On the quality of commercial chemical vapour deposited hexagonal boron nitride

The semiconductors industry has put its eyes on two-dimensional (2D) materials produced by chemical vapour deposition (CVD) because they can be grown at the wafer level with small thickness fluctuations, which is necessary to build electronic devices and circuits. However, CVD-grown 2D materials can contain significant amounts of lattice distortions, which degrades the performance at the device level and increases device-to-device variability. Here we statistically analyse the quality of commercially available CVD-grown hexagonal boron nitride (h-BN) from the most popular suppliers. h-BN is of strategic importance because it is one of the few insulating 2D materials, and can be used as anti-scattering substrate and gate dielectric. We find that the leakage current and electrical homogeneity of all commercially available CVD h-BN samples are significantly worse than those of mechanically exfoliated h-BN of similar thickness. Moreover, in most cases the properties of the CVD h-BN samples analysed don’t match the technical specifications given by the suppliers, and the sample-to-sample variability is unsuitable for the reproducible fabrication of capacitors, transistors or memristors in different batches. In the short term, suppliers should try to provide accurate sample specifications matching the properties of the commercialized materials, and researchers should keep such inaccuracies in mind; and in the middle term suppliers should try to reduce the density of defects to enable the fabrication of high-performance devices with high reliability and reproducibility.


Answers to the comments from reviewer #1
In this paper, the authors used the cross-sectional TEM and C-AFM techniques to evaluate the thickness and crystal/electrical quality of the commercially available "monolayer" and "multilayer" CVD h-BN films.With great efforts, they claimed that some of the most popular suppliers of CVD h-BN provide samples which properties are very far from those advertised in their product specifications.Although this paper can be regarded as the excellent guidance of quantitative electrical analysis on ultrathin insulators by C-AFM, the referee thinks the significance and impact of this work still cannot meet the high standard of Nature Communications.
We thank a lot to the reviewer for indicating that our manuscript can be regarded as an excellent guidance of quantitative electrical analysis on ultrathin insulators by C-AFM.
The number of publications on CVD-grown h-BN and the citations to those publications clearly indicate that this topic is very significant for a wide community.[REDACTED].Regarding impact, the quality of the CVDgrown h-BN in terms of thickness fluctuations, number of lattice defects, tunnelling current and electrical homo geneity has an extremely high impact on the properties of electronic devices.Understanding the quality of co mmercial CVD-grown h-BN can be invaluable for a wide community of scientists employing this material.As our manuscript provides unique information in this direction, we believe it is both significant and impactful.
In the following we provide answers (including additional data when needed) to the technical comments raised by the reviewer.We think the comments raised by the reviewer have been useful and have helped to enhance the quality of our article, and hence we would like again to thank the reviewer for his/her careful revision and constructive feedback.
The main reasons are listed as follows: 1) It is a widely believed fact among 2D community that the quality of CVD-grown 2D materials is typically lower than the mechanically exfoliated one.Therefore, the referee is not surprising to the authors' claim.This paper seems like an accuse of false propaganda on CVD h-BN products of some suppliers, rather than claims all commercial CVD h-BN is of poor quality.However, the names of suppliers of CVD h-BN employed in this study are not disclosed.
We thank the reviewer for this comment.We knew before starting to write this manuscript that CVD-grown h-BN possesses lower quality than mechanically exfoliated.This is known by the community, as the reviewer well pointed.This kind of thinking has been gained from device-level studies.For example, when using mechanical exfoliation, graphene transistors with h-BN substrate show mobilities of 60,000 cm 2 V -1 s -1 (see Dean et al.Nature Nanotechnology 5, 722-736 2010), and when the same experiments are repeated using CVD h-BN the mobility observed is only 2,500 cm 2 V -1 s -1 (see Pandey et al.IEEE Trans. Electron Dev. 65, 4129-4134, 2018).However, the quality of CVD-grown 2D materials evolves, and an updated benchmarking study with CVD h-BN samples from different commercial sources (which has never been done before) is necessary. [REDACTED].

Figure R1 | Example of another study that reports on the quality of commercial 2D materials (in this case
Graphene) without revealing the identity of each company.a, Graphene content per number of companies.b, Number of companies related with the number of layers from AFM (D50 and D90).Reproduced from Kauling, A. P. et al.Advanced Materials 30, 1803784, 2018.
2) This paper mainly focuses on the breakdown strength of CVD h-BN via C-AFM, which is a key parameter for the dielectric layer.
Our manuscript focuses on describing the electrical homogeneity of the samples, which is characterized by the onset potential (VON) measured during ramped voltage stresses and the density and size of conductive spots in lateral scans.
We have noticed that our manuscript had a sentence in the introduction saying: "The main conclusion of our study is that the leakage current, electrical homogeneity and dielectric strength of commercially available CVD h-BN samples are significantly worse than those of mechanically exfoliated h-BN."That is a mistake from our side, we apologize for the confusion created.
In this revision, this sentence has been modified as follows: "The main conclusion of our study is that the leakage current and electrical homogeneity of commercially available CVD h-BN samples are significantly worse than those of mechanically exfoliated h-BN."In other words, we have removed the concept breakdown strength, which now is not mentioned in the manuscript (as we didn't study such thing).However, at current stage, it is the mechanically exfoliated h-BN, rather than the CVD h-BN, is regarded as vdWs dielectric layer to fabricate hysteresis-free and ultrahigh-mobility heterostructure electronic devices.Obviously, the CVD h-BN grown on rough Cu foil is not compatible to the ideal and clean vdW integration with other 2D materials, since contaminations are inevitable during the transfer process.To this end, the referee thinks no one worries about the pinholes in commercially CVD h-BN, but the pinholes of mechanically exfoliated h-BN matters.Hence, if the authors tell us that the commercially available h-BN bulk crystals are all far from satisfactory to fabricate high-performance h-BN based devices, it warrants publication in Nature Communications.
We disagree with this statement.The semiconductors industry only cares about the quality of CVD-grown 2D materials, as stated in multiple technology roadmaps (see The International Roadmap for Devices and Systems.2021 Edition; https://irds.ieee.org/editions/2021).The quality of the h-BN film after the transfer is critical and it is exhaustively studied by many companies and centres, such Imec (see S. Brems et al. in Proc.2023 Symposium on VLSI-TSA, Hsinchu, Taiwan).There is no company using mechanical exfoliation for device fabrication, and hence, whether its quality is good or not has little impact on the semiconductors industry (although studies on mechanical exfoliation are interesting to know the limits of the material and used them for comparison purposes, as we did in our article).
[REDACTED] -3 - The following remarks and questions may be helpful to the authors.1) Typically, the breakdown strength of a dielectric insulator is proportional to its band gap.h-BN has a wide band gap of ~6 eV, which should have a large breakdown voltage even for the ultrathin samples.However, as shown in Fig. 2f, all the mechanically exfoliated h-BN with thickness ranging from monolayer to tri-layer are not insulating at all.Why?It seems like the quality of the mechanically exfoliated h-BN is poor.The authors should do extra experiments, such as fabricating MIM capacitors, to figure out the quality of mechanically exfoliated samples, and compare the breakdown voltage of MIM capacitors to the one measured by C-AFM.
The h-BN films show high leakage currents (despite having a large band gap of ~6 eV) because they are very thin: 0.33 nm for monolayer and 0.99 nm for tri-layer.Due to quantum tunnelling, currents can be measured when the thickness is lower than 1 nm, no matter how large the bandgap is ( As mentioned, we are not studying dielectric strength in this manuscript.Instead, we are measuring onset potential, which is always characterized using CAFM.Hence, we don't see the need of measuring breakdown voltages in MIM capacitors in this study.Moreover, both the onset potential and the breakdown voltage measured via CAFM should never be compared directly with those measured in MIM capacitors, due to the different background currents related to the lateral size of the devices.Moreover, in CAFM the tip-sample contact force plays a very important role.This is explicitly mentioned in different CAFM books (see Celano et al.Electrical Atomic Force Microscopy for Nanoelectronics, Springer-Nature, ISBN 978-3-030-15611-4, 2019 and Lanza et al.Conductive Atomic Force Microscopy: Applications in Nanomaterials, 2017.Wiley-VCH, ISBN: 978-3-527-34091-0).Furthermore, the fact that one device contains more defects does not mean that the h-BN contains more native defects, as many defects can be introduced during device fabrication steps, such as metal evaporation on the 2D material (see for example Zheng et al.Advanced Materials 2022, 34, 2104138).
2) The C-AFM is a very local technique for I-V measurements based on contact mode, in which surface damages are inevitably caused during the tip scanning.Therefore, it may be not a suitable tool for quantitatively determining the amounts of pinholes and defects of ultrathin dielectric layers.To remove the possible influence, laminating another layer of thin Au nanoflakes on top of h-BN is suggested.In this case, the AFM tip will not directly contact the thin dielectric layers.
We disagree with this comment.Local techniques have been used for the detection of pinholes in 2D materials, as the group from Prof. Lain-Jong Li demonstrated using in scanning tunnelling microscopy (see Wan et al. Nature Communications, 13, 4149, 2022).Moreover, hundreds of reputed scientists all around the world use CAFM for the study of nanomaterials, and it has been even highlighted by the International Roadmap of Devices and Systems in its Metrology section (see The International Roadmap for Devices and Systems.2021 Edition (accessed 04 February 2023); https://irds.ieee.org/editions/2021).CAFM has been proven to be a reliable technique that does not damage the surface of the sample if the experiments are done carefully.
In our study we have used a conductive tip with a low spring constant of 0.2 N/m.When we measure the same area of a sample multiple times with this type of tips, we observe zero damage, as seen by the presence of wrinkles in identical positions of the maps when measuring sequentially (see Figure R2a,d and R2b,e), and zoom-out maps also prove that there is no morphology modification in the sample surface (see Figure R2c,f).Lamination of the 2D material is only produced when using very stiff tips (such as diamond tips) and when using very high contact forces.
For clarity, in this revision we have repeated the experiments by applying such a high contact force with a solid diamond tip (model AD-40-AS tip, spring constant 40 N/m), and then we can see such lamination, as shown in Figure R3.Note that all the I-V curves in the CVD h-BN samples presented in our manuscript have been collected without making any scan, just moving the tip from one position to another fresh area and applying ramped voltage stresses at randomly selected positions, ensuring that damage due to lateral forces produced during the scans are avoided.3) The authors seemed to believe that lower Von means higher quality of h-BN.Theoretically speaking, perfect crystals should have higher breakdown voltage.
We thank the reviewer for this comment.In fact, that is not what we believe, and we did not want to express such thing in our manuscript.We are sorry if our text confused the reviewer.If the reviewer can point which sentence gave him/her such impression, we could modify it.
What we think is that (for the same thickness) higher VON means higher quality of h-BN because it is more insulating.This is shown in Figure 7 of our manuscript and discussed throughout the manuscript.In the revised version of this manuscript, we have double-checked that there is no confusing sentence about this point.
The CVD grown h-BN has a much higher Von.Does that mean the quality of monolayer CVD h-BN in author's lab is higher than the mechanically exfoliated one?This is a very good point, and we thank the reviewer for highlighting it.As Figure 7 of our manuscript shows, the VON of multilayer mechanically exfoliated h-BN samples is always higher than in CVD h-BN samples (for the same thickness).This is consistent with the lower number of defects in the mechanically exfoliated samples, as shown via cross-sectional TEM (compare Supplementary Figure 9 with Supplementary Figures 14-18).However, when analysing the value of VON for monolayer h-BN samples produced by mechanical exfoliation (Figure 2f) and CVD method (Figures 3f,l and 4e), the value for CVD h-BN samples is higher.In the case of Figures 3f,l the reason is clearly that the h-BN is not really monolayer, but it has thicknesses of ~2 and ~1.3 nm (which increases VON).However, the I-V curves shown in Figure 4e apply to a sample which seems to be indeed mainly monolayer, as seen from the cross-sectional TEM images (Figure 4a).The possible reasons for the higher VON of monolayer h-BN grown by CVD compared with mechanical exfoliated are: (i) the presence of wrinkles and multilayer islands, as seen from large-area SEM images (Figure 4b); (ii) the presence of impurities in the CVD h-BN sample from the CVD process; (iii) oxidation of the underlying Cu substrate, which oxidizes much more easily than Ru; and (iv) the presence of a slightly higher band gap in the CVD h-BN, as for the mechanically exfoliated large pressure during transfer to the Ru/Ta/SiO2/Si substrate was applied.This explanation has been included in the revised version of the manuscript.4) Surface roughness on Cu foil is much higher than the one on Ru film.Does it affect the Von measured?For a rough surface, the contact area between the surface and tip are relatively small.We thank the reviewer for this interesting comment.No, the surface roughness of the Cu film does not play a relevant role.The parameter that has the highest influence is the tip-sample contact force (see Ranjan et al.Microelectronics Reliability 64, 172-178, 2016).In our study this was maintained always at the same value for different samples, and hence it can be ruled out.5) In Fig. 3e, the authors attributed the conducting area to the amorphous h-BN.However, since no in-situ TEM data were performed, the authors should adopt a more conservative saying.
We thank the reviewer for this comment.Mechanically exfoliated samples show no defects in the TEM images (see Supplementary Figure 14), and the current maps don't show pinholes or low resistivity spots.This was also observed in other studies, such as Britnell, L. et al.Nano Letters 12, 1707-1710, 2012.On the contrary, CVDgrown samples show many defects in the TEM (see Supplementary Figures 5-6 and 8-12) and the current maps show multiple isolated current spots even if no bias is applied.This indicates that the conductive spots are related to the local defects (few-nanometre-wide amorphous regions) in the CVD-grown h-BN.

Figure R5 | CAFM characterization of mechanically exfoliated h-BN and CVD-grown h-BN.
Panel a,c is data of mechanically exfoliated h-BN, panel b,d corresponds to CVD h-BN.a, cross-sectional TEM image of mechanically exfoliated h-BN.b, cross-sectional TEM image of CVD 'monolayer' h-BN from supplier 1. c, CAFM current map of mechanically exfoliated h-BN, collected without applying bias, in an area of 10 #m × 10 #m, shows no current.d, CAFM current map of CVD "monolayer" h-BN from supplier 1, collected without applying bias.Current above 100 pA can be observed.6) In Fig. S1c, please explain the steps and noise burr observed.Besides, please use the standard resistance (for example1 M Ohms) to determine the offset voltage and noise of narrow voltage scan.set 1.215478953 mV.The voltage source has not such a high precision, it works in small steps.The noisy current signal within each step is related to small resistance fluctuations in the tip-sample system, due to by instabilities of the tip-sample contact force and electrical noise in the voltage applied by the CAFM.These two behaviours are characteristic when the CAFM tip is measuring on a metallic sample, and they have been also observed in other CAFMs, such as Multimode V (see Hui et al.Nanoscale, 8, 8466-8473, 2016).This explanation has been included in the caption of Supplementary Figure 2.This paper reports the benchmarking of commercially available CVD-grown hBN (both monolayer and multilayer), comparing with monolayer hBN grown in the authors' lab and multilayer hBN exfoliated from NIMS hBN.The quality assessment of commercial hBN samples is very important for many researchers, because hBN is a key insulating material for 2D research.The authors found that all the commercially available CVD-hBN products do not meet the specifications supplied from the companies.

Answers
We thank a lot to the reviewer for indicating that the topic covered by our manuscript is very important for many researchers.
I think that most of the readers are interested in which company sells the best quality hBN or in the actual quality, such as thickness, crystallinity, of the hBN samples which they are using or they plan to use.However, in this manuscript, the authors do not provide the company names (though Fig. 1 is somehow related to the company name), thus the readers cannot get enough information related to their research.

[REDACTED]
[REDACTED] -8 - Furthermore, since the authors simply examined cross-section TEM images, CAFM data, and SEM images of different samples, it lacks scientific discussion how the hBN quality comes from each CVD process.In other words, scientific insight and findings are not new enough.Therefore, I think that this manuscript does not meet the high standard of Nature Communications and, thus, cannot recommend the publication.
We are sorry that we cannot agree with this statement.The amount of TEM, SEM and CAFM data presented in our manuscript to support the conclusions is much higher than that presented in many other manuscripts in the field of 2D materials published in top Nature journals.Normally most authors present just one TEM image, and when doing CAFM only present one/few I-V curves.On the contrary, our manuscript presents many TEM images in the main text and supplementary information, and the CAFM plots contain data from hundreds of positions.We are not aware of any article showing more TEM and CAFM image about the samples, if the reviewer thinks this is not enough, we would like to kindly request to provide a few references of articles that provide more data than ours.
Regarding the discussion on the CVD process for each sample, this is something that is never included in articles of this type (see Kauling, A. P. et al.Advanced Materials 30, 1803784, 2018 and Bøggild, P. Nature, 502-503, 2018).The reason is that the companies are not willing to disclose such information.We have sent Emails to several suppliers asking for the growth temperature and this question was never answered.In fact, no article that uses commercial samples have ever disclosed such information; if the reviewer is aware of any, we would be happy if he/she could share the reference.
The followings are some small comments on this manuscript.
1.The details of the CVD growth of monolayer hBN in the authors' lab is not well described in the experimental section.Please describe the details of the CVD synthesis, such as the feedstock, CVD temperature, and Cu foil source, because their hBN is used as the standard monolayer sample.
We thank the reviewer for this constructive comment.In the revised version of the manuscript, the required information has been included in the Methods section.The new text included reads as follows: "The CVD h-BN samples grown in our laboratory use a standard ~25-µm-thick Cu foils from Thermo Fisher Scientific as substrate.After introduced in the tube, the temperature is raised to 1050 ºC for 30 minutes in a H2 (10-20 sccm) and Ar (5-10 sccm) atmosphere for annealing and surface cleaning.After that, the valve that controls the flow of the precursor (ammonia borane, H3NBH3, 95%, from Sigma-Aldrich) into the chamber is opened and the temperature is adjusted at 80 ºC during the h-BN growth.Finally, the precursor valve is closed, and the temperature is ramped down to room temperature naturally.The SiO2 samples were synthesized via thermal oxidation on n ++ Si substrates in an industrial foundry." 2. The TEM image of their monolayer hBN (Fig. 4a,b) looks like bilayer hBN.Is this really monolayer?More details explanation is required.
We thank the reviewer for this comment, and we apologize for the confusion created.In the revised version of the manuscript, we replaced Figure 4a by a new one in which the h-BN layer can be better seen (see Figure R2).We thank the reviewer for finding this typo.In the revised version of the manuscript, we have corrected it.
4. It is better to describe why they used Ru/Ta as an electrode.
We thank the reviewer for this constructive comment.The reason that we choose Ruthenium is because it is inert to most other chemicals, not easy to form oxides, and has good electrical conductivity.Moreover, in our group we have the ability of making it very flat (root mean square roughness below 200 pm), which is necessary for CAFM studies.Tantalum is deposited below ruthenium as an adhesion layer.We have also tried Pt, and Au as an electrode, but the surface roughness we achieved is much worse than Ru, so at last we select Ru as a substrate.In the revised version of this manuscript, we have included one sentence to discuss this point.

Answers to the comments from reviewer #3
The manuscript by Yuan et al. reports the structural and electrical characterization of multilayer and "monolayer" CVD-grown h-BN film samples supplied by the main commercial suppliers, and the results are compared with mechanically exfoliated flakes based on h-BN crystals provided by the NIMS group as a reference of highquality (standard) h-BN films.The statistical analysis presented here is of great value for the community and the conclusions of the work are clear: the properties of CVD h-BN films provided by the most popular suppliers are very far from those advertised in their product specifications, regarding film thickness, crystal quality, homogeneity and most critically, electrical properties.In general, I think the conclusions reached by Yuan et al. may serve as a starting point to bring common understanding on the actual quality of samples provided by commercial suppliers, and hopefully to speed up the process of standardization in the market of commercial 2Dmaterials.
the mobility observed is only 2,500 cm 2 V -1 s -1 (see Pandey et al.IEEE Trans.Electron Dev.65, 4129-4134, 2018).However, the quality of CVD-grown 2D materials evolves, and an updated benchmarking study of the available commercial suppliers is necessary.
The goal of this manuscript is to evaluate the status of commercial CVD-grown h-BN.[REDACTED].
In the following we provide answers (including additional data when needed) to the technical comments raised by the reviewer.We think the comments raised by the reviewer have been useful and have helped to enhance the quality of our article, and hence we would like again to thank the reviewer for his/her careful revision and constructive feedback.
1.The main use of h-BN in 2D research is as a dielectric layer, and it has been shown that h-BN encapsulation can drastically increase the mobility of 2D devices.I think it would be more useful to construct devices using various h-BN samples and compare the device performance.
We thank the reviewer for this constructive comment.The figures-of-merit of electronic devices depend not only on the quality of the material as grown, but also on many other factors, such as the density of defects introduced during metal evaporation, contact resistance, residues during transfer, etcetera.For example, some studies have presented transistors with maximum on-state currents up to ~750 µA/µm using defect-rich CVD MoS2 (see Illarionov, Yury Yu, et al.IEEE Electron Device Letters 38, 1763-1766, 2017), while others only reached 6 µA/µm using defect-free MoS2 (see Mitta, Sekhar Babu, et al. 2D Materials 8, 012002, 2020).Hence, having a device with better performance does not mean the quality of the native (as-produced) materials is better.Therefore, fabricating electronic devices is not necessary to assess the quality of as grown 2D materials and their density of native defects.In fact, it is better not to fabricate devices, as defects introduced during device fabrication would also be involved and could lead to incorrect conclusions.
2. The cross-sectional TEM analysis, while is quite useful for thickness measurement, is not typically considered an efficient method for statistical analysis, as the experiment is time consuming and expensive while each sample can only cover regions at a scale of 5-20 microns.It would be more useful if the authors can perform other statistically more efficient analysis, e.g.Raman mapping, to characterize the homogeneity of the samples.
We thank the reviewer for this constructive comment.The lateral resolution of Raman spectroscopy is very low (~1µm), and therefore it only gives averaged information about the sample, and it cannot map local defects as well as TEM and CAFM does.Nevertheless, in this revision we have conducted the experiments requested.The new data are shown in Figure R1 of this letter, and they are also included in the revised version of the manuscript as Supplementary Figure 11.
Here we transferred the CVD-grown 'monolayer' h-BN from supplier 1 onto 300 nm SiO2/Si substrate, and for a better comparison, we also mechanically exfoliated h-BN flakes and transferred them onto 300 nm SiO2/Si substrate.An inhomogeneous contrast was observed in a 100 #m × 100 #m Raman map of the CVD-grown 'monolayer' h-BN from supplier 1 (see Figure R1h), suggesting an uneven film thickness and lack of 2D crystallinity (or presence of amorphous regions).This agrees with the cross-sectional TEM images shown in Figure 3a-b, and the CAFM current map shown in Figure 3e.From 7 out of 12 Raman spectrums, a sharp E2g band of h-BN at 1367.02 cm "1 with a full width at half maximum (FWHM) of 16 cm "1 was observed, while the rest 5 out of 12 Raman spectrums show no clear peak at around 1367 cm "1 (see Figure R1), indicating the absence of h-BN.On the contrary, repeating these experiments on exfoliated h-BN flake show stronger signal in Raman spectrum (see Figure R1b), with a narrower FWHM of 12.8 cm "1 .The new text included in the revised version reads as follows: "Moreover, we transferred this "monolayer" CVD h-BN and mechanically exfoliated h-BN onto a 300 nm SiO2/Si substrate for Raman spectroscopy characterization (see Supplementary Figure 11), and observed that: (i) the mechanically exfoliated sample shows homogeneous and strong E2g band of h-BN at 1367.02 cm -1 with -10 -a full width at half maximum (FWHM) of 12.8 cm -1 ; and (ii) the CVD h-BN from supplier 1 shows very low and inhomogeneous signal, with a FWHM of 16 cm-1, plus at some locations (5 out of 12) no E2g band around 1367 cm -1 is detected.These data demonstrate that the differences observed between the mechanically exfoliated monolayer h-BN sample (Figure 2f) and the CVD h-BN from supplier 1 (Figure 3f) are related to the presence of pinholes, atomic defects, and thickness fluctuations in the CVD h-BN from supplier 1." 3.In the analysis of cross-sectional TEM (for example Figure 3a-b), how can we be sure the "amorphization" is not induced by the FIB sample preparation?For example, in Figure 3b, the Cu foil also looks remarkably damaged as compared to Figure 3a.How to make sure this is the original state of the films after sample preparation?The FIB process can easily damage ultrathin films, especially if they are composed of light elements such as C or B-N.In addition, some of the samples seem to be protected only by amorphous carbon layers.It should be pointed out that even e-beam deposited carbon or thermal evaporated carbon can damage the surface structure of 2D materials.The authors need to be very careful during their sample preparation.
We thank he reviewer for this comment.We are aware that FIB could damage the structure of some samples if it is not done carefully.We have developed a very accurate protocol for the FIB process by adjusting the stage rotation degree, current and voltage of electron beam, current and voltage of ion beam.The fact that our FIB does not damage the samples in this manuscript can be observed from: 1 -The carbon layer on top of the h-BN (as protection layer) was deposited by using a spin coater, which does not damage to the h-BN (see Zheng et al.Advance Materials 2022, 34, 2104138).In our studies, we used spin-coated PMMA as the protection layer.
2 -The mechanically exfoliated samples are defect free because they are extracted from a high-quality crystal, and in Supplementary Figure 9 we do not observe any defects after the FIB and TEM processes.That is perfectly consistent and shows that FIB does not introduce damage or amorphization in our samples.
In the revised version of the manuscript this explanation has been further emphasized, which required us to modify the order of the Supplementary Figures.
The reason why Cu foil in Figure 3b looks 'damaged' as compared to Figure 3a is because of the quality compression and contrast difference in the two images.Here we provided the raw data from Figure 3a-b.The other reason is that the scale of the two images (raw data) is different, so pixel per distance is a bit different in the two images, that's also causing the 'unclear' in Figure 3b.
4. More on this, the authors mention several times throughout the manuscript the possible presence of defects, especially in the "amorphous" areas, but no clear analysis is provided.Do the authors imply here that defective areas are prone to amorphization and is the cause of the observed "amorphous" areas?Seems difficult to correlate both ideas without proper structural analysis.In addition, from the cross-sectional TEM results, one can only describe e.g. the region in Figure 5j as distorted or disordered regions, because such images do not provide conclusive information about the in-plane crystallinity.So, calling it as "amorphous" may not be correct.
We thank the reviewer for this comment.Throughout the manuscript we have used the word "defect" to refer to those areas that do not show perfect layered structure in the cross-sectional TEM images, which in the current maps appear to be more conductive.Sometimes these defects consist of one/few atoms and are observed in the TEM images as a discontinuity of a layer as interstitial atoms between layers.But some others this defective bonding propagates laterally and vertically over larger areas, and that is what we call "amorphous regions".This is mainly observed in the "monolayer" sample from supplier 1, which is the one that exhibited the worst quality.
The in-plane crystallinity in Figure 5j (now Figure 6j in the revised version of the manuscript) can be deduced from the observation of van der Waals gaps between the different layers.That, despite the obvious changes of orientation of the layers (also observed in other articles, see Adithi, K. et al.ACS Nano 16, 2866-2876, 2022), can be clearly observed in Figure 5j.Without 2D in-plane crystallinity, such van der Waals gaps would not form.The multilayer samples in Figure 6 do not show "amorphous" regions and in the manuscript we are not referring to them as such.We only talked about "amorphous" regions when talking about Figure 3, which we believe in that case is correct.
In the revised version of the mansucript, that sentence has been changed as: "We analysed the first sample from supplier 1 by collecting 25 consecutive cross-sectional TEM images and observed that only 80% were 2D layered, although with a thickness ranging from 2 to 2.3 nm, and the remaining 20% contained high density of defects, mainly erratic atomic bonding (see Figure 3a-b and Supplementary Figure 8).Sometimes these defects consist of one/few atoms and are observed in the TEM images as a small discontinuity of one/few layers, or as interstitial atoms between layers (see red arrows in Supplementary Figure 8).But some others this defective bonding propagates laterally and vertically over larger areas, which creates heavily disordered quasiamorphous regions (see yellow arrows in Supplementary Figure 8).Note that these local defects are not related to amorphization produced by the focused ion beam (FIB), as when the same experiments are carried out in mechanically exfoliated samples, perfect layered structure is observed (see Supplementary Figure 9)."We have also inserted some red and yellow arrows in Supplementary Figure 8 to further clarify this point.
5. In Figure 2f, the authors mention that the I-V measurements in mechanically exfoliated monolayer h-BN show good agreement with the calculated curves for monolayer and bilayer h-BN.However, I see that the vast majority of the grey curves (experiments) correlate with the blue line, which corresponds to a trilayer model.Why is this discrepancy in the interpretation?Furthermore, in the following section (3.CVD-grown "monolayer" h-BN), the monolayer model is assumed as reference according to the abovementioned interpretation in Figure 2f.Is this whole interpretation correct and how is this affecting the results from commercial samples?
We thank the reviewer for this comment.We have further discussed the simulations with other experts in the field and finally we have decided to remove them.The reason is that these simulations were carried out years ago when key new knowledge about h-BN was still unknown, mainly simulation parameters.They are not essential for our manuscript, and they can be removed without problem.
6.The authors did not discuss the huge increase in VON for "monolayer" CVD h-BN samples from supplier 2. What is the cause?
We thank the reviewer for pointing out this comment.The reason for this increase of VON is the higher thickness of the h-BN compared to the monolayer samples.The TEM images, SEM image and CAFM topography map (Figure 3g-h, 3i and 3j, respectively), thickness fluctuation, multilayer islands, wrinkles, and particles can be observed, which cause the high variability behaviour in VON.In the revised version, the new text included reads as follows: "However, the value of VON is very large and variable (4.20±1.23 V) indicating the presence of severe thickness fluctuations in the h-BN stack." 7. Figure 4 shows the characterization of in-house CVD-grown monolayer h-BN.However, from the TEM image I can count at least 2 layers, and seemingly up to 4 layers at some points.Despite the films seem to have better crystalline quality than those provided by commercial suppliers, the statement of "truly monolayer" is incorrect.Why in this case the VON is the lowest even if not a monolayer?
We thank the reviewer for this comment, and we apologize for the confusion created.In the revised version of the manuscript, we replaced Figure 4a by a new one in which the h-BN layer can be better seen (see Figure R2).

Figure R2 | TEM characterization of in-house CVD-grown monolayer h-BN grown in our lab.
Crosssectional high-resolution TEM image of the CVD-grown monolayer h-BN sample on Cu foil.
8. The manuscript seems to be written in a rush and lacks many important experimental details.The figure captions were not carefully written, without clear explanation of each panel, and one needs to refer to the main text in order to understand the details. Figure 6 says results from suppliers 3-9, but one has to find out from the fine print in the last column that these samples are from suppliers 5,9,4,7,6, in a very odd arrangement.This is particularly annoying.
We thank the reviewer for finding the typo in the caption of Figure 6, which has been corrected in the revised version of the manuscript.We have also added more details to the captions of all other figures.In the revised version of the manuscript, we have added many more details as requested by the reviewer.9. Section 4 needs to be rewritten and put the information in a more coherent way.It is quite hard to read and follow.For instance, in the beginning the authors mention they want to study the variability from the multilayer samples provided by supplier 1, but one cannot know which parameter are they studying.Looking at Figure 5, one can guess is thickness, but it is confusing since those are supposed to be multilayer samples with thickness >10 nm.The text and the description of the results is incomplete and not possible to follow clearly till the end of the section, where the text reveals there is a thickness mismatch between samples.The authors should rewrite this section of the manuscript.In the same line, it is confusing that the authors describe Figure 6 before figure 5.
We thank the reviewer for this comment.In the revised version of the manuscript, we have replaced some sentences.First, we start the section by clearly stating how the quality of the samples is analysed and compared.We wrote: "Next, we analysed the quality of multilayer CVD h-BN from suppliers 1, 4, 5, 6, 7 and 9 (the other suppliers did not offer multilayer CVD h-BN), discussing mainly surface roughness, average thickness, thickness fluctuations, number of atomic defects, observation of pinholes and electrical homogeneity (through VON)."Second, we have changed the order of Figures 5 and 6, so that they follow the flow of the text.And third, we have added a few more explanations of the images to drive to reader into the conclusions.Those sentences read as follows: "Next, we collected 25 consecutive cross-sectional TEM images for all the samples from supplier 1 and all (100%) of the images show traces of layered structure, although they host large amounts of local defects and lattice distortions (see Figure 6 left column and Supplementary Figures 14-18).The layered structure seems to be more accentuated in the thinnest sample (Figure 6), and for the others the interfaces with C and Cu are blurry, the layers seem to be interrupted and have bifurcated, and for the thickest samples even oblique and even almost vertical layers can be observed.This behaviour has been also observed in 2D materials grown by other academics [25]."And also: "However, the good correlation between thickness (observed in TEM images) and VON (observed in I-V plots) indicates that this parameter plays the most important role (even over crystallinity and density of bonding defects)." 10.In the second paragraph of Section 4, CAFM images of samples from supplier 5 and 9 show pinholes, but in line 3, the authors claim samples from supplier 9 was pinhole free.In addition, in paragraph 3 the authors say Samples from supplier 1 are free of pinholes while Figure 5b-n clearly show the same patterns as in Figure 6.How to understand this?
We thank the reviewer for detecting this problem.We made a mistake in the text.None of the multilayer samples show current (pinholes) when scanned at 0V, as shown in Supplementary Figure 19.The current maps presented in Figures 5 and 6 have been collected while applying 0.5 V. Hence, these currents are related to tunnelling current across the weakest locations of the h-BN stack, not to the presence of pinholes.In the revised version of the manuscript the text has been modified as follows: "From an electrical point of view, none of the multilayer samples show pinholes, as current maps collected when applying 0 V show no current spots (see Supplementary Figure 19)."And also: "When measuring current maps at 0.5 V, the samples from suppliers 5 and 9 show some weak spots (the quantum tunnelling current is higher at those locations), which can represent a problem if the material is used as gate dielectric in transistors, but it has been shown to be beneficial to fabricate memristors.".
We agree with the reviewer, partially.We are not trying to convince anyone that e`URjpd commercial CVD grown h-;E Zd fdVWf] W`c SVZ_X XReV UZV]VTecZT Z_ ecR_dZde`cd* JYV \Vj ^VddRXV `W `fc h`c\ Zd6 nthe quality of CVD-grown h-BN is still NOT enough for being employed as gate dielectric in transistorso( and we explain and quantify in detail how far we are, which is a very valuable information for the community.
Dielectrics have many applications.The current properties of CVD-grown h-BN might still not fulfil the requirements for being used as gate dielectric in transistors, but our group has demonstrated in several articles that its performance is very suitable for the fabrication of memristors.See for example: 1 Nature 2023, 618, 57m62.https://doi.org/10.1038/s41586-023-05973-1 1 Nature Electronics 2020, 3, 638-645.https://doi.org/10.1038/s41928-020-00473-w 1 Nature Electronics 2018, 1, 458m465.https://doi.org/10.1038/s41928-018-0118-9 Hence, saying that the commercial CVD-grown h-BN is not useful for any type of electronic device is incorrect.Note that articles cited present statistics and even report about variability and yield.Other groups have also employed commercial CVD-grown h-BN in other applications, such as: (i) radiofrequency switches [Nature Electronics 2020, Surface roughness and thickness fluctuations is not the same.One material with zero thickness fluctuations and outstanding electrical properties may exhibit a very rough surface if it is placed on a very rough substrate and keep its outstanding electrical properties.The reviewer is using the concept ndfcWRTV c`fXY_Vddo Rd ZW Ze h`f]U SV eYV dR^V e`neYZT\_Vdd W]fTefReZ`_do( and this is incorrect.In the revised version of the manuscript, we have inserted one sentence to emphasize this difference, which reads as follows: "Surface roughness and thickness fluctuations is not the same.The electrical homogeneity is related to only two things: (i) thickness fluctuations, and (ii) presence of atomic defects (dangling bonds, impurities) XX .One material with zero thickness fluctuations and outstanding electrical properties may exhibit a very rough surface if it is placed on a very rough substrate and keep its outstanding electrical properties." However, if the research objectives of this paper are the winker-free CVD-grown h-BN grown on the ultra-flat substrate, such as sapphire, which has the potential for the application of gate dielectrics, it would be much more informative and meaningful.
The reviewer is insisting on having us growing CVD h-BN for its use as gate dielectric in transistors, but that is not the topic of our manuscript.The objective of our work is to understand the quality of commercial 2D materials.
Understanding the quality of commercial 2D materials is of very big global interest for a vast amount of materials scientists and electronic engineers, both in academia and industry.The previous study doing similar analysis (but for liquid-phase exfoliated graphene) [Kauling et al.Advanced Materials 30, 1803784 (2018)] has been cited more than 308 times since its publication in 2018.And now, with the global push of CVD-grown 2D materials, which are being used by companies like TSMC, Intel and Samsung, the push on the samples that we analyse in our paper is even higher [Lanza et al. Advanced Materials 2022, 34, 2207843].
Even though I do not find sufficient significance on evaluating the electrical homogeneity of rough CVD h-BN, I should emphasize that this paper can serve as the excellent guidance of quantitative electrical analysis on ultrathin insulators by C-AFM.If the editor insists on publishing this paper on Nature Communications, I suggest the authors to strength this part by adding more related data of C-AFM on mechanically exfoliated h-BN.
We thank a lot to the reviewer for indicating that our manuscript can be regarded as an excellent guidance of q uantitative electrical analysis on ultrathin insulators by C-AFM.We are sorry that the reviewer cannot find suf ficient significance on evaluating the electrical homogeneity of commercial CVD-grown h-BN. 1) I am delighted to see that authors performed strict comparison experiments to avoid the possible damage caused by the tip.The authors claimed that using soft conductive tip with a low spring constant of 0.2 N/m, rather than stiff diamond tips, can reduce the physical damage during tip scanning.This is a very important information that needs to be emphasized in the main text and supporting information.The Figure R1 and R2 should be added in the SI.Besides, to make the data more reliable, continuous C-AFM maps with more times (zero bias) on the same area are needed.
We thank the reviewer for indicating that the data presented in the past revision were useful.
We are confused, Figure R1 in the previous response letter has nothing to do with this comment.Did the reviewer mean Figures R2 and R3?
Regarding the last sentence of the cVgZVhVcpd comment, in Figure R2 of the previous letter we included 3 consecutive scans.The reviewer is not citing any manuscript showing a longer sequence of scans, and he/she is also not specifying how many scans he/she wants us to measure.In this revision we have included data for 17 scans in the same position of the sample, as it can be seen in Figure R2  In the revised version of the manuscript, this information has been included in the Methods section.
3) In Figure S6b e, with a driving voltage of 0.8 V, the conducting maps undergo obvious changes by multiple scans.However, when zero bias was applied, the damage seems to be less.Suggest the authors to do more comparison experiments on the mechanically exfoliated h-BN, and then emphasize in the main text that "C-AFM mapping with zero bias, small contact force and soft tips is verified as a faithful way to avoid physical damage on the ultrathin insulators".
The increase of quantum tunnelling over time (number of scans that stress the same area) is something normal, but the last image without voltage confirms that no permanent damage is introduced to the sample.We have added the sentence proposed by the reviewer to the main text.We believe this sentence is well supported by Figures S6 and S7  7) The referee is not satisfied with the explanation to the steps and noise burr in Figure S2c.Please use the C-AFM calibration module with a standard resistance to determine the offset voltage and noise of narrow voltage scan of your instrument.
The value of the offset voltage was already indicated in eYV acVgZ`fd gVcdZ`_ `W eYV ^R_fdTcZae6 nThese currents are produced by the inherent offset voltage of the CAFM [17][18], which in our machine is around 7.25 mV.o We have used calibration module of the CAFM and received this same value.
This behaviour is typical in all CAFMs when measure this type of samples (metallic), we have observed it in all the CAFMs that we used independently of the brand, and that includes the Multimode V, Multimode VIII, Dimension Icon, Park NX-HighVac, Nanotech, Agilent 5500, CSInstruments and Omicron.Some of these data have been already published, as mentioned in the previous version of the manuscript, and cited in the text [Hui, F. et al.Moving graphene devices from lab to market: advanced graphene-coated nanoprobes.Nanoscale 8, 8466-8473 (2016)].
To observe the variation of the current (noise) when the offset is compensated, we scan the Ru substrate by applying different biases (0 mV, 7.3 mV, 7.1 mV, 7.2 mV, and 7.25 mV).The current map collected is shown in Figure R5 of this letter.As it can be observed, despite compensating the voltage the current is not zero and fluctuates.This behaviour is only observed when scanning metals and has no effect when analysing the insulating materials explored in this article.
(continue in next page) Thanks for understanding this.
2) Analysis methods >We are not aware of any article showing more TEM and CAFM image about the samples, if the reviewer thinks this is not enough, we would like to kindly request to provide a few references of articles that provide more data than ours.This is not the point I mentioned.What I was concerned is that both TEM and CAFM are local measurement techniques, which does not give large-area information (even though the authors present a number of TEM and CAFM images).For macroscopic analysis, I suggest measuring optical images and Raman mapping images for hBN transferred on SiO2 substrates.Optical and Raman mapping images will give the information on the thickness uniformity as well as the crystallinity (E2g FWHM) in large areas.While the authors have provided Raman maps of exfoliated flakes and commercial CVD-grown hBN films from supplier 1 in Supplementary Fig. 11, more data from the commercial samples obtained from the other suppliers are needed.
We thank the reviewer for clarifying.Optical images should never be used to analyse nanomaterials, as they cannot map any local defect; they can sometimes be used to qualitatively evaluate size of the material and surface roughness in very rough samples, nothing else.
Raman spectroscopy is more precise, but the diameter of the laser light is (in the best cases) of few micrometres wide.Therefore, it gives an averaged information of the locations being analysed.Anyway, as suggested by the reviewer, we have conducted Raman experiments for most of the other commercial samples (except for the multilayer h-BN from supplier 1, as we ran out of that sample during previous experiments).The results are shown in Figure R1 and R2 of this letter, and we also included them in the revised version of the manuscript as Supplementary Figures 14 and 22.The results indicate that no CVD-grown h-BN sample has a quality like the exfoliated one.+81 -IC8>AB 8-J1 CA910 C> -=BK1A <M @I1BD>= K9C8 7A1-C 13>ACBQ (M <-9= />=/1A= 9B C81 ?8MB9/-; 0-<-71 >2 "%( D? C> C81 091;1/CA9/ BIA2-/1 K9C8 C81 />=C-/C <>01Q +81 <1BB-71 ' ?A1J9>IB;M 7>CP <-M.1 the common sense, is the contact mode of AFM will gradually destruct the sample surface, especially for the ultrathin sample.In this paper, the authors seemingly claimed that they can achieve the nearly 0-<-71U2A11 $U"%( <1-BIA1<1=CB 1J1= -C <I;DUB/-=Q '= 2-/CP C89B 9B C81 C1/8=9/-; 2>I=0-D>= >2 C81 work and is also the main interest I found in this paper.This is why I suggest the authors to do more 1L?1A9<1=CBC> 47IA1 >IC K8-C :9=0 >2 1L?1A9<1=C-; ?-A-<1C1AB <-F1A 2>A -/891J9=7 C81 0-<-71U2A11 $U "%( <1-BIA1<1=CQ ,=2>ACI=-C1;MP C81 -IC8>AB /8>>B1 C> 97=>A1 C89B @I1BD>=Q If the reviewer still insists in that the sample might be damaged, please clearly specify which experiments are proposed and we could do them.However, all our experiments clearly indicate that the sample is not damaged when scanned in contact mode (in line with a large amount of literature), and hence there is no reason to keep insisting in this point.If one uses stiffer tips (normally made of diamond) tips with higher spring constant (normally higher than 30 N/m) and uses a contact force (normally above 240 N/nm) he/she may surely damage the 2D material, as shown in other studies that employed diamond tips and high contact forces of 400 nN [Qi, Yizhou, et al.ACS applied materials & interfaces 9.1, 1099-1106, 2017.https://doi.org/10.1021/acsami.6b12916].However, in our study we only use tips with spring constant (0.2 N/m) and contact forces (defection setpoint 0 V) that do not damage the material, as confirmed in Figure R1 of this letter.We do not see why we should investigate the damage of the mechanical 2D material when using other tips or deflection setpoints, as they do not apply to our study.
This has been explicitly mentioned in the first sentence of the aforementioned paragraph, which we copy again here for clarity: We would like to emphasize that the use of CAFM in contact mode (with the types of tips and contact forces employed in this study) does not damage the surface of the CVD-grown h-BN samples.
- We collect current maps without applying any bias in the mechanically exfoliated monolayer samples, and no current is observed (Figure 2g), meaning that the sample is mainly free of pinholes.Some locations next to the edge showed some pinholes (see Supplementary Figure 6), probably due to the higher mechanical stress during peeling, but such behaviour is not representative of the entire surface of the monolayer h-BN flake: the mechanically exfoliated monolayer h-BN is mainly pinhole free (Figure 2g).When a pinhole-free region of the monolayer h-BN flake is scanned under 0.8 V, we observe the presence of some local conductive spots with typical diameters of 3.24±3.21nm, which drive maximum currents of 20.2 pA (Figure 2h).Considering that the mechanically exfoliated h-BN is free of defects (as demonstrated in several studies [21]), these local higher currents could only be explained by a small reduction of the van der Waals gap.If the same area is scanned at 0.8 V for four times, the size and the currents driven by the spots slightly increases (see Supplementary Figure 7b-e), indicating a progressive degradation of the h-BN film.We select four current spots that appear in all scans and plot the resistance in each scan for each spot (see Figure 2i).However, the damage to the h-BN stack is not very significant because subsequent scans without bias do not show remarkable currents above the noise level and no surface modification is observed (see Supplementary Figure 7f).
GTVPaSX]V cWT bT]cT]RT5 jcWT bdaUPRT a^dVW]Tbb P]S cWXRZ]Tbb U[dRcdPcX^]k' we did not add that sentence identical.Instead, we wrote the following sentence in page 3: When analysing the same sample with the CAFM, the RMS surface roughness appears to be high (8.96nm, see Figure 3d), but that is related to the morphology of the Cu foil below the h-BN sheet (see Supplementary Figure 12) and it does not affect the electrical properties of the h-BN stackthe leakage current, depends on the thickness and number of defects [24].
Note that in the previous version of the manuscript, the reference 24 was already added, which is the same reference that we used in the previous response letter to answer that comment.In conclusion, all the information was included and discussed, not using the identical words written by the reviewer but our own explanations.

Figure R2 |
Figure R2 | CAFM maps collected in sequence on multilayer h-BN samples.a-f, consecutive CAFM topography and current maps collected simultaneously by using a CONTV-PT tip (with a spring constant 0.2 N/m).The maps are centred at the same position of the sample, and the topographic maps clearly indicate no damage to the surface of the sample.

Figure R3 |
Figure R3 | CAFM maps collected on CVD h-BN using a solid diamond tip applying high force.a, CAFM topography map collected by using an AD-40-AS diamond tip (with a spring constant 40 N/m).b, Zoom-out CAFM topography map collected at the same point where the scan in a was collected, using a NCHV-A Si tip (in tapping mode).It is clear that the scan with the diamond tip damaged the surface of the sample.c, Crosssectional TEM image after CAFM scan in b; h-BN has been removed and folded at the end of the scan.

Figure R4 |
Figure R4 | Schematic of the effective emission area.Effective emission area through which electrons can flow (Aeff) in a CAFM when the tip is placed on (a) a flat insulating sample and (b) a flat metallic electrode deposited on an insulating sample.

to the comments from reviewer # 2 Figure R1 |
Figure R1 | Example of another study that reports on the quality of commercial 2D materials (in this case Graphene) without revealing the identity of each company.a) Graphene content per number of companies.b) Number of companies related with the number of layers from AFM (D50 and D90).Reproduced from Kauling, A. P. et al.Advanced Materials 30, 1803784, 2018.

Figure R2 |
Figure R2 | TEM characterization of in-house CVD-grown monolayer h-BN grown in our lab.Crosssectional high-resolution TEM image of the CVD-grown monolayer h-BN sample on Cu foil.

Figure R1 |
Figure R1 | Raman characterization of mechanically exfoliated h-BN and CVD-grown 'monolayer' h-BNfrom supplier 1, transferred on 300 nm SiO2 / Si substrates.a-e, Raman and CAFM maps of mechanically exfoliated h-BN flake.a, optical microscopy image of one mechanically exfoliated h-BN flake.b, Typical Raman spectrum at 7 positions marked in a.A sharp E2g band of h-BN at 1367.02 cm "1 with a FWHM of 12 cm "1 was observed.c, a 45 #m × 45 #m Raman map of the intensity of h-BN E2g band.d, AFM topography map collected at the edge of the target mechanically exfoliated h-BN flake, which is the area that marked with yellow dash line in a. e, histogram distribution in d, the distance between two peaks is 3.2 nm, indicating the thickness of this h-BN flake.f-h, Raman experiments of CVD-grown 'monolayer' h-BN from supplier 1. f, photography of 5 mm × 8 mm CVD-grown 'monolayer' h-BN from supplier 1 on a SiO2 (300 nm) / Si substrate after transfer.g, typical Raman spectrum at 12 positions indicated in f. h, a 100 #m × 100 #m Raman map of the intensity of h-BN E2g band.

Figure R3 |
Figure R3 | Example of another study that reports on the quality of commercial 2D materials (in this case Graphene) without revealing the identity of each company.a, Graphene content per number of companies.b, Number of companies related with the number of layers from AFM (D50 and D90).Reproduced from Kauling, A. P. et al.Advanced Materials 30, 1803784, 2018.

Figure R1 |
Figure R1 | Surface roughness of commercial CVD-grown h-BN.a, a, Comparison of the surface roughness of a commercial CVD grown monolayer h-BN on the Cu foil on which it was grown and after being transferred on ultra flat SiO2/Si wafers.b, Comparison of the surface roughness of a commercial CVD grown multilayer h-BN on the Cu foil on which it was grown and after being transferred on ultra-flat SiO2/Si wafers.
Figure R2 CAFM topography maps collected in sequence on multilayer h BN samples.The 1 st scan and the last scan (17 th th ) are a zoom out topography maps with size of 15 xm × 15 xm, while the 2 nd nd ~ 16 th th are taken at the centre of the sample. S7.

Figure R4 |
Figure R4 | CAFM characterization of CVD-grown "monolayer" h-BN.a-c, CAFM results of as-grown <L= n^`_`]RjVco Y-BN on Cu foil.a-b, CAFM topography and current maps collected on the surface of h-BN/Cu without applying bias.c, 100 I-V curves collected on the surface of as-grown CVD h-BN on Cu foil, with 100 pA current limitation.d-f, <:?D cVdf]ed `W ecR_dWVccVU <L= n^`_`]RjVco Y-BN on flat Ru film.d-e, CAFM topography and current maps collected on the surface of h-BN/Ru without applying bias.f, 100 I-V curves collected on the surface of transferred CVD h-BN on Ru film, with 100 pA current limitation.

Figure R5 |
Figure R5 | CAFM maps collected with applying different biases, on Ru substrate.a-b, CAFM topography map and current map, respectively.Biases change during the scanning, as marking in the current map (b).Answers to the comments from reviewer #2

Figure R |
Figure R | Raman characterization of CVD-grown 'monolayer' h-BN from suppliers 2-9, transferred on 300 nm SiO2 / Si substrates.Each Raman spectrum plot contains 12 Raman spectrums collected at 12 different positions.Each Raman map is in a size of 100 x^ w 100 xx ^, selected of the intensity of h BN E2g 2g band.The order from b to to h follows the same order as in Supplementary Figure 8.

Figure R2 |
Figure R2 | Raman characterization of CVD-grown multilayer h-BN from supplier 2, 4, 7, 9 and 12, transferred on 300 nm SiO2 / Si substrates.Each Raman spectrum plot contains 12 Raman spectrums collected at 12 different positions.Each Raman map is in a size of 100 x^w 100 x^, selected of the intensity of h-BN E2g band.The order from a to e follows the same order as in Figure 5.

Figure R1 |
Figure R1 | CAFM topography maps collected in sequence on multilayer h BN samples.The 1 st scan and the last scan (17 th th ) are a zoom out topography maps with size of 15 tm × 15 tm, while the 2 nd nd ~ 16 th th are taken at the centre of the sample.

Figure R1 |
Figure R1 | Optical microscope images of mechanically exfoliated h BN and CVD-grown "monolayer" h-BN from suppliers 1 9, transferred on SiO /Si substrates.a, optical microscope image of mechanically exfoliated h-BN, where large thickness fluctuation can be easily observed by the contrast.b-j, optical microscope images of CVD-Va^f] j\^]^[PhTak W BN from suppliers 1-9.9.
3, 479-485.https://doi.org/10.1038/s41928-020-0416-x],and entropy source for encryption systems [Nanoscale, 2023, 15, 9985-9992.https://doi.org/10.1039/D3NR00030C].I am not surprising that such kind of rough h-BN films will have poor electrical homogeneities and more pinholes than the mechanically exfoliated h-BN with flat surface.Rough surface of h-BN has no relationship with poor electrical homogeneity or pinholes, the reviewer is incorrect in this statement.The electrical homogeneity is related to only two things: (i) thickness fluctuations, and (ii) presence of atomic defects (dangling bonds, impurities) [Chiu, Advances in Materials Science and Engineering, 578168 (2014), http://dx.doi.org/10.1155/2014/578168].The presence of pinholes is related to discontinuities in the material and/or high density of defects that forms a conductive path across the dielectric.
[REDACTED].Moreover, there is a very big global interest on understanding the quality of commercial 2D materials.The pr evious study doing similar analysis (but for liquid-phase exfoliated 2D materials) [Kauling et al.Advanced Ma terials 30, 1803784 (2018)] has been cited more than 308 times since its publication in 2018.And now, with th e global push of CVD-grown 2D materials, which are being used by companies like TSMC, Intel and Samsun g, the push on this type of samples is even higher[Lanza etal.Advanced Materials 2022, 34, 2207843].[RED ACTED].
We would like to emphasize that the use of CAFM in contact mode (with the types of tips and contact forces employed in this study) does not damage the surface of the CVD grown h-BN samples.To confirm this, we make a test experiment that consists of collecting one 15 µm × 15 µm topographic scan in contact mode at a random location of a h BN sample transferred on a SiO2/Si substrate.Then, we zoom-in and scan 15 times with a size of 10 µm × 10 µm, and finally we zoom-out and scan again with a size of 15 µm × 15 µm.Despite the wrinkles in the 2D material are known to be soft regions that could be displaced if enough force is applied[25], all the images collected (see Supplementary Figure1313) are identical and clearly demonstrate that no damage or surface modification is introduced by the tip of the CAFM.