Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics


The miniaturization and integration of frequency-agile microwave circuits—relevant to electronically tunable filters, antennas, resonators and phase shifters—with microelectronics offers tantalizing device possibilities, yet requires thin films whose dielectric constant at gigahertz frequencies can be tuned by applying a quasi-static electric field1. Appropriate systems such as BaxSr1−xTiO3 have a paraelectric–ferroelectric transition just below ambient temperature, providing high tunability1,2,3. Unfortunately, such films suffer significant losses arising from defects. Recognizing that progress is stymied by dielectric loss, we start with a system with exceptionally low loss—Srn+1TinO3n+1 phases4,5—in which (SrO)2 crystallographic shear6,7 planes provide an alternative to the formation of point defects for accommodating non-stoichiometry8,9. Here we report the experimental realization of a highly tunable ground state arising from the emergence of a local ferroelectric instability10 in biaxially strained Srn+1TinO3n+1 phases with n ≥ 3 at frequencies up to 125 GHz. In contrast to traditional methods of modifying ferroelectrics—doping1,2,3,11,12 or strain13,14,15,16—in this unique system an increase in the separation between the (SrO)2 planes, which can be achieved by changing n, bolsters the local ferroelectric instability. This new control parameter, n, can be exploited to achieve a figure of merit at room temperature that rivals all known tunable microwave dielectrics3.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Figure 1: First-principles calculations showing how the index n of Srn+1TinO3n+1 phases strained commensurately to (110) DyScO3 substrates can be used to control the local ferroelectric instability.
Figure 2: Structural characterization by XRD and TEM.
Figure 3: Emergence of ferroelectricity in Srn+1TinO3n+1 films grown on (110) DyScO3 and (110) GdScO3.
Figure 4: In-plane dielectric constant (K11) of n = 6 film on (110) DyScO3, and its tunability at room temperature and high frequency.


  1. Tagantsev, A. K., Sherman, V. O., Astafiev, K. F., Venkatesh, J. & Setter, N. Ferroelectric materials for microwave tunable applications. J. Electroceram. 11, 5–66 (2003)

    Article  CAS  Google Scholar 

  2. Kirchoefer, S. W. et al. Microwave properties of Sr0. 5Ba0. 5TiO3 thin-film interdigitated capacitors. Microw. Opt. Technol. Lett. 18, 168–171 (1998)

    Article  Google Scholar 

  3. Gevorgian, S. S. & Kollberg, E. L. Do we really need ferroelectrics in paraelectric phase only in electrically controlled microwave devices? IEEE Trans. Microw. Theory Tech. 49, 2117–2124 (2001)

    Article  ADS  CAS  Google Scholar 

  4. Nakamura, T. et al. On the perovskite-related materials of high dielectric permittivity with small temperature dependence and low dielectric loss. Ferroelectrics 196, 205–209 (1997)

    Article  CAS  Google Scholar 

  5. Wise, P. L. et al. Structure–microwave property relations in (SrxCa(1−x))n +1TinO3n+1 . J. Eur. Ceram. Soc. 21, 1723–1726 (2001)

    Article  CAS  Google Scholar 

  6. Andersson, S. & Wadsley, A. D. Crystallographic shear and diffusion paths in certain higher oxides of niobium, tungsten, molybdenum and titanium. Nature 211, 581–583 (1966)

    Article  ADS  CAS  Google Scholar 

  7. Anderson, J. S. et al. Point defects and extended defects in niobium oxides. Nature 243, 81–83 (1973)

    Article  ADS  CAS  Google Scholar 

  8. Tilley, R. J. D. Correlation between dielectric constant and defect structure of non-stoichiometric solids. Nature 269, 229–231 (1977)

    Article  ADS  CAS  Google Scholar 

  9. Tilley, R. J. D. An electron microscope study of perovskite-related oxides in the Sr-Ti-O system. J. Solid State Chem. 21, 293–301 (1977)

    Article  ADS  CAS  Google Scholar 

  10. Birol, T., Benedek, N. A. & Fennie, C. J. Interface control of emergent ferroic order in Ruddlesden–Popper Srn +1TinO3n+1 . Phys. Rev. Lett. 107, 257602 (2011)

    Article  ADS  Google Scholar 

  11. Bao, P., Jackson, T. J., Wang, X. & Lancaster, M. J. Barium strontium titanate thin film varactors for room-temperature microwave device applications. J. Phys. D Appl. Phys. 41, 063001 (2008)

    Article  ADS  Google Scholar 

  12. Weiss, C. V. et al. Compositionally graded ferroelectric multilayers for frequency agile tunable devices. J. Mater. Sci. 44, 5364–5374 (2009)

    Article  ADS  CAS  Google Scholar 

  13. Pertsev, N. A., Tagantsev, A. K. & Setter, N. Phase transitions and strain-induced ferroelectricity in SrTiO3 epitaxial thin films. Phys. Rev. B 61, R825–R829 (2000)

    Article  ADS  CAS  Google Scholar 

  14. Antons, A., Neaton, J. B., Rabe, K. M. & Vanderbilt, D. Tunability of the dielectric response of epitaxially strained SrTiO3 from first principles. Phys. Rev. B 71, 024102 (2005)

    Article  ADS  Google Scholar 

  15. Li, Y. L. et al. Phase transitions and domain structures in strained pseudocubic (100) SrTiO3 thin films. Phys. Rev. B 73, 184112 (2006)

    Article  ADS  Google Scholar 

  16. Haeni, J. H. et al. Room-temperature ferroelectricity in strained SrTiO3 . Nature 430, 758–761 (2004)

    Article  ADS  CAS  Google Scholar 

  17. Cole, M. W., Nothwang, W. D., Hubbard, C., Ngo, E. & Ervin, M. Low dielectric loss and enhanced tunability of Ba0. 6Sr0. 4TiO3 based thin films via material compositional design and optimized film processing methods. J. Appl. Phys. 93, 9218–9225 (2003)

    Article  ADS  CAS  Google Scholar 

  18. Cole, M. W., Joshi, P. C. & Ervin, M. H. La doped Ba1−xSrxTiO3 thin films for tunable device applications. J. Appl. Phys. 89, 6336–6340 (2001)

    Article  ADS  CAS  Google Scholar 

  19. Babbitt, R. W., Koscica, T. E. & Drach, W. C. Planar microwave electrooptic phase shifters. Microwave J. 35, 63–79 (1992)

    ADS  Google Scholar 

  20. Gevorgian, S., Carlsson, E., Wikborg, E. & Kollberg, E. Tunable microwave devices based on bulk and thin film ferroelectrics. Integr. Ferroelectr. 22, 765–777 (1998)

    Article  Google Scholar 

  21. Booth, J. C., Takeuchi, I. & Chang, K. S. Microwave-frequency loss and dispersion in ferroelectric Ba0. 3Sr0. 7TiO3 thin films. Appl. Phys. Lett. 87, 082908 (2005)

    Article  ADS  Google Scholar 

  22. Ruddlesden, S. N. & Popper, P. New compounds of the K2NiF4 type. Acta Crystallogr. 10, 538–540 (1957)

    Article  CAS  Google Scholar 

  23. Ruddlesden, S. N. & Popper, P. The compound Sr3Ti2O7 and its structure. Acta Crystallogr. 11, 54–55 (1958)

    Article  CAS  Google Scholar 

  24. Lee, J. & Arias, T. A. Structural phase transitions in Ruddlesden–Popper phases of strontium titanate: ab initio and modulated Ginzburg–Landau approaches. Phys. Rev. B 82, 180104 (2010)

    Article  ADS  Google Scholar 

  25. Xi, X. X. et al. Oxide thin films for tunable microwave devices. J. Electroceram. 4, 393–405 (2000)

    Article  CAS  Google Scholar 

  26. Lee, C.-H. et al. Effect of reduced dimensionality on the optical band gap of SrTiO3 . Appl. Phys. Lett. 102, 122901 (2013)

    Article  ADS  Google Scholar 

  27. Udayakumar, K. R. & Cormack, A. N. Structural aspects of phase-equilibria in the strontium–titanium–oxygen system. J. Am. Ceram. Soc. 71, C469–C471 (1988)

    Article  CAS  Google Scholar 

  28. Udayakumar, K. R. & Cormack, A. N. Non-stoichiometry in alkaline-earth excess alkaline-earth titanates. J. Phys. Chem. Solids 50, 55–60 (1989)

    Article  ADS  CAS  Google Scholar 

  29. Veličkov, B., Kahlenberg, V., Bertram, R. & Bernhagen, M. Crystal chemistry of GdScO3, DyScO3, SmScO3 and NdScO3 . Z. Kristallogr. 222, 466–473 (2007)

    Article  Google Scholar 

  30. Houzet, G., Burgnies, L., Velu, G., Carru, J.-C. & Lippens, D. Dispersion and loss of ferroelectric Ba0. 5Sr0. 5TiO3 thin films up to 110 GHz. Appl. Phys. Lett. 93, 053507 (2008)

    Article  ADS  Google Scholar 

  31. Neaton, J. B. & Rabe, K. M. Theory of polarization enhancement in epitaxial BaTiO3/SrTiO3 superlattices. Appl. Phys. Lett. 82, 1586–1588 (2003)

    Article  ADS  CAS  Google Scholar 

  32. Uecker, R. et al. Properties of rare-earth scandate single crystals (Re = Nd−Dy). J. Cryst. Growth 310, 2649–2658 (2008)

    Article  ADS  CAS  Google Scholar 

  33. Folkman, C. M., Das, R. R., Eom, C. B., Chen, Y. B. & Pan, X. Q. Single domain strain relaxed PrScO3 template on miscut substrates. Appl. Phys. Lett. 89, 221904 (2006)

    Article  ADS  Google Scholar 

  34. Kunc, K. & Martin, R. M. Ab initio determination of static, dynamic and dielectric properties of semiconductors. Physica B 117/118, 511–516 (1983)

    Article  Google Scholar 

  35. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993)

    Article  ADS  CAS  Google Scholar 

  36. Perez-Mato, J. M., Orobengoa, D. & Aroyo, M. I. Mode crystallography of distorted structures. Acta Crystallogr. A 66, 558–590 (2010)

    Article  ADS  CAS  Google Scholar 

  37. Ghosez, P., Gonze, X. & Michenaud, J. P. Ab initio phonon dispersion curves and interatomic force constants of barium titanate. Ferroelectrics 206, 205–217 (1998)

    Article  Google Scholar 

  38. Giannozzi, P. et al. Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009)

    Article  Google Scholar 

  39. Theis, C. D. & Schlom, D. G. Cheap and stable titanium source for use in oxide molecular beam epitaxy systems. J. Vac. Sci. Technol. A 14, 2677–2679 (1996)

    Article  ADS  CAS  Google Scholar 

  40. Haeni, J. H., Theis, C. D. & Schlom, D. G. RHEED intensity oscillations for the stoichiometric growth of SrTiO3 thin films by reactive molecular beam epitaxy. J. Electroceram. 4, 385–391 (2000)

    Article  CAS  Google Scholar 

  41. Kadlec, C. et al. High tunability of the soft mode in strained SrTiO3/DyScO3 multilayers. J. Phys. Condens. Matter 21, 115902 (2009)

    Article  ADS  CAS  Google Scholar 

  42. Noujni, D. et al. Temperature dependence of microwave and THz dielectric response in Srn +1TinO3n+1 (n = 1–4). Integr. Ferroelectr. 62, 199–203 (2004)

    Article  CAS  Google Scholar 

  43. Kamba, S. et al. Composition dependence of the lattice vibrations in Srn +1TinO3n+1 Ruddlesden–Popper homologous series. J. Eur. Ceram. Soc. 23, 2639–2645 (2003)

    Article  CAS  Google Scholar 

  44. Marks, R. B. A multiline method of network analyzer calibration. IEEE Trans. Microw. Theory Tech. 39, 1205–1215 (1991)

    Article  ADS  Google Scholar 

  45. Williams, D. F., Wang, J. C. M. & Arz, U. An optimal vector-network-analyzer calibration algorithm. IEEE Trans. Microw. Theory Tech. 51, 2391–2401 (2003)

    Article  ADS  Google Scholar 

  46. Orloff, N. D. et al. A compact variable-temperature broadband series-resistor calibration. IEEE Trans. Microw. Theory Tech. 59, 188–195 (2011)

    Article  ADS  Google Scholar 

  47. Orloff, N., Mateu, J., Murakami, M., Takeuchi, I. & Booth, J. C. in Proc. IEEE MTT-S Int. Microwave Symp. 1177–1180 (IEEE Publishing, 2007)

    Google Scholar 

  48. Lu, Z. G. & Calvarin, G. Frequency dependence of the complex dielectric permittivity of ferroelectric relaxor. Phys. Rev. B 51, 2694–2702 (1995)

    Article  ADS  CAS  Google Scholar 

  49. Catalan, G., Seidel, J., Ramesh, R. & Scott, J. F. Domain wall nanoelectronics. Rev. Mod. Phys. 84, 119–156 (2012)

    Article  ADS  CAS  Google Scholar 

  50. Xu, G., Shirane, G., Copley, J. R. D. & Gehring, P. M. Neutron elastic diffuse scattering study of Pb(Mg1/3Nb2/3)O3 . Phys. Rev. B 69, 064112 (2004)

    Article  ADS  Google Scholar 

Download references


We acknowledge discussions with S. Trolier-McKinstry and C. A. Randall. Research was supported by Army Research Office (ARO) grants W911NF-09-1-0415 (for C.-H.L., Y.Z., J.A.M. and D.A.M.), W911NF-12-1-0437 (for Y.N., J.Z. and D.G.S.) and W911NF-10-1-0345 (for T.B., N.A.B. and C.J.F.); by the National Science Foundation (NSF) through Materials Research Science and Engineering Centers (MRSEC) grants DMR-0820404 (for R.H., E.V., X.X.X. and V.G.) and DMR-1120296 (for Y.K., J.D.B. and L.F.K.); by the Czech Science Foundation Project no. P204/12/1163 and the Czech Ministry of Education, Youth and Sports project LD12026 (for V.G., D.N. and S.K.); and by the Spanish Government and the European Union through grants EUI-ENIAC-2011-4349 and EUI-ENIAC 2010-04252 (for E.R.). C.-H.L. acknowledges stipend support from NSF grant DMR-0820404. J.A.M. acknowledges financial support from a National Defense Science & Engineering Graduate Fellowship. The dielectric and ferroelectric measurements in Fig. 3c were conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. This work was performed in part at the Cornell NanoScale Factory, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (grant ECCS-0335765). This work made use of the electron microscopy facility of the Cornell Center for Materials Research (CCMR) with support from the NSF MRSEC programme (DMR 1120296) and NSF IMR-0417392.

Author information

Authors and Affiliations



The thin films were synthesized by C.-H.L. on single-crystal substrates grown by M.B. and R.U. The first-principles calculations were performed by T.B., N.A.B. and C.J.F. The films were characterized by microwave measurements by N.D.O., E.R., I.T. and J.C.B.; by SHG by R.H., E.V. and V.G.; by infrared reflectance and terahertz transmission by V.G., D.N. and S.K.; by STEM by Y.Z., J.A.M., L.F.K. and D.A.M.; by XRD by C.-H.L., Y.N., J.-S.Z., Y.K. and J.D.B.; and by capacitance by M.D.B. and S.K. X.X.X. helped analyse the data. C.-H.L., T.B., J.C.B., C.J.F. and D.G.S. wrote the manuscript. The study was conceived and guided by C.J.F. and D.G.S. All authors discussed results and commented on the manuscript.

Corresponding author

Correspondence to Darrell G. Schlom.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 First-principles calculations showing the emergence of a ferroelectric instability in Srn+1TinO3n+1 phases.

a, In-plane polar soft-mode (lowest-frequency transverse optical phonon) square of frequency against index n. Strain values are given with respect to the lattice constant of SrTiO3. The dashed lines are fits to exponentials. b, Zero-frequency isosurface of the soft-mode phonon of SrTiO3 in the first Brillouin zone. From left to right: cubic SrTiO3 under no strain, 0.5%, 1.1% and 1.6% tensile biaxial strain. The last two correspond to (110) DyScO3 and (110) GdScO3 substrates, respectively; the small anisotropy of the substrate surfaces are taken into account in the calculations. The high-symmetry points are provided for the simple tetragonal cell. c, (001)* cuts through the surfaces in b at the qz = 0 plane.

Extended Data Figure 2 θ–2θ XRD scans of the epitaxial Srn+1TinO3n+1 (n = 1–6) films grown on (110) GdScO3.

Substrates peaks are labelled with an asterisk, and the plots are offset for clarity.

Extended Data Figure 3 Superimposed XRD rocking curves of selected film peaks of the Srn+1TinO3n+1 films and the underlying 220 DyScO3 substrate peaks.

a, n = 6 (0026 peak, blue). b, n = 5 (0022 peak, red). c, n = 4 (0020 peak, orange). d, n = 3 (0014 peak, green). e, n = 2 (0010 peak, light blue). f, n = 1 (006 peak, grey). The full-width at half-maximum (FWHM) of the substrate and film peaks are given.

Extended Data Figure 4 Superimposed XRD rocking curves of selected film peaks of the Srn+1TinO3n+1 films and the underlying 220 GdScO3 substrate peaks.

a, n = 6 (0026 peak, blue). b, n = 5 (0022 peak, red). c, n = 4 (0018 peak, orange). d, n = 3 (0016 peak, green). e, n = 2 (008 peak, light blue). f, n = 1 (006 peak, grey). The FWHM of the substrate and film peaks are given.

Extended Data Figure 5 Nonlinear optical SHG temperature scans of Srn+1TinO3n+1 (n = 2–6 and n = ∞) films.

a, Films grown on (110) DyScO3. b, Films grown on (110) GdScO3 substrates. The SHG signal for each temperature scan was normalized with the laser input power, where the SHG signal axis for each scan shows normalized tick labels at 0 and 2 to compare the signal strength between samples. c, d, The paraelectric-to-ferroelectric transition temperatures (TC) measured by SHG were determined as the point where the SHG signal vanishes to zero and are shown for DyScO3 (c) and GdScO3 (d). The error bars are ±10 K, about the height of each square symbol in c and d.

Extended Data Figure 6 Real and imaginary parts of the in-plane complex dielectric constant (K11) of the Sr7Ti6O19/DyScO3 sample at terahertz frequencies.

a, Infrared reflectance spectra of the Sr7Ti6O19/DyScO3 sample (E || []). b, Real and imaginary parts of the measured complex terahertz dielectric spectra (hollow symbols) overlapped with fittings (lines) to the infrared and terahertz spectra.

Extended Data Figure 7 Analysis of the contributions to K11 from phonons and the central mode.

a, Temperature dependence of the real part of the static dielectric constant (K11) of the n = 6/DyScO3 sample. Grey hollow dots show the contribution of solely the low-frequency phonons (soft mode) to K11 calculated from infrared spectra. The blue curve shows contributions from both low-frequency phonons and polar nanoregions (central mode) calculated from infrared and terahertz spectra. b, Temperature dependence of the polar phonons and the central-mode frequencies.

Extended Data Figure 8 Geometry of the coplanar waveguide and interdigitated capacitor device structures measured.

a, Diagram of the test and substrate device layout for the Srn+1TinO3n+1 thin films and DyScO3 and GdScO3 substrates with coplanar waveguides (CPWs) and interdigitated capacitor (IDC) devices. The substrate is shown in light grey, and the 760-nm-thick Ti/Au electrodes in blue. b, Top views and cross-sections of the CPW and IDC device geometry. The cross-section thicknesses are not to scale.

Extended Data Figure 9 Frequency dependence of the real part of the complex dielectric constant of the n = 6/DyScO3 sample at microwave frequencies for various temperatures, T.

a, T > TC. b, T < TC. Solid lines denote fits based on a model that includes effects due to a distribution of relaxation times in the system. Although only the real part of the complex dielectric constant is shown, both real and imaginary parts are included in the fits.

Extended Data Figure 10 Temperature dependence of fit parameters for the results shown in Extended Data Fig. 9.

a, Static and high-frequency dielectric constants. b, The width of the distribution of relaxation times. The value for the relaxation time of the smallest polar clusters is fixed at τ = 10−13 s.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lee, CH., Orloff, N., Birol, T. et al. Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics. Nature 502, 532–536 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing