Multi-scale self-powered authenticated electromechanical transducer with stochastic-defect physically unclonable function

Abstract

A flexible electromechanical transducer comprising: (a) a deformable substrate 10 comprising a polymer material and including at least one strain modifying structural feature configured to generate,

Description

Technical Field

[0001] The present invention relates to flexible electromechanical transducers for sensing, energy harvesting, and hardware security. More particularly, the invention concerns a multi-scale, conformal device that integrates a strain-optimised polymer substrate, piezoelectric and flexoelectric transduction elements, and a physically unclonable function (PUF) element based on stochastic defect-mediated electrical variability in any electrically insulating film, whether layered, quasi-layered, poly crystalline, amorphous, nanocry stalline, mixed-phase or composite. A single coupled multi-physics finite-element simulation simultaneously optimises the positions of all functional elements. The device harvests ambient mechanical energy, senses deformation with microstrain sensitivity, and generates a unique cryptographic identifier within a single flexible patch, enabling self-powered, authenticated, tamper-evident operation for loT, wearable electronics, structural health monitoring, robotics and anti-counterfeiting applications. Background to the Invention

[0002] Flexible transducers for the Internet of Things (loT), wearable electronics and anti-counterfeiting must simultaneously deliver: (i) microstrain sensitivity across a broad dynamic range; (ii) mechanical compliance and conformality; (iii) ultra-low or zero external power consumption; and (iv) intrinsic hardware authentication to prevent cloning or tampering.

[0003] Two distinct lines of prior art exist, but each addresses these requirements only in isolation: (1) Strain-concentrating piezoelectric or flexoelectric transducers optimised solely for mechanical-to-electrical energy conversion and sensing. These devices achieve good power output or sensitivity but are not known to incorporate built-in cryptographic security and substantially require external power or batteries for operation and data transmission. (2) Physically unclonable functions (PUFs) based on defect topology in specific layered insulators, such as hexagonal boron nitride or fluorographene. These provide strong authentication but are not known to provide sensing or energy-harvesting capability, substantially require external power for readout, and are limited to a narrow class of van der Waals materials.

[0004] No prior art provides a single, flexible, self-powered, multi-functional device that combines high-efficiency energy harvesting, high-sensitivity deformation sensing and intrinsic, strain-tunable, tamper-evident authentication in one conformal patch manufactured by low-cost roll-to-roll processing. The present invention addresses these unmet needs.

[0005] Recent work on combined piezoelectric and flexoelectric transducers (for example quadrant-electroded nanogenerators based on one-dimensional ZnO nanostructures) has focused on material-level enhancement of individual transduction mechanisms. The present invention is distinguished by operating at the substrate geometry level: the strain-optimised polymer substrate is specifically engineered to create the spatially non-uniform strain and strain-gradient fields required to activate both piezoelectric and flexoelectric mechanisms simultaneously at a multi-scale level, an approach not contemplated in material-level prior art.

[0006] Prior art PUF devices based on random telegraph signal noise and charge trapping in ALD-grown insulators such as AI2O3 and HfCF (which are known entropy sources in semiconductor contexts) operate as purely electronic, static fingerprints requiring separate electrical excitation. Whilst the defect-trapping physics of these materials is known, their use as strain-modulated PUF elements in a mechanically coupled flexible transducer is novel: prior art exploits these materials in rigid, static configurations where no mechanical coupling exists between the substrate strain state and the defect activation probability. The present invention is further distinguished from structural-randomness PUFs (for example capacitive identity sensors based on random mass distribution, as described in WO2012033837) by the use of defect-mediated quantum tunnelling variability as the entropy source, which is a fundamentally different physical mechanism from geometric mass randomness and provides a PUF response that is intrinsically coupled to the mechanical state of the device. Similarly, prior art on pre-stressed substrates for piezoelectric enhancement (for example US8810113) focuses solely on maximising piezoelectric gain and does not contemplate the joint optimisation of flexoelectric utility and PUF entropy that is central to the present invention.

[0007] Prior PUF devices are further characterised by the following limitations: (i) they are typically static, producing a fixed response independent of applied mechanical state; (ii) they require separate electrical excitation signals to present challenges, adding circuit complexity and power consumption; and (iii) they rely on stored digital states, such as SRAM metastability, flash threshold variation or ring oscillator frequency mismatch, rather than on continuous analogue physical variability. The present invention addresses all three limitations simultaneously. Summary of the Invention

[0008] According to a first aspect of the present invention there is provided a multi-scale self-powered authenticated electromechanical transducer as set out in claim 1.

[0009] According to a second aspect there is provided a method of manufacturing such a transducer as set out in claim 20.

[0010] According to a third aspect there is provided a self-powered authenticated wireless sensor system as set out in claim 21.

[0011] According to a fourth aspect there is provided a sensor array as set out in claim 22.

[0012] According to a fifth aspect there is provided a method of simultaneously sensing mechanical deformation, harvesting energy and authenticating a device as set out in claim 23.

[0013] All embodiments of the invention share the strain-mediated dual-use of the mechanical field (simultaneously as an energy source and as a physical challenge input to the PUF) as the unifying inventive concept. It is this dual-use that eliminates both the need for external power and the need for separate challenge-input circuitry, and that cannot be achieved by independent optimisation of the respective physical domains.

[0014] A particularly powerful consequence of the mechanical integration of the PUF element with the substrate is physical tamper-evidence. Any attempt to delaminate, peel or otherwise separate the device from its host structure subjects the PUF insulator layer to strain amplitudes well outside the calibrated operating envelope. This causes either irreversible dielectric breakdown of the insulator or a permanent shift in the defect conduction topology. Neither outcome can be reversed or reset; the PUF fingerprint is permanently destroyed. Because the PUF is physically bound to the device substrate rather than attached as a separate component, this tamper-evidence cannot be bypassed by removing the PUF alone. This intrinsic, mechanically-enforced tamper-evidence is not achievable by a digital PUF, a separately attached PUF, or any prior art device in which the authentication element is mechanically decoupled from the substrate strain field.

[0015] The inventive step resides in the recognition that coupling these three previously separate disciplines produces unexpected technical effects not predictable from the prior art taken individually or in combination. A skilled person combining a known flexible energy harvester with a known static PUF would not be motivated to mechanically couple the PUF to the substrate strain field, because prior PUF art teaches that the PUF fingerprint should be independent of mechanical state. The present invention inverts this teaching: mechanical state is deliberately exploited as both the power source and the authentication challenge, producing strain-tunable multi-challenge security, tamper-evidence via mechanical overstress, and a synergistic power increase of at least 40% that cannot be predicted by linear superposition of the individual components. These effects are unexpected consequences of the coupling, not predictable outcomes of routine combination.

[0016] The technical effect of the coupled optimisation is to produce a device in which: (a) mechanical strain acts as a physical challenge input to the PUF element; and (b) the same strain field simultaneously maximises energy harvesting efficiency; thereby eliminating the need for separate challenge-input circuitry and external power sources. In contrast to conventional PUF systems requiring external excitation signals, the present invention utilises the mechanically-induced strain field both as an energy source and as a physical challenge input, avoiding the mere juxtaposition of independent components and instead producing a device whose combined performance is greater than the sum of its parts. This power increase relative to independent optimisation is a reproducible consequence of the multi-physics coupling and has been confirmed across a range of substrate geometries and material combinations in representative embodiments. The invention further recognises that the strain field used for energy harvesting can be repurposed as a dynamic input to the PUF element, eliminating the need for separate challenge-input mechanisms while providing inherent tamper-evidence through mechanical stress coupling. The coupled multi-physics simulation produces technical effects in the manufactured device, specifically element positions that exploit non-linear interactions between the strain field and defect activation, which is not obtainable by linear superposition or independent optimisation of the respective physical domains, and is not practically achievable by routine iterative physical prototyping. The resulting element positions deviate by at least 2% of the characteristic length dimension of the substrate from positions that would be predicted for equivalent elements by geometric inspection or single-physics mechanical analysis of the substrate alone, as demonstrated in Table 1. In preferred embodiments the deviation is at least 5% of the characteristic length dimension; in particularly preferred embodiments it is at least 10%. A deviation of at least 2% is sufficient to demonstrate the multi-physics coupling effect, while larger deviations provide greater synergistic benefit. This deviation is not an arbitrary design choice but is indicative of the multi-physics coupling; it is this coupling that produces both the synergistic power increase and the strain-tunable PUF behaviour, and serves as measurable evidence of the core technical feature of the invention. The characteristic length dimension (L) is defined as the length of the longest edge of the substrate for rectangular geometries, the diameter for circular geometries, or more generally the longest dimension of the substrate measured along a principal axis. For the worked example in Table 1, the substrate is 150 mm x 150 mm, giving L = 150 mm.

[0017] In certain embodiments a key structural feature of the invention is that the positions of all functional elements deviate by at least 2% of the characteristic length dimension of the substrate from positions predictable by single-physics analysis alone. This positional deviation is not a design choice but a measurable structural consequence of the multi-physics coupling, and it is this deviation that distinguishes the invention from a mere juxtaposition of known components on a common substrate.

[0018] The joint simulation maximises the objective function Qo + X-H(PUF), where Qo is total harvested power, X is a selectable weighting factor and H(PUF) is the Shannon entropy of the binary PUF response vector, which is maximised when each response bit is equally likely to be 0 or 1, corresponding to an inter-device Hamming distance centred at 0.5. A formal joint optimisation loop treating power output and cryptographic entropy as coupled objectives in a single multi-physics geometric solver is not known in the prior art; optimisation of Q and H separately is known, but the recognition that the same strain field simultaneously determines both, and that joint optimisation produces a configuration superior to either separately optimised configuration, constitutes the core inventive step. This objective function embodies the core inventive concept: the coupling between mechanical power output and cryptographic entropy in a single optimisation, such that improving one does not come at the expense of the other. The resulting configuration produces three emergent technical effects not predictable from the prior art lines taken separately: (1) strain-tunable multi-challenge authentication, wherein different strain levels or directions produce distinct PUF responses; (2) tamper-evidence via irreversible dielectric breakdown under excessive stress; and (3) fully self-powered operation, in which harvested energy powers both sensing and PUF readout.

[0019] The resulting device is greater than the sum of its parts. In representative embodiments, simulation and experimental results demonstrate that the piezoelectric and flexoelectric elements generate at least 40% more power than equivalent separate devices on identical substrates under identical loading conditions. Table 1 shows representative simulation-optimised element positions compared with positions predicted by geometric inspection alone, demonstrating that the deviation from single-physics predictions is characteristic of such embodiments.

[0020] Table 1: Representative element positions for a 150 mm x 150 mm substrate with characteristic length L = 150 mm (longest edge). Deviation (mm) = Euclidean distance between predicted and optimised positions. Deviation (%) = Euclidean distance divided by L x 100. Geometric prediction = centroid of maximum principal strain or strain-gradient region from uncoupled linear elastic analysis. Element Geometric Prediction (mm) Simulation-Optimised (mm) Deviation (mm) Deviation (% ofL) PE-1 (50.0, 50.0) (57.5, 46.5) 8.3 5.5% FE-1 (75.0, 75.0) (86.0, 70.0) 12.1 8.1% PUF electrode pair 1 (100.0, 100.0) (93.5, 107.5) 9.9 6.6% PUF electrode pair 2 (110.0, 100.0) (118.5,95.0) 9.9 6.6%

[0021] The PUF element is mechanically coupled to the substrate such that the applied strain field constitutes a physical challenge to the PUF. Different strain states, arising from different loading directions, magnitudes or spatial distributions, activate different subsets of stochastic defects and thereby produce distinct PUF response vectors. This strain-programmed challenge-response behaviour is an emergent consequence of the multi-physics coupling and cannot be achieved by a conventional static PUF or a digital PUF based on stored data.

[0022] The PUF response arises entirely from analogue physical variability (specifically the spatial distribution of defect-mediated conduction pathways) rather than from stored digital states. This distinguishes the invention from SRAM-PUF, flash-PUF and ring oscillator PUF implementations, and makes the PUF inherently unclonable by digital means. Technical Effects and Advantages

[0023] The invention delivers the following synergistic benefits: (1) Self-powered operation: at least 5.9 pW / cm2 harvested from ambient vibrations or applied strain in measured and simulated representative embodiments, sufficient for autonomous wireless transmission. (2) Generalised PUF materials: any electrically insulating film exhibiting spatially heterogeneous defect distributions, producing a reproducible device-specific response from analogue physical variability rather than stored digital data. (3) Intrinsic authentication: the stochastic defect-mediated fingerprint is appended to every transmitted data packet without additional power consumption. (4) Strain-tunable multi-challenge security: the strain field dynamically alters the PUF response, providing dynamic challenge-response authentication resistant to replay attacks. For example, a first strain level of 0.1% uniaxial tension produces a first PUF response vector, whilst a second strain level of 0.5% uniaxial tension activates a different subset of stochastic defects, producing a second, distinct response vector. The applied strain thus constitutes the authentication challenge. (5) Tamper-evidence: irreversible dielectric breakdown under attempted physical attack. (6) Manufacturing-induced entropy from grain boundaries, variable fluorination / oxidation, vacancy clustering, thickness fluctuations and mixed-phase domains. (7) Low-cost, scalable roll-to-roll fabrication with single-step metallisation. (8) Optically transparent: greater than 80% transmittance at 550 nm; fully flexible and conformal. (9) In-situ self-diagnosis by comparing measured electromechanical response against the simulation-predicted response. (10) Stability: intra-device Hamming distance less than 0.05 across -40°C to +85°C and under repeated strain cycling. Table 2 shows measured intra-device Hamming distances of 0.02-0.04 across 1000 measurement cycles at three temperatures, with maximum observed value 0.048. (11) Broad transduction material compatibility: piezoelectric and flexoelectric elements may comprise bulk, thin-film, nanostructured or composite electromechanical materials including TMDs, ZnO, PVDF and AIN. (12) Broad strain-architecture compatibility: any geometry producing spatially non-uniform strain or strain-gradient fields under load. (13) Extended application scope including medical disposables, smart packaging, supply-chain authentication, secure access tokens and multi-node loT mesh networks.

[0024] Table 2: Measured intra-device Hamming distances across 1000 measurement cycles at three temperatures under repeated strain cycling. Temperature Mean HD (1000 cycles) Max HD Observed Compliant (<0.05) -40°C 0.021 0.038 Yes +25°C 0.018 0.034 Yes +85°C 0.024 0.048 Yes Detailed Description of Preferred Embodiments

[0025] Preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0026] Figure 1 is a plan view of the flexible polymer substrate (10) showing the simulation-optimised positions of all functional elements. Four V-shaped strain-concentrating notches (12) are formed at the mid-points of each edge of the substrate. Piezoelectric transduction elements PE-1 to PE-4 (20), shown as solid-outline rectangles, are located adjacent to each notch in regions of enhanced uniform strain. Flexoelectric transduction elements FE-1 to FE-4 (22), shown as dashed-outline rectangles, are located at the four quadrant positions in regions of enhanced strain gradient, displaced from the substrate centre towards each quadrant. The physically unclonable function (PUF) element (30), shown as a double-outline rectangle, is located at the centre of the substrate. A row of electrode pairs (32) is shown within the PUF element. Uniform strain contours and strain-gradient contours are shown by short-dashed and dotted lines respectively.

[0027] Figure 2 is a flowchart illustrating the joint multi-physics optimisation loop used to determine the positions of all functional elements. The process begins at START (50), proceeds through input of substrate geometry and material parameters (52), initialisation of element positions (54), solution of the coupled finite-element model (56), evaluation of the objective function (58), and a convergence decision (60). If convergence has not been achieved, element positions are updated and the loop returns to block 54. When convergence is achieved, the optimised coordinates for all elements are output (62) and the process ends at END (64).

[0028] Figure 3 is a cross-sectional view of the integrated element stack (not to scale; layer thicknesses are exaggerated for clarity). The flexible polymer substrate (10) forms the base of the stack. The piezoelectric transduction element (20) and the flexoelectric transduction element (22) are deposited in laterally separated regions of the substrate (10) at the simulation-optimised positions. In Figure 3, the cross-section plane is chosen to intersect both of these laterally separated regions sequentially along the length of the substrate, so that each region appears as a distinct lateral zone within the cross-sectional view. The PUF insulator layer (30) is deposited above the transduction elements, with electrode pairs (32) formed within its upper surface. An ALD encapsulation layer (72) and metallisation layer (74) complete the stack.

[0029] Figure 4 shows inter-device Hamming distance distributions measured at -40°C (solid fine), +25°C (long-dash fine) and +85°C (short-dash fine), indicated generally at 80, together with the intra-device Hamming distance distribution (82) shown as a long-short-dash fine. A vertical dashed reference fine marks the HD = 0.05 stability threshold.

[0030] Figure 5 is a block diagram of the complete self-powered authenticated wireless sensor node. The dashed rectangle represents the ASIC boundary enclosing all signal processing and energy management sub-blocks. Inputs from the piezoelectric element (20), flexoelectric element (22) and PUF element (30 / 32) enter the ASIC from above. The wireless transmitter (108) sits outside the ASIC boundary to the right.

[0031] Figure 6 is a plan view of the robotic tactile sensor array embodiment. A plurality of transducer locations are arranged in a two-dimensional grid on a flexible polymer substrate (10). At each location, three piezoelectric element orientation indicators (40) are shown as Une segments oriented at 0°, 60° and 120° to the horizontal, representing three piezoelectric elements with differing crystallographic orientations or a single element with three sensing orientations. A flexoelectric element (22) is shown as a dashed square, and a PUF element (30) is shown as a double rectangle. The orientation indicators are annotated for one representative location, indicated by a circle, for clarity. The 60° angular separation between adjacent piezoelectric orientations is the minimum separation required to resolve the complete in-plane strain tensor (comprising two principal strains and one shear strain component) from three independent electrical outputs; this follows directly from the two-dimensional tensor transformation laws. 1. Substrate Architecture

[0032] The base substrate is a flexible polymer film selected from polyimide, polyethylene naphthalate (PEN), polyethylene terephthalate (PET), thermoplastic polyurethane (TPU) or polydimethylsiloxane (PDMS), having a thickness in the range 25-500 pm. In embodiments intended for wearable, robotic or conformal sensing applications, the substrate may be planar, curved, conformal or three-dimensionally shaped; in stretchable embodiments the substrate may comprise a stretchable elastomeric film such as PDMS or TPU configured to accommodate repeated large-strain deformation without delamination. Textile substrates incorporating conductive yarns or embedded functional layers are also contemplated. In embodiments intended for medical disposable or environmentally sensitive applications, the substrate may additionally comprise biodegradable or bio-derived polymer films, including polylactic acid (PLA) or cellulose-based films, provided they exhibit sufficient mechanical compliance and strain transmission to the functional layers. As used herein, a strain-modifying structural feature is any feature of the substrate geometry that produces a spatially non-uniform strain or strain-gradient field under mechanical load; this definition includes, but is not limited to, the enumerated examples. Strain-modifying structural features comprising any such geometry, including one or more of tapered profiles, notches, kirigami cuts or micro-cavity arrays, are formed in the substrate to create spatially distinct regions of enhanced uniform strain for piezoelectric elements and enhanced strain gradient for flexoelectric elements. These features are designed such that the resulting strain and strain-gradient fields are coupled and cannot be decoupled by geometric inspection alone.

[0033] Referring to Figure 1, the flexible polymer substrate is indicated generally at 10. Four V-shaped strain-concentrating notches 12 are formed at the mid-point of each edge of the substrate 10, one notch at each of the left, right, upper and lower edges. Each notch 12 has a depth of approximately 5 mm and a mouth half-width of approximately 9 mm. The notches 12 locally amplify the strain field and create spatially distinct regions of enhanced uniform strain adjacent to each notch and regions of enhanced strain gradient between the notches, including in the four quadrant regions between adjacent notches. Uniform strain contours and strain-gradient contours are shown by short-dashed and dotted fines respectively. 2. Coupled Multi-Physics Simulation

[0034] A single finite-element model simultaneously solves the fully coupled equations for the mechanical strain tensor; the strain-gradient tensor; piezoelectric polarisation and charge; flexoelectric polarisation and charge; and local PUF electrical behaviour, including leakage, tunnelling probability, ionic migration and Weibull breakdown statistics, for every electrode pair.

[0035] An optimisation loop maximises total harvested power Qo plus a weighted cryptographic entropy term X-H(PUF). The coupled simulation captures non-linear interactions between the strain field and defect activation that are not obtainable by linear superposition or independent optimisation of the respective physical domains, thereby enabling the manufacture of devices with synergistic energy harvesting and authentication performance that is not practically achievable by routine iterative physical prototyping. The physical layout produced by this optimisation cannot be reproduced by standard design rules, geometric centroiding, lookup tables or any rule-of-thumb approach based on single-physics analysis: it is a direct material consequence of the multi-physics coupling embodied in the manufactured device as a measurable positional deviation, and it is this physical consequence that constitutes the technical effect of the algorithm and distinguishes the invention from a computer-implemented mathematical method operating on abstract data alone. Such simulations may be performed using commercially available finite-element analysis software, for example COMSOL Multiphysics or ANSYS, with appropriate coupled physics modules for structural mechanics, piezoelectricity and electrical conduction. Typical simulation parameters include a mesh density of 5-20 elements per minimum feature dimension, a convergence criterion of less than 0.1% change in objective function between successive iterations, and a weighting factor X in the range 0.1 to 10 depending on the relative importance of power output versus cryptographic entropy. Material models for the piezoelectric and flexoelectric layers are taken from published values for the relevant TMD or other electromechanical material. The optimised coordinates of all electrodes and functional layers deviate by at least 2% of the characteristic length dimension of the substrate from positions that would be predicted for equivalent elements by geometric analysis or single-physics simulation of the substrate alone, as demonstrated in Table 1 above (where all entries show deviations of 5.5% or greater in this representative embodiment, with L = 150 mm taken as the longest edge of the 150 mm x 150 mm substrate). This deviation is not an arbitrary design choice but a structural consequence of the multi-physics coupling; it is this coupling that produces both the synergistic 40% power increase and the strain-tunable PUF behaviour.

[0036] In embodiments where exact coupled optimisation is not performed, positioning piezoelectric elements adjacent to regions of highest single-physics strain concentration and flexoelectric elements adjacent to regions of highest single-physics strain-gradient concentration, with the PUF element at the substrate centre, still provides the benefit of self-powered authenticated operation, though with reduced synergistic power output relative to fully coupled optimised configurations.

[0037] In the worked example corresponding to Table 1, the substrate is a polyimide sheet of 150 mm x 150 mm x 50 pm with four V-notches as described in Section 1. Boundary conditions applied to the finite-element model are: fixed displacement (clamped) at one edge; uniform in-plane tensile load of 1 N applied at the opposing edge; zero displacement normal to the substrate plane on all remaining edges; and zero electrical potential on the substrate surface. Material parameters for the M0S2 piezoelectric layer are taken from published density functional theory values (piezoelectric coefficient en = 3.73 x 10 10 C-m1, elastic modulus 270 GPa). For the HfO2 PUF layer, the Weibull breakdown statistics use a characteristic breakdown field of 10 MV-cm1 and a Weibull modulus of 2.5, consistent with published ALD-grown HfO2 data. The objective function weighting factor X is set to 1.0 for this example, giving equal weight to harvested power and PUF entropy. These parameters are sufficient for a person skilled in finite-element analysis and materials characterisation to reproduce the element positions in Table 1 without undue burden; other substrate geometries and material systems may use analogous published parameters.

[0038] Referring to Figure 2, the joint multi-physics optimisation procedure commences at block 50. At block 52, the substrate geometry, material parameters and weighting factor X are supplied. At block 54, initial positions are assigned to all elements 20, 22 and 30. At block 56, the coupled finite-element model is solved. At block 58, the objective function Qo + k-H(PUF) is evaluated. At block 60, a convergence criterion is applied; if not met, positions are updated and the loop returns to block 54. At block 62, optimised coordinates are output. The procedure ends at block 64. 3. Piezoelectric and Flexoelectric Transduction Elements

[0039] Piezoelectric elements are positioned in regions of high uniform strain and may comprise any mechanism or material that converts mechanical deformation into electrical charge, voltage, impedance or capacitance variation, including: transition-metal dichalcogenides (TMDs) such as M0S2, WSc? or alloys thereof; ZnO nanowires; PVDF films; AIN sputtered layers; triboelectric generators based on contact electrification; piezoresistive materials exhibiting strain-dependent resistance; capacitive strain sensors based on deformation-induced capacitance change; and magnetostrictive materials exhibiting strain-dependent magnetic permeability. In the preferred embodiment, the piezoelectric elements comprise monolayer or few-layer TMDs having a thickness in the range 0.6-7 nm, with low-resistance graphene edge contacts providing a contact resistance below 200 Q-pm.

[0040] Flexoelectric elements are positioned in regions of high strain gradient, specifically in the quadrant regions between adjacent strain-concentrating notches where the strain-gradient field is maximised by the coupled multi-physics simulation, and may comprise any material exhibiting flexoelectric coupling, including monolayers of WS2, GeS or SnSe, optionally augmented by integrated micro-scale strain-gradient concentrators that amplify local gradients by at least five times.

[0041] The synergistic placement yields a total electrical power output at least 40% greater than the sum of outputs from equivalent piezoelectric-only and flexoelectric-only devices fabricated on separate identical substrates under identical loading conditions. In representative embodiments: piezo-only output = 3.2 pW / cm2; flexo-only output = 0.9 pW / cm2; combined output = 5.9 pW / cm2, which is approximately 44% greater than the sum (4.1 pW / cm2). 4. Generalised Stochastic-Defect PUF Element

[0042] The PUF element comprises any electrically insulating material capable of exhibiting reproducible stochastic defect-mediated conduction variability under sub-breakdown electrical interrogation. Whilst materials such as AI2O3 and HfO2 are known in semiconductor contexts as charge-trapping layers exhibiting random telegraph signal noise, their use in the present invention as strain-modulated PUF elements in a mechanically coupled flexible transducer is novel: prior art exploits these materials in rigid, static configurations without any mechanical coupling between substrate strain state and defect activation probability. Stochastic defect-mediated electrical variability refers to spatially distributed conduction pathways arising from statistically distributed defects, including grain boundaries, vacancies, trap states, ionic migration pathways and mixed-phase domain boundaries, whose spatial distribution is fixed at manufacture but varies between devices. The response arises from analogue physical variability rather than stored digital data. This distinguishes the invention from SRAM-PUF, flash-PUF and ring oscillator PUF implementations.

[0043] For the purposes of this specification, an electrically insulating material is considered suitable for use as the PUF element if, under fixed electrical and mechanical conditions, repeated readout yields a stable binary response with an intra-device Hamming distance of less than 0.05 over the temperature range -40°C to +85°C and under repeated strain cycling. This functional constraint defines the boundary of the claim scope for the broad material class recited in claims 1 to 3 and excludes materials whose response is insufficiently stable or reproducible for authentication purposes. Intra-device Hamming distance under temperature cycling and repeated strain is a standard PUF characterisation parameter measured by the methods described in, for example, Maiti and Schaumont, IEEE Transactions on Information Forensics and Security, 2012, and the measurement protocol is well known to persons skilled in the hardware security art, such that the constraint is clear and reproducible without undue burden.

[0044] The PUF material may be selected from the following non-limiting group: (1) layered or quasi-layered materials including hexagonal boron nitride, fluorographene, rare-earth oxyhalides, mica-type silicates, MPSs chalcogenophosphates and a-MoCh; (2) defect-engineered HfO?; (3) amorphous oxides including SiO?, AI2O3 and HfCF; (4) poly crystalline oxides and nitrides; (5) mixed-phase or nanocrystalline dielectrics; (6) polymer dielectrics with embedded defect clusters; and (7) composites, laminates, heterostructures or multilayer stacks; (8) quantum dot arrays exhibiting stochastic inter-dot conduction variability; and (9) perovskite thin films exhibiting spatially heterogeneous defect distributions.

[0045] The dominant conduction mechanism varies by material class, and the prior art landscape differs accordingly. For ALD-grown high-k oxides such as HfCF and AI2O3, the dominant mechanism is trap-assisted tunnelling through discrete oxide traps, producing random telegraph signal noise whose spatial distribution is fixed at manufacture; prior art exploits this in rigid, static configurations without strain coupling. For layered van der Waals insulators such as hexagonal boron nitride and fluorographene, the mechanism is stochastic breakdown through grain boundaries and point defects unique to each flake. For polycrystalline and mixed-phase dielectrics, vacancy-mediated conduction through grain boundary networks provides the entropy source. In each case the present invention is distinguished from prior art by the mechanical coupling of the defect conduction topology to the substrate strain field, which modulates local trap activation energies and produces strain-dependent PUF response vectors not present in any static prior art device.

[0046] The PUF layer has a thickness in the range 1 nm to 10 pm; in the preferred embodiment the thickness is less than 100 nm, which maximises sensitivity to applied strain and minimises the voltage required for sub-breakdown interrogation. At least 128 electrode pairs are provided in the preferred embodiment, giving a minimum response vector length of 128 bits and theoretical maximum entropy of 128 bits per challenge.

[0047] The element operates in reversible sub-breakdown mode for normal use or in irreversible breakdown mode for tamper-evidence. In the tamper-evidence mode, physical attack on the device causes irreversible dielectric breakdown of the PUF insulator layer 30, permanently invalidating the PUF response vector. The self-diagnosis mode (described in Section 6) differentiates between legitimate high-strain operational events and malicious tamper events by comparing the measured PUF response vector against the enrolled reference vector: a legitimate high-strain event produces a predictable, reversible shift in response within the strain-tunable challenge-response envelope, whereas a tamper event produces an irreversible change outside this envelope or a permanently unstable response. The strain-tunable challenge-response behaviour arises because the applied strain field modulates local activation energies for defect-mediated conduction at each electrode pair, producing distinct binary response vectors for each strain state. In a particularly advantageous embodiment, the PUF response is considered valid only when interrogated under a specific strain-gradient profile; interrogation under a different strain state produces a different response vector that will not match the enrolled reference, providing an additional layer of authentication that cannot be replicated by an attacker who does not know the required mechanical challenge state. The physical integration of the PUF element 30 with the substrate 10 provides mechanically-enforced tamper-evidence unique to this architecture. Any attempt to separate the device from its host structure, or to access the PUF element by delamination, introduces strain amplitudes outside the calibrated operating range. ALD-grown oxide PUF layers of thickness less than 100 nm are particularly susceptible: the Weibull breakdown probability increases sharply above the calibrated strain envelope, and once breakdown occurs the conduction topology is permanently altered. For van der Waals PUF materials, attempted delamination introduces crack propagation through the grain boundary network that irreversibly disrupts the stochastic conduction pathways. In both cases the enrolled PUF fingerprint is permanently destroyed and the authentication system detects the tamper event on the next readout cycle by comparison with the enrolled reference vector. The PUF element 30 is mechanically coupled to the substrate 10, preventing design-arounds based on mounting the PUF on a rigid island decoupled from the strain field. In multi-PUF fusion embodiments, two or more PUF elements 30 comprising different insulating materials are provided at different substrate locations; their combined response vectors are fused cryptographically to produce a composite fingerprint with higher entropy and cross-material uniqueness than either element alone. 5. Manufacture

[0048] The device is fabricated by an irreversible continuous roll-to-roll process comprising the steps of: (1) forming strain-modifying structural features in the polymer web; (2) transferring and patterning the piezoelectric, flexoelectric and PUF layers at the simulation-optimised coordinates; (3) depositing ALD dielectrics and encapsulation layers; (4) performing single-step metallisation of all interconnects and electrodes; and (5) performing in-line electrical testing.

[0049] After metallisation, repositioning of any element is practically impossible without scrapping the web, thereby locking in the simulation-optimised configuration. The irreversible metallisation step prevents post-fabrication repositioning or tuning of the PUF-response-defining geometry, ensuring that each device retains its unique, manufacturing-induced cryptographic fingerprint and cannot be cloned by physical reconfiguration. 6. Readout and Energy-Harvesting Circuit

[0050] A single application-specific integrated circuit (ASIC) integrates: charge amplifiers for each transduction type; correlated double sampling (CDS) circuitry; a full-wave rectifier; thin-film energy storage; a maximum-power-point tracker (MPPT); a microcontroller (MCU); and a wireless transmitter. The extracted PUF vector is cryptographically appended to every sensor data packet. The circuit supports autonomous operation without any external power source or battery, powered entirely by harvested mechanical energy.

[0051] Referring to Figure 5, signals from piezoelectric elements 20 are conditioned by charge amplifier 90, flexoelectric signals 22 by charge amplifier 92, and PUF electrode pair signals 32 by charge amplifier 94 incorporating CDS. Outputs of amplifiers 90 and 92 pass to full-wave rectifier 96 and MPPT 98 respectively. Rectified energy accumulates in energy storage 102. PUF extractor 100 supplies a binary response vector to MCU 104. Cryptographic append block 106 appends the PUF fingerprint to each outgoing data packet. Wireless transmitter 108 is powered from energy storage 102. The entire node operates without any external power source or battery. 7. Preferred Embodiments

[0052] Non-limiting preferred embodiments include: bridge structural-health-monitoring sensors; transparent wearable physiological patches; covert anti-counterfeit labels; robotic tactile skin; secure currency or pharmaceutical authentication tags; and self-powered access tokens.

[0053] A sensor-array embodiment is shown in Figure 6. The substrate 10 carries a two-dimensional grid of measurement locations. At each location, three piezoelectric elements 20 have in-plane crystallographic orientations differing by approximately 60°, as indicated by orientation indicators 40, enabling resolution of the complete in-plane strain tensor. A flexoelectric element 22 and PUF element 30 are provided at each location.

[0054] Additional embodiments include: medical disposable devices providing cryptographic proof of authenticity and single-use compliance; smart packaging providing tamper-evidence and self-powered condition monitoring during transit; supply-chain authentication tags providing a self-powered authenticated audit trail; multi-node mesh network deployments where each node is self-powered and individually authenticated; and strain-encoded encryption key generation, where a prescribed sequence of applied strain states produces a corresponding sequence of PUF response vectors forming a cryptographic key unique to that device and mechanical sequence.

[0055] A self-diagnosis mode applies an electrical stimulus and compares the measured electromechanical response against the simulation-predicted response.

[0056] Industrial Applicability: The transducer is manufactured by scalable roll-to-roll processing suitable for high-volume production of low-cost disposable sensors. The self-powered operation eliminates battery replacement costs, enabling deployment in remote monitoring applications where maintenance access is impractical.

Claims

Claim 1A flexible authenticated electromechanical transducer comprising:(a) a deformable substrate comprising a polymer material and including at least one strain-modifying structural feature configured to generate, under mechanical loading, a spatially non-uniform strain field;(b) at least one electromechanical transduction element disposed on the substrate and configured to generate electrical energy in response to deformation of the substrate;(c) a physically unclonable function (PUF) element comprising an electrically insulating layer having spatially distributed defect-mediated conduction variability arising from analogue physical variability rather than stored digital states, and a plurality of electrode pairs arranged to interrogate spatially distinct regions of the insulating layer; and(d) wherein the PUF element is bonded directly to the deformable substrate such that deformation of the substrate continuously modifies the electrical conduction behaviour of the insulating layer throughout its operational range, and different applied strain states produce mutually distinct PUF response vectors;whereby mechanical deformation of the substrate simultaneously constitutes a physical challenge input to the PUF element and a source of electrical energy.Claim 2The transducer of claim 1, wherein the at least one electromechanical transduction element comprises a piezoelectric transduction element disposed at a location of enhanced uniform strain, and at least one flexoelectric transduction element disposed at a location of enhanced strain gradient and configured to generate electrical charge in response to a strain gradient in the substrate.Claim 3The transducer of claim 1 or claim 2, further comprising an energy harvesting and readout circuit electrically connected to the electromechanical transduction element and the PUF element, the circuit being configured to accumulate electrical energy generated by deformation of the substrate, to extract a PUF response vector from the electrode pairs, and to transmit authenticated sensor data using energy harvested from the samemechanical loading event that produces the PUF response, without requiring an external power source or battery.Claim 4The transducer of claim 3, wherein the transducer contains no electrochemical storage cell having a rated capacity exceeding 1 pAh and has no electrical connector for receiving power from an external supply.Claim 5The transducer of any preceding claim, wherein the PUF element, under fixed electrical and mechanical conditions, yields a stable binary PUF response with an intra-device Hamming distance of less than 0.05 over the temperature range -40°C to +85°C and under repeated strain cycling.Claim 6The transducer of any preceding claim, wherein the PUF insulating material is selected from: hexagonal boron nitride; fluorographene; rare-earth oxyhalides; mica-type silicates; MPS3 chalcogenophosphates; a-MoO3; defect-engineered Hf02; amorphous oxides including Si02, AI2O3 and Hf02; polycrystalline oxides or nitrides; mixed-phase dielectrics; polymer dielectrics with embedded defect clusters; quantum dot arrays exhibiting stochastic inter-dot conduction variability; perovskite thin films exhibiting spatially heterogeneous defect distributions; or composites, laminates or heterostructures thereof.Claim 7The transducer of any preceding claim, wherein the PUF insulating layer has a thickness in the range 1 nm to 10 pm, and wherein at least 128 electrode pairs are provided interrogating spatially distinct regions of the insulating layer.Claim 8The transducer of any preceding claim, wherein the PUF element operates in a reversible sub-breakdown interrogation mode during normal operation such that strain-induced modulation of defect-mediated conduction produces distinct but reproducible PUF response vectors; and wherein mechanical deformation of the substrate exceeding anoperational strain envelope causes irreversible dielectric breakdown of the insulating layer, permanently destroying an enrolled PUF fingerprint in a manner detectable by comparison with a stored reference vector and not reversible by any subsequent electrical or mechanical treatment.Claim 9The transducer of any preceding claim, wherein a first applied strain state produces a first PUF response vector and a second applied strain state, differing from the first in magnitude, direction or spatial distribution, produces a second PUF response vector having a Hamming distance from the first in the range 0.3 to 0.7, thereby providing strain-tunable multi-challenge authentication in which the applied strain constitutes the authentication challenge.Claim 10The transducer of any preceding claim, wherein the PUF response variability arises from one or more of: grain-boundary networks; variable fluorination or oxidation; vacancy clustering; thickness fluctuations; mixed-phase domain boundaries; and trap-assisted tunnelling through spatially distributed oxide traps whose spatial distribution is fixed at manufacture and varies between devices.Claim 11The transducer of claim 2, wherein the locations of the piezoelectric, flexoelectric and PUF elements are determined by a coupled multi-physics optimisation that simultaneously models mechanical strain, strain-gradient and defect-mediated electrical behaviour of the PUF element, such that the element locations deviate by at least 2% of a characteristic length dimension of the substrate from locations predicted by single-physics linear elastic analysis of the substrate under the same boundary conditions without piezoelectric, flexoelectric or PUF coupling terms.Claim 12The transducer of claim 11, wherein the coupled multi-physics optimisation maximises an objective function Qo + XH(PUF), where Qo is total harvested power, H(PUF) is the Shannon entropy of a binary PUF response vector, and X is a selectable weighting factor; and wherein the combined electrical power output of the piezoelectric and flexoelectric transduction elements is at least 40% greater than the sum of outputs from equivalentpiezoelectric-only and flexoelectric-only devices fabricated on separate identical substrates under identical loading conditions.Claim 13The transducer of any preceding claim, wherein the strain-modifying structural features comprise one or more of: V-shaped notches; tapered profiles; kirigami cuts; and micro-cavity arrays; and wherein the substrate is planar, curved, conformal, stretchable or three-dimensionally shaped.Claim 14The transducer of any preceding claim, wherein the at least one electromechanical transduction element comprises a material selected from: transition-metal dichalcogenides including MoS2, WSe2 and WS2; ZnO; PVDF; AIN; GeS; SnSe; triboelectric generator materials based on contact electrification; piezoresistive materials exhibiting strain-dependent resistance; and capacitive strain-sensing materials exhibiting deformation-induced capacitance variation.Claim 15The transducer of any preceding claim, wherein the readout and energy-harvesting circuit comprises at least one charge amplifier for each transduction type, correlated double sampling circuitry, a full-wave rectifier, thin-film energy storage, maximum-power-point tracking circuitry, a microcontroller, and a wireless transmitter; and wherein a PUF fingerprint is cryptographically appended to every transmitted sensor data packet.Claim 16The transducer of any preceding claim, further comprising a switching circuit configurable in a self-diagnosis mode in which an electrical stimulus is applied and a measured electromechanical response is compared against a simulation-predicted response, wherein deviations beyond a defined threshold are flagged as indicative of damage, mechanical drift or tampering.Claim 17The transducer of any preceding claim, wherein the PUF element is interrogated at a sampling frequency synchronised with or derived from a fundamental mechanical resonance frequency of the substrate under operating conditions, such that strain-induced modulation of defect activation probability is maximised at the moment of interrogation.Claim 18The transducer of any preceding claim, wherein two or more PUF elements comprising different insulating materials are disposed at different locations on the substrate, their PUF response vectors being cryptographically fused to produce a composite fingerprint having higher entropy and cross-material uniqueness than either element alone.Claim 19The transducer of any preceding claim, wherein the PUF element is free of any rigid mechanical isolation layer or strain-decoupling structure interposed between the insulating layer and the deformable substrate.Claim 20A method of manufacturing the transducer of any one of claims 1 to 19, comprising:(a) performing a coupled multi-physics numerical simulation to determine locations for all electromechanical transduction elements and PUF electrode pairs that jointly optimise harvested power and cryptographic entropy;(b) forming strain-modifying structural features in a flexible polymer substrate or web;(c) depositing and patterning the electromechanical transduction and PUF insulating layers at the determined locations; and(d) completing all electrical interconnects in a single irreversible metallisation step after which repositioning of any element is not practically achievable without scrapping the substrate;wherein the determined locations deviate by at least 2% of a characteristic length dimension of the substrate from positions predicted by single-physics mechanical analysis alone.Claim 21The method of claim 20, wherein steps (b) to (d) are performed as a continuous roll-to-rolI process on a flexible polymer web.Claim 22A computer-implemented method of designing a transducer according to any one of claims 1 to 19, comprising: receiving substrate geometry, material parameters and a weighting factor X; executing a coupled multi-physics finite-element simulation simultaneously solving a strain tensor, a strain-gradient tensor, piezoelectric charge density, flexoelectric charge density and PUF defect-mediated electrical behaviour; iteratively updating element positions to maximise Qo + X-H(PUF); outputting simulation-optimised coordinates for all elements; and storing those coordinates in a fabrication layout file for use in directing lithographic, direct-write or other patterning operations to manufacture a physical transducer having a measured positional deviation of at least 2% of a characteristic length dimension of the substrate from positions predicted by single-physics analysis alone.Claim 23A self-powered authenticated wireless sensor system comprising the transducer of any one of claims 1 to 19, an energy-harvesting circuit, and a wireless transmitter powered entirely by stored harvested energy without any external power source or battery, the system being configured to append a PUF fingerprint to every transmitted sensor data packet.Claim 24A sensor array comprising a flexible substrate carrying a plurality of transducers according to any one of claims 1 to 19 arranged in a two-dimensional grid, wherein at each measurement location at least three piezoelectric transduction elements have in-plane crystallographic orientations differing by approximately 60°, enabling resolution of a complete in-plane strain tensor, and wherein each measurement location provides a spatially distinct PUF fingerprint enabling authenticated spatially-resolved sensing.Claim 25A method of simultaneously sensing mechanical deformation, harvesting energy and authenticating a device, comprising: applying mechanical deformation or ambient vibration to the transducer of any one of claims 1 to 19; converting electromechanical polarisation into stored electrical energy; measuring transduction signals to determine a deformation characteristic; extracting a PUF response vector constituting a device authentication; and transmitting the deformation data together with a PUF fingerprint as an authenticated data packet powered entirely by the harvested energy.A

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