Multimodal dynamic and unclonable anti-counterfeiting using robust diamond microparticles on heterogeneous substrate

The growing prevalence of counterfeit products worldwide poses serious threats to economic security and human health. Developing advanced anti-counterfeiting materials with physical unclonable functions offers an attractive defense strategy. Here, we report multimodal, dynamic and unclonable anti-counterfeiting labels based on diamond microparticles containing silicon-vacancy centers. These chaotic microparticles are heterogeneously grown on silicon substrate by chemical vapor deposition, facilitating low-cost scalable fabrication. The intrinsically unclonable functions are introduced by the randomized features of each particle. The highly stable signals of photoluminescence from silicon-vacancy centers and light scattering from diamond microparticles can enable high-capacity optical encoding. Moreover, time-dependent encoding is achieved by modulating photoluminescence signals of silicon-vacancy centers via air oxidation. Exploiting the robustness of diamond, the developed labels exhibit ultrahigh stability in extreme application scenarios, including harsh chemical environments, high temperature, mechanical abrasion, and ultraviolet irradiation. Hence, our proposed system can be practically applied immediately as anti-counterfeiting labels in diverse fields.


POINT-BY-POINT REPLY TO REVIEWER COMMENTS
We thank all the reviewers for their valuable comments, which we have used to improve our work. Please find below the point-by-point reply to the comments, with the reply in blue.

Reviewer #1 (Remarks to the Author):
The authors have investigated the possible application of SiV centres for unclonable labels.
While the study is interesting I feel the authors have over emphasised its utility. the biggest draw back in this process is the CVD growth of diamond which takes place at very high temperature (=> 800C). This fact has also been not mentioned in the script.
Also, it is not clear why SiV was chosen rather than NV which is much easier to fabricate, although, one would need high temperature. Considering this is not that big a breakthrough I feel it is suitable for more specialised journal rather than NComms.

Response:
We are grateful for the reviewer acknowledging that our study is interesting, and would like to take this opportunity to highlight the novelty of our work: (1) multimodal and dynamic diamond-PUF encoding capability adaptable to various anticounterfeiting requirements, e.g., rapid authentication and high-level security; (2) high encoding capacity of the diamond-PUF anti-counterfeiting label; (3) non-toxic and eco-friendly diamond material suitable for practical anti-counterfeiting products requiring high safety, e.g., food and medicine.
(4) ultrahigh stability of the diamond-PUF in extreme application scenarios, e.g., harsh chemical environments, high temperature, mechanical abrasion, and UV light irradiation; (5) scalable fabrication of the diamond-PUF at low-cost by a one-step commercial CVD system; (6) CVD fabrication process of the diamond-PUF has excellent compatibility with different product fabrication lines, e.g., microelectronics.
We have tried our best to address the two major concerns raised by the reviewer. The details are as follows.
(1) About the CVD growth of diamonds at high temperatures: We feel sorry that the reviewer might misunderstand our described CVD growth process of diamond particles. We have strengthened the corresponding description and added the technical details in the Methods section of the revised manuscript, see page 8, line 335. Indeed, our adopted CVD system operated at a temperature of ~900 °C (a commonly used condition for diamond growth as summarized in Table R1); however, we do not see significant side effects/drawbacks of CVD growth for our proposed diamond-PUF product/labels. In general, all the possible methods for growing diamond materials need to work under highly strict conditions (high temperature and high pressure, see Table R1). Compared with the other two commonly known fabrication approaches, detonation and high-pressure high-temperature (HPHT) processes, the CVD process is believed to be the most convenient way to heterogeneously grow large-scale high-quality diamond particles with different color centers on various substrates at a relatively low cost R1-6 . Moreover, a relatively high-temperature growth condition is generally favored in the modern large-scale fabrication of high-quality semiconductor materials R7, 8 , because it normally ensures the great stability of materials. Thus, the CVD growth of diamonds at relatively high temperatures is one strategy for fabricating highly stable diamond-PUF devices. Of course, when needed, the low-temperature CVD growth of diamond is also achievable R9-12 . Do not require high pressure. Used to produce highquality diamonds on large substrates with little contamination and good controllability of the growth process. The method has the flexibility for the choice of substrate, growth rate, and in-situ doping options. R3, 5 The most important motivation of this work is the non-deterministic nature of CVD process, including its seeding, nucleation, and crystal growth procedures, satisfying the critical requirement for fabricating PUF labels. Thus, by taking advantage of this intrinsic property of the CVD process, we directly used the non-deterministic grown diamond microparticles on heterogeneous substrates as PUF anti-counterfeiting labels. In addition, we want to emphasize the great advantage of the one-step heterogeneous CVD growth manner on the substrates, which greatly guarantees the strong adhesion of diamond particles to the silicon substrate, enabling the excellent stability of our diamond-PUF label as a whole device. But those direct methods by dip/spin-coating pre-synthesized particles on substrates as PUF labels (e.g., splitting the materials synthesis and PUF device fabrication into two separate steps) may have stability concerns. From a practical point of view, advanced instruments (e.g., CVD system) and harsh growth conditions (e.g., high temperature) are highly preferred for manufacturing diamond-based anti-counterfeiting labels as replicating them becomes much more challenging (almost being impossible) for general public R15 .
(2) About the utilization of SiV centers rather than NV centers: We strongly believe that the SiV center is much easier to fabricate compared with NV center during CVD diamond fabrication. Actually, the formation of SiV centers in CVD-grown diamond is rather simple, due to the residual silicon sources that are often present in CVD chambers from silicon-containing substrates (or quartz bell jars), as shown by us and many other researchers in the field R6, 16, 17 . In contrast to many other color centers that are normally introduced in the expensively grown monocrystalline diamond, the bright SiV centers can also be prepared in polycrystalline diamond particles at a much lower cost and a larger scale R2-4 , which is exactly what we have done in this work. In our designed experiments, we believe that the fabrication of SiV centers is more proper and convenient (than NV centers), given that the chosen Si substrate is also the Si doping source, and therefore we could "kill two birds with one stone". Moreover, these in-situ incorporated SiV centers during CVD growth have been shown to possess superior fluorescence properties compared to that generated with ion implantation R18 . In contrast, additional processes must be performed to introduce NV centers in our diamond sample, for example, (1) during the CVD process: the adding of nitrogen dopants like nitrogen gas; and/or (2) after the CVD process: (i) the incorporation of nitrogen impurities by doping or implantation, (ii) the creation of lattice vacancies by electron or laser irradiation, and (iii) a final annealing process (e.g., ≥700 °C in high-vacuum or inert gas for several hours) R19 . Thus, the facile creation of high-quality SiV centers in our diamond-PUFs product by the CVD process, in a cost-effective and scalable manner, is one of the key reasons that we adopt SiV centers to demonstrate the anti-counterfeiting applications.
Apart from the easy introduction of SiV centers to our diamond particles, we also prefer the spectroscopic features of SiV centers rather than NV ones. As described in the introduction of the manuscript, "In particular, the SiV center exhibits a naked-eye-invisible near-infrared (NIR) emission at around 737 nm 40 , reducing the difficulty of distinguishing confidential from disturbance information 14 . Thus, the color centers with NIR emissions, like SiV centers in diamond, have great potential to serve as optical PUF labels.", the NIR emission (~737 nm) of SiV center would reduce the difficulty of distinguishing confidential from disturbance information, which is one of the reasons why the color centers with NIR emissions, like SiV centers in diamond were chosen in our project, rather than the NV centers with a broadband emission (ZPL∼638 nm for negatively charged NV, and a large portion falls in the visible region). Moreover, the high photon emission rate of SiV centers (room-temperature emission rates of various single color centers in diamond are summarized in Table R2) would enable a wide distribution of the SiV PL intensities (Fig. 4c), which would lead to a larger encoding capacity of the proposed PL-based anti-counterfeiting applications. To avoid any possible confusion regarding the fabrication of our proposed diamond-PUF product/labels, and to emphasize the reasons for selecting SiV centers for anti-counterfeiting in our work, we have added the above discussion in the revised manuscript, see page 7, line, 282.

Reviewer #2 (Remarks to the Author):
The authors present a anti-counterfeiting strategy by using their previously developed highquality CVD-grown diamond microparticles on heterogeneous substrates. It is a interesting and novel work. However, this manuscript need to solve the following concerned issues before it is considered for publication.

Response:
We gratefully thank the reviewer's time, helpful comments, and appreciation of the novelty of our work. We have thoroughly addressed the reviewer's concerns in our following point-bypoint response.
Q1 To achieve PUFs, the uncertainty of the process is only as a security entry condition, how many methods are there in Fig. 1a(2)? It cannot be outlined by etc., it is not scientific and rigorous. If it is related to the encryption capacity, how sensitive is each method?

Response:
We thank the reviewer for pointing this out, and apologize for this unclear presentation in Fig. 1a (2). A PUF is a physical object with an inherent, unique, and fingerprint-like feature generated in a non-deterministic process. Here, for step (2) "Non-deterministic CVD", we wanted to emphasize that (i) the CVD growth of diamond particles is a non-deterministic process, satisfying the critical requirement for fabricating PUF labels; (ii) the color centers, such as SiV, NV, germanium vacancy (GeV), tin vacancy (SnV) centers, could be stochastically and in-situ introduced into the diamond lattice during the CVD process, which is one of the key points of CVD-grown diamond, without any extra defect-centers generation processes. As a result, a large parameter space offered by CVD process, for example, the concentration, amount, and type of color centers; size, shape, and crystallinity of the diamond particles can be freely modulated by tuning the CVD-growth parameters.
As for the maximum number of anti-counterfeiting methods based on color centers in diamonds, it is highly dependent on the type of color centers introduced by the CVD process ( Fig. 1a(2)).
Until now, there are ∼500 different color centers that have been discovered in diamond R27 , and it has been demonstrated that a large portion (e.g., SiV R28 , NV R29 , GeV R22 , SnV R30 , Nirelated R31 and Cr-related R6 color centers) could be in-situ introduced during CVD process by utilizing suitable substrates or precursors. Although we just demonstrate the optical anti-counterfeiting using the SiV centers in diamond particles, other color centers (e.g., NV, GeV, SnV) in diamonds can also be employed in principle. Each method may have its own encoding capacity, relating to the intrinsic optical properties (e.g., quantum efficiency, photon emission rate, lifetime) of the used color centers. Because the current proposed color center-related anticounterfeiting strategy is based on the PL intensity of the color centers, different types of color centers may have their own level of PL intensity according to their emission rates (roomtemperature emission rates of various single color centers in diamond are summarized in Table   R2). For example, the higher the emission rates of the color centers (which will induce a higher P in C(3) of Fig. 1c), the larger the encoding capacity of the used color centers will be. The ultrahigh room-temperature single-photon emission rate of the SiV centers is one of the important reasons why we used them for high-level PL-related anti-counterfeiting.
Q2 The authors claim: "the developed diamond PUFs exhibit excellent performance in respects such as capacity, diversity, safety, manufacturability, robustness and compatibility ( Fig. 1b)", What is the basis? Is there a consensus among other scholars? Qualitative or quantitative data support is necessary.

Response:
We thank the reviewer for raising a point that allows us to better explain our work. We made such a conclusion based on comparing our results with the most representative optical PUFs shown in the reported works. Previously, some review papers have reviewed the performance of the common anti-counterfeiting materials R32-38 . However, not every reported PUF has all the required quantitative data in the aspects we compared. Here, to support our conclusion, we have summarized the quantitative, semi-quantitative, or qualitative data (see Table R3) of the performance of the most studied optical PUFs with respect to capacity, diversity, safety, manufacturability, robustness, and compatibility from the related reported works. (To be more accurate, we changed the "organic dots" into "polymer dots", as we intended to describe the photoluminescent materials in the form of polymer nanoparticles with a size of 1−100 nm R38 , and we believe "polymer dots" is more accurate.) 7

R49
Capacity: encoding capacity, the maximum number of unique PUFs that can be produced.
Diversity: the number of encoding methods that can be provided.
Safety: the degree of harm or danger the PUF may cause to the environment and human.
Manufacturability: the degree to which a PUF can be effectively manufactured given its design, cost, and distribution requirements.
Robustness: the ability to tolerate perturbations that might affect the PUF function.
Compatibility: the ability to work together in harmony because of well-matched characteristics.

NRs: nanorods
NPs: nanoparticles NA: not available PSMA: polystyrene-maleic acid copolymer To summarize, our diamond-based PUF shows excellent performance in respect of capacity, diversity, safety, manufacturability, robustness, and compatibility. Other optical PUF systems may suffer from drawbacks such as safety concerns, poor stability, complicated chemical synthesis processes, poor compatibility with microelectronics, etc. In our original manuscript, we plotted Fig. 1b under a unified standard by using "High", "Medium", and "Low" to semiqualitatively compare their performance in every aspect. We now feel this is more or less a bit biased due to the un-unified and uncompleted data sets available, therefore, we decide to remove Fig. 1b, and directly show the summarized Table R3 to the audiences, leaving them to be the judge. In replacement of the original Fig. 1b, we have highlighted the novelty of our work as Fig. R1. We have added Table R3 as Supplementary Table 1  Q3 Since the author claims their excellent performance in respects such as capacity, diversity, safety, manufacturability, robustness and compatibility, The authors should provide one-to-one results data to support their views.

Response:
We thank the reviewer for pointing this out. Please see our response to Q2. We have provided a summarized table (Table R3) showing one-to-one quantitative, semi-quantitative, or qualitative data to support our point. From the table, we can clearly see that our diamond-based PUF shows good performance in respect of capacity, diversity, safety, manufacturability, robustness, and compatibility.
Q4 For the application of anti-counterfeit labels, how do users authenticate? What is the ease of use?

Response:
We thank the reviewer for pointing this out. The authentication process and ease of use of a PUF label are essential to its anti-counterfeiting applications. As shown in Fig. 5g of the manuscript, we presented the workflow of the anti-counterfeiting applications using our diamond-PUF label, but it might not be clear enough. Here, to better demonstrate the anticounterfeiting application, we further provide a detailed explanation of the authentication process and ease of use of our diamond-PUF anti-counterfeiting label as follows. As shown in Fig. R2. The execution of authentication can be divided into two steps, including the registration and validation processes.
(1) In the registration stage, input challenges (C1) are projected onto the diamond-PUF to generate the associated response (R1), which is further transformed into the key (K1).
Then, the challenge-response pairs (CRPs) composed of the registered information of C1 as well as K1 are stored in the cloud database.
(2) In the validation stage, the authenticator randomly selects C1 from the cloud database to challenge the candidate PUF, and then obtains a check code K1'. Hereafter, the check code is uploaded to the data cloud to compare the similarity index (I) or Hamming distance between K1 and K1'. If I (K1, K1') is greater than a preset threshold, the verification is true. Otherwise, the verification result is false.
For ease of use, the smartphone-based authentication setup shown in Fig. 3a is expected to have the capability of being detected and read out quickly, cheaply, and conveniently. Due to their high refractive index, the diamond particles on the diamond-PUFs can be easily photographed by any smartphone equipped with a magnifying lens (200~300×). Therefore, the user can readily take and upload the photo to the cloud database for the further authentication process.
To better explain the anti-counterfeiting application, we have added the above discussion about the authentication process and ease of use of our diamond-PUF tag in the revised Supplementary Information as Supplementary Fig. 4 and Supplementary Note 1, see page S-5.
Q5 What is the resolution of Fig. 3a(ii)? How many times can the camera of an ordinary smartphone be enlarged to take such pictures? Are this kind of smartphone ordinary for most users?

Response:
We thank the reviewer for asking these detailed questions. As indicated in Fig. 3a(ii), the actual size of the red dashed square is 200 µm × 200 µm, which is calibrated from the near cross marker (50 µm × 60 µm, fabricated by focused-ion-beam milling). And we used a very portable microscope (with 300× magnification) attached to the camera of an ordinary smartphone to take such pictures. The portable microscope is used for enlargement, and the smartphone is just used to take pictures. This kind of portable microscope is widely available in any stationery store at a relatively low price (we brought it for ~15 USD) R50 , which can be in principle attached to any kind of commonly seen smartphone. Thus, we believe this portable smartphone-based approach is suitable for most users.
Q6 The author is focus on anti-counterfeit labels, why they show some figures for the means of chaos key generation, which is not the same as anti-counterfeit labels, right?

Response:
We thank the reviewer for raising this technical point. When designing a PUF anticounterfeiting system, the digitization (key generation from the readout) of the label is also essential, because the information content of the system is eventually stored in the unique codes generated in such a process. And one of the key points that we want to introduce in our manuscript is the multimodal PUF anti-counterfeiting functions of our diamond-PUF label, ranging from static to dynamic, low-level to high-level encoding, which means that we could have different ways to authenticate our diamond-PUF for different application scenarios. Each level of encoding has its own readout method, for example, physical distribution, scattering spectrum, and PL intensity of the diamond particles, the digitization (means of chaos key generation) process will then be different from each other, depending on the readout method.
The low-level encoding based on physical patterns of diamond particles can be readout quickly, cheaply, and conveniently through mobile devices, which is applicable to applications requiring rapid authentication. At the same time, the high-level encoding (based on the scattering spectrum or PL intensity of diamond particles) requires precision instruments to read, but provides a more secure method, which is applicable to applications requiring high-level security. Therefore, to elaborate and evaluate our claimed multimodal function, we presented the results of chaos key generation from different means.
Q7 Line 213, if for information encryption, decryption is required, please provide a possible decryption scheme.

Response:
We thank the reviewer for asking this technical point. Here, we would like to propose a possible information encryption and decryption scheme using our diamond-PUF label.
Secure communication between two parties is important for everyday information security.
Here, our diamond-PUF label has the application potential in secure information encryption.
As shown in Fig. R3  To better explain the information encryption application, we have added the above discussion about the possible information encryption and decryption scheme using our diamond-PUF label in the revised Supplementary Information as Supplementary Fig. 5

and Supplementary
Note 2, see page S-6.

Q8 The authors should distinguish between the concepts of encryption and anti-counterfeiting.
And the reviewer think the authors need to clarify the role of the mentioned encryption in the manuscript?

Response:
We thank the reviewer for pointing out this unclear description. We apologize for our nonspecific usage of "encryption" which has been mixed with "anti-counterfeiting" in the manuscript. Our intention of mentioning encryption is to remind other possible PUF-related applications using our diamond-PUF tags besides anti-counterfeiting, like information encryption. To clarify this point, we have revised our "encryption" related description in the revised manuscript, as follows, -Page 1, line, 28, "encryption" was changed to "anti-counterfeiting": "Developing advanced anti-counterfeiting materials …" -Page 1, line, 35, "encryption" was changed to "encoding": "… high-capacity optical encoding.

Reviewer #3 (Remarks to the Author):
This manuscript demonstrated multimodal and dynamic PUF labels by using SiV diamond microparticles on Si wafers by CVD fabrication. Authors achieved (1) high anti-counterfeiting capacity due to multimodal optical information like light scattering spectra, shape, and PL intensity; (2) dynamic anti-counterfeiting strategy to enhance the security of the diamond by air oxidation;(3) outstanding stability and durability. The work is significant original progress and offer a new material system for PUF fields.
However, the problems are also evident as follows. Authors conclude that the system exhibits excellent performance in respects such as capacity, diversity, safety, manufacturability, robustness and compatibility, is low cost and can be practically applied immediately as anticounterfeiting labels in diverse fields. However, the fabrication technique by high-temperature CVD, limited substrate (Si), and dynamic strategy by high temperature air oxidation seriously limit its practical application in cryptography.
Overall, this paper can be considered for publication if the authors address the relevant critical problems to support the conclusions.

Response:
We are grateful for the reviewer acknowledging our work is significant original progress, and we have carefully addressed her/his concerns in our following point-by-point response.
Q1 The patterning techniques are critical for optical PUF anticounterfeiting, which can enable PUF with patterns concluding goods information or anticounterfeiting information (that can be authenticated conveniently), and offer the locations for authentication of micro/nano PUF. The patterning strategies of MPCVD PUF should be offered and discussed.

[Response redacted]
Q2 The novelty in diamond microparticles themselves should be explained, such as the preparation or customization for anti-counterfeiting applications.

Response:
We thank the reviewer for this valuable comment. Our large-scale fabrication of high-quality diamond microparticles with SiV centers on heterogeneous substrates offers excellent opportunities for anti-counterfeiting applications: (1) the flexible variability of CVD growth parameters (e.g., gas composition and flow rate, microwave power, pressure, growth time and temperature, diamond seeds, and substrates) and the wafer-scale production (substrate stage

[Response redacted]
with a diameter of 10 cm or even higher) ability make the mass commercial customization of the diamond-PUF labels possible; (2) the micro-size and high refractive index of the diamond particles could enable the convenient readout and authentication processes via a simple portable smartphone-based equipment (Fig. 3a); (3)

Response:
We thank the reviewer for pointing this out. We made such a conclusion based on comparing our results with other most studied optical PUFs shown in the reported works. Please kindly see our response to Q2 of Reviewer #2. We have provided a summarized table (Table R3) showing one-to-one qualitative, semi-quantitative, or quantitative data to support our point. To be unbiased (due to the lack of unified and completed data), we decided to remove Fig. 1b and directly show the summarized Table R3 to the audiences, leaving them to be the judge. In replacement of the original Fig. 1b, we have highlighted the novelty of our work as Fig. R1.
Q4 The calculated the similarity index (Fig. 3e) and Hamming distance are used to quantitatively demonstrate the uniformity, uniqueness, and randomness of the diamond PUFs.
But the calculation process or equations are missing, and the parts should be offered in detail in the Manuscript or Methods.

Response:
We thank the reviewer for pointing this out. The calculation process and equations for the corresponding parameters are as follows, (1) Uniformity. The uniformity metric can be calculated using the following equation: where, Ri is the ith bit response from the n-bit key.
(2) Similarity index. The similarity index (I) is used to detect the degree of similarity between different PUFs, which can be calculated by the following equation: where, A is the same number of pixels between two PUFs, B is the total number of pixels in PUF.
(2) Hamming distance. The Hamming distance between two keys is the minimum number of substitutions required to change one key into the other. The Hamming inter-distance is used to quantify the uniqueness of a PUF, which is the ability to distinguish a PUF from others. And the Hamming intra-distance is used to quantify the reliability of the same PUF label, checking if it has the ability to generate consistent keys under multiple measurements. The uniqueness and reliability are evaluated using the Hamming distance as below: where Ri and Rj are n-bit keys of the ith and jth PUF, and N is the total number of PUFs.
where R0 is the original n-bit key of the PUF, and Ri is the n-bit key generated by the same PUF from ith measurement among total N times of measurements.
We have added the detailed calculation process and equations for the uniformity, similarity index, and Hamming distance as Supplementary Note 4 in the revised Supplementary Information, see page S-11. Q5 Cost on the fabrication and substrate is much higher than the requirement for large-scale commercialization. The fabrication of the diamond PUFs need a high temperature (500℃) and the microwave-plasma assisted chemical vapor deposition (MPCVD) system (Seki 6350) on standard single-crystal Si (100) wafers (2 inches) . The total cost of the diamond PUFs should be calculated and compared.

Response:
We thank the reviewer for this very constructive comment. In general, lab-grown diamonds have existed for more than 60 years, and the synthetic technologies have been well-developed.
The commercialization of CVD technology was realized in the early 2000s, and it has made crucial advances in recent years, allowing companies to grow higher-quality diamonds more rapidly and more cheaply. For example, the cost of producing a 1-carat G-color VS-polished CVD-grown single-crystal diamond (Fig. R5a) dropped significantly from 4000 USD in 2008 to 300-500 USD in 2018, with further reduction expected, according to the Global Diamond Report by the Antwerp World Diamond Centre R58 . At the same time, the global number of CVD systems (Fig. R5b) was ~5300 in 2020, and it is expected to significantly increase to ~31900 by 2025, which is mainly due to the manufacturing and assembly technology of CVD equipment has been mastered by more and more enterprises (such as companies in China, India, and other countries), according to a report by the Sinolink Securities R59 . Therefore, the cost of CVD equipment and fabrication is expected to continuously decrease along with significant technological advancement. In this study, we demonstrated the PUF anti-counterfeiting application by using the heterogeneously grown polycrystalline diamond microparticles, which are believed to have a much lower manufacturing cost than that of the single crystal counterparts R3, 5 . Our diamond-PUF samples were prepared by a Seki 6350 MPCVD system (purchased in 2018), which is indeed expensive (432000 USD). Note that the price of a MPCVD system has been dramatically reduced (~100000 USD) in the market for the low-cost and large-scale commercial fabrication of diamonds (see our uploaded file Supporting Information_MPCVD, showing the quotation and technical description for a standard MPCVD system similar to Seki 6350, which could fully meet all requirement for the fabrication of diamond-PUF labels). Most importantly, the total cost of fabricating the diamond-PUFs could be significantly and continuously reduced when mass production begins, because the MPCVD system is a one-time investment. In addition, we want to emphasize that the repeatability, yield rate, and production efficiency of the MPCVD technology (industrial level) are much higher than those laboratory level methods, which is greatly suitable for massive production. Nevertheless, it is actually beneficial to have complicated instruments (e.g., MPCVD system) and harsh growth conditions (e.g., high temperature) for manufacturing diamond-PUFs as replicating them becomes much more challenging (almost impossible) for the general public R15 .
Here, to provide a general estimation of the total cost of fabricating the diamond-PUFs, we have calculated the cost of fabricating one piece 2-inch sized diamond-PUF in almost all aspects based on our experiment and local situation, as shown in the following Table R4. The local labor cost is ~3 USD/hour. Considering the MPCVD system is highly integrated and does not require complex operations, one person can operate 10 or more equipment at the same time, so the unit labor cost can be converted into ~0.3 USD/hour. In the future, the labor cost will be lower or reduced to zero, because the final production line will develop into full-machine automatic production.

2.427
This cost could be further reduced along with the significant technological advancement over the years.
The above calculated total cost is the unit price for fabricating one piece of 2-inch sized diamond-PUF label. Due to the high encoding capacity of the diamond-PUFs, a tiny working area can meet the purpose of anti-counterfeiting. In our study, the largest area used for encoding is 200 µm × 200 µm (Fig. 3a). Thus, a 2-inch wafer can be cut into a maximum of ~4.9 × 10 4 pieces of working labels, and the cost of an individual working label will be significantly low (~0.0001 USD). And it will be further reduced if a larger-sized substrate is used for the diamond-PUF fabrication. In addition, we might need to consider the extra cost for processing (i.e., cutting the 2-inch wafer into many small pieces for our purpose) the Si wafer (~10 USD/piece), but this is negligible when considering the large number (on the order of ~10 4 pieces) of generated anti-counterfeiting labels from such a 2-inch wafer. In fact, the processing of the wafer-based devices could be well suited by low-cost fabrication techniques (e.g., standardized laser cutting, lithography, etching, etc.) R60-62 used in the LED industry, chip fabrication, and related production lines. Therefore, it can be predicted that the above-estimated cost of the diamond-PUFs (~0.0001 USD per label) would be well-accepted by high-end products with high anti-counterfeiting requirements, such as electronic components, medicine packaging, vehicles, luxury goods, etc.
In addition to the currently adopted Si wafer, it is possible to use many other substrates as well.
It has been reported that diamonds can be CVD grown on other substrates, such as SiO2 R63, 64 , Al2O3 R65 , GaN R66, 67 , or even flexible substrates by later transformation R68, 69 . Moreover, many studies have successfully demonstrated the CVD fabrication of diamonds at relatively low temperatures R9-12 . As shown in Fig. R5 (our unpublished preliminary results, further quality improvements are needed), we have also demonstrated the CVD growth of diamond micro/nanoparticles on SiO2 and sapphire (low growth temperature: <475°C) substrates. To clarify the above points, we have added the above discussion in the revised manuscript, see page 7, line 292, and added Table R4 as Supplementary Table 2 in the revised Supplementary Information, see page S-10.
Q6 In terms of dynamic encoding modulation of the SiV diamond microparticles PUF via air oxidation, the stimulation of air oxidation is high temperature 600°C lasting 15 minutes. That is, the practical application of dynamic encoding is challenging, if not impossible. In addition, the time-dependent encoding is relying on the dynamic emission intensity/brightness of diamond microparticles, which is prone to be affected by the ambient light and exposure time during capturing PUF images. How to deal with this, and the author should explain it.

Response:
We thank the reviewer's comment. For practical applications, we believe a good "threshold" for activating the dynamic encoding is very important for the stable function of the normal anticounterfeiting ability, and dynamic coding is performed on demand when necessary.
Fortunately, the proposed high-temperature air oxidation treatment is such good "threshold" by protecting the diamond-PUF from involuntary transformation (i.e., instability), for example, the diamond-PUF label can function stably in most practical application scenarios (Fig. 6), and it only changes into another new PUF key upon intentional treatment when the original label faces malicious attacks and the risk of being duplicated. At the same time, the air oxidation treatment (600°C, 15 minutes) could be easily achieved by any kind of CVD system, furnace, or heating plate, which is not a challenging requirement. One possible approach for the practical application of dynamic encoding is using the detachable strategy, e.g., detaching the diamond-PUF label for dynamic encoding modulation by air oxidation, and reattaching the label on the product after modulation.
As for the time-dependent encoding process, indeed, it depends on the emission intensity/brightness of the SiV centers in diamond microparticles. However, it was the difference between individual particles that we considered during each encoding process (Fig.   4c); for example, in the quaternary encoding: the intensities ranked between 0~25%, 25~50%, 50~75%, and 75~100% would be encoded as 0, 1, 2, and 3, respectively. And such intensity difference is intrinsically dependent on the SiV concentrations in diamond microparticles, which is determined by the CVD process. The influence of the ambient light and exposure time on the SiV emission is a kind of bulk manner (i.e., the intensity of each particle will increase or decrease to almost the same extent); thus, it will not greatly affect each self-compared encoding process. Here, we have performed additional experiments (Fig. R7) to prove this point by reading out the same label under different conditions (with or without ambient light, exposure time, and laser power). From the results, we can know that the measurement conditions while capturing the PL images may not affect the final keys generated by the same diamond-PUF label because their similarity indexes are within an acceptable value (>80%). Of course, to ensure the accuracy of authentication, we may try to keep the measurement condition of the readout process unchanged. To clarify these points, we have added the above discussion in the revised manuscript, see page 5, line 224, and added Fig. R7 as Supplementary Fig. 8

in the revised Supplementary
Information, see page S-8.

Q7
The authors say that the anti-counterfeiting system could be further combined with machine vision, artificial intelligence, and machine learning to identify and track the diamond-PUF labels efficiently and automatically. However, the relative emission intensity/brightness of diamond microparticles with time changed synchronously (Figure 4b-d); and one of the advantages of machine vision, artificial intelligence, and machine learning is to identify the specific pattern with different brightness, so how to take full use of the dynamic emission intensity/brightness is important.

Response:
We thank the reviewer for pointing this out, and believe there might be some misunderstanding of AI-related discussion. Thus, we have revised the corresponding part so as to make it clear to the audience. We definitely agree with the reviewer that the strength of machine learning is to identify the specific pattern with different brightness, and our intention was to say that those AI techniques could be combined with any fixed diamond-PUF anti-counterfeiting labels to further improve the overall performance. For example, some AI algorithms could be developed for the rapid and accurate authentication of the diamond-PUF label when using the anticounterfeiting based on the shape feature and scattering spectrum of the diamond particles (e.g., one can employ an "internal reference" of a diamond particle with fixed size and shape for the signal normalization). Furthermore, some noise factors (e.g., positioning angle, lighting conditions, magnification, and poor focus) should be considered in the real scenario; thus, robust AI-assisted authentication is desired for practical usage.
As for the mentioned dynamic features in emission intensity/brightness, we actually applied air oxidation treatment (Fig. 5a-d) to generate new PUF keys in the same PUF label when the original key encounters duplicating risks. Once the modification is finished, the PUF label will be fixed without any changes. Therefore, we believe there is no conflict in combining machine vision, artificial intelligence, and machine learning techniques with any fixed diamond-PUF anti-counterfeiting labels for better performance.
To clarify this point, the above discussion about the improvement using advanced algorithms has been rearranged in the newly added Discussion section in the revised manuscript, see page 7, line 303.
Q8 The transformation of capture to binary encoding image is the basis for calculation. Since digital key extraction and performance analysis were conducted by MATLAB, the codes should be offered for the work to be reproduced.

Response:
We thank the reviewer for pointing this out. We have uploaded our MATLAB codes together with our source data of Fig. 3a(ii) and Fig. 4b as a Source Data file upon the submission of our revision files.
Q9 The "multimodal" and "dynamic" are key information and contribution, which can be highlighted and added in the Title.

Response:
We thank the reviewer's suggestion. We have revised the Title accordingly: "Multimodal, dynamic, and unclonable anti-counterfeiting using robust diamond microparticles on heterogeneous substrate"

Other Changes made in the Revised Manuscript
-Page 1, line, 1, the title was revised to: "Multimodal, dynamic, and unclonable anticounterfeiting using robust diamond microparticles on heterogeneous substrate" -Page 1, line, 10, the affiliation of "Jing Wang" and "Lei Shao" was changed to: "State Key Laboratory of Optoelectronic Materials and Technologies, Guangdong Province Key Laboratory of Display Material and Technology, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China" -Page 1, line, 16, the affiliation of 5 was changed to: "Primemax Biotech Limited" -Page 1, line, 27, to meet the formatting requirement, the Abstract was slightly revised to 150 words.
-Page 6, line, 259, "In this way, a kind of dynamic information storage, encryption and transformation material can be successfully developed." was deleted.
-Page 6, line 259, "Therefore", "diamond-PUF" and "for a higher level of security" were added to the last sentence.
-In Fig. 1c, we apologize for our mistake in calculating C (4) in Fig. 1c, and have replaced it with the correct one: C (4) = (n + 1) × P m .
-To meet the formatting requirement, we have provided the figures of the manuscript in individual files.
-To meet the formatting requirement, we have placed the "Acknowledgements", Author Contributions", "Competing Interests", and "Figure Legends" sections after the "References" section.