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An electrode-free method of characterizing the microwave dielectric properties of high-permittivity thin films
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A thin dielectric resonator consisting of a dielectric substrate and the thin film deposited upon it is shown to suffice for microwave characterization and dielectric parameter measurement of high-permittivity thin films without electrodes. The TE <sub>01δ</sub> resonance mode was excited and measured in thin (down to 0.1 mm) rectangular- or disk-shaped low-loss dielectric substrates (D∼10 mm ) with permittivity ε<sup>′</sup>≥10 inserted into a cylindrical shielding cavity or rectangular waveguide. The in-plane dielectric permittivity and losses of alumina, DyScO <sub>3</sub> , SmScO <sub>3</sub> , and ( LaAlO <sub>3</sub>)<sub>0.29</sub>( SrAl <sub>1/2</sub> Ta <sub>1/2</sub> O <sub>3</sub>)<sub>0.71</sub> (LSAT) substrates were measured from 10 to 18 GHz. The substrate thickness optimal for characterization of the overlying thin film was determined as a function of the substrate permittivity. The high sensitivity and efficiency of the method, i.e., of a thin dielectric resonator to the dielectric parameters of an overlying film, was demonstrated by characterizing ultrathin strained EuTiO <sub>3</sub> films. A 22 nm thick EuTiO <sub>3</sub> film grown on a (100) LSAT substrate and strained in biaxial compression by 0.9% exhibited an increase in microwave permittivity at low temperatures consistent with it being an incipient ferroelectric; no strain-induced ferroelectric phase transition was seen. In contrast, a 100 nm thick EuTiO <sub>3</sub> film grown on a (110) DyScO <sub>3</sub> substrate and strained in biaxial tension by 1% showed two peaks as a function of temperature-
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in microwave permittivity and loss. These peaks correspond to a strain-induced ferroelectric phase transition near 250 K and to domain wall motion.
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... Performing measurements of microwave properties often requires complicated and high-precision equipment [7,8]. Resonant techniques can be conditionally divided into 2 groups: those using oscillating circuits (up to 100 MHz) and volume (cavity) resonators ( 100 MHz) [1]. ...
... The dielectric loss constant can be calculated as: Fig. 4b shows the dependences of the attenuation constant on the frequency calculated by (5) for different fillings of the coaxial line and the theoretically determined attenuation constant (7), (8) for an empty line (air). It follows from (7) and (8) that conductor losses are proportional to the square root of the frequency, ~√ , and, from (9), that dielectric losses are proportional to the signal frequency, ~. ...
Dielectric and magnetic powders find their use in a wide spectrum of scientific and technical tasks. For example, micropowders are used as a base of microwave absorbing coverage for the reflection reduction of the electromagnetic waves in the anti-radar systems. In the modern quantum computing and ultra-low noise detectors, they are used as a filling of the coaxial thermal blocking filters. Such filters are extremely necessary to ensure the noise shielding of deeply cooled devices from the measurement equipment under room temperature. For correct calculations of devices based on micropowders, it is essential to obtain their dielectric and magnetic properties. For this reason, parallel plates and induction techniques are used in the low-frequency range, and waveguide methods are used in the HF and SHF ranges. An experimental method for determining the dielectric and magnetic properties of micropowders that covers the meter to centimeter range is proposed. The main idea is to measure frequency dependences of losses and phase changes of the signal transmitted through a coaxial line segment with powder filling. Using the stated technique, we perform the measurements of graphene oxide, graphite and carbonyl iron micropowders, and the values of relative permittivity/permeability and loss tangent in the range 300 kHz – 26.5 GHz are obtained. The structural analysis of the shape and dimensions of micropowders grains is given. Determination of a reliable frequency range for measuring the dielectric/magnetic parameters of investigated micropowders is obtained, and the sensitivity of the offered technique is estimated.
... The microwave response at 5.8 GHz was mea-sured using the composite dielectric resonator method. [59,60]. The TE 01δ resonance frequency, quality factor and insertion loss of the base cylindrical dielectric resonator with and without the sample were recorded during heating from 10 to 400 K with a temperature rate of 0.5 K/min in a Janis closed-cycle He cryostat. ...
The study of magnetic frustration in classical spin systems was motivated by the prediction and discovery of classical spin liquid states. These uncommon magnetic phases are characterized by a massive degeneracy of their ground state implying a finite magnetic entropy at zero temperature. While the classical spin liquid state was originally predicted in the Ising triangular lattice antiferromagnet in 1950, this state has never been experimentally observed in any triangular magnets. We report here the discovery of an electric analogue of classical spin liquids on a triangular lattice of uniaxial electric dipoles in EuAl$_{12}$O$_{19}$. This new type of frustrated antipolar phase is characterized by a highly degenerate state at low temperature implying an absence of long-range antiferroelectric order, despite short range antipolar correlations. Its dynamics are governed by a thermally activated process, slowing down upon cooling towards a complete freezing at zero temperature.
... The measurement methods developed earlier in the millimeter-wave range included the Fabry-Perot open resonator [21][22][23], TE 10n rectangular resonator [24] (used for thin films of TiO 2 on a glass substrate), resonator based on partially filled [25][26][27][28] or cut-off [22] waveguides, and transmission between horns through a ferroelectric sample [27]. Additionally, measurements at frequencies around 10 GHz (a frequency standard for bulk dielectrics) were conducted using a composite dielectric resonator [29,30], microstrip resonator [7,31], and split-post dielectric resonator [28,32]. The most accurate methods are waveguide techniques, but they require the ferroelectric sample to be precisely cut to fit the waveguide cross-section perfectly. ...
The split-cylinder resonator method was adapted to measure the microwave properties (dielectric permittivity and loss tangent) of thin ferroelectric films on a dielectric substrate. The mathematical model for calculating the resonance frequency of the split-cylinder resonator was adjusted for the “ferroelectric film—substrate” structure. An approach for correcting the gap effect based on calibrating with a single-layer dielectric was introduced and used to study two-layer dielectrics. The prototype of a split-cylinder resonator designed to measure single-layer dielectric plates at a frequency of 10 GHz was presented. The resonator calibration was performed using dielectric PTFE samples and fused silica, and an example of the correction function was suggested. The measurement error was estimated, and recommendations on the acceptable parameter range for the material under investigation were provided. The method was demonstrated to measure the microwave properties of a ferroelectric film on a fused silica substrate.
... MW measurements were performed at ~5.8 GHz using the composite dielectric resonator method [12][13][14]. The TE 01δ resonance frequency, quality factor, and insertion loss of the base cylindrical dielectric resonator with and without the samples were recorded during heating from 10 to 400 K with a temperature rate of 0.5 K/min in a Janis closed cycle He cryostat. ...
... This is because the relation of the TE01δ mode to the Curie-Weiss law (Figure 4a) with the microwave dielectric permittivity is similar to that of the soft mode, since is mainly defined by the effective dielectric permittivity of the composite DR; i.e., by the electric permittivity of the base and sample. 21 Because the magnetic permeability of BMCO is ≠ 1 , the electromagnetic response, , should be considered instead of electric permittivity. 22 As the electric permittivity of the base DR is nearly temperature independent, and the relative changes in temperature of the magnetic susceptibility of BMCO are much smaller than the ones in its electrical permittivity (see Figure S4 and reference 8 ), the observed slowing down of the TE01δ mode should be attributed to the Curie-Weiss law for microwave dielectric permittivity (Figure 4a), similarly to the soft mode. ...
Type-II multiferroics, where spin interactions induce a ferroelectric polarization, are interesting for new device functionalities due to large magnetoelectric coupling. We report on a new type of multiferroicity in the quadruple-perovskite $\text{BiMn}_{\text{3}}\text{Cr}_{\text{4}}\text{O}_{\text{12}}$, where an antiferromagnetic phase is induced by the structural change at the ferroelectric phase transition. The displacive nature of the ferroelectric phase transition at 125 K, with a crossover to an order-disorder mechanism, is evidenced by a polar soft phonon in the THz range and a central mode. Dielectric and pyroelectric studies show that the ferroelectric critical temperature corresponds to the previously reported N\'eel temperature of the $\text{Cr}^{\text{3+}}$ spins. An increase in ferroelectric polarization is observed below 48 K, coinciding with the N\'eel temperature of the $\text{Mn}^{\text{3+}}$ spins. This increase in polarization is attributed to an enhanced magnetoelectric coupling, as no change in the crystal symmetry below 48 K is detected from infrared and Raman spectra.
... The complex dielectric permittivity was calculated accounting for the electromagnetic field distribution in the sample. For the MW measurements, we used the composite dielectric resonator method [32][33][34]. TE 01δ resonance frequency, quality factor, and insertion loss of the base cylindrical dielectric resonator with and without the sample were recorded during heating from 10 to 400 K with a temperature rate of 0.5 K/min in a Janis closed-cycle He cryostat. Thin disk-shaped samples without electrodes (thicknesses 50 and 70 μm for KLT4.3 and KLT8, respectively) were placed on top of the base resonator. ...
K1−xLixTaO3 (with x=0.043, 0.08) crystals, characterized by pyroelectric current with calculated spontaneous polarization and zero-field second-harmonic generation, have been studied by broadband dielectric spectroscopy, including time-domain terahertz transmission and infrared reflectivity, and by polarized Raman spectroscopy in the 10–300 K temperature range. This multi-experimental approach has proven the percolative nature of the ferroelectric transition at low temperatures and demonstrated that the ferroelectric phase is inherently inhomogeneous and displays coexistence of ferroelectric and relaxor regions.
We report on the microwave, terahertz (THz), infrared, and Raman spectroscopic studies of BiMn7O12 ceramics, shedding more light onto the nature of two structural phase transitions and their possible relation with ferroelectricity in this compound. We observed a softening of one polar phonon in the THz range on cooling towards 460 and 300 K, i.e., temperatures at which BiMn7O12 undergoes subsequent structural phase transitions from monoclinic I2/m to polar monoclinic Im and triclinic P1 phases. The soft phonon causes dielectric anomalies typical for displacive ferroelectric phase transitions. Microwave measurements performed at 5.8 GHz up to 400 K qualitatively confirmed not only the dielectric anomaly at 300 K, but also revealed two other weak dielectric anomalies near the magnetic phase transitions at 60 and 28 K. This evidences the multiferroic nature of the low-temperature phases, although the relatively high conductivity in the kHz and Hz spectral range prevented us from directly measuring the permittivity and ferroelectric polarization. Some Raman modes sense the magnetic phase transitions occurring near 60 and 25 K, showing that spin-phonon coupling is relevant in this compound and in this temperature range. The deviation of the Mn-O stretching mode frequency from the anharmonic temperature behavior was successfully explained by the spin correlation function calculated from the magnetic contribution to the specific heat.
BaTiO3 (BT) is the best-known ferroelectric and PbMg1/3Nb2/3O3 (PMN) is the best-known relaxor ferroelectric, but their solid solutions were so far studied only very scarcely. Here the high-density perovskite ceramic solid solutions of (1−x)BaTiO3−xPbMg1/3Nb2/3O3 (BT-100x%PMN, x=0.075, 0.10, 0.15) were studied by the infrared reflectivity, time-domain terahertz transmission and microwave spectroscopies (1 MHz–20 THz) and compared with the undoped BT and PMN ceramics. The spectra show presence of a split soft phonon at all temperatures, similar to that observed in BT and PMN. Microwave dielectric dispersion was observed both below and above temperature of the diffuse permittivity maximum. In the case of BT-7.5%PMN and BT-10%PMN, the main dispersion takes place above 1 GHz, in case of the BT-15%PMN, the dispersion covers more homogeneously the 1 MHz–1 THz range. The dielectric response up to the THz range of the BT-10%PMN and BT-15%PMN was fitted with three excitations: soft mode, central mode (lower-frequency component of the split soft phonon), and microwave relaxation, but the soft mode does not soften appreciably and only the latter two excitations contribute substantially to the dielectric permittivity maximum. Dielectric response of the BT-7.5%PMN is similar except for the presence of a second dielectric relaxation in the MHz range, also observed in BT. The relaxations show no PMN-like freezing and can be tentatively attributed to the dynamics of polar nanoregions in the paraelectric phase and to the domain/nanodomain wall dynamics and/or acoustic wave emission and piezoelectric resonances within the grains in the ferroelectric phase. In this way, the BT-100x%PMN ceramics cannot be considered as relaxor ferroelectrics, but rather as ferroelectrics with the diffuse phase transition. The broadband dielectric spectra of undoped BT ceramics revealed a split optical soft mode and two additional dielectric relaxations which are mainly responsible for the dielectric anomaly at the ferroelectric phase transition. It supports the phase transition in BT to be at the crossover from a displacive to an order-disorder type.
The dielectric spectra of different solid dielectrics and semiconductors are discussed in this chapter. These studies allow an understanding of some of the peculiarities of polarization and conductivity in different materials and make recommendations as to their technical application. The data of high-frequency studies of various semiconductors are presented, and special attention is paid to the polar crystals AIIIBV type and semiconductors AIIBV with high dielectric constant. When describing ionic crystals, the values of permittivity, dielectric losses, and temperature stability are analyzed, mainly in those materials that are of interest in electronics. Special attention is given to the thermally stable microwave dielectrics, which are also used in microelectronic transistor gate materials and in microwave engineering as dielectric resonators, substrates of microcircuits, and for filters and phase shifters. Frequency characteristics of the high-permittivity films are described as the components of microwave devices and their perspective in computer engineering. Specific measurement methods are described for most of the investigated materials.
Possibility of microwave characterization of the thin ferroelectric films without electrodes by a composite TE01δ dielectric resonator was checked experimentally. Ferroelectric films PbZr0.52 Ti0.48 O3, Ba0.1Sr0.9 TiO3 and BaTiO3 deposited on the sapphire substrates were measured at ∼5.8 GHz or ∼8.2 GHz in the temperature range 30 K-380 K. TE01δ composite dielectric resonator was demonstrated to be sufficiently sensitive to the ferroelectric films and can be used for their characterization. Moreover, losses of the resonator are mainly defined by the ferroelectric film losses. Temperature dependences of the films dielectric permittivity and tan δ were detected correctly.
An application of a mode dielectric resonator is described for precise measurements of complex permittivity and the thermal effects on permittivity for isotropic dielectric materials. The Rayleigh-Ritz technique was employed to find a rigorous relationship between permittivity, resonant frequency, and the dimensions of the resonant structure, with relative computational accuracy of less than . The influence of conductor loss and its temperature dependence was taken into account in the dielectric loss tangent evaluation. Complex permittivities of several materials, including cross-linked polystyrene, polytetrafluoroethylene, and alumina, were measured in the temperature range of 300-400 K. Absolute uncertainties of relative permittivity measurements were estimated to be smaller than 0.2%, limited mainly by uncertainty in the sample dimensions. For properly chosen sample dimensions, materials with dielectric loss tangents in the range of to can be measured using the mode dielectric resonator.
A procedure is described for measuring the complex permittivity of dielectric thin films with relatively large dielectric constants (ε: about 102–104) and considerable losses (tan δ: about 10−3–1). The ferroelectric films studied here are deposited on a relatively low-ε dielectric substrate and placed in the centre of a rectangular waveguide parallel to the direction of wave propagation. The dielectric constants and losses of thin films are determined not by the shift of the resonant peak, but by numerical analysis of measured scattering parameters using a vector network analyser. The proposed method does not require electrode deposition on the film surface, and provides the natural properties of the film without complications due to conductive electrodes and their interfaces.
Overview of frequency domain measurement techniques of the complex permittivity at microwave frequencies is presented. The methods are divided into two categories: resonant and non-resonant ones. In the first category several methods are discussed such as cavity resonator techniques, dielectric resonator techniques, open resonator techniques and resonators for non-destructive testing. The general theory of measurements of different materials in resonant structures is presented showing mathematical background, sources of uncertainties and theoretical and experimental limits. Methods of measurement of anisotropic materials are presented. In the second category, transmission–reflection techniques are overviewed including transmission line cells as well as free-space techniques.
Benefits of ferroelectric component applications at microwaves is discussed. Experience recently gained in the high-temperature film-production technology has been used for obtaining high-quality ferroelectric tunable components. The disk made from bulk SrTiO3 single crystal covered with double-sided YBa2Cu3Y7 films was used as a high-quality TM010 mode tunable resonator. Planar structures containing thin film ferroelectric layers: planar capacitor, sandwich capacitor, coplanar line, and fin line have been studied. Modeling dielectric response of low-temperature incipient ferroelectrics (SrTiO3, KTaO3) has been applied for simulation of tunable planar structures. The quality factor of a tunable component (QFCT) is suggested to characterize the validity of the component for practical applications. The high-quality planar capacitors are pioneered for the applications. The wide frequency band fin line phase shifter has been studied and simulated. The prospects for applications of ferroelectric planar structures at room temperature is discussed.
Ferroelectric and paraelectric films deposited on dielectric and semiconductor substrates were studied at the frequency range 0.3-100 GHz and temperature interval 300-700 K in comparison with chemically equivalent bulk materials. A dielectric spectroscopy method helps to trace the change of dielectric polarization and dielectric loss mechanisms when the free-stress volume (bulk) ferroelectric is transformed into a thin planar layer (film) that is stressed by its forced accommodation to a rigid substrate. The change in bulk-film properties could be either favourable or an adverse factor for electronic devices.
The dielectric constant of quantum paraelectric EuTiO3, which contains Eu2+ with S=7/2 spin and Ti4+, has been measured under a magnetic field. The dielectric constant shows a critical decrease at the antiferromagnetic ordering of the Eu spins at 5.5 K, as well as a substantial change under a magnetic field (by ∼7% with 1.5 T), indicating a strong coupling between the Eu spins and dielectric properties. We show that the variation of the dielectric constant is dominated by the pair correlation of the nearest-neighbor Eu spins, likely via the variation of the soft-phonon-mode frequency.
Infrared reflectance, terahertz transmittance, and microwave resonance measurements show that SrTiO3 films, strained by similar to 1% in biaxial tension by growing them on (110) DyScO3 substrates, undergo a pronounced phonon softening near 270 K. This in-plane soft-mode drives the ferroelectric transition. The appearance of two new low-frequency modes and splitting of the high-frequency TO4 mode provide evidence of an antiferrodistortive phase below similar to 180 K. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3271179]
Predictions and measurements of the effect of biaxial strain on the properties of epitaxial ferroelectric thin films and superlattices are reviewed. Results for single-layer ferroelectric films of biaxially strained SrTiO3, BaTiO3, and PbTiO3 as well as PbTiO3/SrTiO3 and BaTiO3/SrTiO3 superlattices are described. Theoretical approaches, including first principles, thermodynamic analysis, and phase-field models, are applied to these biaxially strained materials, the assumptions and limitations of each technique are explained, and the predictions are compared. Measurements of the effect of biaxial strain on the paraelectric-to-ferroelectric transition temperature (TC) are shown, demonstrating the ability of percent-level strains to shift TC by hundreds of degrees in agreement with the predictions that predated such experiments. Along the way, important experimental techniques for characterizing the properties of strained ferroelectric thin films and superlattices, as well as appropriate substrates o...
The dielectric constant of ferroelectric ceramics shows strong Debye-like relaxation at GHz frequencies. This relaxation is caused by sound generation inside the crystallites. The ferroelastic domain walls which vibrate in the electric ac field are very effective shear wave transducers. The shear wave emission has a maximum when the wavelength of the sound wave is comparable to the width of the domains. Above this frequency the domain walls can no longer vibrate due to inertia and do not contribute to the dielectric constant. The observed dependence of the microwave dispersion on temperature, doping and grain size of the ferroelectric ceramic is in good agreement with the proposed mechanism of the emission of acoustic shear waves.