Anticounterfeiting tags based on randomly oriented MoSx clusters enabled by capillary and Marangoni flow

Surface-driven flows, including capillary and Marangoni flows, govern solute transport and deposit formation in evaporating thin films and underpin many printed and flexible electronics applications. In parallel, the proliferation of counterfeit products poses significant health, economic, and security risks, motivating the development of anti-counterfeiting tags that are unclonable, unpredictable, and difficult to reproduce. Chemical and solution-based methods offer large parameter spaces and inherent randomness desirable for high-capacity encoding in physical unclonable functions (PUFs). This work investigates whether capillary and Marangoni flow engineering in a mixed-solvent precursor can reproducibly produce random, micrometer-scale MoOx/MoSx cluster morphologies that serve as unclonable tags. The study fabricates such random cluster networks, reads their 3D topographies via confocal laser microscopy, and converts them into digital keys whose randomness, uniqueness, and reproducibility are quantified through entropy, bit uniformity, Hamming distance analyses, and NIST statistical tests. The aim is to demonstrate a robust, rapid, and accessible pathway to high-entropy anticounterfeiting tags using solution-processable functional materials.

Prior studies elucidate coffee-ring and Marangoni effects in evaporating colloidal droplets that shape deposit morphology, with implications for printed electronics and sensors. Anti-counterfeiting research has increasingly explored chemically generated PUFs, including biomimetic microfingerprints, biological and edible PUFs, chaotic organic crystal phosphorescent patterns, quantum dot fluorescent labels with AI authentication, and self-assembled porous polymers. In 2D materials, MoS2-based optical or transistor PUFs have been reported but often require complex or expensive characterization tools. Recent efforts also target expanding key space and improving authentication protocols. The present work builds on these insights by harnessing mixed-solvent-driven capillary/Marangoni instabilities to create random MoOx/MoSx clusters and by adopting a less complex, faster confocal laser microscopy readout to generate and validate digital keys.

Process flow and materials fabrication: A molybdenum-containing precursor was prepared by dissolving 0.05 M ammonium heptamolybdate ((NH4)6Mo7O24) in 5 mL deionized water, stirred at 3000 rpm for ~10 min, and filtered (25 µm). Si/SiO2 substrates (3 × 3 cm2) were solvent cleaned (DI–acetone–DI) and O2 plasma treated (60 W, 60 sccm, 60 s). For random morphology, the precursor was spin-coated (3000 rpm, 60 s) and baked (hotplate 250 °C, 15 min) to form porous MoOx clusters. A co-solvent, 2-methoxyethanol (2-ME), miscible with water, was added at varied vol% to tune surface tension (σ) and contact angle (θ). Pendant drop and contact angle measurements showed decreasing σ and θ with increasing 2-ME, saturating near 10 vol% for θ ~12–13°. Mixed flows and morphology control: In sessile drops, capillary flow (due to evaporation at the pinned edge) and Marangoni flow (surface tension gradient-driven, intensified by 2-ME gradients and temperature) compete, yielding ring-edge or center-dot deposits in the extremes. Volatile 2-ME evaporates faster than water, generating 2-ME-deficient regions near the contact line; higher-σ water-rich droplets with dissolved Mo-salt can form, move, coalesce, and leave random deposits upon evaporation. Precursors with 40–50 vol% 2-ME produced random, spatially distributed Mo-salt patterns via combined flows. Thermal processing and sulfurization: Thermogravimetric/differential thermal analysis indicated MoOx formation requires ≥350 °C. The spin-coated, baked films were thermally decomposed to MoOx. Subsequently, sulfurization in a vacuum CVD chamber with H2S gas at 1000 °C converted MoOx to MoS2. MoS2 formation was confirmed by Raman mapping (E2g ~383 cm−1, A1g ~408 cm−1) matching the random cluster distribution. Patterning and protection: MoS2 clusters were arranged as a 5 × 4 array of tags (20 total), each 50 × 50 µm2. A transparent PDMS overcoat was spin-coated and cured to prevent duplication via molding while allowing optical readout. Topography acquisition: Confocal laser microscopy (VK-X1050; 661 nm laser diode, 6.0 µW, 100× objective) captured 3D topographies (XYZ) of the cluster tags by layer-by-layer scanning. Typical scanned area was 36 × 27 µm2; the system supports up to ~450 × 450 µm2 with ~100 nm in-plane resolution in <60 s and Z resolution to 5 nm. Note: MoOx (bandgap ~3.2 eV) is transparent at 661 nm, limiting pre-sulfurization profiling; MoS2 permits effective scanning. Digital key extraction: From 20 MoS2 tag topographies, height maps were converted to grayscale images via custom Python (3.10.2) code. Images were denoised with a Non-Local Means (NLM) algorithm, and local peaks were detected using peak_local_max (scikit-image). Peaks were binarized (peaks → 1; others → 0). To standardize size and aid reproducibility, binary images were resized to 28 × 20 pixels via binning. As 0s occurred more frequently, von Neumann debiasing was applied to improve bit uniformity; due to nonuniform output lengths, the first 128 bits were selected as the digital key per tag. Statistical characterization: Tag performance metrics included entropy E = −[p log2 p + (1 − p) log2(1 − p)], where p is the probability of 1s; bit uniformity (mean of bits over key size s); reproducibility via intra-device Hamming distance (HD) across repeated acquisitions; uniqueness via inter-device HD across different tags; encoding capacity assessed by degree of freedom DoF = p(1 − p)/σ2 (σ from inter-device HD SD). False positive/negative rates were estimated from intra/inter HD distributions with an optimized HD threshold. NIST SP 800-22 test suite (subset) was run on the concatenated 2560-bit stream (20 keys × 128 bits) with pass criterion p-value > 0.01 and proportion ≥ 19/20. Computation and analysis were performed in Python/Jupyter for image processing and MATLAB for statistics. Cloud storage concept: Digitized keys (rather than raw images) are proposed for efficient storage and on-demand verification over the internet.

- Random morphology generation: Mixed capillary and Marangoni flows in a water/2-ME precursor produced irregular, micrometer-scale Mo-salt cluster deposits; after baking and sulfurization, random MoS2 clusters formed tags (feature size ~1.25 µm). Raman confirmed MoSx formation (E2g ~383 cm−1, A1g ~408 cm−1). - Rapid, robust readout: Confocal laser microscopy captured 2D/3D topographies rapidly over tens of microns with ~100 nm lateral and 5 nm vertical resolution; PDMS overcoat remained transparent to the 661 nm source, enabling readout while hindering molding-based duplication. - Digital key extraction: From 20 tags, grayscale→denoise (NLM)→peak detection→binarization→binning→von Neumann debiasing yielded 128-bit keys per tag. - Entropy and uniformity: Average entropy across 20 keys was 0.9938 (SD 0.0088), close to the ideal 1. Bit uniformity mean was 0.4992 (SD 0.0461), near the ideal 0.5. - Reproducibility and uniqueness: Intra-device and inter-device HD distributions showed clear separation. A decision threshold HD = 0.189 gave estimated false positive and false negative rates on the order of 1e-12. - Degrees of freedom and capacity: From inter-device HD (mean ~0.5022, SD ~0.0425), DoF ≈ 138.41 independent bits, yielding an effective encoding capacity ~2^138 (~3.459 × 10^41). - NIST tests: On 2560 bits (20 × 128), multiple NIST SP 800-22 tests passed (Frequency p=0.115387; Block frequency p=0.115387; Runs p=0.153763; Longest run p=0.115387; Serial p=0.062821; Approximate entropy p=0.085587; Cumulative sums Forward p=0.115387; Cumulative sums Reverse p=0.085587) with per-test proportions ≥0.95–1, meeting the pass criteria. - Practicality: The approach uses accessible confocal microscopy, providing an alternative to more complex/expensive tools often required in prior MoS2-based PUFs.

The study demonstrates that engineering surface-tension-driven flows in mixed-solvent precursor films can reliably produce random, micrometer-scale cluster morphologies that function as unclonable physical tags. By translating the 3D cluster topography into digital keys, the approach achieves high entropy and near-ideal bit balance, supporting randomness. The intra-/inter-device Hamming distance analysis shows strong reproducibility and uniqueness, enabling a clear authentication threshold with vanishingly small false positive/negative rates, addressing the core need for secure verification in anticounterfeiting. The measured degrees of freedom indicate a large effective key space, even after accounting for correlations, supporting high-capacity encoding. Compared with prior MoS2-based PUF implementations that often rely on complex/nanoscale characterization, the use of rapid confocal laser microscopy offers a more accessible, faster, and large-area readout. Protective PDMS coatings prevent simple molding-based duplication without sacrificing optical readout, enhancing practical security. Additionally, MoS2 provides potential electrical and optical dichroism channels for multi-factor authentication. Together, these results validate the hypothesis that capillary–Marangoni-driven random cluster formation, combined with confocal topography readout and robust debiasing/validation, can deliver practical, secure, and scalable anticounterfeiting tags.

The work presents a solution-process compatible method to fabricate anticounterfeiting tags based on random MoSx cluster morphologies generated by the interplay of capillary and Marangoni flows. Confocal laser microscopy enables fast extraction of 3D topographies, which are converted into high-entropy 128-bit digital keys via denoising, peak detection, binarization, binning, and von Neumann debiasing. The tags exhibit near-ideal entropy and bit uniformity, strong reproducibility and uniqueness with negligible false authentication rates, and a large effective key space (DoF ~138). A transparent PDMS overcoat impedes cloning by molding while permitting readout. The findings highlight an accessible route to robust, unclonable tags using functional materials and simple processing. Future work could expand the number of tags and challenges, explore multispectral or electrical readout for multi-factor authentication, optimize solvent/thermal parameters to tune morphology and key statistics, and investigate alternative wavelengths for MoOx profiling and field-deployable readout systems.

- Optical readout constraint for MoOx: MoOx (bandgap ~3.2 eV) is transparent at the 661 nm confocal wavelength, preventing direct topography measurement prior to sulfurization; alternative wavelengths or modalities are needed for MoOx-only tags. - Key length normalization: Von Neumann debiasing produced nonuniform output lengths, necessitating truncation to the first 128 bits per key, which may discard some entropy. - Sample size: Statistical evaluations (including NIST) used 20 tags (2560 bits total), which, while indicative, is a modest dataset; larger cohorts would strengthen statistical confidence and generalizability. - Process complexity/environment: Sulfurization via H2S CVD at 1000 °C adds fabrication complexity and safety considerations; assessing lower-temperature conversions or alternative chalcogenization may improve practicality. - Readout infrastructure: Although more accessible than some nanoscale tools, confocal laser microscopes are still specialized instruments; development of compact, field-deployable readers would facilitate broader adoption.