simple fitting of data to a given model of oxidation.”

 

Comments 2: What is the novelty of the work? and the applications are not highlighted.

Response 2: We improve the introduction and the conclusion in order to highlight the novelty and the objectives of the work and we also compare the advantages/disadvantages of the proposed method relatively to the conventional ones.

We add in the text:

- Page 2, (lines 40-70):

“The objective is the calculation of the activation energy, from successive annealings of the same initial sample, at ambient air pressure and at controlled temperature. The classical methods used to calculate the activation energy from experiments are directly based on the fitting of the oxidation rate using measurement of thicknesses, as a function of the inverse of temperature, assuming a given oxidation law. The main drawbacks of the classical method are:

• the systematic measurement of thicknesses may be destructive, it is also subject to uncertainties and is depending on the method of measurement [21],
• The choice of the fitting function is often based on preliminary hypothesis on the oxidation mechanism [22–24].
• The detection of the possible change of oxidation law is based on visual inspection of the change of slope of the oxidation rate.
• The fitting does not handle the uncertainties of measurement of oxide thicknesses and it strongly depends on the method of measurement [21].
• The time of the full oxidation of copper cannot be retrieved.

To overcome these drawbacks as much as possible, we propose a new method to determine the activation energy. This method has the following properties:

• to prevent oxide and copper damage by excessive manipulations especially for thicknesses measurements, we suppose that the thicknesses are only measured only for both the initial copper sample (after deposition) and the final sample (after full oxidation). Therefore the intermediate thicknesses must be evaluated numerically.
• No a priori hypothesis is made on the oxidation law.
• The possible changes of the oxidation law during the successive annealings are numerically detected and the oxidation time at which it occurs is calculated.
• The proposed method handles the uncertainties on the initial and final oxide thicknesses.
• The time at which the complete copper oxidation takes place can be retrieved.

To achieve these goals, we consider the activation energy as the solution of an inverse problem instead of simply the result of a fitting of experimental data. Such inverse problem resolution necessitates more numerical evaluations than a simple fitting of data to a given model of oxidation.”

 

- Page 16 (lines 438-444)

“The resolution of the inverse problem permits to retrieve the thicknesses of copper and oxide and their uncertainties as a function of time. The main advantages of our method are following. No a priori knowledge on the physic law (or multiple successive laws) governing the oxidation are required. Moreover, only the initial and final measurement of thicknesses are necessary. The times at which the oxidation laws change and at which the complete copper oxidation takes place, can be retrieved.

 

Comments 3. Provide more figures to make easy to the readers to understand.

Response 3: We provide supplementary figures (Fig.2 and Fig.4-6) in order to compare the results on the activation energies on the three samples (including their uncertainties) and comparison with classical method. Figs.4-6 show the comparisons between our results and the results from measured data:

 

- Page 8, we add the Figure 2 showing the values and interval of uncertainties and comparing the results of our method and of the classical one.

 

- Page 7 (lines 270-272):

“Table 1 gives the results and Fig. 2 illustrates the activation energies found for the three samples. The results from both the classical method (ELR ) and the new method (E) can be compared.”

 

- Page 14-16, we add Figures 4-6 showing the values and interval of uncertainties, and comparing the results of the thicknesses obtained from measurement techniques (structural characterization) and our retrieved  thicknesses and comments as following.

+ Page 14 (lines 409-413)

“To assess our method, we compare the retrieved intermediate oxide thicknesses with those obtained from two different measurement techniques based on UV-Visible-NIR Absorbance fitting (see Refs. [6], 9 measured oxide thicknesses for each sample and [8], 6 data for each sample). Figures 4-6 show the three data sets for each of the three substrates (S1, S2 and S3) respectively.”

+ Page 14-16 (lines 414-433):

… Figure 4 …

“For the sample S1, at each oxidation time, we observe the overlap of the uncertainties intervals (Fig. 4). Therefore, the retrieved intermediate oxide thickness we found are in agreement with the indirect measurements in Ref. [6,8]. The ratio of the last oxide thickness to the copper initial one is in [1.1; 2.5] in coherence with the theoretical spatial expansion of crystalline oxide relatively to copper (i.e. in [1.68; 1.77] [21]).

… Figure 5 …

For the sample S2, our results are in agreement with those in Ref. [6] for the corresponding oxidation times (Fig. 5). Only the two last intervals of uncertainties are not overlapping with those of the measurements in Ref. [8]. However, the ratio of the final oxide thickness to the copper initial thickness (between 1.4 and 2.3) is closer to the theoretical spatial expansion of crystalline oxide relatively to copper (between 1.68 and 1.77) than that calculated from data in Ref. [8] (between 0.3 and 1.1).

… Figure 6 …

For each oxidation step of sample S3, the intervals of uncertainties are overlapping (Fig. 6). Moreover, the ratio of the last oxide thickness to the copper initial one is between 1.44 and 1.89. The theoretical spatial expansion of crystalline oxide relatively to copper being between 1.68-1.77 [21], we can conclude that the retrieved oxide thickness have physical sense.

For the three samples, S1, S2 and S3, we obtain oxide thicknesses that are in agreement with the measured ones in Refs. [6,8]. Moreover, our values of ratio of the final oxide thickness to the initial copper one, are in agreement with those obtained from theoretical calculations.”

 

 

Comments 4. Overall the manuscript requires improvement in the presentation.

Response 4: The presentation of the manuscript has been revised and restructured (through the introduction, results and discussion and conclusion) taking into account the different recommendations of the reviewers.

We also add in manuscript an overview of our approach:

 

Page 7 (lines 235-252):

“The resolution of the inverse problem consists in retrieving unknowns parameters of the model from experimental data (the measured initial and final thicknesses of copper and oxide). In our case, the unknown parameters are the copper and oxide thicknesses for each annealing step, the activation energy, the prefactor in the Arrhenius law (Eq. 3), the oxidation laws, and the time at which the complete copper oxidation takes place. The activation energy may depend on the oxide thickness, therefore, we propose four studies, by increasing the degrees of freedom of the problem as following:

• In Sec. 5.1, we calculate the unknown parameters by considering a single oxidation law for all annealing steps. In this case, the classical oxidation laws are tested systematically (the powers in the oxidation law are integers).
• In Sec. 5.2, two oxidation laws are used and the time at which the change of oxidation law occurs, is calculated.
• In Sec. 5.3, two oxidation laws are used and the time at which the change of oxidation law occurs, as well as the powers in the oxidation laws, are computed. In this case, the degree of freedom is increased as we no more consider only the classical laws.
• In Sec. 5.4, three successive oxidation laws are considered, and the two time values at which the oxidation laws change, are retrieved as well as the powers in the oxidation laws.

 

Comments 5. Clearly state how this new proposed method for calculating the activation energy improves upon existing methods.

Response 5: We show how the proposed method improve the existing methods (we also add a discussion on the advantages/disadvantages already described in remarks 1-2).

 

- Page 2, (lines 40-70):

“The objective is the calculation of the activation energy, from successive annealings of the same initial sample, at ambient air pressure and at controlled temperature. The classical methods used to calculate the activation energy from experiments are directly based on the fitting of the oxidation rate using measurement of thicknesses, as a function of the inverse of temperature, assuming a given oxidation law. The main drawbacks of the classical method are:

• the systematic measurement of thicknesses may be destructive, it is also subject to uncertainties and is depending on the method of measurement [21],
• The choice of the fitting function is often based on preliminary hypothesis on the oxidation mechanism [22–24].
• The detection of the possible change of oxidation law is based on visual inspection of the change of slope of the oxidation rate.
• The fitting does not handle the uncertainties of measurement of oxide thicknesses and it strongly depends on the method of measurement [21].
• The time of the full oxidation of copper cannot be retrieved.

To overcome these drawbacks as much as possible, we propose a new method to determine the activation energy. This method has the following properties:

• to prevent oxide and copper damage by excessive manipulations especially for thicknesses measurements, we suppose that the thicknesses are only measured only for both the initial copper sample (after deposition) and the final sample (after full oxidation). Therefore the intermediate thicknesses must be evaluated numerically.
• No a priori hypothesis is made on the oxidation law.
• The possible changes of the oxidation law during the successive annealings are numerically detected and the oxidation time at which it occurs is calculated.
• The proposed method handles the uncertainties on the initial and final oxide thicknesses.
• The time at which the complete copper oxidation takes place can be retrieved.

To achieve these goals, we consider the activation energy as the solution of an inverse problem instead of simply the result of a fitting of experimental data. Such inverse problem resolution necessitates more numerical evaluations than a simple fitting of data to a given model of oxidation.”

 

Comments 6. How this new methodology does make novel contributions in the field of metal-oxide study. Is this method applicable to any type of metal and metal-oxide layers?

Response 6: Such a new method is general and generic, not necessitating any a priori knowledge on oxidation process. Therefore it can be applied to any type of metal and metal-oxyde layer. We also add this remark in the conclusion.

 

- Page 9 (lines 298-301):

“Let us underline that the measurement of intermediate thicknesses is not required for our method (only the measurements of the initial and final thicknesses are necessary, with their uncertainties). That contrasts with the classical method for which all the intermediate thicknesses must be measured at the end of each annealing step.”

 

- Page 16 (lines 438-444):

“The resolution of the inverse problem permits to retrieve the thicknesses of copper and oxide and their uncertainties as a function of time. The main advantages of our method are following. No a priori knowledge on the physic law (or multiple successive laws) governing the oxidation are required. Moreover, only the initial and final measurement of thicknesses are necessary. The times at which the oxidation laws change and at which the complete copper oxidation takes place, can be retrieved.”

 

- Page 16 (lines 451-452):

“Such a method is generic and could be applied to any oxidation or solid state chemical reaction (metal and metal-oxyde layer).”

 

 

Comments 7. Show comparison, particularly by graphical presentation in what ways this new method for calculating activation energy of CuO metal layers improves accuracy to traditional techniques.

Response 7: We also show a comparison (on Fig.2 and Fig.4-6) of the accuracy of our method relatively to the traditional techniques (on the evaluation of the activation energy and on the thicknesses recovered).

 

- Page 8, we add  Figure 2 showing the values and interval of uncertainties and comparing the results of our method and of the classical one.

 

- Page 7 (lines 270-272):

“Table 1 gives the results and Fig. 2 illustrates the activation energies found for the three samples. The results from both the classical method (ELR ) and the new method (E) can be compared.”

 

- Page 14-16, we add Figures 4-6 showing the values and interval of uncertainties, and comparing the results of the thicknesses obtained from measurement techniques (structural characterization) and our retrieved  thicknesses

 

Comments 8. Provide structural characterization such as SEM, TEM, XPS, etc., to claim the accuracy of the new methodology.

Response 8: We show a comparison (on Fig.4-6) of the accuracy of our method relatively to measured thicknesses by spectroscopic methods (in Ref. 6 and 8).

 

- Page 14-16, we add Figures 4-6 showing the values and interval of uncertainties, and comparing the results of the thicknesses obtained from measurement techniques (structural characterization) and our retrieved  thicknesses

 

- Page 14 (lines 409-413)

“To assess our method, we compare the retrieved intermediate oxide thicknesses with those obtained from two different measurement techniques based on UV-Visible-NIR Absorbance fitting (see Refs. [6], 9 measured oxide thicknesses for each sample and [8], 6 data for each sample). Figures 4-6 show the three data sets for each of the three substrates (S1, S2 and S3) respectively.”

 

- Page 14-16 (lines 415-433):

“For the sample S1, at each oxidation time, we observe the overlap of the uncertainties intervals (Fig. 4). Therefore, the retrieved intermediate oxide thickness we found are in agreement with the indirect measurements in Ref. [6,8]. The ratio of the last oxide thickness to the copper initial one is in [1.1; 2.5] in coherence with the theoretical spatial expansion of crystalline oxide relatively to copper (i.e. in [1.68; 1.77] [21]).

For the sample S2, our results are in agreement with those in Ref. [6] for the corresponding oxidation times (Fig. 5). Only the two last intervals of uncertainties are not overlapping with those of the measurements in Ref. [8]. However, the ratio of the final oxide thickness to the copper initial thickness (between 1.4 and 2.3) is closer to the theoretical spatial expansion of crystalline oxide relatively to copper (between 1.68 and 1.77) than that calculated from data in Ref. [8] (between 0.3 and 1.1).

 

For each oxidation step of sample S3, the intervals of uncertainties are overlapping (Fig. 6). Moreover, the ratio of the last oxide thickness to the copper initial one is between 1.44 and 1.89. The theoretical spatial expansion of crystalline oxide relatively to copper being between 1.68-1.77 [21], we can conclude that the retrieved oxide thickness have physical sense.

For the three samples, S1, S2 and S3, we obtain oxide thicknesses that are in agreement with the measured ones in Refs. [6,8]. Moreover, our values of ratio of the final oxide thickness to the initial copper one, are in agreement with those obtained from theoretical calculations.”

Reviewer 2 Report

Comments and Suggestions for Authors

In this manuscript, the authors propose a new method to determine the activation energy of oxidized copper. The authors mentioned that their motivation is the conventional way of calculating activation energy by fitting the oxidation rate as a function of the inverse of temperature has the drawback that the measurement of thickness is subject to uncertainties and strongly depends on the method of measurement. However, the method proposed by the authors also relies on the measurement of the oxide layer thickness. Therefore, isn't the same limitation applicable to the authors' proposed method as well? Consequently, I don't quite understand why the authors have chosen to abandon the simple fitting method that has been conventionally adopted, in favor of such a complicated approach.

At this stage, I am unable to assess whether the method proposed by the authors is novel, and I therefore recommend major revisions. To address my concerns, I suggest the authors:

1. Perform a conventional fitting on the three experimental samples and compare the results with those obtained using their proposed method.

2. Add a detailed discussion that highlights the advantages and disadvantages of the proposed method compared to the conventional fitting method.

Author Response

In this manuscript, the authors propose a new method to determine the activation energy of oxidized copper. The authors mentioned that their motivation is the conventional way of calculating activation energy by fitting the oxidation rate as a function of the inverse of temperature has the drawback that the measurement of thickness is subject to uncertainties and strongly depends on the method of measurement. However, the method proposed by the authors also relies on the measurement of the oxide layer thickness. Therefore, isn't the same limitation applicable to the authors' proposed method as well? Consequently, I don't quite understand why the authors have chosen to abandon the simple fitting method that has been conventionally adopted, in favor of such a complicated approach. At this stage, I am unable to assess whether the method proposed by the authors is novel, and I therefore recommend major revisions.

 

Response : Due to the fact that the measurement of thickness is subject to uncertainties and strongly depends on the method of measurement, the motivation of the method is to avoid the use of conventional way of calculating activation energy (from fitting the oxidation rate as a function of the inverse of temperature and the measurement of thicknesses). In the present paper, the proposed method only necessitates the measurement of the initial and final oxide layer thicknesses (without any measurement of the intermediate thicknesses). That contrast with the classical method which necessitates measurement of  intermediate thicknesses.

We precise such a remark and add in the text (in red) :

- Page 2, (lines 40-70):

“The objective is the calculation of the activation energy, from successive annealings of the same initial sample, at ambient air pressure and at controlled temperature. The classical methods used to calculate the activation energy from experiments are directly based on the fitting of the oxidation rate using measurement of thicknesses, as a function of the inverse of temperature, assuming a given oxidation law. The main drawbacks of the classical method are:

• the systematic measurement of thicknesses may be destructive, it is also subject to uncertainties and is depending on the method of measurement [21],
• The choice of the fitting function is often based on preliminary hypothesis on the oxidation mechanism [22–24].
• The detection of the possible change of oxidation law is based on visual inspection of the change of slope of the oxidation rate.
• The fitting does not handle the uncertainties of measurement of oxide thicknesses and it strongly depends on the method of measurement [21].
• The time of the full oxidation of copper cannot be retrieved.

To overcome these drawbacks as much as possible, we propose a new method to determine the activation energy. This method has the following properties:

• to prevent oxide and copper damage by excessive manipulations especially for thicknesses measurements, we suppose that the thicknesses are only measured only for both the initial copper sample (after deposition) and the final sample (after full oxidation). Therefore the intermediate thicknesses must be evaluated numerically.
• No a priori hypothesis is made on the oxidation law.
• The possible changes of the oxidation law during the successive annealings are numerically detected and the oxidation time at which it occurs is calculated.
• The proposed method handles the uncertainties on the initial and final oxide thicknesses.
• The time at which the complete copper oxidation takes place can be retrieved.

To achieve these goals, we consider the activation energy as the solution of an inverse problem instead of simply the result of a fitting of experimental data. Such inverse problem resolution necessitates more numerical evaluations than a simple fitting of data to a given model of oxidation.”

 

- Page 6 (lines 220-223):

“..and for a given value of hOx1, randomly chosen within the intervals of uncertainties of measurement (appendix B), we numerically evaluate the successive intermediate thicknesses h2..9 (Eq. 8).”

 

Comments 1. Perform a conventional fitting on the three experimental samples and compare the results with those obtained using their proposed method.

Response1: A conventional fitting on the three experimental samples has been achieved in order to compare the results of the classical method with obtained results from the proposed method and are given in Table 1 (comparison for each sample and each law the activation energies E and ERL). Such results are also illustrated in a new Fig,2 (page 8) showing the activation energy (ELR) calculated from classical method and the activation energy (E) calculated from the new method (including their uncertainties). We also add in the manuscript the explanation of the differences between the obtained results (including uncertainties on the Activation Energies).

- Page 7 (lines 263-272):

“We also evaluate the activation energy (ELR ) obtained from the classical method, that consists in calculating the slope of the logarithm of oxidation rate as a function of 1/T, by using linear regression. For the classical method, it is necessary to achieve the measurement of the intermediate thicknesses and their uncertainties (given in [8]). To take into account these uncertainties, we use the method described in appendix C. That contrasts with the new proposed method which only necessitate the measurement of the initial and final thicknesses (the intermediate ones are numerically evaluated).

Table 1 gives the results and Fig. 2 illustrates the activation energies found for the three samples. The results from both the classical method (ELR ) and the new method (E) can be compared..”

 

- Page 8, we add a new Figure 2 showing the values and interval of uncertainties by comparing the results of our method and of the classical one.

 

- Page 9, (lines 276-282):

“The other retrieved parameters are of the same order of magnitude for the three samples and for the three oxidation laws, respectively. The values of the activation energies obtained from the classical method (ELR ) are smaller than those obtained from our method (E). The mean value of the activation energy calculated with our method is in the interval of uncertainties of the classical method. The uncertainty on ELR is about 10 times that of our method (see Fig. 2 and Tab. 1). Therefore, our method appears to be more efficient than the classical one.”

 

- Page 9, (lines 298-301):

“Let us underline that the measurement of intermediate thicknesses is not required for our method (only the measurements of the initial and final thicknesses are necessary, with their uncertainties). That contrasts with the classical method for which all the intermediate thicknesses must be measured at the end of each annealing step.”

 

 

Comments 2. Add a detailed discussion that highlights the advantages and disadvantages of the proposed method compared to the conventional fitting method.

Response 2: A discussion that highlights the advantages/disadvantages of the new proposed method, relatively to the conventional methods has been added. We modify the introduction (see Page 2 lines 38-70), we add a remark in the introduction and in the conclusion in order to highlight such elements.

- Page 2, (lines 40-70):

“The objective is the calculation of the activation energy, from successive annealings of the same initial sample, at ambient air pressure and at controlled temperature. The classical methods used to calculate the activation energy from experiments are directly based on the fitting of the oxidation rate using measurement of thicknesses, as a function of the inverse of temperature, assuming a given oxidation law. The main drawbacks of the classical method are:

• the systematic measurement of thicknesses may be destructive, it is also subject to uncertainties and is depending on the method of measurement [21],
• The choice of the fitting function is often based on preliminary hypothesis on the oxidation mechanism [22–24].
• The detection of the possible change of oxidation law is based on visual inspection of the change of slope of the oxidation rate.
• The fitting does not handle the uncertainties of measurement of oxide thicknesses and it strongly depends on the method of measurement [21].
• The time of the full oxidation of copper cannot be retrieved.

To overcome these drawbacks as much as possible, we propose a new method to determine the activation energy. This method has the following properties:

• to prevent oxide and copper damage by excessive manipulations especially for thicknesses measurements, we suppose that the thicknesses are only measured only for both the initial copper sample (after deposition) and the final sample (after full oxidation). Therefore the intermediate thicknesses must be evaluated numerically.
• No a priori hypothesis is made on the oxidation law.
• The possible changes of the oxidation law during the successive annealings are numerically detected and the oxidation time at which it occurs is calculated.
• The proposed method handles the uncertainties on the initial and final oxide thicknesses.
• The time at which the complete copper oxidation takes place can be retrieved.

To achieve these goals, we consider the activation energy as the solution of an inverse problem instead of simply the result of a fitting of experimental data. Such inverse problem resolution necessitates more numerical evaluations than a simple fitting of data to a given model of oxidation.”

 

- Page 9, (lines 298-301):

“Let us underline that the measurement of intermediate thicknesses is not required for our method (only the measurements of the initial and final thicknesses are necessary, with their uncertainties). That contrasts with the classical method for which all the intermediate thicknesses must be measured at the end of each annealing step.”

 

- Page 16 (lines 438-444):

“The resolution of the inverse problem permits to retrieve the thicknesses of copper and oxide and their uncertainties as a function of time. The main advantages of our method are following. No a priori knowledge on the physic law (or multiple successive laws) governing the oxidation are required. Moreover, only the initial and final measurement of thicknesses are necessary. The times at which the oxidation laws change and at which the complete copper oxidation takes place, can be retrieved.”

 

- Page 16 (lines 451-452):

“Such a method is generic and could be applied to any oxidation or solid state chemical reaction (metal and metal-oxyde layer).”

Reviewer 3 Report

Comments and Suggestions for Authors

Cooper oxidation is a fundamental technological challenge. The authors propose a novel and innovative theoretical model that, without any a priori hypothesis on the oxidation law, helps to determine the activation energy. The proposed method allows to overcome uncertainties as much as possible in activation energy determination. It is shown that this method works on successive annealing of the same initial sample at ambient air pressure and at controlled temperature.

The research design is appropriate, and numerical presumptions and results were well supported by experimental observations, making the manuscript valuable for the readers. The author's findings supported the conclusions well. However, some minor improvements should be made before publishing:

1.        The introduction part of the manuscript is based on rather old literature references. It could be upgraded by citing more novel sources.

 

2.        The manuscript is interesting to read; however, it is not easy to understand. Proofreading by a native speaker would make the manuscript more attractive and understandable.

Comments on the Quality of English Language

1.        The manuscript is interesting to read; however, it is not easy to understand. Proofreading by a native speaker would make the manuscript more attractive and understandable.

Author Response

Cooper oxidation is a fundamental technological challenge. The authors propose a novel and innovative theoretical model that, without any a priori hypothesis on the oxidation law, helps to determine the activation energy. The proposed method allows to overcome uncertainties as much as possible in activation energy determination. It is shown that this method works on successive annealing of the same initial sample at ambient air pressure and at controlled temperature. The research design is appropriate, and numerical presumptions and results were well supported by experimental observations, making the manuscript valuable for the readers. The author's findings supported the conclusions well. However, some minor improvements should be made before publishing:

Comments 1. The introduction part of the manuscript is based on rather old literature references. It could be upgraded by citing more novel sources.

Response 1: An update in sources in literature references have been added (see new references in red in the revised manuscript: [3,4,5,9,12,16,20] (from 2019 to 2024). Moreover, the introduction has been revised in order to enhance the advantages/disadvantages of the new method relatively to the conventional methods.

 

Comments 2. The manuscript is interesting to read; however, it is not easy to understand. Proofreading by a native speaker would make the manuscript more attractive and understandable.

Response 2: The English has been revised and the manuscript has been reread by an English native speaker. We hope that it is now more attractive and understandable.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author can think of a structural investigation like SEM/FESEM to determine the oxidation part of CuO films, which will make the manuscript stronger and worthy to read by the scientific community. 

Author Response

Comments 1: The author can think of a structural investigation like SEM/FESEM to determine the oxidation part of CuO films, which will make the manuscript stronger and worthy to read by the scientific community. 

Response 1: Structural investigations like SEM/FESEM and AFM could be used to measure the oxidation thicknesses.  Nevertheless, the systematic measurement of thicknesses may be destructive, and is also subject to uncertainties and is depending on the method of measurement [21].

The method we propose allows to calculate the activation energy of copper oxidation and simultaneously, the calculation of thicknesses for intermediate annealings. As stated in the article (page 2, lines 46-47), we avoid direct measurements of intermediate thicknesses to maintain sample integrity (lines 56-59). In addition, intermediate samples are no longer available for measurements since successive annealings are performed on the same sample until total oxidation.

However, we based the validation of the method on comparison with indirect measurements by UV-visible spectroscopy on the same samples, given in references [6] and [8]. This method is non destructive. In addition, we verified that the ratio of oxide to copper thickness corresponds well with the theoretical values given by crystallography (page 14, lines 409-416). We also specify that if the intermediate thicknesses were known, the method is also applicable.

As a result, we cannot fully satisfy the referee’s request but we have proposed a validation with the above mentioned methods.

However, to improve clarity, we add in the text the following information:

- Page 2 (lines 46-47):

“The systematic measurement of thicknesses may be destructive, it is also subject to uncertainties and is depending on the method of measurement [21].”

Therefore, we suppressed the mention of uncertainties in line 52 to avoid duplication.

 

- Page 5 (lines 214-217)

“… and on the measurement of initial and final thicknesses  of copper and oxide by Scanning Electron Microscopy, Multi Angle Incident spectroscopy, Atomic Force Microscopy, Spectroscopic Ellipsometry and UV-Visible Spectroscopy. The intermediate thicknesses are not measured to avoid possible destruction of the samples.”

 

- Page 14 (lines 411-418)

“Only the initial and final thicknesses are measured by Scanning Electron Microscopy, Multi Angle Incident spectroscopy, Atomic Force Microscopy, Spectroscopic Ellipsometry (see Appendix B). To assess our method, we compare the retrieved intermediate oxide thicknesses with those obtained from two different indirect measurement techniques (UV- visible spectroscopy) that are not destructive (see Refs. [6], 9 measured oxide thicknesses for each sample and [8], 6 data for each sample). Moreover, we verified that the ratio of oxide to copper thickness corresponds well with the theoretical values given by crystallography.”