Tunable High-Frequency Thin-Film Inductor through Stress-Induced Magnetic Anisotropy

Tunable High-Frequency Thin-Film Inductor through Stress-Induced Magnetic Anisotropy | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Tunable High-Frequency Thin-Film Inductor through Stress-Induced Magnetic Anisotropy Jian Zhang, Tianlong Fu, Hongjin Ji, Ningning Wang, Hongxia Li, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8769909/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Thin-film solenoid-type inductors, owning low flux leakage and low parasitic capacitance, is required with high stability and tunability for flexible electronics. The existing solutions for flexible and tunable thin-film solenoid-type inductors is limited with the operations ease, device size and compatibility in flexible electronics. This work demonstrates a general approach to realize thin-film solenoid-type inductors on flexible substrate via stencil lithography. Ultrathin solenoid-type inductors were achieved with the total thickness less than 1 µm, and this ultrathin construction benefited the pliability and deformation uniformity during deformation regulation. The magnetic anisotropy and the permeability of permalloy magnetic core were directly impacted by bending the substrate through the magnetoelastic coupling. Based on this, the applied tensile/compressive strains gave rise to the multi-directional tunability of the thin-film inductors, showing the maximum enhancement over 140% of the inductance value at 800 MHz by bending. With the highly stability over 1,000 bending cycle tests, this method for thin-film solenoid-type inductors with easy-access turnability is expected for the future applications of flexible electronics in RF circuit and wireless communication. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 Introduction Inductor, composed with coil and magnetic core which can induce electric current and magnetic field respectively, can realize the electrical power transfer and energy storage. As being broadly applied in circuits, inductors are used for filtering, choking, power transfer, and voltage transformation [ 1 , 2 ]. Beyond these traditional applications, recent advances in dynamically responsive materials have enabled inductors to function as power generators [ 3 ], anemometers [ 4 – 6 ], humidity sensors [ 7 – 9 ], and multi-parameter detectors [ 10 ]. As a crucial passive component, the miniaturization, adjustability and high-frequency operation of tunable and flexible thin-film inductors have become particularly important for the rapid development of flexible electronics [ 11 , 12 ]. Current mainstream of thin-film inductors primarily includes planar inductors [ 13 – 16 ] and solenoid-type inductors [ 17 – 21 ]. Planar inductors composed of track-shape coil are typically fabricated via single-step patterning (e.g. photolithography, nanoimprint, inkjet printing [ 22 ] ), followed plating [ 23 ], physical vapor deposition (PVD), or direct cutting by femtosecond laser on metallic layer [ 24 – 27 ]. Though with simple structure, the leakage flux and the accumulation of parasitic capacitance is hardly to be avoided, thereby limiting its potential application. In contrast, solenoid-type thin-film inductors adopt the coil around magnetic core, where the encapsulated magnetic core further improves both inductor performance and integration density [ 28 ]. Compared to planar inductors, the solenoid-type inductors reduce flux leakage, enhance inductor efficiency and improve overall performance [ 29 , 30 ]. Additionally, their lower parasitic capacitance and resistance enable stable high-frequency inductance, making them suitable for high-speed digital circuits and RF applications [ 31 – 33 ]. For a solenoid-type inductor with the coil turns N, the cross-sectional area of the core A c , and the length of each turn of the coil l 0 , the inductance L and DC resistance R dc of the coupled inductor can be respectively expressed as [ 28 ]: $$\:L=\frac{{\mu\:}_{0}{\mu\:}_{r}{N}^{2}{A}_{c}}{{l}_{m}}$$ 1 $$\:{R}_{dc}=\frac{{l}_{0}N\rho\:}{{A}_{\omega\:}}$$ 2 where µ 0 and µ r are the vacuum permeability and relative permeability of the magnetic core respectively, ρ is the resistivity of the coil metal material, l m is the length of the magnetic core, and A ω is the cross-sectional area of the wire. Aiming to the tunable thin-film inductor which are commonly required for voltage-controlled oscillators, low noise amplifiers, radio frequency identification, etc., people can change the conductive or magnetic parameters in Eq. ( 1 )&( 2 ) to real-time adjust the inductance. For example, Lazarus et al. fabricated a pneumatically tunable inductor using liquid metal as conductive traces and silicone elastomer as pneumatic chambers [ 34 ]. Through aerodynamic deformation, the inductor exhibits volume expansion and compression, and achieves inductance modulation between 100–400 nH at -15 ~ 10 kPa. Meyer et al. fabricated a stretchable inductor based on silicone elastomer and liquid metal, of which the inductance is enhanced up to 20% with twice its original length [ 35 ]. However, most tunable inductors are reported in macroscale, and research on microscaled thin-film inductors still face a challenge in terms of size [ 36 ]. Furthermore, the great volume change may lead the plastic deformation of metal and the failure of coils. There is a great demand for a gentle and easy-access tuning method for thin-film inductor in flexible electronics. While the improvement of inductor performance through strain has been reported, the current research has mainly focused on the geometric changes induced by deformation [ 37 ]. Based on Eq. ( 1 ), the inductor performance is directly decided by permeability, and the permeability of the magnetic core is closely relative to the magnetic anisotropy [ 38 ]. For the magnetic film on flexible substrate, the stress status (bending, stretching, or compression) applied on the film directly orients the spontaneous magnetization (M) through magnetoelastic coupling, and thus effect the magnetic anisotropy and the permeability at microscale. Based on this, mechanically bending thin-film inductors containing magnetic core on flexible substrate should enable tunable inductance without altering the inductor's physical dimensions or components. In this work, we demonstrated an ultrathin-film inductor fabricated via stencil lithography, incorporating gold (Au) coil around a permalloy (Py) magnetic core, with a total thickness < 1 µm. The bending of flexible substrate induced the strain and changed the magnetic anisotropy of magnetic core through magnetoelastic coupling, so as to adjust the inductance value. Compared with the inductor without Py magnetic core which were insensitive to bending, the inductor with Py magnetic core showed over 140% enhancement of the inductance value at 800MHz by bending. The multi-directional adjustability of this ultrathin-film inductor was further investigated by bending at different direction. The stability test of over 1000 bending/releasing cycles demonstrated it suitable as the adjustable and flexible ultrathin-film inductor which is expected for the future applications in RF circuit and wireless communication. 2 Experimental section For the fabrication of flexible electronics, conventional photolithography faces challenges on flexible substrates, and alternative techniques such as nanoimprint lithography, stencil lithography, and inkjet printing have emerged as the viable fabrication strategies [ 39 – 41 ]. Polyethylene terephthalate (PET) as one of the most common substrates in flexible electronics was selected with the thickness of 0.125 mm. PET surface was firstly annealed at 120 ℃ for 10 min and cleaned with O 2 plasma to improve the smoothness and adhesion ( Fig. 1 a ) . A solenoid-type inductor was multilayered as bottom- and top-side coils, SiO 2 insulator layers and magnetic core, and were fabricated through stencil lithography with multi-shape shadow masks in electron-beam evaporation. Detailedly, 10-nm Cr and 150-nm Au were deposited through shadow mask to form the bottom-side electrode ( Fig. 1 b ) . SiO 2 /Py/SiO 2 layers with the thicknesses of 160 nm/120 nm/160 nm were respectively deposited ( Fig. 1 c-e ) . The permalloy owns high permeability and high saturation magnetic induction, making it commonly used for high-frequency inductor. Here, Py film including 81 wt% Ni and 19 wt% Fe with a negative magnetostrictive coefficient of ~ -2 ppm was selected as the magnetic core [ 42 , 43 ]. 10-nm Cr and 150-nm Au were deposited again to complete the coil around the Py core ( Fig. 1 f ) . By this way, organic solvents were totally avoided on organic substrate and a multilayer-stacked solenoid-type inductor was ideally realized. The structural parameters of the inductor illustrated in Fig. 1 h &g are summarized in Table 1 . Table 1 Parameters of inductors with different turns. L m (mm) W m (mm) R (mm) W A (mm) L A (mm) W v (mm) g (mm) Py. core 8/15/20 2 0.4 6 4.2/9.2/13.3 0.2 0.6 Air core / 2 0.4 6 4.2/9.2/13.3 0.2 0.6 The calculation of strain induced by bending is detailedly descripted in Fig. S1 . The magnetic properties of the Py magnetic core with and without applied stress were measured by using the magnetic-optical Kerr microscope (MOKE, from Evico Magnetics GmbH, Germany). The inductance L and the quality factor Q were tested by using the impedance analyzer (from Keysight, USA E49918 1MHz − 1GHz). The final samples were characterized by magnetic force microscope (AFM, from Nano Wizard 4-NanoScience, JPK Instruments S3 AG, Germany) and scanning electron microscopy (SEM, from Sigma 300, Carl Zeiss, Germany). 3 Results and discussion 3.1 The study of the as-fabricated thin-film inductor The previously reported microfabrication processes of thin-film inductors normally involved multistep patterning with photolithography, in which the usage of organic solvents could damage the organic substrates. Aiming to flexible thin-film inductor, we developed stencil lithography to totally avoid organic solvents on organic substrate and a multilayer-stacked solenoid-type inductor with the minimum linewidth of 100 µm is ideally realized, as the sample shown in Fig. 2 a. The SEM image with cross-sectional view in Fig. 2 b show the layers including the insulator layers, the Py magnetic core, and the top-side electrode, proving the total thickness of 600 nm. Considering the bottom-side electrode with the additional thickness of 160 nm, the total thickness of our proposed device is only 760 nm. This ultrathin construction ensured the pliability and deformation uniformity in the following bending test. As shown in Fig. 2 c &d , the inductance (L) and quality factor (Q) of the as-fabricated thin-film inductors with varying numbers of turns were measured on both PET and SiO₂ substrates. L for the thin-film inductors fabricates on PET substrate is over 20 nL at 100 ~ 1000 MHz (shown in the solid lines in Fig. 2 a ), while L on SiO2 substrate is less than 10 nL (shown in the dash lines in Fig. 2 a ). The difference of L on PET and SiO2 substrates is even increased with increasing frequency. For example, L with 15 turns on PET and SiO₂ substrate is 29.2 and 3.8 nH at 800 MHz, respectively, presenting a sevenfold enhancement on flexible substrate. The quality factor Q, defined as the ratio of reactive power to active power, is derived in Fig. 2 d. The dash lines show that Q for the thin-film inductors on SiO₂ substrate is less than 0.5, indicating the significant energy loss and more resistive characteristics [ 28 , 29 ]. For comparison, Q value is enhanced over 2 with higher frequency on PET substrate, as the solid lines shown in Fig. 2 d. 3.2 The study of the magnetic anisotropy with strain This superiority for the thin-film inductors on flexible substrate is notable, and can be attributed to the additional tension distribution caused in the magnetic layer deposited on flexible substrate [ 44 , 45 ]. It was reported that this tension specially generated on flexible substrate is mainly attributed to the Young’s moduli mismatch between different layers during stress recovery (E Py : ~113 GPa and E PET : 2-2.7 GPa) [ 46 ], and thermal expansion mismatch between Py/PET layers [ 47 – 49 ]. The in-plane stress distribution on PET substrate pronounced in-plane magnetic anisotropy [ 50 , 51 ], resulting in superior inductance (L) and quality factor (Q) values compared to the one on rigid substrates. The slightly reduced L and Q for inductors with more turns were also noticed in this work, which could be attributed to the increased resistance with longer conductive coil [ 52 – 54 ]. To evaluate the magnetic core's contribution, we fabricated air-core inductors with identical geometries on both rigid and flexible substrates (Fig. S2) . The results clearly show that air-core inductors on both of PET and SiO 2 substrates maintain Q below 1 across a broad frequency range, exhibiting predominantly resistive behaviour. Bending the flexible substrate could easily induce the tensile and compressive stress in Py magnetic core. As described in Introduction , the spontaneous magnetization (M) and magnetic anisotropy is immediately related to the applied stress status. Considering the electron-beam deposited magnetic films, which is commonly polycrystalline and magnetically isotropic, the magnetoelastic coupling mechanism can be elementarily described as : $$\:{E}_{\sigma\:}=-\frac{3}{2}\sigma\:\lambda\:{{cos}}^{2}\theta\:$$ 3 where E σ , σ, λ, and θ present the magnetoelastic energy, stress, magnetostrictive coefficient, and angle between M and σ direction, respectively. For negative magnetostrictive films (Py used in our system with λ ~ -2 ppm), minimizing E σ requires θ = 90° or 270° and M perpendicular to the direction of tension (σ > 0). Conversely, θ = 0° or 180° and M is parallel to the direction of compression stress (σ < 0). Figure 3 a shows the relationship between M and the applied tensile/compressive stresses with the mechanism of magnetoelastic coupling for the cases when bending the Py magnetic core on the flexible substrate. To experimentally investigate the impact of stress on the magnetic anisotropy of magnetic thin films, we measured the magnetic hysteresis loops using MOKE at room temperature under in-plane magnetic fields applied perpendicular (H x ) and parallel (H y ) to the tension direction. Figure 3 b shows the magnetic hysteresis loop with H y , and the remanence ratio (M r ) are reduced to be 0.31 from 0.75. This means the dampening effect on magnetic anisotropy along the magnetic core by tension. On the contrary , Fig. 3 c shows the magnetic hysteresis loops with H x , and M r is increased to be 0.90 from 0.73, meaning the enhancement of the magnetic anisotropy perpendicular to the magnetic core by tension. The condition for applying compression stress should be reversed based on Eq. ( 3 ). 3.3 The study of the dynamic inductance with strain In an inductor, the change of stress status directly impacts the stress anisotropy on Py magnetic core, which are relative to the initial permeability µ i : [ 55 ] $$\:{\mu\:}_{i}\propto\:\frac{{M}_{s}^{2}}{{K}_{1}+{K}_{2}}\propto\:\frac{{M}_{s}^{2}}{{K}_{1}+\lambda\:\sigma\:}$$ 4 where M s , K 1 and K 2 are the saturation magnetization, the magnetocrystalline anisotropy and the stress anisotropy. Thus, the applied stress may change µ i and make the thin-film inductor tunable. We tested L for the 5-turn inductor under different bending states along the Py magnetic core as illustrated in Fig. 4 a &d . Figure 4 b indicates that under tensile strain, L increased with larger bending deformation. At maximum tensile strain of 1.8%, L reached at 43.7 nH at 800 MHz, with the 39.6% increasement compared to the flat status (31.3 nH at 800 MHz). Correspondingly, Q was also enhanced with larger tensile strain ( Fig. 4 c ). In contrast, under compressive strain, L and Q decreased stepwise with larger bending deformation ( Fig. 4 e &f ). At maximum compressive strain of 1.8%, the inductance was decreased by 5.1% @ 800 MHz, demonstrating an opposite responsibility to the revered strain states, matching Eq. ( 4 ). In Fig. S3 , the inductor without the Py magnetic core is also examined by bending. Regardless of tensile or compressive strain, L and Q remain stable at 44.5 nH and 1.28 at 800 MHz, respectively. This conclusively demonstrates that the magnetoelastic coupling in the magnetic core plays a key role in regulating the thin-film inductance. Besides bending along the Py magnetic core, we also examined the impact from bending perpendicularly to the Py magnetic core in Fig. 5 a &d , which interestingly shows the reversed tunability corresponding to the applied tensile or compressive strain. In this case, both of L and Q were weaken under tensile strain ( Fig. 5 b &c ), and were enhanced under compressive strain ( Fig. 5 e &f ). For instance, L is reduced from 31.3 nH to 28.1 nH at 800 MHz with the tensile strain of 1.8%, and is enhanced from 31.3nH to 32.4nH at 800 MHz with the compressive strain of 1.8%. This revered result can be explained by Poisson’s ratio: ε x =-υε y . Considering that the average ratio υ for or Fe-Ni invar alloys is ~ 0.29 [ 56 ], the tensile strain along the lateral direction can considered as the compressive strain along the longitudinal direction. Thus, the applied tensile/compressive strain perpendicularly to the Py magnetic core can be respectively switched as the applied compressive/tensile stress along the Py magnetic core, and thus lead the reversed tunability. 3.4 The stability test To evaluate the stability of this flexible and tunable thin-film inductor, we conducted cyclic tests by alternating tensile and compressive strains. In each cycle, a 5-turn inductor is bended to 1.8% tensile strain and 1.8% compressive strain in turn, and then record the inductance performance at 800 MHz in flat status. Figure 6 a shows that L is stable at 33 ~ 34 nH after 600 cycles and slightly reduced to be 27 nH in 700 ~ 1000 cycles. Correspondingly, Q is maintained at 3.0 in 600 cycles, and slightly reduced to be 2.4 in 700 ~ 1000 cycles. In Fig. S4a&b , optical image and AFM image prove that the Py magnetic core maintains its structural integrity after 100 cycles due to the coverage of SiO 2 insulator layer. Without SiO 2 insulator layer, however, the Py magnetic core shows the cracks after once bending as shown in Fig. S4c&d . As compared with the previous report in Fig. 6 b, a thinnest solenoid-type thin-film inductors with considerable and stable tunability is achieved in this work. 4.Conclusions In summary, this study demonstrates a new method to realize ultrathin and tunable solenoid-type thin-film inductors on flexible substrates. Using stencil lithography through shadow-mask-assisted evaporation, solenoid-type thin-film inductors were ideally fabricated with the total thickness < 1 µm, and the pliability and deformation uniformity of this ultrathin configuration benefited the tunability. The measurement of hysteresis loops proved that the magnetic anisotropy of Py magnetic core is directly impacted with the bending status due to the magnetoelastic coupling. Based on this, the applied tensile/compressive strains gave rise to the multi-directional tunability of the thin-film inductors, showing the maximum enhancement over 140% of the inductance value at 800 MHz by bending. Our work allows easy access to realize flexible electronics with highly stability and turnability, which is expected for the future applications in RF circuit and wireless communication. Declarations Competing interests Not applicable. Ethics approval Not applicable. Consent to participate Not applicable. Consent to publish Not applicable. Funding The authors gratefully acknowledge the National Science Fund for Distinguished Young Scholars (52225312), the National Natural Science Foundation of China (52272292), and the Zhejiang Provincial Key Research and Development Program (2023C01053). Author Contribution Conceptualization, J. Z. and T. F.; Methodology, J. Z. and T. F.; Formal analysis, T. F., and H. J., Validation, N. W. and H. L.; Resources, Z. K. and F. Z.; Supervision, F. Z. and X. Z.; Project administration, X. Z.; Writing - Original Draft, J. Z. and T. F. All authors reviewed the manuscript. Data Availability The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request. References Zhang W, Zhou G, Hong Y et al (2024) Organic package substrate embedded coupled magnetic core inductors using lithographic via technology for power supply in package. Results Phys 60:107628. http://doi.org/10.1016/j.rinp.2024.107628 Michel JP, Sibuet H, Buffet N et al (2019) Ultra-low profile integrated magnetic inductors and transformers for HF applications. IEEE Trans Magn 55(7):1–7. http://doi.org/10.1109/tmag.2019.2905985 Zhang J, Hou XJ, Qian S et al (2024) Flexible multilayer MEMS coils and their application in energy harvesters. Sci China Technological Sci 67(4):1282–1293. http://doi.org/10.1007/s11431-023-2474-9 Liu C, Yi Z, Qin M et al (2021) Passive and wireless anemometer based on inductor bending effect. J Microelectromech Syst 31(1):3–5. http://doi.org/10.1109/jmems.2021.3124230 Yi Z, Wan Y, Qin M et al (2020) Quadruple sensitivity improvement for wind speed sensor using dual-layer bended inductors. Sens Actuators A: Phys 303:111786. http://doi.org/10.1016/j.sna.2019.111786 Yi Z, Wan Y, Qin M et al (2019) Novel anemometer based on inductor bending effect. J Microelectromech Syst 28(3):321–323. http://doi.org/10.1109/jmems.2019.2909103 Deng WJ, Wang LF, Dong L et al (2018) Experimental study of the bending effect on LC wireless Humidity Sensors fabricated on flexible PET substrates. J Microelectromech Syst 27(5):761–763. http://doi.org/10.1109/jmems.2018.2856912 Wang B, Han B, Wang K et al (2024) Air vehicle humidity sensor based on PVA film humidity sensing principle. APL Mater 12(7):071116. http://doi.org/10.1063/5.0213766 Zhang C, Guo L, Wang LF et al (2014) Passive wireless integrated humidity sensor based on dual-layer spiral inductors. Electron Lett 50(18):1287–1289. http://doi.org/10.1049/el.2014.1240 Dong L, Deng WJ, Wang LF et al (2018) Multi-parameters detection implemented by LC sensors with branching inductors. IEEE Sens J 19(1):304–310. http://doi.org/10.1109/jsen.2018.2876060 Scidà A, Haque S, Treossi E et al (2018) Application of graphene-based flexible antennas in consumer electronic devices. Mater Today 21(3):223–230. http://doi.org/10.1016/j.mattod.2018.01.007 Escobedo P, de Pablos-Florido J, Carvajal MA et al (2020) The effect of bending on laser-cut electro-textile inductors and capacitors attached on denim as wearable structures. Text Res J 90(21–22):2355–2366. http://doi.org/10.1177/0040517520920570 Talekar PM, Pulijala V (2021) Improvement of inductor performance parameters with thin 20 nm permalloy patterns. IEEE Mangn Lett 12:1–5. http://doi.org/10.1109/lmag.2021.3130833 Pulijala V, Syed A (2016) Comparison of the effects of 60 nm and 96 nm thick patterned permalloy thin films on the performance of on-chip spiral inductors. J Magn Magn Mater 419:245–248. http://doi.org/10.1016/j.jmmm.2016.06.031 Gardner DS, Schrom G, Paillet F et al (2009) Review of on-chip inductor structures with magnetic films. IEEE Trans Magn 45(10):4760–4766. http://doi.org/10.1109/tmag.2009.2030590 Tumma SK, Nistala BR (2020) A novel hybrid series stacked differential fractal inductor for MMIC applications. Circuit World 46(2):137–145. http://doi.org/10.1108/cw-06-2019-0058 Anthony R, Wang N, Casey DP et al (2016) MEMS based fabrication of high-frequency integrated inductors on Ni-Cu-Zn ferrite substrates. J Magn Magn Mater 406:89–94. http://doi.org/10.1016/j.jmmm.2015.12.099 Wang T, Jiang W, Divan R et al (2017) Novel electrically tunable microwave solenoid inductor and compact phase shifter utilizing permaloy and PZT thin films. IEEE Trans Microwave Theory Tech 65(10):3569–3577. http://doi.org/10.1109/tmtt.2017.2731765 Bellaredj MLF, Kohl P, Swaminathan M (2021) Design and characterization of package-embedded solenoidal magnetic core inductors for high-frequency and high-efficiency sip integrated voltage regulators. IEEE Trans Compon Packag Manuf Technol 11(4):625–634. http://doi.org/10.1109/tcpmt.2021.3068189 Mishra D, Raj PM, Tummala R (2016) Design, fabrication and characterization of thin power inductors with multilayered ferromagnetic-polymer composite structures. Microelectron Eng 160:34–38. http://doi.org/10.1016/j.mee.2016.02.071 Chikazumi Sōshin (1997) and Chad D. Graham. Physics of ferromagnetism. Oxford University Press. https://doi.org/10.1093/oso/9780198517764.001.0001 Lou J, Ren H, Chao X et al (2022) Recent progress in the preparation technologies for micro metal coils. Micromachines 13(6):872. http://doi.org/10.3390/mi13060872 Gao LY, Liu ZQ (2022) Electroplating low coercivity nanocrystalline Fe-Ni magnetic cores for high performance on-chip microinductor. IEEE Trans Magn 58(4):1–7. http://doi.org/10.1109/tmag.2022.3144488 Zhou G, Zhang W, He D et al (2019) A novel structured spiral planar embedded inductor: Electroless-plating NiCoP alloy on copper coil as magnetic core. J Magn Magn Mater 489:165363. http://doi.org/10.1016/j.jmmm.2019.165363 Chen Y, Zhang Y, Wang J et al (2024) Flexible mini-inductors with ultra‐high inductance density directly cut from soft magnetic amorphous alloys by femtosecond laser. Adv Funct Mater 34(27):2313355. http://doi.org/10.1002/adfm.202313355 Bjelica JM, Djuric NM, Djuric SM (2020) Modeling and performance analysis of planar fractal inductors. IEEE Trans Magn 56(11):1–8. http://doi.org/10.1109/tmag.2020.3018428 Djuric SM, Dubourg G (2017) Fractal inductors on flexible plastic substrate fabricated by laser ablation. Microelectron Eng 168:10–14. http://doi.org/10.1016/j.mee.2016.10.008 Djuric SM, Dubourg G (2017) Fractal inductors on flexible plastic substrate fabricated by laser ablation. Microelectron Eng 168:10–14. http://doi.org/10.1016/j.mee.2016.10.008 Gao Y, Zardareh SZ, Yang X et al (2014) Significantly Enhanced Inductance and Quality Factor of GHz Integrated Magnetic Solenoid Inductors With FeGaB/Al 2 O 3 Multilayer Films. IEEE Trans Electron Devices 61(5):1470–1476. http://doi.org/10.1109/ted.2014.2313095 Wang X, Chen H, Shi X et al (2017) A novel NiZn ferrite integrated magnetic solenoid inductor with a high quality factor at 0.7-6 GHz. AIP Adv 7(5). http://doi.org/10.1063/1.4973283 Pan P, Chen C, Gu J et al (2024) High-performance 3-D silicon-embedded coupled solenoid inductors with inserted magnetic core. IEEE Trans Electron Devices. http://doi.org/10.1109/ted.2024.3381920 Zhou N, Liu C, Lewis JA et al (2017) Gigahertz electromagnetic structures via direct ink writing for radio-frequency oscillator and transmitter applications. Adv Mater 29(15):1605198. http://doi.org/10.1002/adma.201605198 Huang W, Yang Z, Kraman MD et al (2020) Monolithic mTesla-level magnetic induction by self-rolled-up membrane technology. Sci Adv 6(3):eaay4508. http://doi.org/10.1126/sciadv.aay4508 Shi Q, Chen H, Pang K et al (2020) Permalloy/polydimethylsiloxane nanocomposite inks for multimaterial direct ink writing of gigahertz electromagnetic structures[J]. J Mater Chem C 8(43):15099–15104. http://doi.org/10.1039/d0tc03244a Lazarus N, Sarah S (2018) Bedair. Bubble inductors: pneumatic tuning of a stretchable inductor. AIP Adv. http://doi.org/10.1063/1.5003372 . 8.5 Lazarus N, Meyer CD (2016) Stretchable inductor with liquid magnetic core. Mater Res Express 3(3):036103. http://doi.org/10.1088/2053-1591/3/3/036103 Chen L, Qiao Z, Liu S et al (2025) High inductance density in CMOS-compatible magnetically integrated 3D microinductors for radio-frequency applications. Nat Commun 16(1):10072. http://doi.org/10.1038/s41467-025-65032-3 Hubert A, Schäfer R (1998) Magnetic domains: the analysis of magnetic microstructures. Springer Sci Bus Media. https://doi.org/10.1007/978-3-540-85054-0 Zhang M, Xia L, Dang S et al (2019) Electrical properties of double-sided polymer surface nanostructures. Nanoscale Res Lett 14(1):230. http://doi.org/10.1186/s11671-019-3071-2 Zhou N, Liu C, Lewis JA et al (2017) Gigahertz electromagnetic structures via direct ink writing for radio-frequency oscillator and transmitter applications. Adv Mater 29(15):1605198. http://doi.org/10.1002/adma.201605198 Zhang L, He Y, Deng W et al (2024) High-efficiency flexible organic solar cells with a polymer-incorporated pseudo-planar heterojunction. Discover Nano 19(1):39. http://doi.org/10.1186/s11671-024-03982-1 Yang Z, Khandelwal A, Wang AT et al (2024) Unleashing the performance of self-rolled‐up 3d inductors via deterministic electroplating on cylindrical surfaces. Adv Mater Technol 9(10):2400092. http://doi.org/10.1002/admt.202470043 Long TR (1966) Magnetoelastic sensitivity and composition of Permalloy films. J Appl Phys 37(3):1470–1471. http://doi.org/10.1063/1.1708521 Lei T, Zhang W, Bo G et al (2024) Tuning the Ferromagnetic Resonance Frequency of Microstructured Permalloy Film on Flexible Substrate. physica status solidi (RRL)-Rapid Research Letters. 18(9):2400081. http://doi.org/10.1002/pssr.202400081 Kumar D, Singh S, Vishawakarma P et al (2016) Tailoring of in-plane magnetic anisotropy in polycrystalline cobalt thin films by external stress. J Magn Magn Mater 418:99–106. http://doi.org/10.1016/j.jmmm.2016.03.072 Ohashi Y, Matsushima Y, Kaiju H (2023) Modulation of magnetic anisotropy by bending in Ni and Ni 78 Fe 22 thin films on polycarbonate organic substrates. J Magn Magn Mater 570:170497. http://doi.org/10.1016/j.jmmm.2023.170497 Freitas WJ, Manera LT, Swart JW (2022) Functional cyclic bending test for integrated inductors on flexible Kapton substrate[J]. Microelectron Reliab 135:114592. http://doi.org/10.1016/j.microrel.2022.114592 Greek S, Ericson F (1998) Young's modulus, yield strength and fracture strength of microelements determined by tensile testing. MRS Online Proceedings Library (OPL) , 518: 110183. https://doi.org/10.1557/PROC-518-51 Zhang J, Lee WK, Tu R et al (2021) Spontaneous formation of ordered magnetic domains by patterning stress[J]. Nano Lett 21(12):5430–5437. http://doi.org/10.1021/acs.nanolett.1c00070 Bowden N, Brittain S, Evans AG et al (1998) Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer[J]. Nature 393(6681):146–149. http://doi.org/10.1038/30193 Dai G, Zhan Q, Yang H et al (2013) , . Controllable strain-induced uniaxial anisotropy of Fe81Ga19 films deposited on flexible bowed-substrates. Journal of Applied Physics, 114(17): 173913. http://doi.org/10.1063/1. 4829670 Gueye M, Wague BM, Zighem F et al (2014) , . Bending strain-tunable magnetic anisotropy in Co 2 FeAl Heusler thin film on Kapton. Applied Physics Letters, 105(6): 062409. http://doi.org/10.1063/1. 4893157 Ota S, Hibino Y, Bang D et al (2016) Strain-induced reversible modulation of the magnetic anisotropy in perpendicularly magnetized metals deposited on a flexible substrate. Appl Phys Express 9(4):043004. http://doi.org/10.7567/apex.9.043004 Zhao L et al (2024) Artificial magnetic disclination through local stress engineering. Acta Mater 265:119579. http://doi.org/10.1016/j.actamat.2023.119579 Li Z et al (2023) Strength, plasticity and coercivity tradeoff in soft magnetic high-entropy alloys by multiple coherent interfaces. Acta Mater 254:118970. http://doi.org/10.1016/j.actamat.2023.118970 Pandya NY, Mevada AD, Gajjar PN (2016) Lattice dynamical and thermodynamic properties of FeNi3, FeNi and Fe3Ni invar materials[J]. Comput Mater Sci 123:287–295. http://doi.org/10.1016/j.commatsci.2016.07.001 Additional Declarations No competing interests reported. Supplementary Files Supportinginformation.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 09 Mar, 2026 Reviews received at journal 25 Feb, 2026 Reviews received at journal 24 Feb, 2026 Reviewers agreed at journal 21 Feb, 2026 Reviewers agreed at journal 21 Feb, 2026 Reviewers agreed at journal 20 Feb, 2026 Reviewers invited by journal 16 Feb, 2026 Editor invited by journal 16 Feb, 2026 Editor assigned by journal 10 Feb, 2026 Submission checks completed at journal 10 Feb, 2026 First submitted to journal 10 Feb, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8769909","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":595013360,"identity":"ec20afbe-7d99-4df6-ae95-ae043758bd9b","order_by":0,"name":"Jian Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYBACxmYQ0QAk2HsYJGBsIrXwnCFSC0QfSJlEDpFamNuZnz38ucMuTz7y7cHbPAw2shsOMD97gN9hbOYGkmeSiw1v5yVb8zCkGW84ABQh4BczCcM25sSNs3PMpHkYDiduOMDDJoFfC/s3icS2+sSNM8+AtPwnRguPmcTBtsOJ8yV4QFoOEKWlTLKx7XjiBp4cY8s5BsnGMw+zmeHVYth/fJvkz7bqxPntZwxvvKmwk+073vwMv5YGKMPgAJgEYmZ86oFAHs5owKNqFIyCUTAKRjYAAC48RlQELPMLAAAAAElFTkSuQmCC","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":true,"prefix":"","firstName":"Jian","middleName":"","lastName":"Zhang","suffix":""},{"id":595013361,"identity":"0526cb3a-b8aa-41e1-8582-92182fa5d81f","order_by":1,"name":"Tianlong Fu","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Tianlong","middleName":"","lastName":"Fu","suffix":""},{"id":595013362,"identity":"0420bbe5-d3a3-4926-95d2-5a590ef6a836","order_by":2,"name":"Hongjin Ji","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Hongjin","middleName":"","lastName":"Ji","suffix":""},{"id":595013363,"identity":"d48e3fa5-a99f-4202-ab36-e98807c92bbc","order_by":3,"name":"Ningning Wang","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Ningning","middleName":"","lastName":"Wang","suffix":""},{"id":595013364,"identity":"c9960392-5724-41d0-9b74-d08f037c5645","order_by":4,"name":"Hongxia Li","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Hongxia","middleName":"","lastName":"Li","suffix":""},{"id":595013365,"identity":"ece7039e-071e-4aef-a097-12f38a7990b4","order_by":5,"name":"Zhe Kong","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Zhe","middleName":"","lastName":"Kong","suffix":""},{"id":595013366,"identity":"50d9cc55-59c2-4669-b794-f98d3725a93d","order_by":6,"name":"Xiaoyu Zhao","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyu","middleName":"","lastName":"Zhao","suffix":""},{"id":595013367,"identity":"a3717c1d-ca56-4aa2-ac8f-e08efbf2af2c","order_by":7,"name":"Feng Zhou","email":"","orcid":"","institution":"Changzhou Booming New Material Technology Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Feng","middleName":"","lastName":"Zhou","suffix":""},{"id":595013368,"identity":"c1ee5f7b-dc32-467f-9e51-d407dc2cecbb","order_by":8,"name":"Xuefeng Zhang","email":"","orcid":"","institution":"Hangzhou Dianzi University","correspondingAuthor":false,"prefix":"","firstName":"Xuefeng","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-02-03 02:08:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8769909/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8769909/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103255540,"identity":"e2489732-a707-4690-8df4-401c8f68f670","added_by":"auto","created_at":"2026-02-23 16:47:15","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":237117,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e(a-f) Fabrication process of the flexible thin-film inductor. (g) Schematic top view and (h) cross-sectional view of the flexible thin-film inductor illustrating the key design parameters and the components, respectively.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/5d77615135ee95f7e7e21284.png"},{"id":103505649,"identity":"c6305e33-f68e-47d5-8982-bf451838ed11","added_by":"auto","created_at":"2026-02-26 13:32:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":421670,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e(a) Digital image of the as-fabricated thin-film inductor on PET substrate. (b) Cross-sectional SEM image of the as-fabricated thin-film inductor including multilayers of the insulator layers, the Py magnetic core, and the top-side electrode. (c) L and (d) Q of inductors fabricated on PET substrate (solid line) and SiO2 substrate (dashed line) with different turns N.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/ca48f64455fe50cbc2878a8c.png"},{"id":103255546,"identity":"bd1b25de-aeb3-46c2-a03d-c5f890b34a3d","added_by":"auto","created_at":"2026-02-23 16:47:17","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":293345,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e(a) Scheme showing the impact of tensile/compressive stress on the orientation of M in magnetic film with negative magnetostriction coefficient. Hysteresis loop of Py magnetic film under applied tensile stress, measured with the in-plane magnetic fields (b) parallel (Hx) and (c) perpendicular (Hy) to the tension direction.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/e0ce68c54b912736ee0615a3.png"},{"id":103505950,"identity":"c4b30323-73a0-4a30-8eab-562c5ed0bedb","added_by":"auto","created_at":"2026-02-26 13:33:36","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":427567,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e(a) Digital image of tensile strain applied along the Py magnetic core of the thin-film inductor. (b) L and (c) Q variation of a 5-turn inductor under different tensile strains. (d) Digital image of compressive strain applied along the Py magnetic core of the thin-film inductor. (e) L and (f) Q variation of a 5-turn inductor under different compressive strains.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/87f9f3e63d0c165017c0e06a.png"},{"id":103505313,"identity":"fe3b74bf-04e7-4062-a6b9-39265880cd9f","added_by":"auto","created_at":"2026-02-26 13:29:45","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":387733,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e(a) Digital image of tensile strain applied perpendicularly to the Py magnetic core of the thin-film inductor. (b) L and (c) Q variation of a 5-turn inductor under different tensile strains . (d) Digital image of compressive strain applied perpendicularly to the Py magnetic core of the thin-film inductor. (e) L and (f) Q variation of a 5-turn inductor under different compressive strains.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/f8e69610fbcf2a39895b259a.png"},{"id":103255545,"identity":"7aa55efb-baa9-47bb-a4b2-8f267266e366","added_by":"auto","created_at":"2026-02-23 16:47:17","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":110602,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e(a) L and Q at 800 MHz of a 5-turn solenoid-type thin-film inductor recorded with 1000 bending cycles of 1.8% tensile/compressive strains. (b) Comparison of the overpotentials of our results with recently reported solenoid-type thin-film inductors.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/5bb30cd63e0d2d8a5e313909.png"},{"id":104397509,"identity":"458f3278-b3d2-44f1-90ab-8d0ed0668bb9","added_by":"auto","created_at":"2026-03-11 11:50:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2565381,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/55410a1a-0f19-4e6b-ac60-e8f074d588fe.pdf"},{"id":103505502,"identity":"7b029e55-dba5-4889-a86b-86cd082ca3de","added_by":"auto","created_at":"2026-02-26 13:31:31","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2242292,"visible":true,"origin":"","legend":"","description":"","filename":"Supportinginformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-8769909/v1/dc0292c3f44b592aa3630984.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Tunable High-Frequency Thin-Film Inductor through Stress-Induced Magnetic Anisotropy","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003e \u003cem\u003eInductor, composed with coil and magnetic core which can induce electric current and magnetic field respectively, can realize the electrical power transfer and energy storage. As being broadly applied in circuits, inductors are used for filtering, choking, power transfer, and voltage transformation\u003c/em\u003e [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. \u003cem\u003eBeyond these traditional applications, recent advances in dynamically responsive materials have enabled inductors to function as power generators\u003c/em\u003e [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], \u003cem\u003eanemometers\u003c/em\u003e [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], \u003cem\u003ehumidity sensors\u003c/em\u003e [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], \u003cem\u003eand multi-parameter detectors\u003c/em\u003e [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. \u003cem\u003eAs a crucial passive component, the miniaturization, adjustability and high-frequency operation of tunable and flexible thin-film inductors have become particularly important for the rapid development of flexible electronics\u003c/em\u003e [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cem\u003eCurrent mainstream of thin-film inductors primarily includes planar inductors\u003c/em\u003e [\u003cspan additionalcitationids=\"CR14 CR15\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] \u003cem\u003eand solenoid-type inductors\u003c/em\u003e [\u003cspan additionalcitationids=\"CR18 CR19 CR20\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. \u003cem\u003ePlanar inductors composed of track-shape coil are typically fabricated via single-step patterning (e.g. photolithography, nanoimprint, inkjet printing\u003c/em\u003e [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003cem\u003e), followed plating\u003c/em\u003e [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], \u003cem\u003ephysical vapor deposition (PVD), or direct cutting by femtosecond laser on metallic layer\u003c/em\u003e [\u003cspan additionalcitationids=\"CR25 CR26\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. \u003cem\u003eThough with simple structure, the leakage flux and the accumulation of parasitic capacitance is hardly to be avoided, thereby limiting its potential application. In contrast, solenoid-type thin-film inductors adopt the coil around magnetic core, where the encapsulated magnetic core further improves both inductor performance and integration density\u003c/em\u003e [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. \u003cem\u003eCompared to planar inductors, the solenoid-type inductors reduce flux leakage, enhance inductor efficiency and improve overall performance\u003c/em\u003e [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. \u003cem\u003eAdditionally, their lower parasitic capacitance and resistance enable stable high-frequency inductance, making them suitable for high-speed digital circuits and RF applications\u003c/em\u003e [\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cem\u003eFor a solenoid-type inductor with the coil turns N, the cross-sectional area of the core A\u003c/em\u003e \u003csub\u003e \u003cem\u003ec\u003c/em\u003e \u003c/sub\u003e, \u003cem\u003eand the length of each turn of the coil l\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003ethe inductance L and DC resistance R\u003c/em\u003e\u003csub\u003e\u003cem\u003edc\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eof the coupled inductor can be respectively expressed as\u003c/em\u003e [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:L=\\frac{{\\mu\\:}_{0}{\\mu\\:}_{r}{N}^{2}{A}_{c}}{{l}_{m}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{R}_{dc}=\\frac{{l}_{0}N\\rho\\:}{{A}_{\\omega\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ewhere \u0026micro;\u003c/em\u003e \u003csub\u003e \u003cem\u003e0\u003c/em\u003e \u003c/sub\u003e \u003cem\u003eand \u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eare the vacuum permeability and relative permeability of the magnetic core respectively, ρ is the resistivity of the coil metal material, l\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eis the length of the magnetic core, and A\u003c/em\u003e\u003csub\u003e\u003cem\u003eω\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eis the cross-sectional area of the wire. Aiming to the tunable thin-film inductor which are commonly required for voltage-controlled oscillators, low noise amplifiers, radio frequency identification, etc., people can change the conductive or magnetic parameters in\u003c/em\u003e Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e)\u0026amp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) \u003cem\u003eto real-time adjust the inductance. For example, Lazarus et al. fabricated a pneumatically tunable inductor using liquid metal as conductive traces and silicone elastomer as pneumatic chambers\u003c/em\u003e [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. \u003cem\u003eThrough aerodynamic deformation, the inductor exhibits volume expansion and compression, and achieves inductance modulation between 100\u0026ndash;400 nH at -15\u0026thinsp;~\u0026thinsp;10 kPa. Meyer et al. fabricated a stretchable inductor based on silicone elastomer and liquid metal, of which the inductance is enhanced up to 20% with twice its original length\u003c/em\u003e [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. \u003cem\u003eHowever, most tunable inductors are reported in macroscale, and research on microscaled thin-film inductors still face a challenge in terms of size\u003c/em\u003e [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. \u003cem\u003eFurthermore, the great volume change may lead the plastic deformation of metal and the failure of coils. There is a great demand for a gentle and easy-access tuning method for thin-film inductor in flexible electronics.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003eWhile the improvement of inductor performance through strain has been reported, the current research has mainly focused on the geometric changes induced by deformation\u003c/em\u003e [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. \u003cem\u003eBased on\u003c/em\u003e Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), \u003cem\u003ethe inductor performance is directly decided by permeability, and the permeability of the magnetic core is closely relative to the magnetic anisotropy\u003c/em\u003e [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. \u003cem\u003eFor the magnetic film on flexible substrate, the stress status (bending, stretching, or compression) applied on the film directly orients the spontaneous magnetization (M) through magnetoelastic coupling, and thus effect the magnetic anisotropy and the permeability at microscale. Based on this, mechanically bending thin-film inductors containing magnetic core on flexible substrate should enable tunable inductance without altering the inductor's physical dimensions or components.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003eIn this work, we demonstrated an ultrathin-film inductor fabricated via stencil lithography, incorporating gold (Au) coil around a permalloy (Py) magnetic core, with a total thickness \u0026lt; 1 \u0026micro;m. The bending of flexible substrate induced the strain and changed the magnetic anisotropy of magnetic core through magnetoelastic coupling, so as to adjust the inductance value. Compared with the inductor without Py magnetic core which were insensitive to bending, the inductor with Py magnetic core showed over 140% enhancement of the inductance value at 800MHz by bending. The multi-directional adjustability of this ultrathin-film inductor was further investigated by bending at different direction. The stability test of over 1000 bending/releasing cycles demonstrated it suitable as the adjustable and flexible ultrathin-film inductor which is expected for the future applications in RF circuit and wireless communication.\u003c/em\u003e \u003c/p\u003e"},{"header":"2 Experimental section","content":"\u003cp\u003e \u003cem\u003eFor the fabrication of flexible electronics, conventional photolithography faces challenges on flexible substrates, and alternative techniques such as nanoimprint lithography, stencil lithography, and inkjet printing have emerged as the viable fabrication strategies\u003c/em\u003e [\u003cspan additionalcitationids=\"CR40\" citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. \u003cem\u003ePolyethylene terephthalate (PET) as one of the most common substrates in flexible electronics was selected with the thickness of 0.125 mm. PET surface was firstly annealed at 120 ℃ for 10 min and cleaned with O\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eplasma to improve the smoothness and adhesion\u003c/em\u003e \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea\u003cb\u003e)\u003c/b\u003e. \u003cem\u003eA solenoid-type inductor was multilayered as bottom- and top-side coils, SiO\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003einsulator layers and magnetic core, and were fabricated through stencil lithography with multi-shape shadow masks in electron-beam evaporation. Detailedly, 10-nm Cr and 150-nm Au were deposited through shadow mask to form the bottom-side electrode\u003c/em\u003e \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb\u003cb\u003e)\u003c/b\u003e. \u003cem\u003eSiO\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/Py/SiO\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003elayers with the thicknesses of 160 nm/120 nm/160 nm were respectively deposited\u003c/em\u003e \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec-e\u003cb\u003e)\u003c/b\u003e. \u003cem\u003eThe permalloy owns high permeability and high saturation magnetic induction, making it commonly used for high-frequency inductor. Here, Py film including 81 wt% Ni and 19 wt% Fe with a negative magnetostrictive coefficient of ~ -2 ppm was selected as the magnetic core\u003c/em\u003e [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. \u003cem\u003e10-nm Cr and 150-nm Au were deposited again to complete the coil around the Py core\u003c/em\u003e \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef\u003cb\u003e)\u003c/b\u003e. \u003cem\u003eBy this way, organic solvents were totally avoided on organic substrate and a multilayer-stacked solenoid-type inductor was ideally realized. The structural parameters of the inductor illustrated in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eh\u003cb\u003e\u0026amp;g\u003c/b\u003e \u003cem\u003eare summarized in\u003c/em\u003e Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters of inductors with different turns.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eg (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ePy. core\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e8/15/20\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e2\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e0.4\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003e4.2/9.2/13.3\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e0.2\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eAir core\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e/\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e2\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e0.4\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003e4.2/9.2/13.3\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e0.2\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eThe calculation of strain induced by bending is detailedly descripted in\u003c/em\u003e \u003cb\u003eFig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e. \u003cem\u003eThe magnetic properties of the Py magnetic core with and without applied stress were measured by using the magnetic-optical Kerr microscope (MOKE, from Evico Magnetics GmbH, Germany). The inductance L and the quality factor Q were tested by using the impedance analyzer (from Keysight, USA E49918 1MHz \u0026minus;\u0026thinsp;1GHz). The final samples were characterized by magnetic force microscope (AFM, from Nano Wizard 4-NanoScience, JPK Instruments S3 AG, Germany) and scanning electron microscopy (SEM, from Sigma 300, Carl Zeiss, Germany).\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3 Results and discussion","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 The study of the as-fabricated thin-film inductor\u003c/h2\u003e \u003cp\u003e \u003cem\u003eThe previously reported microfabrication processes of thin-film inductors normally involved multistep patterning with photolithography, in which the usage of organic solvents could damage the organic substrates. Aiming to flexible thin-film inductor, we developed stencil lithography to totally avoid organic solvents on organic substrate and a multilayer-stacked solenoid-type inductor with the minimum linewidth of 100 \u0026micro;m is ideally realized, as the sample shown in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea. \u003cem\u003eThe SEM image with cross-sectional view in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb \u003cem\u003eshow the layers including the insulator layers, the Py magnetic core, and the top-side electrode, proving the total thickness of 600 nm. Considering the bottom-side electrode with the additional thickness of 160 nm, the total thickness of our proposed device is only 760 nm. This ultrathin construction ensured the pliability and deformation uniformity in the following bending test.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eAs shown in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec\u003cb\u003e\u0026amp;d\u003c/b\u003e, \u003cem\u003ethe inductance (L) and quality factor (Q) of the as-fabricated thin-film inductors with varying numbers of turns were measured on both PET and SiO₂ substrates. L for the thin-film inductors fabricates on PET substrate is over 20 nL at 100\u0026thinsp;~\u0026thinsp;1000 MHz (shown in the solid lines in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea\u003cem\u003e), while L on SiO2 substrate is less than 10 nL (shown in the dash lines in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea\u003cem\u003e). The difference of L on PET and SiO2 substrates is even increased with increasing frequency. For example, L with 15 turns on PET and SiO₂ substrate is 29.2 and 3.8 nH at 800 MHz, respectively, presenting a sevenfold enhancement on flexible substrate. The quality factor Q, defined as the ratio of reactive power to active power, is derived in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed. \u003cem\u003eThe dash lines show that Q for the thin-film inductors on SiO₂ substrate is less than 0.5, indicating the significant energy loss and more resistive characteristics\u003c/em\u003e [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. \u003cem\u003eFor comparison, Q value is enhanced over 2 with higher frequency on PET substrate, as the solid lines shown in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 The study of the magnetic anisotropy with strain\u003c/h2\u003e \u003cp\u003e \u003cem\u003eThis superiority for the thin-film inductors on flexible substrate is notable, and can be attributed to the additional tension distribution caused in the magnetic layer deposited on flexible substrate\u003c/em\u003e [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. \u003cem\u003eIt was reported that this tension specially generated on flexible substrate is mainly attributed to the Young\u0026rsquo;s moduli mismatch between different layers during stress recovery (E\u003c/em\u003e\u003csub\u003e\u003cem\u003ePy\u003c/em\u003e\u003c/sub\u003e: \u003cem\u003e~113 GPa and E\u003c/em\u003e\u003csub\u003e\u003cem\u003ePET\u003c/em\u003e\u003c/sub\u003e: \u003cem\u003e2-2.7 GPa)\u003c/em\u003e [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e], \u003cem\u003eand thermal expansion mismatch between Py/PET layers\u003c/em\u003e [\u003cspan additionalcitationids=\"CR48\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. \u003cem\u003eThe in-plane stress distribution on PET substrate pronounced in-plane magnetic anisotropy\u003c/em\u003e [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e], \u003cem\u003eresulting in superior inductance (L) and quality factor (Q) values compared to the one on rigid substrates. The slightly reduced L and Q for inductors with more turns were also noticed in this work, which could be attributed to the increased resistance with longer conductive coil\u003c/em\u003e [\u003cspan additionalcitationids=\"CR53\" citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eTo evaluate the magnetic core's contribution, we fabricated air-core inductors with identical geometries on both rigid and flexible substrates\u003c/em\u003e \u003cb\u003e(Fig. S2)\u003c/b\u003e. \u003cem\u003eThe results clearly show that air-core inductors on both of PET and SiO\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003esubstrates maintain Q below 1 across a broad frequency range, exhibiting predominantly resistive behaviour. Bending the flexible substrate could easily induce the tensile and compressive stress in Py magnetic core. As described in\u003c/em\u003e \u003cb\u003eIntroduction\u003c/b\u003e, \u003cem\u003ethe spontaneous magnetization (M) and magnetic anisotropy is immediately related to the applied stress status. Considering the electron-beam deposited magnetic films, which is commonly polycrystalline and magnetically isotropic, the magnetoelastic coupling mechanism can be elementarily described as\u003c/em\u003e:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{E}_{\\sigma\\:}=-\\frac{3}{2}\\sigma\\:\\lambda\\:{{cos}}^{2}\\theta\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ewhere E\u003c/em\u003e \u003csub\u003e \u003cem\u003eσ\u003c/em\u003e \u003c/sub\u003e, \u003cem\u003eσ, λ, and θ present the magnetoelastic energy, stress, magnetostrictive coefficient, and angle between\u003c/em\u003e \u003cb\u003eM\u003c/b\u003e \u003cem\u003eand σ direction, respectively. For negative magnetostrictive films (Py used in our system with λ ~ -2 ppm), minimizing E\u003c/em\u003e\u003csub\u003e\u003cem\u003eσ\u003c/em\u003e\u003c/sub\u003e \u003cem\u003erequires θ\u0026thinsp;=\u0026thinsp;90\u0026deg; or 270\u0026deg; and\u003c/em\u003e \u003cb\u003eM\u003c/b\u003e \u003cem\u003eperpendicular to the direction of tension (σ\u0026thinsp;\u0026gt;\u0026thinsp;0). Conversely, θ\u0026thinsp;=\u0026thinsp;0\u0026deg; or 180\u0026deg; and\u003c/em\u003e \u003cb\u003eM\u003c/b\u003e \u003cem\u003eis parallel to the direction of compression stress (σ\u0026thinsp;\u0026lt;\u0026thinsp;0).\u003c/em\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea \u003cem\u003eshows the relationship between\u003c/em\u003e \u003cb\u003eM\u003c/b\u003e \u003cem\u003eand the applied tensile/compressive stresses with the mechanism of magnetoelastic coupling for the cases when bending the Py magnetic core on the flexible substrate. To experimentally investigate the impact of stress on the magnetic anisotropy of magnetic thin films, we measured the magnetic hysteresis loops using MOKE at room temperature under in-plane magnetic fields applied perpendicular (H\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e) and parallel (H\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e) to the tension direction.\u003c/em\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb \u003cem\u003eshows the magnetic hysteresis loop with H\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eand the remanence ratio (M\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e) are reduced to be 0.31 from 0.75. This means the dampening effect on magnetic anisotropy along the magnetic core by tension. On the contrary\u003c/em\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec \u003cem\u003eshows the magnetic hysteresis loops with H\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eand M\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eis increased to be 0.90 from 0.73, meaning the enhancement of the magnetic anisotropy perpendicular to the magnetic core by tension. The condition for applying compression stress should be reversed based on\u003c/em\u003e Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 The study of the dynamic inductance with strain\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eIn an inductor, the change of stress status directly impacts the stress anisotropy on Py magnetic core, which are relative to the initial permeability \u0026micro;\u003c/em\u003e \u003csub\u003e \u003cem\u003ei\u003c/em\u003e \u003c/sub\u003e: [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e]\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\mu\\:}_{i}\\propto\\:\\frac{{M}_{s}^{2}}{{K}_{1}+{K}_{2}}\\propto\\:\\frac{{M}_{s}^{2}}{{K}_{1}+\\lambda\\:\\sigma\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ewhere M\u003c/em\u003e \u003csub\u003e \u003cem\u003es\u003c/em\u003e \u003c/sub\u003e, \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eand K\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eare the saturation magnetization, the magnetocrystalline anisotropy and the stress anisotropy. Thus, the applied stress may change \u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eand make the thin-film inductor tunable. We tested L for the 5-turn inductor under different bending states along the Py magnetic core as illustrated in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea\u003cb\u003e\u0026amp;d\u003c/b\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb \u003cem\u003eindicates that under tensile strain, L increased with larger bending deformation. At maximum tensile strain of 1.8%, L reached at 43.7 nH at 800 MHz, with the 39.6% increasement compared to the flat status (31.3 nH at 800 MHz). Correspondingly, Q was also enhanced with larger tensile strain (\u003c/em\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec\u003cem\u003e). In contrast, under compressive strain, L and Q decreased stepwise with larger bending deformation (\u003c/em\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee\u003cb\u003e\u0026amp;f\u003c/b\u003e\u003cem\u003e). At maximum compressive strain of 1.8%, the inductance was decreased by 5.1% @ 800 MHz, demonstrating an opposite responsibility to the revered strain states, matching\u003c/em\u003e Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). \u003cem\u003eIn\u003c/em\u003e \u003cb\u003eFig. S3\u003c/b\u003e, \u003cem\u003ethe inductor without the Py magnetic core is also examined by bending. Regardless of tensile or compressive strain, L and Q remain stable at 44.5 nH and 1.28 at 800 MHz, respectively. This conclusively demonstrates that the magnetoelastic coupling in the magnetic core plays a key role in regulating the thin-film inductance.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eBesides bending along the Py magnetic core, we also examined the impact from bending perpendicularly to the Py magnetic core in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea\u003cb\u003e\u0026amp;d\u003c/b\u003e, \u003cem\u003ewhich interestingly shows the reversed tunability corresponding to the applied tensile or compressive strain. In this case, both of L and Q were weaken under tensile strain (\u003c/em\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb\u003cb\u003e\u0026amp;c\u003c/b\u003e\u003cem\u003e), and were enhanced under compressive strain (\u003c/em\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee\u003cb\u003e\u0026amp;f\u003c/b\u003e\u003cem\u003e). For instance, L is reduced from 31.3 nH to 28.1 nH at 800 MHz with the tensile strain of 1.8%, and is enhanced from 31.3nH to 32.4nH at 800 MHz with the compressive strain of 1.8%. This revered result can be explained by Poisson\u0026rsquo;s ratio: ε\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e=-υε\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e. \u003cem\u003eConsidering that the average ratio υ for or Fe-Ni invar alloys is ~\u0026thinsp;0.29\u003c/em\u003e [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e], \u003cem\u003ethe tensile strain along the lateral direction can considered as the compressive strain along the longitudinal direction. Thus, the applied tensile/compressive strain perpendicularly to the Py magnetic core can be respectively switched as the applied compressive/tensile stress along the Py magnetic core, and thus lead the reversed tunability.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 The stability test\u003c/h2\u003e \u003cp\u003e \u003cem\u003eTo evaluate the stability of this flexible and tunable thin-film inductor, we conducted cyclic tests by alternating tensile and compressive strains. In each cycle, a 5-turn inductor is bended to 1.8% tensile strain and 1.8% compressive strain in turn, and then record the inductance performance at 800 MHz in flat status.\u003c/em\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea \u003cem\u003eshows that L is stable at 33\u0026thinsp;~\u0026thinsp;34 nH after 600 cycles and slightly reduced to be 27 nH in 700\u0026thinsp;~\u0026thinsp;1000 cycles. Correspondingly, Q is maintained at 3.0 in 600 cycles, and slightly reduced to be 2.4 in 700\u0026thinsp;~\u0026thinsp;1000 cycles. In\u003c/em\u003e \u003cb\u003eFig. S4a\u0026amp;b\u003c/b\u003e, \u003cem\u003eoptical image and AFM image prove that the Py magnetic core maintains its structural integrity after 100 cycles due to the coverage of SiO\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003einsulator layer. Without SiO\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003einsulator layer, however, the Py magnetic core shows the cracks after once bending as shown in\u003c/em\u003e \u003cb\u003eFig. S4c\u0026amp;d\u003c/b\u003e. \u003cem\u003eAs compared with the previous report in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb, a \u003cem\u003ethinnest solenoid-type thin-film inductors with considerable and stable tunability is achieved in this work.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4.Conclusions","content":"\u003cp\u003e \u003cem\u003eIn summary, this study demonstrates a new method to realize ultrathin and tunable solenoid-type thin-film inductors on flexible substrates. Using stencil lithography through shadow-mask-assisted evaporation, solenoid-type thin-film inductors were ideally fabricated with the total thickness \u0026lt; 1 \u0026micro;m, and the pliability and deformation uniformity of this ultrathin configuration benefited the tunability. The measurement of hysteresis loops proved that the magnetic anisotropy of Py magnetic core is directly impacted with the bending status due to the magnetoelastic coupling. Based on this, the applied tensile/compressive strains gave rise to the multi-directional tunability of the thin-film inductors, showing the maximum enhancement over 140% of the inductance value at 800 MHz by bending. Our work allows easy access to realize flexible electronics with highly stability and turnability, which is expected for the future applications in RF circuit and wireless communication.\u003c/em\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003e \u003cem\u003eNot applicable.\u003c/em\u003e \u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eEthics approval\u003c/strong\u003e \u003cp\u003e \u003cem\u003eNot applicable.\u003c/em\u003e \u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to participate\u003c/strong\u003e \u003cp\u003e \u003cem\u003eNot applicable.\u003c/em\u003e \u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to publish\u003c/strong\u003e \u003cp\u003e \u003cem\u003eNot applicable.\u003c/em\u003e \u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThe authors gratefully acknowledge the National Science Fund for Distinguished Young Scholars (52225312), the National Natural Science Foundation of China (52272292), and the Zhejiang Provincial Key Research and Development Program (2023C01053).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, J. Z. and T. F.; Methodology, J. Z. and T. F.; Formal analysis, T. F., and H. J., Validation, N. W. and H. L.; Resources, Z. K. and F. Z.; Supervision, F. Z. and X. Z.; Project administration, X. Z.; Writing - Original Draft, J. Z. and T. F. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eZhang W, Zhou G, Hong Y et al (2024) Organic package substrate embedded coupled magnetic core inductors using lithographic via technology for power supply in package. Results Phys 60:107628. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.rinp.2024.107628\u003c/span\u003e\u003cspan address=\"10.1016/j.rinp.2024.107628\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMichel JP, Sibuet H, Buffet N et al (2019) Ultra-low profile integrated magnetic inductors and transformers for HF applications. IEEE Trans Magn 55(7):1\u0026ndash;7. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/tmag.2019.2905985\u003c/span\u003e\u003cspan address=\"10.1109/tmag.2019.2905985\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang J, Hou XJ, Qian S et al (2024) Flexible multilayer MEMS coils and their application in energy harvesters. Sci China Technological Sci 67(4):1282\u0026ndash;1293. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1007/s11431-023-2474-9\u003c/span\u003e\u003cspan address=\"10.1007/s11431-023-2474-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu C, Yi Z, Qin M et al (2021) Passive and wireless anemometer based on inductor bending effect. J Microelectromech Syst 31(1):3\u0026ndash;5. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/jmems.2021.3124230\u003c/span\u003e\u003cspan address=\"10.1109/jmems.2021.3124230\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYi Z, Wan Y, Qin M et al (2020) Quadruple sensitivity improvement for wind speed sensor using dual-layer bended inductors. Sens Actuators A: Phys 303:111786. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.sna.2019.111786\u003c/span\u003e\u003cspan address=\"10.1016/j.sna.2019.111786\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYi Z, Wan Y, Qin M et al (2019) Novel anemometer based on inductor bending effect. J Microelectromech Syst 28(3):321\u0026ndash;323. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/jmems.2019.2909103\u003c/span\u003e\u003cspan address=\"10.1109/jmems.2019.2909103\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDeng WJ, Wang LF, Dong L et al (2018) Experimental study of the bending effect on LC wireless Humidity Sensors fabricated on flexible PET substrates. J Microelectromech Syst 27(5):761\u0026ndash;763. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/jmems.2018.2856912\u003c/span\u003e\u003cspan address=\"10.1109/jmems.2018.2856912\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang B, Han B, Wang K et al (2024) Air vehicle humidity sensor based on PVA film humidity sensing principle. APL Mater 12(7):071116. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1063/5.0213766\u003c/span\u003e\u003cspan address=\"10.1063/5.0213766\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang C, Guo L, Wang LF et al (2014) Passive wireless integrated humidity sensor based on dual-layer spiral inductors. Electron Lett 50(18):1287\u0026ndash;1289. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1049/el.2014.1240\u003c/span\u003e\u003cspan address=\"10.1049/el.2014.1240\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDong L, Deng WJ, Wang LF et al (2018) Multi-parameters detection implemented by LC sensors with branching inductors. IEEE Sens J 19(1):304\u0026ndash;310. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/jsen.2018.2876060\u003c/span\u003e\u003cspan address=\"10.1109/jsen.2018.2876060\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScid\u0026agrave; A, Haque S, Treossi E et al (2018) Application of graphene-based flexible antennas in consumer electronic devices. Mater Today 21(3):223\u0026ndash;230. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.mattod.2018.01.007\u003c/span\u003e\u003cspan address=\"10.1016/j.mattod.2018.01.007\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEscobedo P, de Pablos-Florido J, Carvajal MA et al (2020) The effect of bending on laser-cut electro-textile inductors and capacitors attached on denim as wearable structures. Text Res J 90(21\u0026ndash;22):2355\u0026ndash;2366. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1177/0040517520920570\u003c/span\u003e\u003cspan address=\"10.1177/0040517520920570\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTalekar PM, Pulijala V (2021) Improvement of inductor performance parameters with thin 20 nm permalloy patterns. IEEE Mangn Lett 12:1\u0026ndash;5. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/lmag.2021.3130833\u003c/span\u003e\u003cspan address=\"10.1109/lmag.2021.3130833\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePulijala V, Syed A (2016) Comparison of the effects of 60 nm and 96 nm thick patterned permalloy thin films on the performance of on-chip spiral inductors. J Magn Magn Mater 419:245\u0026ndash;248. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.jmmm.2016.06.031\u003c/span\u003e\u003cspan address=\"10.1016/j.jmmm.2016.06.031\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGardner DS, Schrom G, Paillet F et al (2009) Review of on-chip inductor structures with magnetic films. IEEE Trans Magn 45(10):4760\u0026ndash;4766. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/tmag.2009.2030590\u003c/span\u003e\u003cspan address=\"10.1109/tmag.2009.2030590\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTumma SK, Nistala BR (2020) A novel hybrid series stacked differential fractal inductor for MMIC applications. Circuit World 46(2):137\u0026ndash;145. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1108/cw-06-2019-0058\u003c/span\u003e\u003cspan address=\"10.1108/cw-06-2019-0058\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAnthony R, Wang N, Casey DP et al (2016) MEMS based fabrication of high-frequency integrated inductors on Ni-Cu-Zn ferrite substrates. J Magn Magn Mater 406:89\u0026ndash;94. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.jmmm.2015.12.099\u003c/span\u003e\u003cspan address=\"10.1016/j.jmmm.2015.12.099\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang T, Jiang W, Divan R et al (2017) Novel electrically tunable microwave solenoid inductor and compact phase shifter utilizing permaloy and PZT thin films. IEEE Trans Microwave Theory Tech 65(10):3569\u0026ndash;3577. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/tmtt.2017.2731765\u003c/span\u003e\u003cspan address=\"10.1109/tmtt.2017.2731765\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBellaredj MLF, Kohl P, Swaminathan M (2021) Design and characterization of package-embedded solenoidal magnetic core inductors for high-frequency and high-efficiency sip integrated voltage regulators. IEEE Trans Compon Packag Manuf Technol 11(4):625\u0026ndash;634. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/tcpmt.2021.3068189\u003c/span\u003e\u003cspan address=\"10.1109/tcpmt.2021.3068189\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMishra D, Raj PM, Tummala R (2016) Design, fabrication and characterization of thin power inductors with multilayered ferromagnetic-polymer composite structures. Microelectron Eng 160:34\u0026ndash;38. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.mee.2016.02.071\u003c/span\u003e\u003cspan address=\"10.1016/j.mee.2016.02.071\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChikazumi Sōshin (1997) and Chad D. Graham. Physics of ferromagnetism. Oxford University Press. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1093/oso/9780198517764.001.0001\u003c/span\u003e\u003cspan address=\"10.1093/oso/9780198517764.001.0001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLou J, Ren H, Chao X et al (2022) Recent progress in the preparation technologies for micro metal coils. Micromachines 13(6):872. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.3390/mi13060872\u003c/span\u003e\u003cspan address=\"10.3390/mi13060872\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGao LY, Liu ZQ (2022) Electroplating low coercivity nanocrystalline Fe-Ni magnetic cores for high performance on-chip microinductor. IEEE Trans Magn 58(4):1\u0026ndash;7. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/tmag.2022.3144488\u003c/span\u003e\u003cspan address=\"10.1109/tmag.2022.3144488\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou G, Zhang W, He D et al (2019) A novel structured spiral planar embedded inductor: Electroless-plating NiCoP alloy on copper coil as magnetic core. J Magn Magn Mater 489:165363. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.jmmm.2019.165363\u003c/span\u003e\u003cspan address=\"10.1016/j.jmmm.2019.165363\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen Y, Zhang Y, Wang J et al (2024) Flexible mini-inductors with ultra‐high inductance density directly cut from soft magnetic amorphous alloys by femtosecond laser. Adv Funct Mater 34(27):2313355. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1002/adfm.202313355\u003c/span\u003e\u003cspan address=\"10.1002/adfm.202313355\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBjelica JM, Djuric NM, Djuric SM (2020) Modeling and performance analysis of planar fractal inductors. IEEE Trans Magn 56(11):1\u0026ndash;8. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/tmag.2020.3018428\u003c/span\u003e\u003cspan address=\"10.1109/tmag.2020.3018428\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDjuric SM, Dubourg G (2017) Fractal inductors on flexible plastic substrate fabricated by laser ablation. Microelectron Eng 168:10\u0026ndash;14. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.mee.2016.10.008\u003c/span\u003e\u003cspan address=\"10.1016/j.mee.2016.10.008\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDjuric SM, Dubourg G (2017) Fractal inductors on flexible plastic substrate fabricated by laser ablation. Microelectron Eng 168:10\u0026ndash;14. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.mee.2016.10.008\u003c/span\u003e\u003cspan address=\"10.1016/j.mee.2016.10.008\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGao Y, Zardareh SZ, Yang X et al (2014) Significantly Enhanced Inductance and Quality Factor of GHz Integrated Magnetic Solenoid Inductors With FeGaB/Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e Multilayer Films. IEEE Trans Electron Devices 61(5):1470\u0026ndash;1476. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/ted.2014.2313095\u003c/span\u003e\u003cspan address=\"10.1109/ted.2014.2313095\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang X, Chen H, Shi X et al (2017) A novel NiZn ferrite integrated magnetic solenoid inductor with a high quality factor at 0.7-6 GHz. AIP Adv 7(5). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1063/1.4973283\u003c/span\u003e\u003cspan address=\"10.1063/1.4973283\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePan P, Chen C, Gu J et al (2024) High-performance 3-D silicon-embedded coupled solenoid inductors with inserted magnetic core. IEEE Trans Electron Devices. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1109/ted.2024.3381920\u003c/span\u003e\u003cspan address=\"10.1109/ted.2024.3381920\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou N, Liu C, Lewis JA et al (2017) Gigahertz electromagnetic structures via direct ink writing for radio-frequency oscillator and transmitter applications. Adv Mater 29(15):1605198. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1002/adma.201605198\u003c/span\u003e\u003cspan address=\"10.1002/adma.201605198\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang W, Yang Z, Kraman MD et al (2020) Monolithic mTesla-level magnetic induction by self-rolled-up membrane technology. Sci Adv 6(3):eaay4508. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1126/sciadv.aay4508\u003c/span\u003e\u003cspan address=\"10.1126/sciadv.aay4508\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShi Q, Chen H, Pang K et al (2020) Permalloy/polydimethylsiloxane nanocomposite inks for multimaterial direct ink writing of gigahertz electromagnetic structures[J]. J Mater Chem C 8(43):15099\u0026ndash;15104. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1039/d0tc03244a\u003c/span\u003e\u003cspan address=\"10.1039/d0tc03244a\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLazarus N, Sarah S (2018) Bedair. Bubble inductors: pneumatic tuning of a stretchable inductor. AIP Adv. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1063/1.5003372\u003c/span\u003e\u003cspan address=\"10.1063/1.5003372\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. 8.5\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLazarus N, Meyer CD (2016) Stretchable inductor with liquid magnetic core. Mater Res Express 3(3):036103. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1088/2053-1591/3/3/036103\u003c/span\u003e\u003cspan address=\"10.1088/2053-1591/3/3/036103\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen L, Qiao Z, Liu S et al (2025) High inductance density in CMOS-compatible magnetically integrated 3D microinductors for radio-frequency applications. Nat Commun 16(1):10072. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1038/s41467-025-65032-3\u003c/span\u003e\u003cspan address=\"10.1038/s41467-025-65032-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHubert A, Sch\u0026auml;fer R (1998) Magnetic domains: the analysis of magnetic microstructures. Springer Sci Bus Media. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/978-3-540-85054-0\u003c/span\u003e\u003cspan address=\"10.1007/978-3-540-85054-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang M, Xia L, Dang S et al (2019) Electrical properties of double-sided polymer surface nanostructures. Nanoscale Res Lett 14(1):230. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1186/s11671-019-3071-2\u003c/span\u003e\u003cspan address=\"10.1186/s11671-019-3071-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou N, Liu C, Lewis JA et al (2017) Gigahertz electromagnetic structures via direct ink writing for radio-frequency oscillator and transmitter applications. Adv Mater 29(15):1605198. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1002/adma.201605198\u003c/span\u003e\u003cspan address=\"10.1002/adma.201605198\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang L, He Y, Deng W et al (2024) High-efficiency flexible organic solar cells with a polymer-incorporated pseudo-planar heterojunction. Discover Nano 19(1):39. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1186/s11671-024-03982-1\u003c/span\u003e\u003cspan address=\"10.1186/s11671-024-03982-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang Z, Khandelwal A, Wang AT et al (2024) Unleashing the performance of self-rolled‐up 3d inductors via deterministic electroplating on cylindrical surfaces. Adv Mater Technol 9(10):2400092. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1002/admt.202470043\u003c/span\u003e\u003cspan address=\"10.1002/admt.202470043\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLong TR (1966) Magnetoelastic sensitivity and composition of Permalloy films. J Appl Phys 37(3):1470\u0026ndash;1471. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1063/1.1708521\u003c/span\u003e\u003cspan address=\"10.1063/1.1708521\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLei T, Zhang W, Bo G et al (2024) Tuning the Ferromagnetic Resonance Frequency of Microstructured Permalloy Film on Flexible Substrate. physica status solidi (RRL)-Rapid Research Letters. 18(9):2400081. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1002/pssr.202400081\u003c/span\u003e\u003cspan address=\"10.1002/pssr.202400081\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar D, Singh S, Vishawakarma P et al (2016) Tailoring of in-plane magnetic anisotropy in polycrystalline cobalt thin films by external stress. J Magn Magn Mater 418:99\u0026ndash;106. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.jmmm.2016.03.072\u003c/span\u003e\u003cspan address=\"10.1016/j.jmmm.2016.03.072\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOhashi Y, Matsushima Y, Kaiju H (2023) Modulation of magnetic anisotropy by bending in Ni and Ni\u003csub\u003e78\u003c/sub\u003eFe\u003csub\u003e22\u003c/sub\u003e thin films on polycarbonate organic substrates. J Magn Magn Mater 570:170497. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.jmmm.2023.170497\u003c/span\u003e\u003cspan address=\"10.1016/j.jmmm.2023.170497\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFreitas WJ, Manera LT, Swart JW (2022) Functional cyclic bending test for integrated inductors on flexible Kapton substrate[J]. Microelectron Reliab 135:114592. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.microrel.2022.114592\u003c/span\u003e\u003cspan address=\"10.1016/j.microrel.2022.114592\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGreek S, Ericson F (1998) \u003cem\u003eYoung's modulus, yield strength and fracture strength of microelements determined by tensile testing. MRS Online Proceedings Library (OPL)\u003c/em\u003e, 518: 110183. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1557/PROC-518-51\u003c/span\u003e\u003cspan address=\"https://doi.org/10.1557/PROC-518-51\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang J, Lee WK, Tu R et al (2021) Spontaneous formation of ordered magnetic domains by patterning stress[J]. Nano Lett 21(12):5430\u0026ndash;5437. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1021/acs.nanolett.1c00070\u003c/span\u003e\u003cspan address=\"10.1021/acs.nanolett.1c00070\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBowden N, Brittain S, Evans AG et al (1998) Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer[J]. Nature 393(6681):146\u0026ndash;149. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1038/30193\u003c/span\u003e\u003cspan address=\"10.1038/30193\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDai G, Zhan Q, Yang H et al (2013) ,\u003cem\u003e. Controllable strain-induced uniaxial anisotropy of Fe81Ga19 films deposited on flexible bowed-substrates. Journal of Applied Physics, 114(17): 173913.\u003c/em\u003e \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1063/1.\u003c/span\u003e\u003cspan address=\"http://doi.org/10.1063/1.\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cem\u003e4829670\u003c/em\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGueye M, Wague BM, Zighem F et al (2014) ,\u003cem\u003e. Bending strain-tunable magnetic anisotropy in Co\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eFeAl Heusler thin film on Kapton. Applied Physics Letters, 105(6): 062409.\u003c/em\u003e \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1063/1.\u003c/span\u003e\u003cspan address=\"http://doi.org/10.1063/1.\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cem\u003e4893157\u003c/em\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOta S, Hibino Y, Bang D et al (2016) Strain-induced reversible modulation of the magnetic anisotropy in perpendicularly magnetized metals deposited on a flexible substrate. Appl Phys Express 9(4):043004. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.7567/apex.9.043004\u003c/span\u003e\u003cspan address=\"10.7567/apex.9.043004\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao L et al (2024) Artificial magnetic disclination through local stress engineering. Acta Mater 265:119579. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.actamat.2023.119579\u003c/span\u003e\u003cspan address=\"10.1016/j.actamat.2023.119579\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi Z et al (2023) Strength, plasticity and coercivity tradeoff in soft magnetic high-entropy alloys by multiple coherent interfaces. Acta Mater 254:118970. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.actamat.2023.118970\u003c/span\u003e\u003cspan address=\"10.1016/j.actamat.2023.118970\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePandya NY, Mevada AD, Gajjar PN (2016) Lattice dynamical and thermodynamic properties of FeNi3, FeNi and Fe3Ni invar materials[J]. Comput Mater Sci 123:287\u0026ndash;295. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.1016/j.commatsci.2016.07.001\u003c/span\u003e\u003cspan address=\"10.1016/j.commatsci.2016.07.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-nano","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"narl","sideBox":"Learn more about [Discover Nano](https://www.springer.com/journal/11671)","snPcode":"11671","submissionUrl":"https://submission.nature.com/new-submission/11671/3","title":"Discover Nano","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8769909/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8769909/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThin-film solenoid-type inductors, owning low flux leakage and low parasitic capacitance, is required with high stability and tunability for flexible electronics. The existing solutions for flexible and tunable thin-film solenoid-type inductors is limited with the operations ease, device size and compatibility in flexible electronics. This work demonstrates a general approach to realize thin-film solenoid-type inductors on flexible substrate via stencil lithography. Ultrathin solenoid-type inductors were achieved with the total thickness less than 1 \u0026micro;m, and this ultrathin construction benefited the pliability and deformation uniformity during deformation regulation. The magnetic anisotropy and the permeability of permalloy magnetic core were directly impacted by bending the substrate through the magnetoelastic coupling. Based on this, the applied tensile/compressive strains gave rise to the multi-directional tunability of the thin-film inductors, showing the maximum enhancement over 140% of the inductance value at 800 MHz by bending. With the highly stability over 1,000 bending cycle tests, this method for thin-film solenoid-type inductors with easy-access turnability is expected for the future applications of flexible electronics in RF circuit and wireless communication.\u003c/p\u003e","manuscriptTitle":"Tunable High-Frequency Thin-Film Inductor through Stress-Induced Magnetic Anisotropy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-23 16:47:10","doi":"10.21203/rs.3.rs-8769909/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-09T15:28:48+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-25T08:43:55+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-25T03:48:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"314591350778702908374627803572618800662","date":"2026-02-22T01:49:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"337309386931015973235589042325626916480","date":"2026-02-22T00:52:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"62325110300424604492988890543991501555","date":"2026-02-20T14:05:34+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-16T22:50:42+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-02-16T07:42:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-11T04:39:51+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-11T00:55:33+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Nano","date":"2026-02-11T00:50:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-nano","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"narl","sideBox":"Learn more about [Discover Nano](https://www.springer.com/journal/11671)","snPcode":"11671","submissionUrl":"https://submission.nature.com/new-submission/11671/3","title":"Discover Nano","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f719c294-522f-46bf-bfdf-05601b27ee47","owner":[],"postedDate":"February 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-27T14:55:01+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-23 16:47:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8769909","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8769909","identity":"rs-8769909","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}