Noise Reduction of Atomic Force Microscopy Measurement Data for Fitting Verification of Chemical Mechanical Planarization Model

Round 1

Reviewer 1 Report

The manuscript “Noise reduction of atomic force microscopy measurement data for fitting verification of chemical mechanical planarization model” proposes a new approach of noise reduction by combining Wavelet Transform and Fourier Transform.  The authors provide the details of the method and the verification in an AFM setting.  The paper is acceptable to Electronics until the following issues are resolved:

 

1. The introduction needs more work.  1) Too many experimental details and results (Figs 1-3, Table 1) are shown in the introduction.  This makes the introduction not generic for the examples in the field, but only for the authors’ specific designs. 2) The references used in the introduction need to be reordered.  References 19-22 appeared earlier than 7-18.

2. Page 8, line 220-228.  It would be better to show figures of the results from 2sigma and 3sigma cases to explain why 2sigma is used as the noise threshold.  The figures might explain it better for readers to understand why “the damage to the signal increases” when the hard threshold is set to 3sigma.

3. Figure 12.  The SEM images need be larger to reflect the dishings on the images. 

4. Figure 13.  The chart type should be scatters without lines, since the dishing is not dependent on the number of the test sample.  The authors may consider combining Figs 13-14 (the number is 15 for figure 14 in the Figure title) together since they are from the same sets of data.

5. In Figure 14, for smapleL1-3, the absolute error is higher after denoising.  Please explain.

6. Minor errors. Examples: 1) Please double check the page numbers.  2) Line 18, missing period. 3) Figure 9, the caption “wavelet coefficient” above l=1 figure is confusing.

Author Response

1. The introduction needs more work. 1) Too many experimental details and results (Figs 1-3, Table 1) are shown in the introduction. This makes the introduction not generic for the examples in the field, but only for the authors’ specific designs. 2) The references used in the introduction need to be reordered. References 19-22 appeared earlier than 7-18.

 

A: Thank you for your guidance. The purpose of this article is not simply AFM data noise reduction. My research work and the research of the research group mainly focus on the establishment of chemical mechanical planarization(CMP) morphology prediction model. This research direction involves the measurement of chip topography data. At the same time, we find that the measurement noise will affect the accuracy of the modeling. However, previous studies in CMP modeling did not consider the noise effect of measurement data. Since this is a pioneering sub-research in the field of CMP modeling, and its application is limited to data noise reduction required for CMP modeling, you may feel that the introduction of the experiment is too detailed and lacks generality. But this experiments or the trench structure shown in Fig 1-3 is commonly used experimental methods in CMP modeling. So, I think these detailed descriptions of experiments are what researchers in the field of CMP modeling need to know. So, I don't think the experimental details can be deleted.

The order of references will be changed in the new version.

 

2. Page 8, line 220-228. It would be better to show figures of the results from 2sigma and 3sigma cases to explain why 2sigma is used as the noise threshold. The figures might explain it better for readers to understand why “the damage to the signal increases” when the hard threshold is set to 3sigma.

 

A : I think this is a very meaningful suggestion. I will add a comparison of noise reduction results with a threshold value of 3sigma to the mentioned position, so that readers can better understand why an excessively high threshold value will cause damage to the original signal

 

3. Figure 12. The SEM images need be larger to reflect the dishings on the images.

 

A : The concept of dishing is shown in figure1, which may not be obvious. I will add the presentation of dishing in SEM.

 

4. Figure 13. The chart type should be scatters without lines, since the dishing is not dependent on the number of the test sample. The authors may consider combining Figs 13-14 (the number is 15 for figure 14 in the Figure title) together since they are from the same sets of data.

 

A: I reworked Fig14 into a histogram. But I tried many ways and still can't merge Fig14 with Fig15. So I finally decided to keep two plots to show the dishing comparison and root mean square error comparison respectively

 

5. In Figure 14, for smapleL1-3, the absolute error is higher after denoising. Please explain.

 

A: I think it can be explain from two point:

 

First, both AFM data and SEM data have observational random errors in human measurement. The random observation error of L1-3 is large, so the absolute error of the data after noise reduction is similar to that before noise reduction. This is just a case of coincidence.

Second, the dishing measured in AFM data is the mean height difference average of a region. But that measured from SEM data is the height difference of a local point. Therefore, there may be a high absolute error between local dishing and regional average dishing.

Reviewer 2 Report

Dear Author(s), the manuscript ‘Noise reduction of atomic force microscopy measurement data for fitting verification of chemical mechanical planarization model’, Manuscript ID: electronics-2391448, have some weakness that must be revised appropiately.

Please refer to the listed below of the most crucial issues:

1.      In the ‘Abstract’ section, the problem in noise is not comprehensively introduced. Its removal as crucial task is not improved. This section should present more about requirements. Generally, this section is poor and must be improved suitably.

2.      Moreover, the shortcuts should not be presented in the ‘Abstract’ section or, respectively, should be provided when firstly presented in text. For example, the IC abbreviation was not introduced at firstly written in this section.

3.      The origin of the noise occurrence was not presented in an appropriate order. Moreover, the source of the noise is not reflected to the SEM analysis as well.

4.      The review in the ‘Introduction’ section is not comprehensive enough. There are many limitations that must be studied considering the noise components of the raw measured data. From that matter, this issues must be studied in a wider range of analysis. Please present more previous studies and, respectively, lacks in the currect state of knowledge which, correspondingly, will provide some requirements in the further studies.

5.      According to the previous issue, the motivation of work does not derived straightly from the critical review, which, in fact, does not exist. Moreover, the advantages and disadvantages of previous studies results are not introduced suitably.

6.      Furthermore to the previous comment, what type of noise is usually found for the AFM measurements? If various types of noises, it should be even reviewed in the ‘Introduction’ section. Please try to refer for various types of noises:

(1)   https://www.doi.org/10.1088/0957-0233/23/3/035008

(2)   https://doi.org/10.1007/s41871-020-00057-4

(3)   https://doi.org/10.3390/ma14020333

7.      Generally, from the ‘Introduction’ section, the motivation of work is not clear, especially which type of noise (which frequency, amplitude) is considered as that dominant and must be reduced firstly. The Author(s) must highlight the main problem to be resolved. In that matter, it is difficult to follow what is the main axis of the studies presented.

8.      In section 2, it is not obvious which equations are newly considered and, respectively, which already studied and presented in previous papers. The Author(s) must separate their proposals and previous results to encourage their work.

9.      Some practical applications of Fourier Tranform, and other algorithms, must be presented that can justify usage of them. Look for some exaples:

(4)   http://dx.doi.org/10.17531/ein.2021.1.9

(5)   https://doi.org/10.1007/s00170-015-7509-0

(6)   https://doi.org/10.1016/j.measurement.2013.10.036

10.  The assumptions from lines 173-181 are not supported by advantages and disadvantages of the wavelet Fourier characteristics. The wavelet transform, connected with Fourier transform, can add some significant value to the data characteristics. They are not presented and included in the proposals.

11.  The thresholding of the AFM measurement data is not references to the current results. Please improve the section 3.3. for the (a) subsection and justify the value of hard thresholding with some previous studies, the Author(s) or other sources, if exist.

12.  The critical discussion in section 4, which is significant in the method validation, is not presented. As in many previous cases, the prons and cons are not included.

13.  The ‘Conclusion’ section is messy. Firstly, is too long with one sentences, it should be divided in some separated and numbered gaps. Secondly, the main purpose must be highlighted and introduced appropriately. Currently, this section is a lot of various sentences. Finally, the main purpose must be more highlitghted and reader informaed around the main objective of the paper.

14.  The further studies should be proposed, any ‘the Outlook’ idea to continue the proposals applications.

Moreover, some additional (editorial) modifications are required as well:

15.  The empty page before ‘References’ must be removed.

16.  The numbering of pages is mixed, it looks confusing.

17.  The formatting of the ‘References’ must be unified that, in some cases, there is no DOI link and in some it was provided.

From the above, the reviewed manuscript must be improved significantly before any further processing of the Electronics journal, if allowed by the Editor.

Author Response

1. In the ‘Abstract’ section, the problem in noise is not comprehensively introduced. Its removal as crucial task is not improved. This section should present more about requirements. Generally, this section is poor and must be improved suitably.

 

A: At the beginning of the writing abstract, the introduction to the problem was not perfect for the sake of length. In the new edition, I will add the introduction to noise and the description of noise problems in the abstract.

 

2. Moreover, the shortcuts should not be presented in the ‘Abstract’ section or, respectively, should be provided when firstly presented in text. For example, the IC abbreviation was not introduced at firstly written in this section.

 

A:  Problem of shortcuts will be addressed in the new version of abstract. Each shortcuts will be introduced with full name at firstly written.

 

3. The origin of the noise occurrence was not presented in an appropriate order. Moreover, the source of the noise is not reflected to the SEM analysis as well.

 

A: This paper was originally written for an audience of researchers in the field of CMP modeling. In previous modeling studies, the effect of measurement noise was not considered in the modeling process due to the large design size. However, as the feature size decreases, the impact of noise in the data measurement phase becomes more severe. As the earliest study discussing this issue, this paper is low on the introduction of noise types and noise mechanisms in AFM measurement, focusing on the introduction of experiments and noise phenomena. This is indeed an oversight in my writing, and I will increase the introduction of noise mechanisms and AFM noise classification in the new version.

For the second point I don't quite understand what you mean, why do we need to analyze the noise mechanism of AFM data in SEM data, SEM and AFM are different morphological measurement methods and different measurement mechanisms, SEM measurement methods cannot analyze the cause of noise in AFM data. In this paper, we show SEM photos only as a comparison data with AFM data, and use the noise reduction AFM data with higher similarity to SEM data to prove the effectiveness of noise reduction. For the explanation of the noise mechanism, I think it is impossible to analyze the noise mechanism of AFM data by SEM measurement.

 

4. The review in the ‘Introduction’ section is not comprehensive enough. There are many limitations that must be studied considering the noise components of the raw measured data. From that matter, this issues must be studied in a wider range of analysis. Please present more previous studies and, respectively, lacks in the currect state of knowledge which, correspondingly, will provide some requirements in the further studies.

 

A: I have shown and analyzed the characteristics of noise and the restricted range of noise studies in the frequency domain characterization chapter. In the original paper, the cause of the noise I refer to the literature [17]. It is considered that the noise appearing in this AFM data is due to the tilt of the probe as well as jitter. And after analyzing the frequency domain characteristics of the noise, I refer to the literature [24-25] that the high frequency noise due to the jitter of the probe belongs to Gaussian random noise. Also, I believe that the noise satisfies the Gaussian characteristics in the local segment of the frequency domain as far as possible based on its spectral characteristics. I consider this to be a restriction on the type of noise as well as its characteristics

 

5. According to the previous issue, the motivation of work does not derived straightly from the critical review, which, in fact, does not exist. Moreover, the advantages and disadvantages of previous studies results are not introduced suitably.

 

A: The motivation for this work is not a critique or optimization of existing or pre-existing noise reduction methods. Rather, it is an analysis of noise problems for a completely new domain (wafer morphology measurement for CMP modeling) and a preliminary noise reduction treatment. The comparison of the noise reduction data shows that the noise reduction method is optimized (AFM vs SEM). I believe that it is interesting to discuss such new problems and to make preliminary attempts to solve them.

 

6. Furthermore to the previous comment, what type of noise is usually found for the AFM measurements? If various types of noises, it should be even reviewed in the ‘Introduction’ section. Please try to refer for various types of noises:

 

(1)   https://www.doi.org/10.1088/0957-0233/23/3/035008

(2)   https://doi.org/10.1007/s41871-020-00057-4

(3)   https://doi.org/10.3390/ma14020333

A: Thank you very much for the literature support. I think the study of noise types you mentioned is very important to the overall elaboration of noise reduction work. The noise mechanism and the morphological characterization parameters described in the references you gave are very important to improve the noise study. However, there is a problem of realizability here. As you know, our institution is not focused on morphological measurement or noise reduction, and AFM data measurement and noise reduction is only a derivative of our research. Therefore, all AFM data are obtained from third-party measurement organizations. Such organizations do not disclose much about the measurement equipment and the impact of the measurement environment. For example, the 'measurement noise test' and the 'residual test' described in your reference 'https://www.doi.org/10.1088/0957-0233/23/3/035008' and 'residual flatness test' that you have given us cannot be implemented in our own experimental environment. This is the reason why in the article line53-62, multiple repetitions of measurement can be effective in reducing noise but cannot be applied. Therefore, in the new version of the article I will add a description of the noise characteristics in the background. However, it is difficult to further define the noise characteristics and types as you have done in the references you have given.

 

7. Generally, from the ‘Introduction’ section, the motivation of work is not clear, especially which type of noise (which frequency, amplitude) is considered as that dominant and must be reduced firstly. The Author(s) must highlight the main problem to be resolved. In that matter, it is difficult to follow what is the main axis of the studies presented.

 

A: In Figure 3 and the related introduction, the two main types of noise present in the AFM data are illustrated: slope noise and glitch noise. The study of the noise characteristics (frequency and amplitude) of these two types of noise needs to be discussed categorically. Slope noise does not have frequency characteristics because it belongs to DC noise. The noise reduction method used is also achieved by linear flattening. According to the observation of the spectral characteristics of the glitch noise in Fourier analysis, the noise belongs to Gaussian noise in the frequency band (the distribution of the frequency components in the frequency band is the same), so there is no dominant frequency.

8. In section 2, it is not obvious which equations are newly considered and, respectively, which already studied and presented in previous papers. The Author(s) must separate their proposals and previous results to encourage their work.

 

A: Because Fourier transform and wavelet transform formulas are basically public knowledge. In writing this section, I used these formulas directly and ignored references to them. This is my negligence in writing the paper. Thank you for your correction. I will try my best to find the original source of these formulas in the new version.

 

9. Some practical applications of Fourier Tranform, and other algorithms, must be presented that can justify usage of them. Look for some exaples:

 

(4)   http://dx.doi.org/10.17531/ein.2021.1.9

(5)   https://doi.org/10.1007/s00170-015-7509-0

(6)   https://doi.org/10.1016/j.measurement.2013.10.036

A: I think it is necessary to discuss with you about this point. Fourier transform is just a signal analysis tool rather than a specific means of noise reduction. Its function is to allow one to interpret the signal from the frequency domain perspective. In the article Zhang, the Fourier transform is used to process the signal in order to observe the frequency domain energy distribution of the signal. From the spectrum of the AFM signal shown in Figure5, it can be seen that the signal and the noise appear to be significantly different in the energy distribution in the spectrum. Therefore, I choose to process the signal by thresholding the energy spectrum to achieve noise reduction. If the Fourier transform is a specific noise reduction algorithm, then I think showing several noise reduction cases of similar AFM signals can enhance the convincingness of noise reduction achieved by using the Fourier transform. However, as a signal analysis tool, the Fourier transform is used only to facilitate the researcher's observation of the signal, and there is no such thing as suitability or otherwise. Therefore, I think there is no need to add practical cases to prove that Fourier transform is more suitable for AFM data noise reduction.

 

10. The assumptions from lines 173-181 are not supported by advantages and disadvantages of the wavelet Fourier characteristics. The wavelet transform, connected with Fourier transform, can add some significant value to the data characteristics. They are not presented and included in the proposals.

 

A: The advantage of wavelet transform is that wavelet coefficients can retain both time domain information and frequency domain information of the signal. Therefore, the multilayer coefficient components of the signal after wavelet transform are essentially the time domain information in different frequency bands. The conjecture in lines 173-181 starts from the actual frequency domain of the signal and finds that the noise of the signal components in each frequency band is closer to the Gaussian noise if the signal is band split. Therefore, the wavelet transform of the signal is equivalent to the frequency band segmentation of the signal, and the noise in the signal components of each frequency band after the frequency band segmentation is closer to Gaussian noise, so it is more conducive to the use of threshold noise reduction. This is the advantage of the complex wavelet transform. Secondly, the advantage of wavelet transform is also reflected in the subsequent screening of signal components, where each signal component (wavelet coefficients) after threshold noise reduction retains time-domain information. Therefore, it is possible to determine whether the components will be added to the reshaped signal based on their time domain neatness or not. And the use of Fourier transform is due to the significant difference between noise and signal in the energy spectrum of the signal found in the frequency domain analysis. This is also reflected in the hypothesis in lines 173-181, specifically 'It exhibited significant energy concentration (peak) in the frequency domain. The instantaneous power of the signal was higher than that of the noise; hence, hard thresholding could be used for noise reduction.'

Of course, the above wavelet transform advantages are only my personal understanding, so I hope you can help correct me if there are any mistakes. At the same time, I do not quite understand what you call ‘The wavelet transform, connected with Fourier transform, can add some significant value to the data characteristics’. I am not sure which kind of characteristics you mean in the AFM data. I hope you can clarify this so that I can optimize and revise the article.

 

11. The thresholding of the AFM measurement data is not references to the current results. Please improve the section 3.3. for the (a) subsection and justify the value of hard thresholding with some previous studies, the Author(s) or other sources, if exist.

 

A: As I mentioned in my previous answer, the Fourier transform is only a signal analysis tool, not a specific noise reduction algorithm. The subsequent noise reduction operation is determined by the spectral characteristics obtained from the Fourier transform of the signal. Therefore, there is no uniform standard or regulation for the noise reduction threshold based on the Fourier transform. Unfortunately, there is no reference for this purpose. The noise reduction thresholds in the article are also determined based on the Gaussian distribution properties, provided that the noise is Gaussian distributed.

12. The critical discussion in section 4, which is significant in the method validation, is not presented. As in many previous cases, the prons and cons are not included.

 

A: I will add the discussion of algorithm and noise reduction results in the new version, so as to facilitate readers' understanding and use of the algorithm

 

13. The ‘Conclusion’ section is messy. Firstly, is too long with one sentences, it should be divided in some separated and numbered gaps. Secondly, the main purpose must be highlighted and introduced appropriately. Currently, this section is a lot of various sentences. Finally, the main purpose must be more highlitghted and reader informaed around the main objective of the paper.

 

A: Your suggestion is very appropriate. I will optimize the language expression in the new conclusion paragraph to make it easier to understand.At the same time, according to your suggestion, the new version will present clearer research objectives and conclusions.And I'll highlight the important objective explanations and conclusions

 

14. The further studies should be proposed, any ‘the Outlook’ idea to continue the proposals applications.

 

A: Outlook is in final paragraph. To be honest, it is indeed too short to give the reader much thought, and in the new edition I go into more detail about possible future research points on this issue

 

15. The empty page before ‘References’ must be removed.
16. The numbering of pages is mixed, it looks confusing.
17. The formatting of the ‘References’ must be unified that, in some cases, there is no DOI link and in some it was provided.

 

A: All of the formatting issues will all be addressed in the new version. However, some references themselves just don't have DOI anymore.

Round 2

Reviewer 1 Report

The manuscript can be accepted.

Reviewer 2 Report

Dear Author(s), the manuscript titled ‘Noise reduction of atomic force microscopy measurement data for fitting verification of chemical mechanical planarization model’, Manuscript ID: electronics-2391448, has been improved according to the minimum requirements so, if allowed by the Editor, can be further processed by the Electronics journal.