Tunable Permittivity Research Articles

Tunable bound states in the continuum with loss compatibility

Dynamic control of bound states in the continuum (BICs) is usually achieved by engineering structural geometries of lossless optical systems, leading to a passive nature for most current BIC devices. Introducing materials with tunable permittivity, i.e., refractive index and loss, may offer a new degree of freedom in designing reconfigurable BIC metadevices with active functionalities. However, achieving loss-accompanied or loss-driven BIC manipulation while preserving its ultrahigh Q factor is extremely challenging. Here, we report a loss-compatible BIC manipulation mechanism based on far-field interference in a mirror-assisted photonic crystal slab, wherein the loss of tunable material not only harmoniously coexists with ultrahigh Q factor, but also serves as a pivotal joystick of BIC dynamics in momentum space. By modulating loss and refractive index of tunable material through the amorphous-crystalline phase transition, simulation results show the active switching of topological charge for BICs, as well as the multidimensional control of chiroptical effect for quasi-BICs, including steerable response/emission direction and chirality continuum with far-field ellipticity ranging from −0.944 to +0.943. Our findings suggest a distinct route to construct BIC metadevices with active functionalities and foster deeper exploration of intrinsic loss applications within the ultrahigh-Q photonic system.

Realizing high-performance four active plasmonic filters using a single structure

This research aims to contribute significantly to the field of plasmonic filtering technology within modern optical communication systems. By focusing on the development of a high-performance, more compact, and efficient design, this study explores the potential of hybrid plasmonic filters to revolutionize optical filtering applications. The approach leverages an innovative active material with electrically tunable permittivity, allowing for dynamic control over the filter’s optical properties. The research specifically examines four types of filters: low-pass filters (LPF), high-pass filters (HPF), band-pass filters (BPF), and band-reject filters (BRF). These filters are designed to operate effectively across a broad wavelength range of 1200–1800 nm, achieving a transmittance exceeding 98% at the output port, while maintaining isolation with transmittance below 2% at the isolated ports. The structure demonstrates a FWHM of approximately 216 nm for the band-pass filter and approximately 223 nm for the band-reject filter, which are considered moderate values, ensuring the versatility and multifunctionality of the design. The ultra-compact size, with a footprint of just 21 µm2, makes these filters particularly advantageous for integration into space-constrained optical communication systems.

Novel HPMC/PEDOT:PSS nanocomposite for optoelectronic and energy storage applications.

This study investigates a class of materials known as polymer nanodielectrics, which are formed by incorporating ceramic fillers into polymers. These materials offer the unique advantage of tunable electrical and optical properties. The research focuses on the incorporation of high-purity stannic oxide nanoparticles (SnO2 NPs) into a ternary blend matrix of hydroxypropyl methylcellulose (HPMC) and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) using a solution casting method. Characterization techniques like X-ray diffraction (XRD) and Fourier-transform infrared spectroscopy (FT-IR) revealed alterations in the amorphous nature of the HPMC/PEDOT:PSS blend upon the introduction of SnO2 NPs. These analyses also suggest the formation of interactions between the polymer and nanoparticles. Scanning electron microscopy (SEM) images confirmed the successful dispersion of SnO2 NPs on the surface of the polymer blend, particularly at lower concentrations. The optical properties of the nanocomposite films were investigated using UV-vis spectrophotometry. This analysis allowed for the calculation of optical constants like the bandgap and refractive index. The results showed a dual-bandgap structure, with the direct and indirect bandgaps ranging from 4.92 eV to 4.26 eV and 3.52 eV to 1.68 eV, respectively. Electrical characterization using AC conductivity and dielectric permittivity measurements revealed a dependence on the SnO2 NPs concentration within the frequency range of 0.1 Hz to 10 MHz. The relaxation processes and interfacial polarization effects within these nanocomposites are further discussed in the study. At a frequency of 10 Hz, the AC conductivity exhibited a significant increase, rising from 1.85 × 10-12 S m-1 to 1.04 × 10-9 S m-1 upon the addition of 0.7 wt% SnO2 NPs. These findings highlight the multifunctional nature of the developed nanocomposites. They hold promise for various applications, including UV blockers, optical bandgap tuners, and optical coatings in advanced optoelectronic devices. Additionally, their tunable high permittivity suggests potential use as dielectric substrates for next-generation, high-performance energy storage devices.

Innovative enhancements in polymer nanocomposites: Integrating ZnO nanorods into Hydroxypropyl methylcellulose/Polyvinyl pyrrolidone blend for advanced energy storage devices

Polymer nanocomposites are promising for various industrial and scientific applications due to their flexibility, diverse functionalities, and unique properties. In this study, zinc oxide nanorods (ZnO NRs) were incorporated into a blend of polymers (Hydroxypropyl methylcellulose - HPMC and Polyvinyl pyrrolidone - PVP) using a solution-casting technique, with concentrations varying from 2 % to 8 % by weight. Transmission electron microscopy (TEM) revealed that the ZnO NRs had an average diameter of 140 nm and a length of 3.22 μm. X-ray diffraction (XRD) analysis showed reduced crystallinity in the samples as the ZnO NR content increased. Fourier-transform infrared spectroscopy (FTIR) indicated changes in vibrational peaks due to interactions between functional groups in the blend and the nanorods. The addition of ZnO NRs significantly influenced the optical bandgap energies and UV/visible light absorption spectra of the samples. The bandgap of the nanocomposites significantly decreased upon ZnO NR incorporation, with direct and indirect bandgaps ranging from 5.19 to 4.70 eV and 4.74–3.66 eV, respectively. Electrical conductivity and dielectric characteristics were assessed across frequencies ranging from 0.1 to 10 MHz, revealing increasing AC conductivity, dielectric permittivity, and dielectric loss with higher ZnO NR content. Notably, at 10 Hz, the electrical conductivity increased from 3.5 × 10⁻12 S/m to 3.62 × 10⁻10 S/m upon loading with ZnO NR. The combination of adjustable optical bandgaps, frequency-dependent AC conductivity, and a wide range of tunable permittivity highlights the potential of these HPMC/PVP-ZnO NR nanocomposites for developing flexible optoelectronic and energy storage devices.

Versatile Landscape of Low-k Polyimide: Theories, Synthesis, Synergistic Properties, and Industrial Integration.

The development of microelectronics and large-scale intelligence nowadays promotes the integration, miniaturization, and multifunctionality of electronic and devices but also leads to the increment of signal transmission delays, crosstalk, and energy consumption. The exploitation of materials with low permittivity (low-k) is crucial for realizing innovations in microelectronics. However, due to the high permittivity of conventional interlayer dielectric material (k ∼ 4.0), it is difficult to meet the demands of current microelectronic technology development (k < 3.0). Organic dielectric materials have attracted much attention because of their relatively low permittivity owing to their low material density and low single bond polarization. Polyimide (PI) exhibits better application potential based on its well permittivity tunability (k = 1.1-3.2), high thermal stability (>500 °C), and mechanical property (modulus of elasticity up to 3.0-4.0 GPa). In this review, based on the synergistic relationship of dielectric parameters of materials, the development of nearly 20 years on low-k PI is thoroughly summarized. Moreover, process strategies for modifying low-k PI at the molecular level, multiphase recombination, and interface engineering are discussed exhaustively. The industrial application, technological challenges, and future development of low-k PI are also analyzed, which will provide meaningful guidance for the design and practical application of multifunctional low-k materials.

Highly Sensitive Lossy Tunable Permittivity Sensor

Highly Sensitive Lossy Tunable Permittivity Sensor

Tunable metamaterials with carrier-induced effective permittivity for active control of electromagnetic fields in semiconductor manufacturing device

Precise control of electromagnetic fields is critical in many advanced manufacturing processes, such as those used in the semiconductor industry, where device performance relies on precision and uniformity. Here, we introduce a solution to control electromagnetic fields via permittivity modulation without the limitations of resonance-based approaches, through a patterned semiconductor enabling permittivity tuning via carrier-density modulation. This carrier-responsive metamaterial (CRM) exhibits frequency-independent performance over a broad frequency spectrum and significant permittivity tunability through controlled semiconductor conductivity. Furthermore, the conductivity response and the tuning range can be easily modulated through the variation of semiconductor materials and geometrical parameters. We present an intuitive model that explains the relationship between the CRM’s structure and properties, including its effective permittivity and loss tangent. Supported by comprehensive simulations and experimental validations, our findings show that the effective permittivity can be increased by over 3.5 times with low dielectric loss across a wide frequency range. As an application, we explore the CRM’s potential in plasma control, revealing its ability to influence plasma density nearly 30% by modulating its effective permittivity, exhibiting CRM’s versatile functionality and potential impact across diverse technological domains.

A comprehensive study on crystal structure, phase compositions of the BiVO4-LaVO4 binary dielectric ceramic system and a typical design of dielectric resonator antenna for C-band applications

Novel multi-component (Bi1-xLax)VO4 (BLVOx) (0.05 ≤ x ≤ 0.9) solid-solution/composite ceramics crystal structures, phase compositions as well as its applications in the C-band dielectric resonator antenna have been designed and investigated. With the increased substitution of La3+, phase transitions among the monoclinic scheelite (mBiVO4), tetragonal zircon (zt(La,Bi)VO4) and monoclinic monazite (mLaVO4), driven by the compositional changes, were detected. La3+ played an essential role in the optimization of the dielectric properties of BLVOx. The measured Q × f values at the microwave band are considerably larger around the range of compositions forming the zircon phase and reached the maximum value (12,800 GHz) at pure zircon phase (x = 0.5), demonstrating that the impact of zircon structure on the intrinsic loss should not be disregarded and is beneficial for low dielectric loss. Meanwhile, the εr and TCF values could be tuned by regulating the concentration ratio of Bi3+/La3+ to obtain composites or solid-solutions with appropriate εr and near-zero TCF values. Additionally, a cylindrical dielectric resonator antenna (CDRA) of BVLO0.5 ceramic was designed with high simulated radiation efficiency (99.8%) and gain (4.58 dBi) at the center frequency (6.73 GHz), indicating its potential application in C-band because of its tunable permittivity and low-loss.

Plasma-Driven Tuning of Dielectric Permittivity in Graphene.

Materials with tunable negative electromagnetic performance, i.e., where dielectric permittivity becomes negative, have long been pursued in materials research due to their peculiar electromagnetic (EM) characteristics. Here, this promising feature is reported in materials on the case of plasma-synthesized nitrogen-doped graphene sheets with tunable permittivity over a wide (1-40GHz) frequency range. Selectively incorporated nitrogen atoms in a graphene scaffold tailor the electronic structure in a way that provides an ultra-low energy (0.5-2eV) 2D surface plasmon excitation, leading to subunitary and negative dielectric constant values in the Ka-band, from 30 up to 40GHz. By allowing the tailoring of structures at atomic scale, this novel plasma-based approach creates a new paradigm for designing 2D nanomaterials like nanocarbons with controllable and tunable permittivity, opening a path to the next generation of 2D metamaterials.

Magnetic vortex configuration in Fe3O4 nanorings/nanotubes for aspect ratio and magnetic orientation regulated microwave absorption

Morphological structure can greatly affect the magnetic domain of magnetic materials, which plays a significant role on regulating the magnetic characteristics and electromagnetic properties. Herein, Fe3O4 nanorings/nanotubes with adjustable aspect ratio were fabricated through a hydrothermal route followed by reduction annealing treatment. The magnetic flux distributions in radial and axial direction were characterized by electron holography, suggesting that the Fe3O4 nanorings/nanotubes show magnetic vortex structure. The magnetic vortex-domain structure is favored to break the Snoek’s limit of Fe3O4, improving the high-frequency permeability and boosting the natural resonance band to 1 ∼ 10 GHz. Meanwhile the complex permittivity is highly sensitive to the aspect ratio. The Fe3O4 nanorings/nanotubes perform excellent comprehensive microwave absorption properties, owing to the special magnetic vortex structure, tunable complex permittivity, big complex permeability, large magnetization and high natural resonance. The Fe3O4 nanorings with the smallest aspect ratio show a minimum reflection loss (RL) value of −47.9 dB at 2.6 mm and EAB of 4 GHz at 3 mm. Besides, rotational orientation by an external magnetic field can cause the parallel arrangement of nanorings/nanotubes, which can increase both the complex permittivity and broad the resonance band. Rotational orientation can realize effective absorption efficiency at a broader frequency range with a thinner thickness, further improving the comprehensive microwave absorption. These findings not only suggest that designing particular magnetic-domain structures by morphologies can break the Snoek’s limit of magnetic materials, but also demonstrate that aspect ratio and magnetic field-assisted rotational orientation is promising ways to regulate the electromagnetic parameters, resulting in high-performance microwave absorption.

ZnO nanofiller concentrations modified P(VDF-HFP)/PEO polymer matrix-based nanocomposites of enhanced optical and dielectric properties for emerging optoelectronic and energy storage devices

Wide bandgap metal oxide nanoparticles incorporated polymer blend matrix-based polymer nanocomposites (PNCs) are established as innovative multifunctional and properties tunable materials in the dimensional design and fabrication of promising performance extensive flexible type advanced devices. For further progress in these materials, herein, the detailed structural and promising properties of solution-cast prepared ternary PNC films, composed of poly(vinylidene fluoride-co-hexafluoropropylene) P(VDF-HFP)/ poly(ethylene oxide) PEO (50/50 wt%) host matrix and zinc oxide (ZnO) nanofiller (0, 1, 2, 5, and 10 wt%), are characterized. A sequence of employed experimental techniques, namely SEM, XRD, FTIR, and DSC, confirm that the surface morphology, polymorphic crystallographic character, polymer-polymer interactions, polymer-nanoparticle interfaces, crystalline phase thermal transitions, and degree of crystallinity of these PNCs largely affected with varying nanofiller concentrations. The optical study conducted with a UV–Vis spectrophotometer revealed high photo sensing and UV shielding characteristics with an energy bandgap of about 3.0 eV, demonstrating widespread applications of these semiconducting PNC materials in emerging optoelectronic device technologies. The broadband dielectric spectroscopic (BDS) characterization over the 20 Hz–1 GHz range explained harmonic field frequency and nanofiller concentration tunable dielectric permittivity (about 3 to 13) with low losses and multiple relaxation processes, predominantly ruled by microstructural interfaces and interactions developed in these ternary hybrid complex materials. The meaningful broadband dielectric characteristics of P(VDF-HFP)/PEO/ZnO materials demonstrated that they could be used as innovative nanodielectrics for energy storage purposes in capacitive devices, and flexible dielectric substrate and insulators for the fabrication of frequency-adjustable discrete and integrated microelectronic devices.

MgF2-based microwave dielectric ceramics with ultra-low sintering temperature and high thermal expansion coefficient

Ultralow-temperature co-fired ceramic (ULTCC) materials with low permittivity and dielectric loss are considered promising materials for 5 G communication applications. Herein, a novel multiphase xMgF2-(1x)LiF (x = 0.20, 0.35, 0.50, 0.65) microwave dielectric ceramic was prepared via a conventional solid-state method for ULTCC applications. The ceramic achieves densification at a sintering temperature of 625 °C. The xMgF2-(1-x)LiF ceramics exhibit tunable permittivity ranging from 5.21 to 7.30, Q×f from 39400 to 52800 GHz, and τf from − 61 to − 98 ppm °C−1. Analysis of the crystal structure and microstructure revealed that the volatilisation of fluoride ions in the ceramics led to an increase in defect concentration, contributing to an unfavourable decrease in dielectric loss. The 0.35MgF2-0.65LiF ceramic shows comprehensive properties with the highest Q×f value (52800 GHz) and low permittivity (6.40). Furthermore, the thermal expansion coefficient is an important performance parameter in ceramic packaging with the 0.35 MgF2-0.65 LiF ceramic exhibiting a colossal thermal expansion coefficient of 28.69 ppm °C−1, thus enabling excellent compatibility with printed circuit board (PCB) substrates. Moreover, these high thermal expansion coefficient ceramics are excellent candidates for packaging.

Magnetic Properties and Applications of Glass-coated Ferromagnetic Microwires

A remarkable magnetic softness and giant magnetoimpedance (GMI) effect at GHz frequency range havebeen observed in glass-coated microwires subjected to appropriate postprocessing. Co-based microwires present higher GMI effect. Insulating and flexible glass-coating allows use of magnetically soft amorphous glass-coated microwires for stresses or temperature monitoring insmartcomposites using free space facility. Such composites with magnetic microwire inclusions can present tunable magnetic permittivity. We report on in-situ the evolution of the transmission and reflection parameters of the polymer containing magnetic microwire inclusions during the polymerization process. A remarkable change of the reflection and transmission in the range of 4-7 GHz upon the matrix polymerization is observed. Observed dependencies are discussed in terms of the effect of the temperature and stresses variation on magnetic properties of glass-coated microwires during the thermoset matrix polymerization. Obtained results are considered as a base for novel sensing technique allowing non-destructive and non-contact monitoring of the composites utilizing ferromagnetic glass-coated microwire inclusions with magnetic properties sensitive to tensile stress and temperature.

Study of Tunable Dielectric Permittivity of PBDB-T-2CL Polymer in Ternary Organic Blend Thin Films Using Spectroscopic Ellipsometry.

The ellipsometric analyses reported in this paper present a novelty by bringing an in-depth optical investigation of some ternary organic blends. This study focuses on the tunability and control of the relative permittivity of active layers by varying the weight ratio of blended materials spin-coated as thin films. To investigate this, an extensive approach based on spectroscopic ellipsometry was conducted on ternary blend (D:A1:A2) thin films, involving a donor [D = chlorinated conjugated polymer (PBDB-T-2Cl)] and two acceptor materials [A1 = a non-fullerene (ITIC-F) and A2 = a fullerene (PCBM)]. The refractive index constitutes a key parameter that exposes insights into the feasibility of photovoltaic cells by predicting the trajectory of light as it transits the device. In this term, higher obtained refractive indexes support higher absorption coefficients. Notably, the dielectric constant can be rigorously tuned and finely calibrated by modest variations in the quantity of the third element, resulting in considerable modifications. Moreover, the inclusion of fullerene in blends, as the third element, results in a smooth topographical profile, further refining the surface of the film. From an electrical point of view, the ternary blends outperform the polymer thin films. The synergistic interaction of constituents emphasizes their potential to enhance solar conversion devices.

Enhanced low-frequency microwave absorption of N-doped biomass derived carbon

Hierarchical porous undoped and N-doped carbon derived from the natural spinach roots was prepared by a facile carbonization process at 600–800 ℃ respectively. The electromagnetic properties were carefully investigated in the range of 1–18 GHz in order to study the effect of the tunable permittivity on the microwave absorbing and shielding performance by modulating the intrinsic polarization of the biomass carbon. Compared with the other samples, the undoped one sintered at 650 ℃ shows the minimum reflection loss (RL) of − 42.93 dB at 16.72 GHz with a thickness of 2.0 mm, while the effective absorbing bandwidth achieves 6.46 GHz at 2.4 mm. With the N-doping, the permittivity is obviously affected by the nitrogen-containing groups and compounds induced dipolar and interfacial polarization. The RLmin of the N-doped carbon sample sintered at 700 ℃ has arrived at − 49.96 dB at 15.88 GHz with a very thin thickness of 1.5 mm. Besides, the impedance matching bandwidth can cover the L-C band in the N-doped carbon with the excellent RL of − 43.195 dB at d= 8.4 mm and f= 2.4 GHz. The competitive and tunable mechanism of the dielectric property are also studied for the tunable impedance and microwave absorption.

Tunable Complex Permittivity and Strong Microwave Absorption Properties of Novel Dielectric-Conductive ZnO/C Hybrid Composite Absorbents

Modern electronic information technology has led social life into inevitable electromagnetic pollution, making microwave absorbing materials more and more important. Herein, dielectric-conductive ZnO/C hybrid composite absorbents were prepared by two-step carbonization with ZnO powders and glucose as critical materials. The electrical conductivity, complex permittivity, and reflection loss were analyzed to study the dielectric and microwave absorption properties. Results show that the prepared ZnO/C composite absorbents exist in the form of rod-like ZnO dispersed in the irregular block carbon, and the complex permittivity of the composite absorbents can be adjusted via varying the carbonization temperature. The minimum reflection loss of −25.64 dB is achieved at 1.8 mm thickness for the composite absorbent with 50 wt.% absorbent content as the final carbonization temperature is 750 °C, and the optimum effective absorption bandwidth is 2.21 GHz at 9.64–11.85 GHz. The excellent microwave absorption properties of ZnO/C composite absorbents are attributed to the combination actions of dipole polarization, conductance loss, and interface polarization, which is significant for the purposeful design of superior microwave-absorbing materials with dielectric and conductive absorbents.

Wavelength-tunable infrared chiral metasurfaces with phase-change materials.

Optical phase-change materials exhibit tunable permittivity and switching properties during phase transition, which offers the possibility of dynamic control of optical devices. Here, a wavelength-tunable infrared chiral metasurface integrated with phase-change material GST-225 is demonstrated with the designed unit cell of parallelogram-shaped resonator. By varying the baking time at a temperature above the phase transition temperature of GST-225, the resonance wavelength of the chiral metasurface is tuned in the wavelength range of 2.33 µm to 2.58 µm, while the circular dichroism in absorption is maintained around 0.44. The chiroptical response of the designed metasurface is revealed by analyzing the electromagnetic field and displacement current distributions under left- and right-handed circularly polarized (LCP and RCP) light illumination. Moreover, the photothermal effect is simulated to investigate the large temperature difference in the chiral metasurface under LCP and RCP illumination, which allows for the possibility of circular polarization-controlled phase transition. The presented chiral metasurfaces with phase-change materials offer the potential to facilitate promising applications in the infrared regime, such as chiral thermal switching, infrared imaging, and tunable chiral photonics.

Broadband tuning of plasma photonic crystal bandgaps using pixilated plasma distributions within a supercell

Plasma photonic crystals (PPCs) are photonic crystals formed from plasma that allows them an electrically tunable structure and permittivity. PPCs are potential microwave bandgap components with frequency ranges theoretically limited only by the physical control of the plasma distribution. In practice, they are limited by the controllability of the plasma distribution. Traditional approaches have minimal control and range of PPC reconfigurability because the plasma distribution is fixed. In contrast, this work explores reconfiguring the PPC structure by treating individual columns as pixels within a larger PPC structure. While the location of each plasma column is fixed, individual columns are adjusted to change the macroscopic plasma distribution of the total PPC. This work shows for the first time that individual plasma column control can tune a PPC bandgap frequency by an order of magnitude, from 190–300 GHz to 26–37 GHz. The changes to the larger supercell structure emulate changes to PPC parameters such as the lattice constant, column radius, and permittivity. This enables a wider tunable frequency range for PPC bandgaps as well as improved manipulation over the range. The collision frequency imposes a lower limit on the variable frequency range. The results demonstrate an expanded frequency variability for PPCs that highlight their potential as a wideband tunable bandgap device when each column is individually controlled.

Highly efficient graphene terahertz modulator with tunable electromagnetically induced transparency-like transmission

Graphene-based optical modulators have been extensively studied owing to the high mobility and tunable permittivity of graphene. However, weak graphene-light interactions make it difficult to achieve a high modulation depth with low energy consumption. Here, we propose a high-performance graphene-based optical modulator consisting of a photonic crystal structure and a waveguide with graphene that exhibits an electromagnetically-induced-transparency-like (EIT-like) transmission spectrum at terahertz frequency. The high quality-factor guiding mode to generate the EIT-like transmission enhances light-graphene interaction, and the designed modulator achieves a high modulation depth of 98% with a significantly small Fermi level shift of 0.05 eV. The proposed scheme can be utilized in active optical devices that require low power consumption.

Versatile spider-web-like cross-linked polyimide aerogel with tunable dielectric permittivity for highly sensitive flexible sensors

With the development of intelligent electronic power systems, the performance of flexible electronic sensors with portability and miniaturization is increasingly in demand. It is extremely challenging to achieve high modulus and high elasticity of polymer matrix simultaneously due to the inherent strength-elasticity conflict of elastic polymer. Here, a series of “spider-web-like” cross-linked polyimide aerogels (CPAs) had been successfully prepared. Benefiting from the robust dynamic network structure, the CPAs exhibited excellent compressive resilience, tunable dielectric permittivity, high thermal insulation property (λ = 0.040 W/m∙K) and modulus (E = 1073 KPa). Additionally, due to the excellent resilience of the CPAs and tunable permittivity, a CNTs/CPA-3 composite aerogel-based strain sensor obtained by assembling the CPA-3 with carbon nanotubes (CTNs) possessed synergistically enhanced sensitivity, high selectivity and “multi-touch” stress detection, without deterioration even after 2000 cycles. Furthermore, the established mathematical model revealed the internal mechanism of the synergistic enhancement of sensing performance of sensor with strain-controllable permittivity. Thus, the fabricated CPAs might be an ideal substrate material for flexible electronic sensors in electronic power systems, and the mathematical model established could also provide a reliable reference for improving the sensitivity and detection limits of sensors.