Electrostatically driven dielectric anomaly in mesoscopic ferroelectric–paraelectric bilayers

Acta Materialia 105 (2016) 68e74

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Electrostatically driven dielectric anomaly in mesoscopic ferroelectriceparaelectric bilayers H. Khassaf a, N. Khakpash a, S. Vijayan a, M. Aindow a, S.P. Alpay a, b, * a b

Department of Materials Science and Engineering and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA Department of Physics, University of Connecticut, Storrs, CT 06269, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 October 2015 Received in revised form 9 December 2015 Accepted 13 December 2015 Available online xxx

We study the dielectric properties of 220 nm thick PbZr0.2Ti0.8O3/SrTiO3 (PZT/STO) ferroelectric (FE) eparaelectric (PE) bilayers with varying PZT/STO layer fractions grown onto Pt/Ti/TiO2/SiO2/Si substrates using metaleorganic solution deposition. The films are characterized using a combination of Xeray diffraction and scanning transmission electron microscopy (STEM). A letype anomaly in the dielectric response is observed near a critical PZT/STO ratio of 0.25 STO. At this layer fraction, the smallesignal dielectric permittivity exceeds 1600, which is significantly larger that the dielectric response of monolithic PZT and STO films deposited at the same conditions (~600 and ~200, respectively). In order to explain this behavior, a thermodynamic model is employed taking into account the electrostatic and electromechanical interactions between PZT and STO layers. We conclude that the observed dielectric anomaly is due to internal fields that result from the polarization mismatch between FE PZT and PE STO layers. Our results indicate that such internal fields can be used as a design parameter to produce structures with enhanced dielectric, piezoelectric, and pyroelectric properties as compared to those achievable for monolithic monolayer ferroelectric materials. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Ferroelectric multilayers Dielectric properties Dielectric anomaly

1. Introduction Composites consist of a combination of two or more materials. These are typically multiecomponent, multiephase systems with specific (combined) properties that are designed to be superior to their building blocks. There are several prominent classes of composites that were developed for structural applications in aerospace and transportation industries for which materials with high strength but low density (weight) are required. In electrical, magnetic, and electromagnetic applications, multiecomponent multieferroic composites have received significant attention [1e5]. For such materials, it is difficult to apply continuumelevel composite materials laws because the ferroic order parameters are nonelinear and hysteretic in nature. The simplest constructs are multilayers and superlattices consisting of a combination of ferroelectric (FE) e paraelectric (PE) linear dielectric (LDE) materials. Such heterostructures have been studied intensely because of the unique properties that they exhibit compared to monolithic FEs. Early work

* Corresponding author. Department of Materials Science and Engineering and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA. E-mail address: [email protected] (S.P. Alpay). http://dx.doi.org/10.1016/j.actamat.2015.12.023 1359-6454/© 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

has shown that it is possible to enhance the pyroelectric coefficients of FE multilayers with concentration gradients. The increase in the pyroelectric coefficients is significant; effective pyroelectric coefficients as large as 20 mC/cm2
C have been measured in compositionally graded potassium tantalum niobate (KTN) [6] and barium strontium titanate (BST) [7]. These values are three orders of magnitude larger than what is typically measured in monolithic FEs (0.02e0.04 mC/cm2
C) [8]. Erbil, Kim and Gerhardt's experimental investigation clearly demonstrates that dielectric permittivity values exceeding 4  105 can be realized in carefully synthesized epitaxial PbTiO3/Pb0.72La0.28TiO3 superlattices [9]. Similar results have been observed in a number of FE multilayers and superlattices [10e15]. For example, epitaxial equiefraction BaTiO3/SrTiO3(STO) ultrathin superlattices on MgO substrates display much larger capacitances compared to monolithic BST 50/ 50 synthesized under identical conditions [16]. There are several theoretical approaches that were developed to explain the peculiar properties of FE multilayers. These include ab initio calculations, phase field models, and Isingetype of computations [17e20]. The simplest explanation employs basic thermodynamics wherein the free energy densities of the individual FE, PE and LDE layers are described using a LandaueDevonshire type of

H. Khassaf et al. / Acta Materialia 105 (2016) 68e74

expansion of the (total) polarization. The coupling in FE/FE, FE/PE, and FE/LDE bilayers is established through electromechanical and electrostatic interactions across the interlayer interface. It has been shown that these electrostatic fields result from the polarization and polarizability mismatch between the layers and, depending on the relative layer fractions, may be large enough to completely suppress the FE response in the monodomain multilayers. Associated with the disappearance of the spontaneous polarization, there is a letype anomaly at this critical layer fraction. This is analogous to the response of a monolithic ferroelectric near the PEeFE phase transformation at TC. Theoretical results also indicate that the degree of the coupling is reduced significantly if the layers are electrostatically screened from each other such that the bilayers can be treated as simple capacitors in series [21]. Strain coupling between the layers and the layers with the substrates can readily be included in such an approach and the effect of misfit strain and/or thermal strains can be interrogated. Quantitative computations of the dielectric permittivity, dielectric tunability, pyroelectric coefficients, and adiabatic temperature changes in several FE multilayer systems were carried out using this approach [22e24]. Most recent computations predict large pyroelectric and electrocaloric responses in monoedomain FE multilayers [25]. Misirlioglu and Levanyuk showed that electrical domains may form in such constructs to minimize the internal depolarizing fields, thereby maintaining ferroelectricity even in multilayers with large volume fractions of the PE or LDE phase [26]. While there is now a better understanding on the nonelinear coupling across interfaces in multilayered multiferroic composites, the concept of utilizing the anomaly near the critical layer fraction in a FE/PE or FE/LDE layered heterostructure has not been explored systematically or exploited in potential applications. Such an investigation would enable the design and engineering of FE multilayers, superlattices, and other heterostructures with far superior dielectric, electromechanical, and electrothermal properties with potential applications in sensors and actuators, tunable dielectric devices, and solidestate heating/cooling. Here, we demonstrate conclusively that electrostatic coupling can be used as a design parameter to enhance dielectric properties. Our results show that a dielectric anomaly exists even in simple bilayers such as PbZr0.2Ti0.8O3(PZT)/STO that were grown onto commercial platinized Si (Pt/Ti/TiO2/SiO2/Si) using industry standard metaleorganic solution deposition (MOSD). Furthermore, this anomaly is predicted using a theoretical methodology that is based on nonelinear thermodynamics and continuum electrostatic/electromechanical relations. Combined with the experimental findings, this indicates that strong electrostatic coupling can be established in mesoscale and microscale FE multilayers. These findings pave the way for devices that have higher charge storage capacity, dielectric tunability, and pyroelectric coefficients. 2. Experimental methods Lead acetate hydrate (SigmaeAldrich 99.9965%), titanium (IV) isopropoxide (SigmaeAldrich, 99.995%), and zirconium (IV) tertebutoxide (SigmaeAldrich, 99.999%), and strontium acetate hydrate (SigmaeAldrich, 99.995%), and titanium (IV) isopropoxide were used as precursors for PZT and STO. In the case of PZT, 10% excess Pb was used to compensate for the volatility of lead. For both layers, 2emethoxyethanol (2MOE) was used as the main solvent and glacial acetic acid (AA) was added to obtain clear and uniform solutions with the desired molarity of 0.3 M. In all samples, the ratio of 2MOE/AA was 1/1. The precursors were spun onto platinized Si substrates at 4000 rpm for 50 s. Each layer was then dried at 150
C for 1 min before the next layer was grown. All organic addenda and the remaining solvents were pyrolyzed at 300
C for

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15 min. Films were then annealed at 750
C for 30 min which resulted in crackefree crystalized films. Annealing of PZT and STO layers were done separately in order to minimize interediffusion between the layers [27]. Using this methodology we have deposited PZT/STO bilayer structures with a total thickness of h ¼ 220 nm and STO layer fraction aSTO ¼ 0 (PZT), 0.25, 0.50, 0.75, and 1.00 (STO). Structural characterization was performed by XRD and STEM. The XRD data was acquired using a Bruker D8 diffractometer with CuKa radiation at 40 kV through a smalleangle locked beam detector scan. Crossesectional STEM samples were prepared by focused ion beam (FIB) milling in an FEI Helios Nanolab 460. Protective Pt layers were deposited over the region of interest using first the electron beam and then the Gaþ ion beam. Trenches were then cut through the deposits to form preethinned lamellae, and these were then lifted out and mounted onto copper Omni grids. A scanning transmission electron microscopy (STEM) detector and flipestage were used for final thinning. Gaþ beam currents were reduced iteratively to a value of 9.7 pA during final milling to avoid excessive Gaþ implantation and beam damage. The resulting samples were examined in an FEI Talos F200X STEM equipped with supereX siliconedrift EDXS detectors, and operating at an accelerating voltage of 200 kV. Electrical characterization was performed by producing MIM capacitor test structures: top Pt electrodes 150 nm in thickness were sputtered through a stainless steel shadow mask, yielding Pt pads 200 mm in diameter. The capacitanceevoltage (CeV) and capacitanceefrequency dissipation factor (Cetan d) were measured with an HP 4194A impedance/gainephase analyzer and a Radiant tester was used to obtain polarizationeelectric field (PeE) hysteresis loops. 3. Results The PZT and STO films were grown via MOSD onto platinized Si. A schematic representation of the resultant structure is shown in Fig. 1(a) where a ¼ aSTO ¼ hSTO/(hPZT þ hSTO) and h ¼ hPZT þ hSTO. Structural characterization of these layers was performed by a combination of grazing incidence Xeray diffraction (GIXRD) and scanning transmission electron microscopy (STEM). A fixed 5
angle of incidence was used in GIXRD to limit the intensity of peaks from the substrate in the pattern since the depth of Xeray penetration in this geometry is far smaller than that in the conventional BraggeBrentano geometry. The GIXRD results (Fig. 1(b)) indicate that PZT and STO layers are phase pure and polycrystalline in each case. Bright field (BF) STEM images obtained from focused ion beam (FIB) cut cross sections through the structures (Fig. 1(c)) confirm that the deposited layers are dense, uniform and have thicknesses that correspond closely to the nominal values. Examples of higheangle annular darkefield (HAADF) STEM images together with Pb and Sr maps from each of the samples are presented in Fig. 2. In each case these correspond to a region 300  300 nm. HAADF and spectrum images were acquired at a resolution of 512  512 pixels with a dwell time of 2 ms/pixel. The Pb and Sr maps were obtained by performing standardeless quantification of the energy dispersive Xeray spectrometry (EDXS) signals in the La and Ka peaks, respectively. The HAADF images confirm that the layers are dense with welledefined interfaces, and that the STO layers are polycrystalline. The sizes of the STO grains measured from such images are 11.9 ± 4.1 nm, 24.7 ± 10.8 nm, and 18.9 ± 6 nm for aSTO ¼ 0.75, 0.50, and 0.25, respectively. In each case these values are the arithmetic means of 30 separate caliper diameter measurements, and the stated variances are the standard deviations. The strong Z contrast in such HAADF images masks the grain structure in the PZT layers, but high magnification BF STEM images from such regions (not shown) indicate that these grains are finer than those in the

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Fig. 1. Heterostructure Geometry, XRD, and SEM: (a) Schematic of the PZTeSTO bilayer structure sandwiched between top and bottom Pt electrodes on a thick substrate. Here hPZT and hSTO are the thicknesses of PZT and STO layers and aSTO ¼ hSTO/(hPZT þ hSTO) is fraction of the STO layer in the multilayer heterostructure. (b) XRD pattern from the PZT/STO bilayer with aSTO ¼ 0.50. (c) BFeSTEM image obtained from a FIBecut crossesection of the PZT/STO/Pt/Ti/SiO2/Si structure with aSTO ¼ 0.75.

Fig. 2. STEM analysis: HAADF images with corresponding Pb and Sr elemental maps obtained from FIBecut crossesections of the samples with: (a) aSTO ¼ 0.75, (b) aSTO ¼ 0.50, and (c) aSTO ¼ 0.25.

STO layers. The measured PZT grain sizes are 6.0 ± 0.9 nm, 9.0 ± 1.4 nm, and 8.8 ± 1.8 nm for aSTO ¼ 0.75, 0.50, and 0.25, respectively. The Pb and Sr maps show that there is minimal interediffusion of Sr and Pb in these layers. We note that Pb diffuses readily into Si even through the metallization and the native SiO2 layer [28]. As such, the Pb signal in STO could be interpreted as a

result of Pb transport during the annealing process at TG ¼ 750
C, although it is also possible that this is a TEM specimen preparation artifact induced during FIB milling. To measure capacitanceevoltage (CeV), capacitanceefrequency dissipation factor (Cetan d) and polarizationeelectric field (PeE) responses of the PZT/STO bilayers, we formed MIM capacitors by

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sputtering Pt top electrodes. In Fig. 3, we plot the polarizationeapplied electric field behavior of the PZT/STO bilayers. For aSTO ¼ 0, there is a welledeveloped hysteresis loop with a spontaneous polarization of PS ¼ 40.7 mC/cm2 and a coercive field of EC ¼ 99 kV/cm. This value matches well with previous results from the literature for PZT with the PbZr0.2Ti0.8O3 composition (c.f. PS ~40 mC/cm2 in Ref. [29] for PbZr0.2Ti0.8O3 on platinized Si). For aSTO ¼ 0.25, PS decreases to 5.7 mC/cm2 but the heterostructure still displays FE behavior with EC ¼ 37.5 kV/cm. For films with aSTO > 0.25, however, the hysteresis response, which is a key signature of ferroelectricity, disappears entirely. The PeE curves are nonelinear indicating paraelectric behavior with a dielectric tunability of 30% at E ¼ 230 kV/cm for aSTO ¼ 0.50. The inset in Fig. 3 shows the tenability of the sample with aSTO ¼ 1. All samples with aSTO ¼ 0.5 and higher show the same behavior (Not shown due to brevity). Fig. 4 is a plot of the smallesignal (E ¼ 0) average dielectric permittivity (εr) of PZT/STO bilayers with different STO relative layer fractions. εr for aSTO ¼ 0 corresponding to a monolithic PZT film is comparable with reported values for polycrystalline PZT produced using similar deposition techniques [29,30]. The magnitude of εr increases substantially from 631 for aSTO ¼ 0 to 1674 for aSTO ¼ 0.25. We note that this remarkable effect was measured reproducibly for four different samples with aSTO ¼ 0.25 and for over two hundred different Pt contact pads across the sample. The individual data points from these measurements are shown in the inset to Fig. 4. With increasing aSTO, εr decreases; for aSTO ¼ 0.50 and aSTO ¼ 1 εr ¼ 455 and εr ¼ 184, respectively. Fig. 5 presents the frequency dependence of dielectric permittivity and loss tangent for representative samples. We note that all samples exhibit relatively low tan d values (~0.05) and low leakage currents (~107 A) regardless of aSTO.

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Fig. 4. Dielectric Properties: Relative dielectric permittivity of PZT/STO bilayers with different STO layer fractions on Si substrate. The inset shows the data for dielectric permittivity measurements for four samples with aSTO ¼ 0.25. The mean and the standard deviation of the dielectric permittivity at aSTO ¼ 0.25 are 1574 and 120, respectively. The solid line is the theoretical smallesignal average relative dielectric permittivity of polycrystalline PZT/STO bilayer as a function of aSTO. The computations were carried out for TG ¼ 750
C.

4. Theoretical analysis and discussion To explain these results and to provide guidance for future studies we employed a thermodynamic model. The free energy density of a monoedomain, monolayer FE film with uniaxial polarization P ¼ (0,0,P) is [31]:

Fig. 3. Polarization Response: Comparison of polarizationevoltage hysteresis behavior of PZT/STO for different STO layer fractions. Polarization vanishes for films with aSTO > 0.25. The inset shows that the bilayer with aSTO ¼ 0.50 displays a non-linear dielectric permittivity as a function of the applied electric field which is consistent with paraelectric response. Similar behavior is observed in samples with aSTO ¼ 0.75 and aSTO ¼ 0.25 (not shown).

Fig. 5. Dielectric loss: (a) Relative smallesignal dielectric permittivity and (b) loss of PZT/STO bilayers as a function of frequency and aSTO.

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GðP; T; uT ; EÞ ¼ G0 þ e aP 2 þ e bP 4 þ cP 6 þ

u2T S11 þ S12

(1)

where ae and be are renormalized dielectric stiffness coefficients given by: ae ¼ a[2Q12/(S11þS12)]uT, and be ¼ bQ212/(S11þS12), a ¼ (TTC)/2ε0C, b, and c are the bulk dielectric stiffness coefficients, ε0 is the permittivity of free space, C is the CurieeWeiss constant, and Sij and Qij are the elastic compliances and electrostrictive coefficients respectively at constant polarization. uT in Equation (1) is the ineplane thermal strain given by:

ZTG uT ðTG Þ ¼

ðaF  aS ÞdT

(2)

T

where aF and aS are the coefficients of thermal expansion (CTEs) of the film and substrate, respectively. For a bilayer with layer thicknesses h1 ¼ hSTO and h2 ¼ hPZT as shown in Fig. 1(a), the total energy of the system has to include the electrostatic coupling between the layers. The free energy density of such a configuration can be expressed as [32].

G ¼ ð1  aÞ½G1 ðP1 Þ  EP1  þ a½G2 ðP2 Þ  EP2  þ

að1  aÞ F ðP1  P2 Þ2 þ S 2ε0 h

(3)

where a ¼ aSTO ¼ hSTO/(hPZT þ hPZT). Here, Gi (i ¼ 1,2) are the free energy densities of layers i with a polarization Pi (i ¼ 1,2). These are given by Equation (1). The second term establishes the electrostatic coupling between the two layers and follows from the electrical boundary conditions V,D ¼ 0 and E1h1 þ E2h2 ¼ 0, where D is the dielectric displacement vector, and E1 and E2 are the internal (depolarizing) electric fields in layers 1 and 2, respectively. Since h1 and h2 are much larger than the correlation length of ferroelectricity (1e10 nm), we neglect interfacial effects [the last term in Equation (3)] [33]. The details of the derivations of Equations (1) and (3) are given elsewhere [23]. The equilibrium polarization in each layer (PS,1 and PS,2) are computed from the equations of state vGi/vPi ¼ 0. The smallesignal average relative dielectric permittivity of the bilayer is then:

εR ¼ ε1 0

dP dE

!

     dPS;1 dPS;2 ð1 þ a  aÞ ¼ ε1 0 dE dE

(4)

The same set of relations hold for multilayer structures (or “superlattices”) consisting of repeating units of bilayers with individual layer thicknesses larger than the correlation length of ferroelectricity (1e10 nm) [34]. The results of the theoretical treatment described above as applied to PZT/STO multilayers are shown in Fig. 4, where the solid line is the computed average smallesignal dielectric permittivity. All coefficients and materials constants for PZT and STO entering Equation (1) were compiled from the literature [31,35,36], and TG is taken to be 750
C, which is the temperature of the final anneal. We note that since the thicknesses of the layers are of the order of only several hundred nanometers and are much smaller than the thickness of the platinized Si substrate (~0.5 mm), all thermal stresses are concentrated in the bilayer construct. Furthermore, because the substrate thickness is much larger than the thickness of the layers, the reference for the distribution of thermal strains is the substrate, i.e., uT in each layer is given by Equation (2) and not by relative thicknesses of PZT and STO. For TG ¼ 750
C, uT is ~0.006 for both STO and PZT due to the almost identical CTEs of both materials.

While there are small differences between the experimental results and the predictions of the theoretical analysis, the overall agreement is remarkable considering that there are no fitting/ floating parameters employed in the calculations. Theoretical results predict the presence of a critical fraction at which FE vanishes and the dielectric response displays a letype anomaly. The differences between experimental results and the calculations could be due to several parameters that were neglected in the model for the sake of simplicity. For instance, polycrystalline microstructure of PZT and STO films vs. the monodomain approximation polarization employed in the computations could be a cause of deviation, which would essentially reduce the polarization response [37,38], and thus the magnitude of the coupling between layers, but would not alter the physics of the coupling. Other sources include polarization fluctuations near the interfaces, defects such as space/bound charges, and inhomogeneous distributions of internal stresses [39]. We also note that the grain size for PZT layers is in the range of the critical size below which polarization is reduced in FE powders and nanostructures [40,41]. This means that the dielectric permittivity could be even larger for a given aSTO if the synthesis method or the processing conditions would produce larger PZT grains. The theoretical approach can also be used to investigate the effect of CTE mismatch between the ferroelectric bilayers and the substrate on the polarization response and dielectric permittivity. Expanding the model further, we can analyze the role of processing temperatures during synthesis. The results of this analysis are shown in Fig. 6 for PZT/STO bilayers. Fig. 6(a) and (b) plot the contours of spontaneous electric polarization variations of PZT/STO multilayers for a wide range of CTEs of the substrate and STO layer fractions. As a general trend, with increasing STO layer volume fraction, the average spontaneous polarization of the system decreases until it vanishes completely at a critical relative STO thickness. This behavior is because of the electrostatic fields that are generated due to the polarization mismatch. The magnitude of this internal field increases with increasing STO layer fraction. Depending on the CTE of the substrate, this critical thickness at which the polarization disappears varies. For substrates with lower CTEs than the average CTE of the PZT/STO bilayer (~11  106
C1), this critical fraction becomes smaller. For example, for PZT/STO stacks on sapphire (aeAl2O3), Si, and SiO2 (which induce ineplane tensile thermal strains), the critical STO layer fractions are 0.37, 0.32, and 0.26, respectively. On the other hand, for MgO as substrate that induces compressive ineplane thermal strains, the critical fraction increases to 0.49. Fig. 6(b) displays the dependence of the average dielectric permittivity of the PZT/STO bilayer as a function of the CTE of substrate and aSTO. It shows that the critical aSTO and the region where extremely large dielectric permittivity can be expected can be tailored by changing the substrate material. Fig. 6(c) and (d) highlight the importance of the processing temperature on the critical aSTO. Here we plot the average polarization of PZT/STO stacks as a function of aSTO for two different TG values. 500
C < TG < 750
C represents the typical spectrum of annealing/ growth temperatures for PZT and similar ferroelectrics [42]. The shaded regions in both figures show the range of critical aSTO for substrates with CTEs from ~0.5  106
C1 (SiO2) to ~13  106
C1 (MgO). The corresponding dielectric anomalies for SiO2 and MgO substrates are at aSTO ¼ 0.32 and aSTO ¼ 0.47 for TG ¼ 500
C and at aSTO ¼ 0.26 and aSTO ¼ 0.49 for TG ¼ 750
C (see Fig. 6(e) and (f)). 5. Conclusions and outlook We presented here the findings of a combined experimental and theoretical study on the dielectric properties of 220 nm thick PZT/ STO films with varying layer fractions grown onto Pt/Ti/TiO2/SiO2/Si

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Fig. 6. Mesoscopic Modeling: (a) Contour maps of the variations in the spontaneous polarization and the (b) relative dielectric permittivity as functions of the STO thickness ratio and the CTE of the substrate. Dashed lines correspond to the average CTEs of commercial substrates SiO2, Si, sapphire (aeAl2O3), SrTiO3, and MgO. The critical thickness ratio for anomaly shifts to higher STO layer fractions for substrates with higher CTEs. (c) and (d) plot the polarization response of the PZT/STO bilayer system as a function of aSTO for SiO2 and MgO substrates for growth temperatures of 500
C and 750
C, respectively. The shaded regions in (c) and (d) correspond to polarization values as a function of aSTO for substrates with CTEs between 0.5  106
C1 (SiO2) and 13  106
C1 (MgO). (e) and (f) are the relative dielectric permittivities as a function of aSTO for PZT/STO on SiO2 and MgO for TG ¼ 500
C and TG ¼ 750
C, respectively.

substrates using MOSD. The results show conclusively that there exists a critical layer fraction (~0.25e0.30 STO) above which ferroelectricity vanishes. Associated with the disappearance of ferroelectric behavior, there is a significant increase in the smallesignal dielectric permittivity. We attributed this to internal fields that result from electrostatic interactions between ferroelectric and paraelectric layers. Regardless of the limitations of the theoretical analysis, it is abundantly clear that the electrostatic interactions between the layers define the polarization response and the average dielectric permittivity. Since the internal fields are sizeeindependent, such interactions are not limited to ultraethin (1e10 nm) multilayers and superlattices. This means that because of the very nature of electrostatic fields, FE multilayers and superlattices do not have to be synthesized using complex and costly techniques such as molecular beam epitaxy or metaleorganic chemical vapor deposition to obtain unique dielectric responses. As shown here, relatively simple and industryestandard solution deposition or solegel methods that lend themselves to scaleeup can be employed for growth of such constructs on industryestandard substrates. When viewed from an application standpoint, these internal fields that are generated from the polarization mismatch between dielectrically dissimilar materials present a significant opportunity to maximize the dielectric properties. An obvious application where

such multilayers would generate immediate benefit is in charge storage. Capacitors are already manufactured as multilayers and FE composites would provide more storage capability in a given volume/foot print of a capacitor [43]. There are several other examples. For instance, the dielectric tunability, a key parameter in solidestate telecommunication antennas, is also enhanced near this critical layer fraction; this has been shown experimentally and theoretically [44]. Indeed, the dielectric anomaly displayed in Fig. 4 would also be observed in other property coefficients that describe piezoelectric, pyroelectric, and electrocaloric responses. Improvements in such properties would enable more efficient acoustic resonators, IR devices, solidestate heating/cooling devices, and waste energy recovery. References [1] C.-W. Nan, M. Bichurin, S. Dong, D. Viehland, G. Srinivasan, Multiferroic magnetoelectric composites: historical perspective, status, and future directions, J. Appl. Phys. 103 (2008) 031101. [2] S.A. Harrington, J. Zhai, S. Denev, V. Gopalan, H. Wang, Z. Bi, S.A. Redfern, S.H. Baek, C.W. Bark, C.-B. Eom, Thick lead-free ferroelectric films with high Curie temperatures through nanocomposite-induced strain, Nat. Nanotechnol. 6 (2011) 491e495. [3] I.A. Kornev, L. Bellaiche, P.-E. Janolin, B. Dkhil, E. Suard, Phase diagram of Pb(Zr,Ti)O3 solid solutions from first principles, Phys. Rev. Lett. 97 (2006) 157601. [4] Y. Bastani, N. Bassiri-Gharb, Enhanced dielectric and piezoelectric response in

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