Electrically Reconfigurable Optical PUFs Based on MoS2 Photoluminescence Modulation

Electrically Reconfigurable Optical PUFs Based on MoS2 Photoluminescence Modulation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Electrically Reconfigurable Optical PUFs Based on MoS2 Photoluminescence Modulation Guanhai Li, Xianjie Lin, Xin Li, Xiaofang Wang, Jin Chen, Feilong Yu, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7074604/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Conventional optical security keys are fundamentally static-offering fixed encoding states and relying on irreversible processes or bulky apparatus-rendering them vulnerable to modeling, duplication, and physical attacks. Here, we present an electrically reconfigurable optical PUFs based on photoluminescence (PL) modulation in structurally disordered MoS 2 microstructures. By leveraging a multidimensional “one-static-two-dynamic” encoding strategy, our system integrates electrically invariant grayscale patterns with gate-tunable PL intensity and emission wavelength, enabling pixel-specific, high-entropy responses that are both reprogrammable and non-volatile. The devices are fabricated via lithography-free van der Waals stacking, generating intrinsic spatial randomness without compromising scalability. Electrostatic gating induces reversible and layer-sensitive bandstructure modulation-mechanistically validated by first-principles calculations-which governs the observed PL shifts across 41 gate voltages. Binary keys extracted from these states yield near-ideal Hamming distance statistics and an exceptionally low total authentication error probability (< 2 × 10 − 38 ), with a maximum selection entropy of 6.375-surpassing conventional PUFs benchmarks. We further implement a dual-stage authentication protocol that couples zero-bias grayscale screening with voltage-controlled PL verification. This framework provides a practical, tamper-resilient, and quantum-attack-resistant solution for next-generation hardware security. Physical sciences/Materials science/Materials for devices/Electronic devices Physical sciences/Nanoscience and technology/Nanoscale devices/Quantum information Physically Unclonable Function Electrically Reconfigurable Photoluminescence MoS2 Microstructure Disorder High-Entropy Optical Encoding Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction As the digital economy scales, the demand for robust, future-proof data security has become a global imperative. 1–3 . Traditional cryptographic systems, based on deterministic algorithms and mathematical hardness assumptions, are increasingly vulnerable to advances in quantum computing 4,5 . With Shor’s algorithm threatening to render Rivest-Shamir-Adleman (RSA) and Elliptic Curve Cryptography (ECC) obsolete, new paradigms for securing information are imperative—particularly in resource-constrained and widely distributed environments such as the Internet of Things (IoT) 6–8 . Physically Unclonable Functions (PUFs) offer a hardware-centric solution to this challenge, generating non-reproducible responses from intrinsic randomness of microstructures for identity authentication and anti-counterfeiting 9–15 . Compared to conventional electrical PUFs, optical PUFs offer high parallelism, fast readout, and rich encoding capacity, with applications ranging from integrated electronics to intelligent sensing and labeling. However, most reported optical PUFs remain fixed after fabrication, with limited capacity for reconfiguration. The inability to update or renew keys compromises resilience against adaptive attacks and imposes practical limitations in long-term secure deployments. In pursuit of reconfigurability, recent efforts have introduced tunable optical PUFs based on mechanical deformation, thermal reshaping, or phase-change materials. Yet these approaches often suffer from irreversibility, complex setup, or limited reconfiguration cycles, restricting their scalability and real-world applicability. Electrically controllable PUFs, particularly those based on two-dimensional (2D) materials with strong light–matter interactions and gate-tunable properties, represent a promising direction—but practical implementations remain rare. Here, we report an electrically reconfigurable optical PUFs based on PL modulation in spatially disordered MoS 2 microstructures. The device integrates static grayscale contrast with gate-tunable PL intensity and wavelength, forming a “one-static-two-dynamic” multidimensional encoding scheme. Randomness is physically encoded by iteratively assembling exfoliated MoS 2 nanosheets onto a silicon substrate via van der Waals transfer, resulting in a lithography-free, disordered emission landscape. Applying gate voltages from − 40 V to + 40 V modulates the local band structure of MoS 2 , enabling pixel-specific and reversible shifts in PL, as confirmed by first-principles simulations. To characterize the security capacity of such devices, we propose a generalized entropy model that incorporates both static and dynamic optical features. This model not only provides a quantitative framework for evaluating hybrid PUFs but also demonstrates the advantage of electrically reconfigurable systems in expanding encoding capacity without sacrificing stability. In our implementation, 41 gate voltage states yield near-ideal Hamming distance statistics, an authentication error probability below 2 × 10 − 38 , and a massive configuration space from a single device. This work delivers a scalable and low-power optical security platform featuring rewritability, multidimensional encoding, and universal entropy evaluation. It also establishes electrically tunable PL in disordered 2D materials as a powerful mechanism for next-generation quantum-resilient hardware security. Results In the encoding stage (Fig. 1 a), a 532 nm laser excites PL from the MoS 2 microstructure, and spatially resolved PL intensity and peak wavelength data are acquired using a confocal mapping spectrometer. The observed PL heterogeneity arises from nanoscale variations in interlayer coupling, local strain, and thickness—randomly introduced during stochastic flake deposition. These spatial irregularities yield unique PL fingerprints for each device. When a gate voltage is applied, the band structure of MoS 2 is modulated, altering excitonic recombination pathways and inducing pixel-specific, reversible shifts in both PL intensity and wavelength. In contrast, the optical grayscale pattern-captured via bright-field microscopy-remains invariant across all gate biases, since it reflects static morphological contrast determined solely by the spatial distribution of MoS 2 flakes. The co-existence of dynamic PL responses and stable grayscale values forms the foundation of our “one-static-two-dynamic” encoding architecture, enabling robust, multidimensional physical security primitives. The fabrication process (Fig. 1 b) begins with mechanical exfoliation of bulk MoS 2 , followed by sequential dry-transfer of flakes onto a doped Si substrate with a 285 nm thermal SiO 2 layer. Each transfer cycle disrupts and reconstructs the local flake arrangement, progressively amplifying structural randomness. After multiple iterations, a highly disordered MoS 2 network is formed, with no deterministic control over flake placement or orientation-an essential condition for generating high-entropy optical responses. Silver paste electrodes are screen-printed and etched to define a planar back-gate structure. Optical images of the same region across successive transfers reveal increasing coverage and heterogeneity, visually confirming the system’s physically unclonable nature. This modular, mask-free fabrication strategy offers a low-cost and scalable route toward densely integrated PUFs arrays with electrically reconfigurable functionality. The optical PUFs architecture exploits the physical randomness inherent in disordered MoS 2 microstructures as the entropy source for secure key generation. As shown in Fig. 2 a, two nominally similar regions display clearly distinguishable textures under optical microscopy, a direct consequence of the stochastic flake distribution introduced during sequential exfoliation and transfer. To quantify this disorder, a representative 50 × 50 µm 2 region is divided into a 20 × 20 pixel array (Fig. 2 b), and grayscale intensity is extracted by converting RGB image data into scalar luminance values ( Supplementary Note 1 ). The resulting heatmap reveals spatial variations in grayscale levels originating from differences in flake thickness, surface interference effects, and stacking disorder. The corresponding intensity histogram (Fig. 2 c) spans a wide range with no evident periodicity, confirming the suitability of grayscale encoding for entropy-based applications. Although the substrate can theoretically support ~ 25,600 such units within a standard 0.8 × 0.8 cm 2 area, practical yields are limited by exfoliation randomness and transfer efficiency. Nonetheless, the process remains highly scalable, cost-effective, and lithography-free—offering a compelling route to dense PUFs arrays. To assess the security strength of grayscale-based binary keys, NIHD values were computed across 50 independently fabricated PUFs units ( Supplementary Note 2 ). The distribution, centered at µ ≈ 0.50008, aligns closely with the ideal uncorrelated case (see Supplementary Fig. S1 ), indicating strong inter-device uniqueness and cryptographic reliability. Beyond grayscale, PL responses offer additional encoding dimensions. Figure 2 d presents 3D PL maps from 200 pixels, demonstrating substantial spatial variation in both intensity (500–2400 counts) and emission wavelength (680–800 nm). These variations stem from localized strain, interlayer coupling, and band structure modulation—all intrinsic to the disordered stacking process. Statistical analyses of PL intensity and wavelength (Figs. 2 e–f) reveal Gaussian-like distributions, indicative of high entropy. Binary keys derived from PL features also satisfy stringent cryptographic metrics. NIHD distributions (Figs. 2 g–h) show mean values of µ = 0.49945 (intensity) and µ = 0.50236 (wavelength), both closely approximating the theoretical optimum of 0.5. These results confirm that grayscale contrast, PL intensity, and PL wavelength form statistically independent and physically robust encoding modalities—together enabling multidimensional key generation with enhanced capacity and unpredictability. To enable cryptographic reconfiguration without altering the underlying material structure, we exploit the sensitivity of MoS 2 PL to external gating fields. As schematically outlined in Fig. 3 a, PL spectra are collected across a 20 × 20 pixel matrix under 532 nm excitation (18.2 mW), while V g is swept from − 40 V to + 40 V in 2 V steps. For each pixel, PL intensity and peak wavelength are extracted and independently binarized using adaptive thresholds, yielding a new binary key for each voltage configuration. This process defines an electrically driven, reversible challenge–response architecture built atop a static flake layout. The underlying mechanism of electrical tunability is clarified via first-principles calculations.To elucidate the mechanism underlying electrical reconfiguration, we performed density functional theory (DFT) simulations of MoS 2 band structure evolution under an external electric displacement field (D) ( Supplementary Note 3 ). As shown in Fig. 3 b, monolayer MoS 2 undergoes a direct-to-indirect bandgap transition and ultimately a semimetallic phase under increasing displacement field (D), altering its radiative recombination efficiency. This band structure evolution, absent any structural rearrangement, offers a low-power, repeatable means of tuning PL output. Figure 3 c extends the simulation to multilayer systems (1–6 layers), revealing strong layer-dependent sensitivity: monolayers exhibit minor shifts (< 0.01 eV across ± 0.5 V/Å), while thicker flakes display significant nonlinear responses due to interlayer interactions. Supplementary Fig. 2–4 present the corresponding calculation results for bilayer, quadrilayer, and hexalayer MoS 2 , respectively. This physics manifests experimentally in the pixel-wise optical response. As shown in Fig. 3 d–f, six representative pixels display distinct, non-monotonic modulation of both PL intensity (Fig. 3 e) and emission wavelength (Fig. 3 f) under varying V g . These variations originate from local differences in flake thickness, strain, and band bending, producing a richly entropic, yet fully reversible optical landscape. Unlike thermal or mechanical tuning methods, this approach preserves the integrity of the flake structure while enabling rapid and renewable PUFs reconfiguration. To quantify the effectiveness of electrically induced reconfiguration, we performed extensive statistical analyses on the PL intensity-derived binary keys across 41 voltage states. As shown in Fig. 4a , the average bit-wise probability of binary “1” is 0.50 ± 0.0125, closely approximating ideal randomness. This statistical balance ensures maximal entropy for key generation and confirms that electrical gating introduces no systematic bias. The ability to generate decorrelated keys under different voltages is evaluated in Fig. 4b , which presents a similarity heatmap of binary keys across all V g configurations. Pairwise similarity values remain consistently below 7%, indicating that the gate voltage serves as an effective and orthogonal control knob for key reconfiguration. Each voltage step produces a statistically independent identity, supporting scalable deployment of dynamic security primitives. In Fig. 4c , we assess repeatability by measuring the same region under a fixed gate voltage (V g = + 40 V) across 41 sequential trials. The resulting PL intensity-derived keys exhibit > 97.5% similarity, highlighting the robustness of the system against temporal and environmental noise. This low intra-state variability is essential for reliable authentication. Normalized HDs are used to compare keys derived under identical and distinct voltages. As shown in Fig. 4d , intra-V g HDs are narrowly distributed around zero (µ = 0.01537, max < 0.045), while inter-V g HDs are centered near 0.5 (µ = 0.49722), as expected for independent binary strings. The sharp separation between the two distributions demonstrates strong reconfigurability while maintaining readout consistency. Figure 4e provides a zoomed-in view near the crossover point of the intra- and inter-HD curves, from which the optimal decision threshold (HD d = 0.14638) is defined. The FAP and FRP are calculated as 4.87 × 10 − 39 and 1.31 × 10 − 38 , respectively, yielding a total authentication error probability (TAEP) below 2 × 10 − 38 . These near-zero error rates confirm that our PL-based optical PUFs provide not only high entropy and reconfigurability but also strong authentication fidelity. To rigorously evaluate the reconfigurability and capacity of our optical PUFs, we introduce a generalized entropy framework applicable to both static and dynamic PUFs systems. For a PUFs with N statistically orthogonal identities, the selection entropy is defined as log 2 (N), reflecting the logarithmic scaling of the accessible key space. In our implementation, the baseline device supports three encoding dimensions—grayscale (static), PL intensity (dynamic), and PL wavelength (dynamic). Without applying gate modulation (i.e., zero reconstructions), the system already achieves an entropy of log 2 (3) ≈ 1.585, surpassing conventional static optical PUFs that typically rely on a single dimension. Upon electrical reconstruction, two of these dimensions (PL intensity and wavelength) become reconfigurable via gate-induced modulation. Since each reconfiguration adds two new states to the original system, the total number of configurations becomes 2n + 1, yielding a selection entropy of log 2 (2n + 1). As shown in Fig. 4f , for n = 41 gate voltages (− 40 V to + 40 V in 2 V steps), the entropy reaches log 2 (83) ≈ 6.375—substantially exceeding those of other reported PUFs systems. This entropy scaling, however, is conservative. In practice, our system allows for quasi-continuous electrical tuning. Minor variations in gate voltage (e.g., − 39.9 V vs. −40 V) yield distinct and stable PL responses, suggesting the theoretical reconfiguration space is continuous rather than discrete. This expands the potential identity pool far beyond the already high 83-state model. Furthermore, the PUFs array—with a 20 × 20 pixel structure—offers ~ 3 400 usable bits, resulting in a base-level key space of ~ 7.06 × 10 190 , assuming ideal independence across bits. This is orders of magnitude larger than conventional optical PUFs, which typically offer key spaces on the order of 10 20 . In combination, the high base entropy, dynamic electrical tunability, and multidimensional response space enable our MoS 2 -based optical PUFs to serve as physically compact yet cryptographically expansive platforms. The near-infinite instantiation space and reconfiguration fidelity make them exceptionally resilient to cloning and model-based prediction attacks, positioning them as a powerful new class of electrically reprogrammable hardware security primitives. To fully harness the multidimensional encoding capability of the MoS 2 -based PUFs system, we propose a hierarchical authentication framework that integrates both static and reconfigurable optical responses. This architecture balances speed, energy efficiency, and cryptographic robustness by combining grayscale-based rapid screening with dynamically reconfigurable PL verification. In the first authentication tier, grayscale patterns—captured via standard bright-field optical imaging without electrical bias—serve as a low-power, rapidly accessible entropy layer. This enables real-time, non-invasive preliminary checks, ideal for mobile or constrained environments. The grayscale response R A (1, j) of Device A is used to encrypt a gate voltage V G1 , producing a ciphertext M 1 that is shared with Device B. Device B generates its own grayscale R B (1, j) and performs a bitwise XOR with R A (1, j); the result is then verified against the cloud-stored key P(1, j). If the match falls within a preset tolerance, the system proceeds to deeper verification. In the second tier, the system leverages the gate-dependent PL characteristics of MoS 2 to generate high-entropy, device-specific responses. Devices A and B operate under a shared gate voltage derived through the grayscale-mediated key exchange. PL intensity and wavelength data from each device are binarized into R A (2, j, k), R A (3, j, k) and R B (2, j, k), R B (3, j, k), respectively. These responses, governed by nanoscale material nonuniformities and electric field–modulated band structures, are highly sensitive to even minimal variations in physical configuration or voltage mismatch. Final authentication is completed by comparing the XOR outputs of the PL responses with their corresponding public keys P(2, j, k) and P(3, j, k). Thanks to the nonlinear and spatially variant PL behavior under electrical gating, any discrepancy in grayscale responses during the initial tier propagates into large differences in derived V G and downstream PL keys—amplifying the system’s resistance to impersonation, replay attacks, or cloning. By orthogonally combining grayscale (static), PL intensity (dynamic), and PL wavelength (dynamic) modalities, the framework offers scalable and reconfigurable security primitives, capable of supporting distributed authentication across large numbers of devices. Its hybrid nature ensures not only rapid and energy-efficient verification but also ultra-high-fidelity identity discrimination, underpinned by the intrinsic material disorder and electro-optic tunability of MoS 2 . Conclusion In this work, we have demonstrated an electrically reconfigurable optical PUFs platform based on the PL properties of MoS 2 microstructures, offering a high-capacity, low-error solution for hardware-level security. By integrating grayscale features, PL intensity, and PL wavelength as three orthogonal entropy sources, the system achieves a multidimensional encoding strategy with exceptional uniqueness, unpredictability, and robustness. The use of gate-tunable PL responses enables dynamic generation of cryptographic keys without altering the physical structure of the device, significantly expanding the key space through a quasi-continuous spectrum of configurations. Comprehensive experimental characterization, supported by first-principles modeling, reveals that electrostatic gating induces layer- and pixel-specific modulation of PL spectra through field-dependent band structure evolution. This mechanism allows reliable and reversible key reconfiguration, with inter-Hamming distance distributions tightly centered near the theoretical ideal (µ ≈ 0.5) and negligible authentication error probabilities (TAEP < 2 × 10 − 38 ). Moreover, we proposed a dual-tier authentication protocol that capitalizes on fast grayscale screening and secure PL validation, providing a practical route to scalable and energy-efficient device authentication. By combining the inherent material disorder of MoS 2 with its electro-optic tunability, this work establishes a physically grounded, high-entropy platform for next-generation security primitives, with promising applications in secure communication, anti-counterfeiting, and the Internet of Things. The presented strategy paves the way for electrically reconfigurable, optically addressable PUFs with unprecedented flexibility and cryptographic performance. Methods Fabrication of Electrically Reconfigurable Optical PUFs Devices Few-layer MoS 2 nanosheets were prepared via mechanical exfoliation from bulk crystals using adhesive tape. The exfoliated flakes were sequentially transferred onto a heavily doped p-type silicon substrate (resistivity: 0.01–0.02 Ω·cm) using a PDMS-mediated van der Waals assembly method. Through multiple transfer cycles, a hierarchically disordered network of MoS 2 flakes was constructed, enhancing spatial randomness across the device surface. To realize electrical tunability, a bottom-gate architecture was fabricated by integrating a patterned silver nanopaste electrode via screen printing. Standard photolithographic etching steps were used to define the gate structure, enabling precise control of electric field modulation across the MoS₂ domain. This process yielded fully integrated, electrically reconfigurable two-dimensional material-based optical PUFs devices. Optical and Electrical Characterization A Zeiss Lab5 optical microscope was employed to examine the morphological distribution and optical contrast of the MoS 2 flakes, confirming the random and non-reproducible topography across the device. PL mapping was performed over a 50 × 50 µm 2 area using a compact confocal Raman spectrometer (Nanobase XperRam C) with a 532 nm continuous-wave laser as the excitation source. A galvanometric scanner provided high-resolution raster scanning with a spatial step size of 10 nm. To apply gate voltages for PUFs reconfiguration, a Keysight B2912B precision source meter was used to sweep the back-gate voltage from − 40 V to + 40 V in 2 V increments. All measurements were conducted on an air-floated vibration isolation optical platform to minimize mechanical noise and ensure high spectral fidelity during PL acquisition. Declarations Supporting Information Supporting Information Available: Energy band diagram of MoS 2 under different layers and different electric displacement field calculated by first principles, calculation of grayscale value and performances of the PUFs, and some supplementary data. Competing interests The authors declare no competing interests. Acknowledgement This work was supported by National Key Research and Development Program of China (2023YFA1406900); Strategic Priority Research Program (B) of Chinese Academy of Sciences (XDB0580000, GJ0090406); National Natural Science Foundation of China (62222514, 62350073, U2341226, 12227901, U23A6002); Shanghai Science and Technology Committee (23ZR1482000, 22JC1402900); Shanghai Municipal Science and Technology Major Project (2019SHZDZX01). This work was partially carried out at the Soft Matter Nanofab (SMN180827) in ShanghaiTech University. 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Additional Declarations There is NO Competing Interest. Supplementary Files Supplementaryinformation.docx Electrically Reconfigurable Optical PUFs Based on MoS2 Photoluminescence Modulation Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7074604","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":485072888,"identity":"927fdee2-e3b3-4e03-8ffc-c6f75847789a","order_by":0,"name":"Guanhai Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIie3RP4oCMRQG8AwBt3lgGxnRKzyxWlj0INskDGgjIthYSWRhKw8wMMcY2DpD7iCCFusNUgourC9aiWS0XNh8VQL55csfxmJi/mIE10biGzRpbL4ZgydIoo2bjTotTUQSeWyIJLmzfTQ0IfK4pvu+WllArsqNPVDLsj1MdeKObDANkd6+0kQa6ms3QiIWoG14a82yeZDkyhMgIj0xAEKylO6ldD0RqizGzh/ME36qI12hdJUj9jGd+BbuSaO2hfanR0bZEbvJjD6I7rKvPl/XmIVb8sw6+fMLzWJcOrdYDl+KD7s9LgbhFnM7ZZefug5CLfd7ifDqmJiYmP+ZM76MXAZOQJneAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-2745-055X","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Guanhai","middleName":"","lastName":"Li","suffix":""},{"id":485072889,"identity":"dc82c4f1-8eba-4c9a-946d-7089104e97c3","order_by":1,"name":"Xianjie Lin","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Xianjie","middleName":"","lastName":"Lin","suffix":""},{"id":485072890,"identity":"a6f7adc7-0c78-4738-abf8-0f3fa80a88d8","order_by":2,"name":"Xin Li","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"Li","suffix":""},{"id":485072891,"identity":"d6cfb7ec-ad7b-4479-b6d8-2204bd60ec3f","order_by":3,"name":"Xiaofang Wang","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Xiaofang","middleName":"","lastName":"Wang","suffix":""},{"id":485072892,"identity":"8689bea5-1e8c-4b18-9661-c906c6e5dd96","order_by":4,"name":"Jin Chen","email":"","orcid":"https://orcid.org/0000-0003-4183-4629","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Jin","middleName":"","lastName":"Chen","suffix":""},{"id":485072893,"identity":"1d36f45e-fe74-4cf7-a0e7-e8166b5e1a50","order_by":5,"name":"Feilong Yu","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Feilong","middleName":"","lastName":"Yu","suffix":""},{"id":485072894,"identity":"dcc47936-09bb-4f70-bfd4-f452b07224b3","order_by":6,"name":"Juntong Liu","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Juntong","middleName":"","lastName":"Liu","suffix":""},{"id":485072895,"identity":"fd7ae222-774d-4c86-954f-3f483f702a50","order_by":7,"name":"Yuxin Song","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Yuxin","middleName":"","lastName":"Song","suffix":""},{"id":485072896,"identity":"67b07c6e-c8d1-4765-b707-c2c2a7ca906f","order_by":8,"name":"Jiaji Yang","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Jiaji","middleName":"","lastName":"Yang","suffix":""},{"id":485072897,"identity":"053b7a3f-96bc-4389-aa0a-b06b8c470f62","order_by":9,"name":"Junzhe Gu","email":"","orcid":"","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Junzhe","middleName":"","lastName":"Gu","suffix":""},{"id":485072898,"identity":"e65b3dd1-2abf-415f-b0b9-9f18cfa9c0ae","order_by":10,"name":"Xiaoshuang Chen","email":"","orcid":"https://orcid.org/0000-0003-0131-9454","institution":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Xiaoshuang","middleName":"","lastName":"Chen","suffix":""},{"id":485072899,"identity":"4a1cba97-97f2-41f2-81ad-2e1b35dc4129","order_by":11,"name":"Wei Lu","email":"","orcid":"https://orcid.org/0000-0001-9859-8394","institution":"Shanghai Institute of Technical Physics","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Lu","suffix":""}],"badges":[],"createdAt":"2025-07-08 11:55:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7074604/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7074604/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86762361,"identity":"ff1c3028-e370-43ea-b18a-ef4299876780","added_by":"auto","created_at":"2025-07-15 10:32:40","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2140802,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConcept and fabrication of electrically reconfigurable optical PUFs based on disordered MoS\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e microstructures.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Schematic illustration of the multidimensional encoding framework. Optical grayscale contrast serves as a static identifier, remaining invariant under varying gate voltages (V\u003csub\u003eg\u003c/sub\u003e), while the PL intensity and emission wavelength exhibit dynamic, gate-tunable modulation. This hybrid encoding—combining static grayscale with dual dynamic PL features-enables high-entropy key generation for applications in secure authentication, anti-counterfeiting, and encryption. \u003cstrong\u003eb\u003c/strong\u003e, Fabrication workflow of the reconfigurable PUFs. MoS\u003csub\u003e2\u003c/sub\u003e flakes are mechanically exfoliated and transferred layer-by-layer onto a p-doped silicon substrate via PDMS-assisted van der Waals assembly. Iterative transfer cycles induce spatially random stacking, forming a lithography-free, disordered optical landscape. Back-gated control is established by etching and depositing silver nanopaste electrodes, completing a scalable and reconfigurable PUFs device platform.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-7074604/v1/7edb9533b407ee0596111fee.png"},{"id":86762368,"identity":"6ad42988-e18a-44af-bb49-3fa827f03005","added_by":"auto","created_at":"2025-07-15 10:32:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":3314176,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCryptographic analysis of grayscale and PL-based encoding parameters in MoS\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e optical PUFs.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Bright-field optical microscopy images of two representative MoS\u003csub\u003e2\u003c/sub\u003e regions. Subareas marked by circles reveal clear morphological differences, reflecting the intrinsic randomness induced by uncontrolled exfoliation and transfer. \u003cstrong\u003eb\u003c/strong\u003e, Grayscale heatmap extracted from a 50 × 50 μm\u003csup\u003e2\u003c/sup\u003e region segmented into a 20 × 20 pixel matrix, where each pixel spans 2.5 × 2.5 μm\u003csup\u003e2\u003c/sup\u003e. RGB values are converted into scalar grayscale intensity to quantify morphological contrast. \u003cstrong\u003ec\u003c/strong\u003e, Statistical histogram of grayscale intensities across multiple device areas, showing a broad, nonuniform distribution suitable for entropy encoding. \u003cstrong\u003ed\u003c/strong\u003e, Three-dimensional PL mapping of 200 randomly sampled pixels under 532 nm excitation, revealing pronounced spatial heterogeneity in both intensity and peak wavelength. \u003cstrong\u003ee–f\u003c/strong\u003e, Probability distributions of PL intensity (\u003cstrong\u003ee\u003c/strong\u003e) and peak wavelength (\u003cstrong\u003ef\u003c/strong\u003e) at V\u003csub\u003eg\u003c/sub\u003e = 0 V. \u003cstrong\u003eg–h\u003c/strong\u003e, Normalized inter-Hamming distance (NIHD) distributions for binary keys derived from PL intensity (\u003cstrong\u003eg\u003c/strong\u003e) and wavelength (\u003cstrong\u003eh\u003c/strong\u003e), both exhibiting near-ideal Gaussian statistics.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-7074604/v1/9a310e535d00e5d3b1853fc1.png"},{"id":86762375,"identity":"87609939-0713-478b-9ebf-3e84f6959b86","added_by":"auto","created_at":"2025-07-15 10:32:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2613737,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eElectrically driven reconfiguration of PL-based optical PUFs and first-principles modeling of gate-dependent band structures. a\u003c/strong\u003e, Schematic of the reconfiguration process. (i) Gate voltage (V\u003csub\u003eg\u003c/sub\u003e) modulates PL intensity and emission wavelength; (ii) PL data are binarized via adaptive thresholding; (iii) unique cryptographic keys are generated from a single static flake pattern. \u003cstrong\u003eb\u003c/strong\u003e, First-principles simulations of the monolayer MoS\u003csub\u003e2\u003c/sub\u003e band structure under increasing electric displacement fields (D), showing a progression from a direct to indirect bandgap and eventual metallization. \u003cstrong\u003ec\u003c/strong\u003e, Calculated bandgap modulation of MoS\u003csub\u003e2\u003c/sub\u003e as a function of D across layer numbers (monolayer to hexalayer), revealing distinct tunability profiles due to interlayer coupling and quantum confinement. \u003cstrong\u003ed\u003c/strong\u003e, Six representative pixels randomly selected from a 20 × 20 PL mapping array. \u003cstrong\u003ee–f\u003c/strong\u003e, Experimentally measured PL intensity (\u003cstrong\u003ee\u003c/strong\u003e) and emission wavelength (\u003cstrong\u003ef\u003c/strong\u003e) responses for these pixels under gate modulation from −40 V to +40 V with highly localized, reversible, and non-monotonic behavior.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-7074604/v1/6e682d93779aa893e05e010b.png"},{"id":86763664,"identity":"a54c201e-6d9b-4aca-95c5-f4624211559e","added_by":"auto","created_at":"2025-07-15 10:40:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1538487,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStatistical evaluation of reconfigurable PL-based optical PUFs and generalized entropy analysis. a\u003c/strong\u003e, Bit distribution across 41 voltage states (−40 V to +40 V in 2 V steps) for PL intensity-derived binary keys. The probability of “1” occurrence at each bit position demonstrates excellent balance. \u003cstrong\u003eb\u003c/strong\u003e, Heatmap of pairwise similarity between binary keys at different gate voltages, revealing low correlation and high decorrelation efficiency. \u003cstrong\u003ec\u003c/strong\u003e, Repeatability test of PL intensity keys under V\u003csub\u003eg\u003c/sub\u003e = +40 V over 41 consecutive measurements, confirming high intra-state stability. \u003cstrong\u003ed\u003c/strong\u003e, Distributions of normalized Hamming distances (HDs) for intra-V\u003csub\u003eg\u003c/sub\u003e and inter-V\u003csub\u003eg\u003c/sub\u003e states. \u003cstrong\u003ee\u003c/strong\u003e, Zoom-in view of the decision threshold (HD\u003csub\u003ed\u003c/sub\u003e) defined by the intersection of Gaussian fits to intra- and inter-V\u003csub\u003eg\u003c/sub\u003e HD distributions. Shaded areas denote false acceptance (FAP, red) and false rejection (FRP, blue) probabilities. \u003cstrong\u003ef\u003c/strong\u003e. Comparison of selection entropy for PUFs with varying reconfiguration capabilities. Our electrically reconfigurable optical PUFs demonstrate superior entropy scaling due to multidimensional encoding and reversible key renewal.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-7074604/v1/8ab8544910ee74b45839760e.png"},{"id":86763665,"identity":"54ea49c2-4894-478c-b927-6b4c8b02fcae","added_by":"auto","created_at":"2025-07-15 10:40:41","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":592215,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHierarchical device authentication using MoS₂-based electrically reconfigurable optical PUFs. \u003c/strong\u003eThe proposed two-tiered framework leverages a static grayscale layer for rapid pre-authentication, followed by a reconfigurable PL-based verification utilizing both intensity and wavelength responses. ① Device A generates a grayscale value response R\u003csub\u003eA\u003c/sub\u003e (1, j) through challenge. Encrypt the gate voltage value V\u003csub\u003eG1\u003c/sub\u003e using R\u003csub\u003eA\u003c/sub\u003e (1, j) to obtain encrypted information M\u003csub\u003e1\u003c/sub\u003e, and then send the excitation and M\u003csub\u003e1\u003c/sub\u003e to device B. ② Device B generates its own grayscale value response R\u003csub\u003eB\u003c/sub\u003e (1, j) through excitation. ③ \u003cstrong\u003eStage I – Preliminary Verification\u003c/strong\u003e: Compare R\u003csub\u003eA\u003c/sub\u003e (1, j) ⊕ R\u003csub\u003eB\u003c/sub\u003e (1, j) with the public key P (1, j) to roughly determine the legitimacy of device B. ④ \u003cstrong\u003eStage II – Secure PL-Based Authentication\u003c/strong\u003e: Device A obtains the PL intensity response R\u003csub\u003eA\u003c/sub\u003e (2, j, k) and PL wavelength response R\u003csub\u003eA\u003c/sub\u003e (3, j, k) based on the gate voltage value V\u003csub\u003eG1\u003c/sub\u003e. Device B uses R\u003csub\u003eB\u003c/sub\u003e (1, j) ⊕ P (1, j) and M\u003csub\u003e1\u003c/sub\u003e decryption to obtain the gate voltage value V\u003csub\u003eG2\u003c/sub\u003e, which generates the PL intensity response R\u003csub\u003eB\u003c/sub\u003e (2, j, k) and PL wavelength response R\u003csub\u003eB\u003c/sub\u003e (3, j, k). ⑤ Final authentication is achieved by XOR comparisons of R\u003csub\u003eA\u003c/sub\u003e and R\u003csub\u003eB\u003c/sub\u003e PL keys with reference public keys P(2, j, k) and P(3, j, k), confirming device identity.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-7074604/v1/884932d45754c2169dcb4ff2.png"},{"id":89908383,"identity":"53452753-3e88-49ab-8b9f-bef2d56760bf","added_by":"auto","created_at":"2025-08-26 10:25:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9802293,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7074604/v1/d2fd43c8-3cf4-4e46-9a8b-34198de6c63e.pdf"},{"id":86763667,"identity":"6cebf376-f580-4ded-a3f7-8419ee590996","added_by":"auto","created_at":"2025-07-15 10:40:41","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":13462149,"visible":true,"origin":"","legend":"Electrically Reconfigurable Optical PUFs Based on MoS2 Photoluminescence Modulation","description":"","filename":"Supplementaryinformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7074604/v1/2b7f812ec98a3a3184eb5451.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Electrically Reconfigurable Optical PUFs Based on MoS2 Photoluminescence Modulation","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAs the digital economy scales, the demand for robust, future-proof data security has become a global imperative.\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. Traditional cryptographic systems, based on deterministic algorithms and mathematical hardness assumptions, are increasingly vulnerable to advances in quantum computing\u003csup\u003e4,5\u003c/sup\u003e. With Shor\u0026rsquo;s algorithm threatening to render Rivest-Shamir-Adleman (RSA) and Elliptic Curve Cryptography (ECC) obsolete, new paradigms for securing information are imperative\u0026mdash;particularly in resource-constrained and widely distributed environments such as the Internet of Things (IoT)\u003csup\u003e6\u0026ndash;8\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003ePhysically Unclonable Functions (PUFs) offer a hardware-centric solution to this challenge, generating non-reproducible responses from intrinsic randomness of microstructures for identity authentication and anti-counterfeiting\u003csup\u003e9\u0026ndash;15\u003c/sup\u003e. Compared to conventional electrical PUFs, optical PUFs offer high parallelism, fast readout, and rich encoding capacity, with applications ranging from integrated electronics to intelligent sensing and labeling. However, most reported optical PUFs remain fixed after fabrication, with limited capacity for reconfiguration. The inability to update or renew keys compromises resilience against adaptive attacks and imposes practical limitations in long-term secure deployments.\u003c/p\u003e\u003cp\u003eIn pursuit of reconfigurability, recent efforts have introduced tunable optical PUFs based on mechanical deformation, thermal reshaping, or phase-change materials. Yet these approaches often suffer from irreversibility, complex setup, or limited reconfiguration cycles, restricting their scalability and real-world applicability. Electrically controllable PUFs, particularly those based on two-dimensional (2D) materials with strong light\u0026ndash;matter interactions and gate-tunable properties, represent a promising direction\u0026mdash;but practical implementations remain rare.\u003c/p\u003e\u003cp\u003eHere, we report an electrically reconfigurable optical PUFs based on PL modulation in spatially disordered MoS\u003csub\u003e2\u003c/sub\u003e microstructures. The device integrates static grayscale contrast with gate-tunable PL intensity and wavelength, forming a \u0026ldquo;one-static-two-dynamic\u0026rdquo; multidimensional encoding scheme. Randomness is physically encoded by iteratively assembling exfoliated MoS\u003csub\u003e2\u003c/sub\u003e nanosheets onto a silicon substrate via van der Waals transfer, resulting in a lithography-free, disordered emission landscape. Applying gate voltages from \u0026minus;\u0026thinsp;40 V to +\u0026thinsp;40 V modulates the local band structure of MoS\u003csub\u003e2\u003c/sub\u003e, enabling pixel-specific and reversible shifts in PL, as confirmed by first-principles simulations. To characterize the security capacity of such devices, we propose a generalized entropy model that incorporates both static and dynamic optical features. This model not only provides a quantitative framework for evaluating hybrid PUFs but also demonstrates the advantage of electrically reconfigurable systems in expanding encoding capacity without sacrificing stability. In our implementation, 41 gate voltage states yield near-ideal Hamming distance statistics, an authentication error probability below 2 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;38\u003c/sup\u003e, and a massive configuration space from a single device. This work delivers a scalable and low-power optical security platform featuring rewritability, multidimensional encoding, and universal entropy evaluation. It also establishes electrically tunable PL in disordered 2D materials as a powerful mechanism for next-generation quantum-resilient hardware security.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eIn the encoding stage (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea), a 532 nm laser excites PL from the MoS\u003csub\u003e2\u003c/sub\u003e microstructure, and spatially resolved PL intensity and peak wavelength data are acquired using a confocal mapping spectrometer. The observed PL heterogeneity arises from nanoscale variations in interlayer coupling, local strain, and thickness\u0026mdash;randomly introduced during stochastic flake deposition. These spatial irregularities yield unique PL fingerprints for each device. When a gate voltage is applied, the band structure of MoS\u003csub\u003e2\u003c/sub\u003e is modulated, altering excitonic recombination pathways and inducing pixel-specific, reversible shifts in both PL intensity and wavelength. In contrast, the optical grayscale pattern-captured via bright-field microscopy-remains invariant across all gate biases, since it reflects static morphological contrast determined solely by the spatial distribution of MoS\u003csub\u003e2\u003c/sub\u003e flakes. The co-existence of dynamic PL responses and stable grayscale values forms the foundation of our \u0026ldquo;one-static-two-dynamic\u0026rdquo; encoding architecture, enabling robust, multidimensional physical security primitives.\u003c/p\u003e\n\u003cp\u003eThe fabrication process (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb) begins with mechanical exfoliation of bulk MoS\u003csub\u003e2\u003c/sub\u003e, followed by sequential dry-transfer of flakes onto a doped Si substrate with a 285 nm thermal SiO\u003csub\u003e2\u003c/sub\u003e layer. Each transfer cycle disrupts and reconstructs the local flake arrangement, progressively amplifying structural randomness. After multiple iterations, a highly disordered MoS\u003csub\u003e2\u003c/sub\u003e network is formed, with no deterministic control over flake placement or orientation-an essential condition for generating high-entropy optical responses. Silver paste electrodes are screen-printed and etched to define a planar back-gate structure. Optical images of the same region across successive transfers reveal increasing coverage and heterogeneity, visually confirming the system\u0026rsquo;s physically unclonable nature. This modular, mask-free fabrication strategy offers a low-cost and scalable route toward densely integrated PUFs arrays with electrically reconfigurable functionality.\u003c/p\u003e\n\u003cp\u003eThe optical PUFs architecture exploits the physical randomness inherent in disordered MoS\u003csub\u003e2\u003c/sub\u003e microstructures as the entropy source for secure key generation. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea, two nominally similar regions display clearly distinguishable textures under optical microscopy, a direct consequence of the stochastic flake distribution introduced during sequential exfoliation and transfer. To quantify this disorder, a representative 50 \u0026times; 50 \u0026micro;m\u003csup\u003e2\u003c/sup\u003e region is divided into a 20 \u0026times; 20 pixel array (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb), and grayscale intensity is extracted by converting RGB image data into scalar luminance values (\u003cstrong\u003eSupplementary Note 1\u003c/strong\u003e). The resulting heatmap reveals spatial variations in grayscale levels originating from differences in flake thickness, surface interference effects, and stacking disorder. The corresponding intensity histogram (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec) spans a wide range with no evident periodicity, confirming the suitability of grayscale encoding for entropy-based applications.\u003c/p\u003e\n\u003cp\u003eAlthough the substrate can theoretically support\u0026thinsp;~\u0026thinsp;25,600 such units within a standard 0.8 \u0026times; 0.8 cm\u003csup\u003e2\u003c/sup\u003e area, practical yields are limited by exfoliation randomness and transfer efficiency. Nonetheless, the process remains highly scalable, cost-effective, and lithography-free\u0026mdash;offering a compelling route to dense PUFs arrays. To assess the security strength of grayscale-based binary keys, NIHD values were computed across 50 independently fabricated PUFs units (\u003cstrong\u003eSupplementary Note 2\u003c/strong\u003e). The distribution, centered at \u0026micro;\u0026thinsp;\u0026asymp;\u0026thinsp;0.50008, aligns closely with the ideal uncorrelated case (see \u003cstrong\u003eSupplementary Fig. \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/strong\u003e), indicating strong inter-device uniqueness and cryptographic reliability.\u003c/p\u003e\n\u003cp\u003eBeyond grayscale, PL responses offer additional encoding dimensions. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ed presents 3D PL maps from 200 pixels, demonstrating substantial spatial variation in both intensity (500\u0026ndash;2400 counts) and emission wavelength (680\u0026ndash;800 nm). These variations stem from localized strain, interlayer coupling, and band structure modulation\u0026mdash;all intrinsic to the disordered stacking process. Statistical analyses of PL intensity and wavelength (Figs. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee\u0026ndash;f) reveal Gaussian-like distributions, indicative of high entropy.\u003c/p\u003e\n\u003cp\u003eBinary keys derived from PL features also satisfy stringent cryptographic metrics. NIHD distributions (Figs. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eg\u0026ndash;h) show mean values of \u0026micro;\u0026thinsp;=\u0026thinsp;0.49945 (intensity) and \u0026micro;\u0026thinsp;=\u0026thinsp;0.50236 (wavelength), both closely approximating the theoretical optimum of 0.5. These results confirm that grayscale contrast, PL intensity, and PL wavelength form statistically independent and physically robust encoding modalities\u0026mdash;together enabling multidimensional key generation with enhanced capacity and unpredictability.\u003c/p\u003e\n\u003cp\u003eTo enable cryptographic reconfiguration without altering the underlying material structure, we exploit the sensitivity of MoS\u003csub\u003e2\u003c/sub\u003e PL to external gating fields. As schematically outlined in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea, PL spectra are collected across a 20 \u0026times; 20 pixel matrix under 532 nm excitation (18.2 mW), while V\u003csub\u003eg\u003c/sub\u003e is swept from \u0026minus;\u0026thinsp;40 V to +\u0026thinsp;40 V in 2 V steps. For each pixel, PL intensity and peak wavelength are extracted and independently binarized using adaptive thresholds, yielding a new binary key for each voltage configuration. This process defines an electrically driven, reversible challenge\u0026ndash;response architecture built atop a static flake layout.\u003c/p\u003e\n\u003cp\u003eThe underlying mechanism of electrical tunability is clarified via first-principles calculations.To elucidate the mechanism underlying electrical reconfiguration, we performed density functional theory (DFT) simulations of MoS\u003csub\u003e2\u003c/sub\u003e band structure evolution under an external electric displacement field (D) (\u003cstrong\u003eSupplementary Note 3\u003c/strong\u003e). As shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb, monolayer MoS\u003csub\u003e2\u003c/sub\u003e undergoes a direct-to-indirect bandgap transition and ultimately a semimetallic phase under increasing displacement field (D), altering its radiative recombination efficiency. This band structure evolution, absent any structural rearrangement, offers a low-power, repeatable means of tuning PL output. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec extends the simulation to multilayer systems (1\u0026ndash;6 layers), revealing strong layer-dependent sensitivity: monolayers exhibit minor shifts (\u0026lt;\u0026thinsp;0.01 eV across \u0026plusmn;\u0026thinsp;0.5 V/\u0026Aring;), while thicker flakes display significant nonlinear responses due to interlayer interactions. \u003cstrong\u003eSupplementary Fig.\u0026nbsp;2\u0026ndash;4\u003c/strong\u003e present the corresponding calculation results for bilayer, quadrilayer, and hexalayer MoS\u003csub\u003e2\u003c/sub\u003e, respectively.\u003c/p\u003e\n\u003cp\u003eThis physics manifests experimentally in the pixel-wise optical response. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ed\u0026ndash;f, six representative pixels display distinct, non-monotonic modulation of both PL intensity (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ee) and emission wavelength (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ef) under varying V\u003csub\u003eg\u003c/sub\u003e. These variations originate from local differences in flake thickness, strain, and band bending, producing a richly entropic, yet fully reversible optical landscape. Unlike thermal or mechanical tuning methods, this approach preserves the integrity of the flake structure while enabling rapid and renewable PUFs reconfiguration.\u003c/p\u003e\n\u003cp\u003eTo quantify the effectiveness of electrically induced reconfiguration, we performed extensive statistical analyses on the PL intensity-derived binary keys across 41 voltage states. As shown in \u003cstrong\u003eFig.\u0026nbsp;4a\u003c/strong\u003e, the average bit-wise probability of binary \u0026ldquo;1\u0026rdquo; is 0.50\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0125, closely approximating ideal randomness. This statistical balance ensures maximal entropy for key generation and confirms that electrical gating introduces no systematic bias. The ability to generate decorrelated keys under different voltages is evaluated in \u003cstrong\u003eFig.\u0026nbsp;4b\u003c/strong\u003e, which presents a similarity heatmap of binary keys across all V\u003csub\u003eg\u003c/sub\u003e configurations. Pairwise similarity values remain consistently below 7%, indicating that the gate voltage serves as an effective and orthogonal control knob for key reconfiguration. Each voltage step produces a statistically independent identity, supporting scalable deployment of dynamic security primitives.\u003c/p\u003e\n\u003cp\u003eIn \u003cstrong\u003eFig.\u0026nbsp;4c\u003c/strong\u003e, we assess repeatability by measuring the same region under a fixed gate voltage (V\u003csub\u003eg\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;+\u0026thinsp;40 V) across 41 sequential trials. The resulting PL intensity-derived keys exhibit\u0026thinsp;\u0026gt;\u0026thinsp;97.5% similarity, highlighting the robustness of the system against temporal and environmental noise. This low intra-state variability is essential for reliable authentication. Normalized HDs are used to compare keys derived under identical and distinct voltages. As shown in \u003cstrong\u003eFig.\u0026nbsp;4d\u003c/strong\u003e, intra-V\u003csub\u003eg\u003c/sub\u003e HDs are narrowly distributed around zero (\u0026micro;\u0026thinsp;=\u0026thinsp;0.01537, max\u0026thinsp;\u0026lt;\u0026thinsp;0.045), while inter-V\u003csub\u003eg\u003c/sub\u003e HDs are centered near 0.5 (\u0026micro;\u0026thinsp;=\u0026thinsp;0.49722), as expected for independent binary strings. The sharp separation between the two distributions demonstrates strong reconfigurability while maintaining readout consistency.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure\u0026nbsp;4e\u003c/strong\u003e provides a zoomed-in view near the crossover point of the intra- and inter-HD curves, from which the optimal decision threshold (HD\u003csub\u003ed\u003c/sub\u003e = 0.14638) is defined. The FAP and FRP are calculated as 4.87 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;39\u003c/sup\u003e and 1.31 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;38\u003c/sup\u003e, respectively, yielding a total authentication error probability (TAEP) below 2 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;38\u003c/sup\u003e. These near-zero error rates confirm that our PL-based optical PUFs provide not only high entropy and reconfigurability but also strong authentication fidelity.\u003c/p\u003e\n\u003cp\u003eTo rigorously evaluate the reconfigurability and capacity of our optical PUFs, we introduce a generalized entropy framework applicable to both static and dynamic PUFs systems. For a PUFs with N statistically orthogonal identities, the selection entropy is defined as log\u003csub\u003e2\u003c/sub\u003e(N), reflecting the logarithmic scaling of the accessible key space. In our implementation, the baseline device supports three encoding dimensions\u0026mdash;grayscale (static), PL intensity (dynamic), and PL wavelength (dynamic). Without applying gate modulation (i.e., zero reconstructions), the system already achieves an entropy of log\u003csub\u003e2\u003c/sub\u003e(3)\u0026thinsp;\u0026asymp;\u0026thinsp;1.585, surpassing conventional static optical PUFs that typically rely on a single dimension. Upon electrical reconstruction, two of these dimensions (PL intensity and wavelength) become reconfigurable via gate-induced modulation. Since each reconfiguration adds two new states to the original system, the total number of configurations becomes 2n\u0026thinsp;+\u0026thinsp;1, yielding a selection entropy of log\u003csub\u003e2\u003c/sub\u003e(2n\u0026thinsp;+\u0026thinsp;1). As shown in \u003cstrong\u003eFig.\u0026nbsp;4f\u003c/strong\u003e, for n\u0026thinsp;=\u0026thinsp;41 gate voltages (\u0026minus;\u0026thinsp;40 V to +\u0026thinsp;40 V in 2 V steps), the entropy reaches log\u003csub\u003e2\u003c/sub\u003e(83)\u0026thinsp;\u0026asymp;\u0026thinsp;6.375\u0026mdash;substantially exceeding those of other reported PUFs systems.\u003c/p\u003e\n\u003cp\u003eThis entropy scaling, however, is conservative. In practice, our system allows for quasi-continuous electrical tuning. Minor variations in gate voltage (e.g., \u0026minus;\u0026thinsp;39.9 V vs. \u0026minus;40 V) yield distinct and stable PL responses, suggesting the theoretical reconfiguration space is continuous rather than discrete. This expands the potential identity pool far beyond the already high 83-state model. Furthermore, the PUFs array\u0026mdash;with a 20 \u0026times; 20 pixel structure\u0026mdash;offers\u0026thinsp;~\u0026thinsp;3\u003csup\u003e400\u003c/sup\u003e usable bits, resulting in a base-level key space of ~\u0026thinsp;7.06 \u0026times; 10\u003csup\u003e190\u003c/sup\u003e, assuming ideal independence across bits. This is orders of magnitude larger than conventional optical PUFs, which typically offer key spaces on the order of 10\u003csup\u003e20\u003c/sup\u003e. In combination, the high base entropy, dynamic electrical tunability, and multidimensional response space enable our MoS\u003csub\u003e2\u003c/sub\u003e-based optical PUFs to serve as physically compact yet cryptographically expansive platforms. The near-infinite instantiation space and reconfiguration fidelity make them exceptionally resilient to cloning and model-based prediction attacks, positioning them as a powerful new class of electrically reprogrammable hardware security primitives.\u003c/p\u003e\n\u003cp\u003eTo fully harness the multidimensional encoding capability of the MoS\u003csub\u003e2\u003c/sub\u003e-based PUFs system, we propose a hierarchical authentication framework that integrates both static and reconfigurable optical responses. This architecture balances speed, energy efficiency, and cryptographic robustness by combining grayscale-based rapid screening with dynamically reconfigurable PL verification.\u003c/p\u003e\n\u003cp\u003eIn the first authentication tier, grayscale patterns\u0026mdash;captured via standard bright-field optical imaging without electrical bias\u0026mdash;serve as a low-power, rapidly accessible entropy layer. This enables real-time, non-invasive preliminary checks, ideal for mobile or constrained environments. The grayscale response R\u003csub\u003eA\u003c/sub\u003e(1, j) of Device A is used to encrypt a gate voltage V\u003csub\u003eG1\u003c/sub\u003e, producing a ciphertext M\u003csub\u003e1\u003c/sub\u003e that is shared with Device B. Device B generates its own grayscale R\u003csub\u003eB\u003c/sub\u003e(1, j) and performs a bitwise XOR with R\u003csub\u003eA\u003c/sub\u003e(1, j); the result is then verified against the cloud-stored key P(1, j). If the match falls within a preset tolerance, the system proceeds to deeper verification. In the second tier, the system leverages the gate-dependent PL characteristics of MoS\u003csub\u003e2\u003c/sub\u003e to generate high-entropy, device-specific responses. Devices A and B operate under a shared gate voltage derived through the grayscale-mediated key exchange. PL intensity and wavelength data from each device are binarized into R\u003csub\u003eA\u003c/sub\u003e(2, j, k), R\u003csub\u003eA\u003c/sub\u003e(3, j, k) and R\u003csub\u003eB\u003c/sub\u003e(2, j, k), R\u003csub\u003eB\u003c/sub\u003e(3, j, k), respectively. These responses, governed by nanoscale material nonuniformities and electric field\u0026ndash;modulated band structures, are highly sensitive to even minimal variations in physical configuration or voltage mismatch.\u003c/p\u003e\n\u003cp\u003eFinal authentication is completed by comparing the XOR outputs of the PL responses with their corresponding public keys P(2, j, k) and P(3, j, k). Thanks to the nonlinear and spatially variant PL behavior under electrical gating, any discrepancy in grayscale responses during the initial tier propagates into large differences in derived V\u003csub\u003eG\u003c/sub\u003e and downstream PL keys\u0026mdash;amplifying the system\u0026rsquo;s resistance to impersonation, replay attacks, or cloning. By orthogonally combining grayscale (static), PL intensity (dynamic), and PL wavelength (dynamic) modalities, the framework offers scalable and reconfigurable security primitives, capable of supporting distributed authentication across large numbers of devices. Its hybrid nature ensures not only rapid and energy-efficient verification but also ultra-high-fidelity identity discrimination, underpinned by the intrinsic material disorder and electro-optic tunability of MoS\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn this work, we have demonstrated an electrically reconfigurable optical PUFs platform based on the PL properties of MoS\u003csub\u003e2\u003c/sub\u003e microstructures, offering a high-capacity, low-error solution for hardware-level security. By integrating grayscale features, PL intensity, and PL wavelength as three orthogonal entropy sources, the system achieves a multidimensional encoding strategy with exceptional uniqueness, unpredictability, and robustness. The use of gate-tunable PL responses enables dynamic generation of cryptographic keys without altering the physical structure of the device, significantly expanding the key space through a quasi-continuous spectrum of configurations. Comprehensive experimental characterization, supported by first-principles modeling, reveals that electrostatic gating induces layer- and pixel-specific modulation of PL spectra through field-dependent band structure evolution. This mechanism allows reliable and reversible key reconfiguration, with inter-Hamming distance distributions tightly centered near the theoretical ideal (µ ≈ 0.5) and negligible authentication error probabilities (TAEP \u0026lt; 2 × 10\u003csup\u003e− 38\u003c/sup\u003e). Moreover, we proposed a dual-tier authentication protocol that capitalizes on fast grayscale screening and secure PL validation, providing a practical route to scalable and energy-efficient device authentication.\u003c/p\u003e\u003cp\u003eBy combining the inherent material disorder of MoS\u003csub\u003e2\u003c/sub\u003e with its electro-optic tunability, this work establishes a physically grounded, high-entropy platform for next-generation security primitives, with promising applications in secure communication, anti-counterfeiting, and the Internet of Things. The presented strategy paves the way for electrically reconfigurable, optically addressable PUFs with unprecedented flexibility and cryptographic performance.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cb\u003eFabrication of Electrically Reconfigurable Optical PUFs Devices\u003c/b\u003e\u003c/p\u003e\u003cp\u003eFew-layer MoS\u003csub\u003e2\u003c/sub\u003e nanosheets were prepared via mechanical exfoliation from bulk crystals using adhesive tape. The exfoliated flakes were sequentially transferred onto a heavily doped p-type silicon substrate (resistivity: 0.01–0.02 Ω·cm) using a PDMS-mediated van der Waals assembly method. Through multiple transfer cycles, a hierarchically disordered network of MoS\u003csub\u003e2\u003c/sub\u003e flakes was constructed, enhancing spatial randomness across the device surface. To realize electrical tunability, a bottom-gate architecture was fabricated by integrating a patterned silver nanopaste electrode via screen printing. Standard photolithographic etching steps were used to define the gate structure, enabling precise control of electric field modulation across the MoS₂ domain. This process yielded fully integrated, electrically reconfigurable two-dimensional material-based optical PUFs devices.\u003c/p\u003e\u003cp\u003e\u003cb\u003eOptical and Electrical Characterization\u003c/b\u003e\u003c/p\u003e\u003cp\u003eA Zeiss Lab5 optical microscope was employed to examine the morphological distribution and optical contrast of the MoS\u003csub\u003e2\u003c/sub\u003e flakes, confirming the random and non-reproducible topography across the device. PL mapping was performed over a 50 × 50 µm\u003csup\u003e2\u003c/sup\u003e area using a compact confocal Raman spectrometer (Nanobase XperRam C) with a 532 nm continuous-wave laser as the excitation source. A galvanometric scanner provided high-resolution raster scanning with a spatial step size of 10 nm. To apply gate voltages for PUFs reconfiguration, a Keysight B2912B precision source meter was used to sweep the back-gate voltage from − 40 V to + 40 V in 2 V increments. All measurements were conducted on an air-floated vibration isolation optical platform to minimize mechanical noise and ensure high spectral fidelity during PL acquisition.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eSupporting Information\u003c/h2\u003e\u003cp\u003eSupporting Information Available: Energy band diagram of MoS\u003csub\u003e2\u003c/sub\u003e under different layers and different electric displacement field calculated by first principles, calculation of grayscale value and performances of the PUFs, and some supplementary data.\u003c/p\u003e\u003ch2\u003eCompeting interests\u003c/h2\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis work was supported by National Key Research and Development Program of China (2023YFA1406900); Strategic Priority Research Program (B) of Chinese Academy of Sciences (XDB0580000, GJ0090406); National Natural Science Foundation of China (62222514, 62350073, U2341226, 12227901, U23A6002); Shanghai Science and Technology Committee (23ZR1482000, 22JC1402900); Shanghai Municipal Science and Technology Major Project (2019SHZDZX01). This work was partially carried out at the Soft Matter Nanofab (SMN180827) in ShanghaiTech University.\u003c/p\u003e\u003ch2\u003eCode availability\u003c/h2\u003e\u003cp\u003eThe code used for data analysis during this study is available upon reasonable request from the corresponding authors.\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e\u003cp\u003eRelevant data supporting the key findings of this study are available in the article and Supplementary Information file. All raw data generated in this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003ePilarczyk, K., Daly, B., Podborska, A. et al. 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All-optical multilevel physical unclonable functions. \u003cem\u003eNature Materials.\u003c/em\u003e \u003cb\u003e23\u003c/b\u003e, 369\u0026ndash;376 (2024).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":false,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Physically Unclonable Function, Electrically Reconfigurable Photoluminescence, MoS2 Microstructure Disorder, High-Entropy Optical Encoding","lastPublishedDoi":"10.21203/rs.3.rs-7074604/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7074604/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eConventional optical security keys are fundamentally static-offering fixed encoding states and relying on irreversible processes or bulky apparatus-rendering them vulnerable to modeling, duplication, and physical attacks. Here, we present an electrically reconfigurable optical PUFs based on photoluminescence (PL) modulation in structurally disordered MoS\u003csub\u003e2\u003c/sub\u003e microstructures. By leveraging a multidimensional \u0026ldquo;one-static-two-dynamic\u0026rdquo; encoding strategy, our system integrates electrically invariant grayscale patterns with gate-tunable PL intensity and emission wavelength, enabling pixel-specific, high-entropy responses that are both reprogrammable and non-volatile. The devices are fabricated via lithography-free van der Waals stacking, generating intrinsic spatial randomness without compromising scalability. Electrostatic gating induces reversible and layer-sensitive bandstructure modulation-mechanistically validated by first-principles calculations-which governs the observed PL shifts across 41 gate voltages. Binary keys extracted from these states yield near-ideal Hamming distance statistics and an exceptionally low total authentication error probability (\u0026lt;\u0026thinsp;2 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;38\u003c/sup\u003e), with a maximum selection entropy of 6.375-surpassing conventional PUFs benchmarks. We further implement a dual-stage authentication protocol that couples zero-bias grayscale screening with voltage-controlled PL verification. This framework provides a practical, tamper-resilient, and quantum-attack-resistant solution for next-generation hardware security.\u003c/p\u003e","manuscriptTitle":"Electrically Reconfigurable Optical PUFs Based on MoS2 Photoluminescence Modulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-15 10:32:36","doi":"10.21203/rs.3.rs-7074604/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8b4b5f7e-fe5f-440d-9512-6589325ded35","owner":[],"postedDate":"July 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":51490934,"name":"Physical sciences/Materials science/Materials for devices/Electronic devices"},{"id":51490935,"name":"Physical sciences/Nanoscience and technology/Nanoscale devices/Quantum information"}],"tags":[],"updatedAt":"2025-11-11T16:29:02+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-15 10:32:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7074604","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7074604","identity":"rs-7074604","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}