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Nonlinear Effective Dielectric Properties of Barium Strontium Titanate Composites from 300MHz to 4GHz

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Abstract

The nonlinear effective dielectric properties of barium strontium titanate (BST) composites at microwave frequencies are important for designing microwave phase shifters, tunable capacitors, and nonlinear transmission lines (NLTLs) for high-power microwave applications. Previous studies have reported the dielectric properties of these nonlinear materials in the linear regime at microwave frequencies or in the nonlinear regime at sub-microwave frequencies; however, a detailed assessment of the nonlinear permittivity of BST composites at microwave frequencies is lacking. In this study, we used two bias tees and a DC power supply to apply a volume-averaged bias field from 0 to 1.43\(\times {10}^{6}\) V/m to composites located in a coaxial air line to measure the nonlinear effective permittivity of BST composites with volume fractions up to 30% BST (Ba2/3Sr1/3TiO3) from 300MHz to 4GHz. The measured permittivity exhibits negligible nonlinearity and loss over these frequencies and volume fractions at the highest applied bias field. A nonlinear effective medium theory based on the Maxwell-Garnett law suggests that achieving strong nonlinearity for composites containing volume fractions from 20 to 50% of BST requires a bias field above \({10}^{7}\) V/m. Thus, while including BST in NLTL composites may be important for increasing dielectric breakdown strength, it may only enhance nonlinear permittivity for strong bias fields and high volume fractions.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  • 1. Nadaud, K., Borderon, C., Renoud, R., Ghalem, A., Crunteanu, A., Huitema, L., Dumas-Bouchiat, F., Marchet, P., Champeaux, C., Gundel, H.W.: Effect of the incident power on permittivity, losses and tunability of BaSrTiO3 thin films in the microwave frequency range. Appl. Phys. Lett. 110, 212902 (2017). https://doi.org/10.1063/1.4984089

  • 2. Ghalem, A., Rammal, M., Huitema, L., Crunteanu, A., Madrangeas, V., Dutheil, P., Dumas-Bouchiat, F., Marchet, P., Champeaux, C., Trupina, L., Nedelcu, L., Banciu, M.G.: Ultra-high tunability of Ba(2/3)Sr(1/3)TiO3-based capacitors under low electric fields. IEEE Microw. Wirel. Components Lett. 26, 504–506 (2016). https://doi.org/10.1109/LMWC.2016.2576455

  • 3. DePaolis, R., Payan, S., Maglione, M., Guegan, G., Coccetti, F.: High-tunability and high-Q-factor integrated ferroelectric circuits up to millimeter waves. IEEE Trans. Microw. Theory Tech. 63, 2570–2578 (2015). https://doi.org/10.1109/TMTT.2015.2441073

  • 4. Selmi, F., Hughes, R., Varadan, V.V.K., Varadan, V.V.K.: Tunable ceramic phase shifters and their applications. 1916, 180–188 (1993). https://doi.org/10.1117/12.148472

  • 5. Liu, Y., Acikeia, B., Nagra, A.S., Taylor, T.R., Hansen, P.J., Speck, J.S., York, R.A.: Distributed phase shifters using (Ba,Sr)TiO3 thin films on sapphire and glass substrates. In: Integr. Ferroelectr. pp. 313–320 (2001)

  • 6. Galt, D., Price, J.C., Beall, J.A., Ono, R.H.: Characterization of a tunable thin film microwave YBa2Cu3O7 − x/SrTiO3 coplanar capacitor. Appl. Phys. Lett. 63, 3078 (1998). https://doi.org/10.1063/1.110238

  • 7. Nguyen, H.V., Benzerga, R., Borderon, C., Delaveaud, C., Sharaiha, A., Renoud, R., Paven, C.Le, Pavy, S., Nadaud, K., Gundel, H.W.: Miniaturized and reconfigurable notch antenna based on a BST ferroelectric thin film. Mater. Res. Bull. 67, 255–260 (2015). https://doi.org/10.1016/j.materresbull.2015.02.034

  • 8. Sherman, V.O., Tagantsev, A.K., Setter, N., Iddles, D., Price, T.: Ferroelectric-dielectric tunable composites. J. Appl. Phys. 99, 074104 (2006). https://doi.org/10.1063/1.2186004

  • 9. Ponchel, F., Legier, J.F., Soyer, C., Ŕmiens, D., Midy, J., Lasri, T., Gúguan, G.: Rigorous extraction tunability of Si-integrated Ba0.3Sr0.7TiO3 thin film up to 60 GHz. Appl. Phys. Lett. 96, 252906 (2010). https://doi.org/10.1063/1.3454772

  • 10. Fairbanks, A.J., Darr, A.M., Garner, A.L.: A review of nonlinear transmission line system design. IEEE Access. 8, 148606–148621 (2020). https://doi.org/10.1109/ACCESS.2020.3015715

  • 11. Liou, J.W., Chiou, B.S.: Dielectric tunability of barium strontium titanate/silicone-rubber composite. J. Phys. Condens. Matter. 10, 2773–2786 (1998). https://doi.org/10.1088/0953-8984/10/12/015

  • 12. Strumpler, R., Rhyner, J., Greuter, F., Kluge-Weiss, P.: Nonlinear dielectric composites. Smart Mater. Struct. 4, 215–222 (1995). https://doi.org/10.1088/0964-1726/4/3/009

  • 13. Wang, Z., Nelson, J.K., Hillborg, H., Zhao, S., Schadler, L.S.: Dielectric constant and breakdown strength of polymer composites with high aspect ratio fillers studied by finite element models. Compos. Sci. Technol. 76, 29–36 (2013). https://doi.org/10.1016/j.compscitech.2012.12.014

  • 14. Wang, Z., Nelson, J.K., Miao, J., Linhardt, R.J., Schadler, L.S., Hillborg, H., Zhao, S.: Effect of high aspect ratio filler on dielectric properties of polymer composites: a study on barium titanate fibers and graphene platelets. IEEE Trans. Dielectr. Electr. Insul. 19, 960–967 (2012). https://doi.org/10.1109/TDEI.2012.6215100

  • 15. Hu, T., Juuti, J., Jantunen, H.: RF properties of BST–PPS composites. J. Eur. Ceram. Soc. 27, 2923–2926 (2007). https://doi.org/10.1016/J.JEURCERAMSOC.2006.11.027

  • 16. Sambyal, P., Singh, A.P., Verma, M., Farukh, M., Singh, B.P., Dhawan, S.K.: Tailored polyaniline/barium strontium titanate/expanded graphite multiphase composite for efficient radar absorption. RSC Adv. 4, 12614–12624 (2014). https://doi.org/10.1039/C3RA46479B

  • 17. Pandya, R.J., Joshi, U.S., Caltun, O.F.: Microstructural and electrical properties of barium strontium titanate and nickel zinc ferrite composites. Procedia Mater. Sci. 10, 168–175 (2015). https://doi.org/10.1016/J.MSPRO.2015.06.038

  • 18. Huang, X., Sun, B., Zhu, Y., Li, S., Jiang, P.: High-k polymer nanocomposites with 1D filler for dielectric and energy storage applications. Prog. Mater. Sci. 100, 187–225 (2019). https://doi.org/10.1016/j.pmatsci.2018.10.003

  • 19. Wang, N., Cotton, I., Robertson, J., Follmann, S., Evans, K., Newcombe, D.: Partial discharge control in a power electronic module using high permittivity non-linear dielectrics. IEEE Trans. Dielectr. Electr. Insul. 17, 1319–1326 (2010). https://doi.org/10.1109/TDEI.2010.5539704

  • 20. Robertson, J., Varlow, B.R.: Non-linear ferroelectric composite dielectric materials. IEEE Trans. Dielectr. Electr. Insul. 12, 779–790 (2005). https://doi.org/10.1109/TDEI.2005.1511103

  • 21. Guo, J., Wang, X., Jia, Z., Wang, J., Chen, C.: Nonlinear electrical properties and field dependency of BST and nano-ZnO-doped silicone rubber composites. Molecules. 23, 3153 (2018). https://doi.org/10.3390/molecules23123153

  • 22. Chou, X., Zhai, J., Yao, X.: Dielectric tunable properties of low dielectric constant Ba 0.5Sr0.5TiO3 - Mg2TiO4 microwave composite ceramics. Appl. Phys. Lett. 91, 1–4 (2007). https://doi.org/10.1063/1.2784202

  • 23. Zhang, J., Zhai, J., Jiang, H., Yao, X., Haitao, J., Jiwei, Z., Jiang, H., Xi, Y.: Dielectric tunable properties of BaTi4O9-doped Ba0.6Sr0.4TiO3 microwave composite ceramics. Artic. Sci. China Ser. E Technol. Sci. 52, 116–122 (2009). https://doi.org/10.1007/s11431-008-0333-0

  • 24. Fairbanks, A.J., Crawford, T.D., Garner, A.L.: Nonlinear transmission line implemented as a combined pulse forming line and high- power microwave source. Rev. Sci. Instrum. 92, 104702 (2021). https://doi.org/10.1063/5.0055916

  • 25. Fairbanks, A.J., Crawford, T.D., Vaughan, M.E., Garner, A.L.: Simulated and measured output from a composite nonlinear transmission line driven by a Blumlein pulse generator. IEEE Trans. Plasma Sci. 49, 3383–3391 (2021). https://doi.org/10.1109/TPS.2021.3114449

  • 26. Crawford, T.D., Fairbanks, A.J., Hernandez, J.A., Tallman, T.N., Garner, A.L.: Nonlinear permeability measurements for nickel zinc ferrite and nickel zinc ferrite/ barium strontium titanate composites from 1–4 GHz. IEEE Trans. Magn. 57, 6100810 (2021). https://doi.org/10.1109/TMAG.2021.3068820

  • 27. Fairbanks, A.J., Crawford, T.D., Hernandez, J.A., Mateja, J.D., Zhu, X., Tallman, T.N., Garner, A.L.: Electromagnetic measurements of composites containing barium strontium titanate or nickel zinc ferrite inclusions from 1–4 GHz. Compos. Sci. Technol. 210, 108798 (2021). https://doi.org/10.1016/j.compscitech.2021.108798

  • 28. Fairbanks, A.J., Crawford, T.D., Hernandez, J.A., Mateja, J.D., Zhu, X., Tallman, T.N., Garner, A.L.: Electromagnetic properties of multiphase composites containing barium strontium titanate and nickel zinc ferrite inclusions from 1–4 GHz. Compos. Sci. Technol. 211, 108826 (2021). https://doi.org/10.1016/j.compscitech.2021.108826

  • 29. Farcich, N.J., Salonen, J., Asbeck, P.M.: Single-length method used to determine the dielectric constant of polydimethylsiloxane. IEEE Trans. Microw. Theory Tech. 56, 2963–2971 (2008). https://doi.org/10.1109/TMTT.2008.2007182

  • 30. Trajkovikj, J., Zurcher, J.F., Skrivervik, A.K.: Soft and flexible antennas on permittivity adjustable PDMS substrates. LAPC 2012–2012 Loughbrgh. Antennas Propag. Conf. (2012). https://doi.org/10.1109/LAPC.2012.6402953

  • 31. Gale, B.K., Eddings, M.A., Sundberg, S.O., Hatch, A., Kim, J., Ho, T.: Low-cost MEMS technologies. In: Yogesh B. Gianchandani, Osamu Tabata, H.Z. (ed.) Comprehensive Microsystems. pp. 341–378. Elsevier (2008)

  • 32. Zhu, X., Fairbanks, A.J., Crawford, T.D., Garner, A.L.: Modelling effective electromagnetic properties of composites containing barium strontium titanate and/or nickel zinc ferrite inclusions from 1–4 GHz. Compos. Sci. Technol. 214, 108978 (2021). https://doi.org/10.1016/j.compscitech.2021.108978

  • 33. Pozar, D.M.: Microwave Engineering. John Wiley &Sons, Inc (2012)

  • 34. Bartley, P.G., Begley, S.B.: A new technique for the determination of the complex permittivity and permeability of materials. 2010 IEEE Int. Instrum. Meas. Technol. Conf. I2MTC 2010 - Proc. 54–57 (2010). https://doi.org/10.1109/IMTC.2010.5488184

  • 35. Sihvola, A.: Electromagnetic mixing formulas and applications. IEF (1999)

  • 36. Padurariu, L., Curecheriu, L., Buscaglia, V., Mitoseriu, L.: Field-dependent permittivity in nanostructured BaTiO3 ceramics: modeling and experimental verification. Phys. Rev. B. 85, 224111 (2012). https://doi.org/10.1103/PhysRevB.85.224111

  • 37. Johnson, K.M.: Variation of dielectric constant with voltage in ferroelectrics and its application to parametric devices. J. Appl. Phys. 33, 2826–2831 (1962). https://doi.org/10.1063/1.1702558

  • 38. Astafiev, K.F., Sherman, V.O., Tagantsev, A.K., Setter, N.: Can the addition of a dielectric improve the figure of merit of a tunable material? J. Eur. Ceram. Soc. 23, 2381–2386 (2003). https://doi.org/10.1016/S0955-2219(03)00139-0

  • 39. Myroshnychenko, V., Smirnov, S., Mulavarickal Jose, P.M., Brosseau, C., Förstner, J.: Nonlinear dielectric properties of random paraelectric-dielectric composites. Acta Mater. 203, 116432 (2021). https://doi.org/10.1016/j.actamat.2020.10.051

  • 40. Zhou, K., Boggs, S.A., Ramprasad, R., Aindow, M., Erkey, C., Alpay, S.P.: Dielectric response and tunability of a dielectric-paraelectric composite. Appl. Phys. Lett. 93, 102908 (2008). https://doi.org/10.1063/1.2982086

  • 41. Padurariu, L., Curecheriu, L.P., Mitoseriu, L.: Nonlinear dielectric properties of paraelectric-dielectric composites described by a 3D Finite Element Method based on Landau-Devonshire theory. Acta Mater. 103, 724–734 (2016). https://doi.org/10.1016/j.actamat.2015.11.008

  • 42. Garnett, J.C.M.: Colours in metal glasses and in metallic films. Proc. R. Soc. London. 73, 443–445 (1904). https://doi.org/10.1098/rsta.1904.0024

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Acknowledgements

This work was supported by the Office of Naval Research under Grant N00014-18-1-2341. We thank Haoxuan Wang for his assistance when performing the high voltage measurements.

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Authors and Affiliations

  1. Elmore Family School of Electrical and Computer Engineering, Purdue University, 47907, West Lafayette, IN, USA

    Xiaojun Zhu & Allen L. Garner

  2. School of Nuclear Engineering, Purdue University, 47906, West Lafayette, IN, USA

    Andrew J. Fairbanks, Travis D. Crawford & Allen L. Garner

  3. Department of Agricultural and Biological Engineering, Purdue University, 47907, West Lafayette, IN, USA

    Allen L. Garner

  4. Naval Surface Warfare Center, 22448, Dahlgren, VA, USA

    Andrew J. Fairbanks

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  1. Xiaojun Zhu
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Correspondence to Allen L. Garner.

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Zhu, X., Fairbanks, A.J., Crawford, T.D. et al. Nonlinear Effective Dielectric Properties of Barium Strontium Titanate Composites from 300MHz to 4GHz. Appl Compos Mater 30, 93–109 (2023). https://doi.org/10.1007/s10443-022-10065-w

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