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.
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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.
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.
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.
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Lee, CH., Orloff, N., Birol, T. et al. Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics. Nature 502, 532–536 (2013). https://doi.org/10.1038/nature12582
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