In the field of oxide electronics, there has been tremendous progress in the recent years in atomic engineering of functional oxide thin films with controlled interfaces at the unit cell level. However, some relevant devices such as tunable ferroelectric microwave capacitors (varactors) based on BaxSr1−xTiO3 are stymied by the absence of suited compatible, very low resistive oxide electrode materials on the micrometer scale. Therefore, we start with the epitaxial growth of the exceptionally highly conducting isostructural perovskite SrMoO3 having a higher room-temperature conductivity than Pt. In high-frequency applications such as tunable filters and antennas, the desired electrode thickness is determined by the electromagnetic skin depth, which is of the order of several micrometers in the frequency range of a few gigahertz. Here, we report the pulsed laser deposition of a fully layer-by-layer grown epitaxial device stack, combining a several micrometers thick electrode of SrMoO3 with atomically engineered sharp interfaces to the substrate and to the subsequently grown functional dielectric layer. The difficult to achieve epitaxial thick film growth makes use of the extraordinary ability of perovskites to accommodate strain well beyond the critical thickness limit by adjusting their lattice constant with small shifts in the cation ratio, tuned by deposition parameters. We show that our approach, encompassing several orders of magnitude in film thickness scale whilst maintaining atomic layer control, enables the fabrication of metal-insulator-metal (MIM) varactors based on 50–100 nm thin BaxSr1−xTiO3 layers with high tunability above three at the Li-ion battery voltage level (3.7 V).

The use of the perovskite BaxSr1−xTiO3 (BST) in frequency-agile microwave applications is based on the possibility to tune its permittivity, ε, by cation displacement through a quasistatic electric field.1–3 The most suitable device design for energy-efficient low-voltage applications in mobile communication consists of a metal-insulator-metal (MIM) varactor where the tunable BST is sandwiched between two electrode layers each having a thickness exceeding the skin depth.2 Due to the lack of structurally matching oxide electrode materials, existing devices combine a metal bottom electrode such as Pt with the subsequently grown BST layer on top, resulting in a defect-rich, strained, polycrystalline BST with so-called size effects associated with local polarized nanoregions and moveable charge defects.1,4 In today’s technology, the choice of metal electrode materials structurally incompatible with BST has to be compensated by rather thick (typically 200–300 nm) BST layers which, in turn, require rather large tuning voltages in the range of several tens of volts. In consequence, a MIM varactor with metal bottom electrodes, showing low losses at the working frequency (1–3 GHz) and being tunable at Li-ion battery voltage level (3.7 V) is as desirable as elusive.

Due to the ever increasing importance of high-frequency varactors, there have been several approaches to overcome the described material limitations. Attempts to use conducting oxides like SrRuO3 as an isostructural bottom electrode material have been given up due to insufficient conductivity.5 Another approach was to further optimize the growth of BST on Pt by molecular beam epitaxy,6 yielding MIM varactors with outstanding performance in the low-frequency region far below 1 GHz.7 The minimum thickness of BST is severely limited due to the growth onto a metal layer and the formation of three-dimensional defects in such metal films.8 Further approaches took advantage of the low defect density in the Ruddlesden-Popper structural derivatives of BST,9 which, however, are only applicable in interdigital capacitors (IDC) requiring rather high tuning voltages of the order of 100 V because of the specific device geometry.10,11

A comparison of the resistivities of the commonly used noble metals Au and Pt to some of the most common conducting perovskite oxides as a function of the in-plane lattice parameter is presented in Fig. 1(a). It shows that single-crystalline SrMoO3 has a low room-temperature resistivity of 5 μΩ cm,12 not only outperforming all other perovskites and even Pt (10.6 μΩ cm) but also providing a perfect lattice match to BST in the desired composition range for high tunability at room-temperature. The high conductivity of SrMoO3 (Mo 4d t2g2 electronic state) as compared to its particle-hole analog SrRuO3 (Ru 4d t2g4 electronic state with two holes in the t2g orbital) is related to the absence of magnetic interactions and weaker correlation effects.21 Due to its outstandingly low resistivity, SrMoO3 emerges as a favorable material for several applications including microelectronics,14 solid oxide fuel cells,22 transparent conductors,23,24 and plasmonics.25 As the range of lattice constants of perovskite substrates is broad, a “match made in heaven” can be formed by heteroepitaxy of GdScO3, SrMoO3, and Ba0.5Sr0.5TiO3 (BST50) with all involved lattice mismatches below 0.5%. BST50 has been chosen as a tunable dielectric for the varactors due to its high permittivity in the paraelectric phase at room temperature and, therefore, high tunability with comparably low losses.4 

FIG. 1.

(a) Comparison of some common conducting perovskite oxides (filled blue circles)5,12–20 to Au and Pt (green open diamonds) with respect to resistivity and lattice parameters. SrMoO3 s.c. denotes SrMoO3 single crystal. The BST lattice parameter range between SrTiO3 and BaTiO3 is indicated by dashed lines. The lattice constants of Ba0.5Sr0.5TiO3 (BST50) and GdScO3 are indicated by red and black arrows, respectively. The following data is for a sample with a 5 µm thick bottom electrode of SrMoO3 and a 50 nm BST50 layer: (b) X-ray diffraction (XRD) θ–2θ - scan near the GdScO3 220 reflection. (c) XRD ω-scan of the 002 reflections of SrMoO3 (FWHM = 0.008°) and BST50 (FWHM = 0.008°), as well as of the GdScO3 220 (FWHM = 0.008°) measured with Ge(220) × 2 monochromators at source and detector side. (d) XRD reciprocal space map near the GdScO3 332 reflection.

FIG. 1.

(a) Comparison of some common conducting perovskite oxides (filled blue circles)5,12–20 to Au and Pt (green open diamonds) with respect to resistivity and lattice parameters. SrMoO3 s.c. denotes SrMoO3 single crystal. The BST lattice parameter range between SrTiO3 and BaTiO3 is indicated by dashed lines. The lattice constants of Ba0.5Sr0.5TiO3 (BST50) and GdScO3 are indicated by red and black arrows, respectively. The following data is for a sample with a 5 µm thick bottom electrode of SrMoO3 and a 50 nm BST50 layer: (b) X-ray diffraction (XRD) θ–2θ - scan near the GdScO3 220 reflection. (c) XRD ω-scan of the 002 reflections of SrMoO3 (FWHM = 0.008°) and BST50 (FWHM = 0.008°), as well as of the GdScO3 220 (FWHM = 0.008°) measured with Ge(220) × 2 monochromators at source and detector side. (d) XRD reciprocal space map near the GdScO3 332 reflection.

Close modal

Here, we report MIM oxide ferroelectric varactors with thin tunable epitaxial dielectric BST50 layers, operating at low voltages below 10 V and at high frequencies up to 3 GHz, which were enabled using a 5 µm thick highly conducting epitaxial oxide SrMoO3 bottom electrode. There is a major challenge in combining SrMoO3 and BST as they grow in different extremes of the thermodynamic phase diagram. The Mo4+ (4d2) valence state in SrMoO3 is highly unstable against oxidation to Mo6+ (4d0) forming the insulating scheelite SrMoO4 exactly when subjected to the required growth conditions of BST50, which has to be fully oxidized to avoid oxygen defects. In order to achieve an acceptable compromise between a high quality dielectric with high tunability, low losses, and low leakage currents on the one hand, and a highly conductive electrode on the other hand, suited interface engineering has to be applied. In this case, we used a SrTiO3 (or BST50) interlayer grown in reducing atmosphere (ultra-high vacuum), consisting of only 10 unit cells.26 SrTiO3 was chosen due to the structural compatibility and because it undergoes a transition from a gapped insulator to a conducting material as a function of increasing oxygen vacancy concentration. Moreover, only a few unit cells of SrTiO3 can maintain sharp and stable oxidation gradients.27 

Epitaxial BST50/SrTiO3/SrMoO3/SrTiO3 thin-film heterostructures were grown by pulsed laser deposition (PLD) onto (110) GdScO3 substrates with a size of 5 × 5 mm2. A KrF excimer laser was used to ablate SrTiO3 single crystals, sintered SrMoO4 and BST50 pellets serving as PLD targets. More than 300 000 laser pulses with a fluence of 0.6 J/cm2 were shot to grow 5 µm thick SrMoO3 layers in Ar atmosphere at a pressure of 30 mTorr. The 50–100 nm thick BST50 films were deposited in oxygen atmosphere at a pressure of 8 mTorr and a laser fluence of 0.6 J/cm2. Two and 4 nm thick SrTiO3 layers were grown between SrMoO3 film and GdScO3 substrate,28,29 as well as between BST50 and SrMoO3 film, respectively, at a laser fluence of 1 J/cm2 in ultra-high vacuum (base pressure below 1 × 10−8 Torr). All samples were deposited at a substrate temperature of 630–650 °C, measured by a pyrometer on the back side of the sample holder. The growth of the layers was performed sequentially without exposing the sample to air. The growth of the aforementioned thin-film layers was monitored in situ by a 50 kV Torr® RHEED system from Staib Instruments. After the BST50 growth, the samples were cooled down to room temperature and transferred in vacuum for deposition of 10 nm thick Pt and Au seed layers followed by a thick (>4 µm) Au layer grown by electroplating. Finally, the Au/Pt top electrode of the varactors was structured using photolithography and Ar+ ion-beam etching. The top electrode of the varactor test structure consists of a central circular patch with a diameter of 20–60 µm, surrounded by a concentric ring-shaped ground plane with an outer diameter of 350 µm. The layout of the varactor top electrodes is shown in the supplementary material Fig. S1.

X-ray diffraction (XRD) measurements of the BST50/SrTiO3/SrMoO3/SrTiO3/GdScO3 heterostructures were performed with monochromatic Cu Kα1 radiation using a Rigaku SmartLab® diffractometer with a Ge 2-bounce monochromator. In preparation for the scanning transmission electron microscopy (STEM) measurements, cross-sectional cuts of the samples were made using a Jeol JIB-4600F focused ion beam (FIB) instrument. The atomic resolution images were acquired using an Atomic Resolution Microscope (ARM) Jeol 200 F equipped with a Schottky emitter and a Cs-probe corrector. The microscope was operated at 200 kV. High-angle annular dark-field (HAADF) STEM images were acquired using the 8 C spot size setting and were filtered using a principal component analysis (PCA) for improved noise reduction.30 

The Keysight Technologies impedance analyzer E4991B and vector network analyzer (VNA) E5071C were used to measure the reflection coefficient S11 of the varactor test structures in the f = 40 MHz–20 GHz frequency range, using ground-signal-ground (GSG) on-wafer probes with a 150 µm pitch. An open-short-load calibration was performed for both devices, using a standard calibration substrate [calibration kit with short-open-load-thru (SOLT) structures on alumina]. The DC bias voltage was applied either by the impedance analyzer itself or by an external voltage source for the VNA measurement.

The full heterostructure of the device stack is in a highly coherent crystalline state as shown by XRD analysis in Figs. 1(b)–1(d). The in-plane lattice parameters are locked to the substrate throughout the full stack thickness of several micrometers as revealed by the reciprocal space map [see Fig. 1(d)]. The rocking curves at the 002 reflections of SrMoO3 and BST50 show low diffuse backgrounds, and the full width at half maxima (FWHM) of 0.008° is remarkably only limited by the crystallinity of the substrate [see Fig. 1(c)].

It is well known that a lattice mismatched layer acquires increasing strain energy with increasing thickness leading eventually to strain relaxation by misfit dislocation formation when a certain critical thickness is reached, which is typically in the range of several tens to hundreds on nanometer for perovskites.

One would therefore assume that the growth of a five-micrometers-thick and fully coherent atomically smooth SrMoO3 layer is impossible. Here, however, the reciprocal space map clearly shows that coherent growth beyond the critical thickness is viable. Note that the SrMoO3 in-plane lattice constant is locked to the substrate, which leads to an enlarged c-axis lattice constant (0.3989 nm) deviating from the bulk value (0.3975 nm). This is a first hint for a mechanism allowing such thick bottom electrode growth in a layer-by-layer mode. Only based on this achievement, the subsequent functional BST50 layer can be grown with similar crystalline quality as if grown directly onto the substrate. The full coherency of the complete stack is evidenced by a set of characterizations including streaky RHEED patterns and intensity oscillations of the specular spot indicating atomic layer-by-layer growth of all layers [see Fig. 2(b)]. The growth oscillation amplitude during growth of the thick SrMoO3 layer remains constant over the full period of time. The oscillation period slightly increases towards the end of the SrMoO3 growth due to laser gas exhaustion.

FIG. 2.

(a) RHEED patterns of the GdScO3 substrate, bottom SrTiO3, SrMoO3, top SrTiO3, and BST50 layers of the heterostructure. (b) Intensity of the specular diffracted spot, recorded during the growth of the bottom SrTiO3 (black), SrMoO3 (blue), top SrTiO3 (green), and BST50 (red) layers. Black arrows denote deposition start and stop times. (c) Low-resolution HAADF-STEM image of the varactor heterostructure. [(d) and (e)] High-resolution HAADF-STEM images along with [(f) and (g)] elemental intensity line profiles of the SrMoO3/SrTiO3/GdScO3 and BST50/SrTiO3/SrMoO3 interfaces, respectively.

FIG. 2.

(a) RHEED patterns of the GdScO3 substrate, bottom SrTiO3, SrMoO3, top SrTiO3, and BST50 layers of the heterostructure. (b) Intensity of the specular diffracted spot, recorded during the growth of the bottom SrTiO3 (black), SrMoO3 (blue), top SrTiO3 (green), and BST50 (red) layers. Black arrows denote deposition start and stop times. (c) Low-resolution HAADF-STEM image of the varactor heterostructure. [(d) and (e)] High-resolution HAADF-STEM images along with [(f) and (g)] elemental intensity line profiles of the SrMoO3/SrTiO3/GdScO3 and BST50/SrTiO3/SrMoO3 interfaces, respectively.

Close modal

High-resolution STEM images reveal the remarkable fact that the interface between the substrate, the SrTiO3 buffer layer, and the lower end of the SrMoO3 electrode [see Fig. 2(d)] is of the same high crystalline quality and displays close-to-perfect dislocation-free atomic layering as does the interface between the upper end of the SrMoO3 electrode and the subsequent SrTiO3/BST layer [see Fig. 2(e)] – with 5 µm grown SrMoO3 in between [see low resolution overview in Fig. 2(c)].

The physics behind the possibility to grow perovskite layers to unprecedented high thicknesses with atomic control, is the ability of perovskites to change their lattice spacings as a function of cation ratio, which, in turn, can be tuned by deposition parameters in thin film growth. Provided that the growth parameters can be kept constant over the long deposition time, which is a technical challenge but feasible, PLD at pulse repetition rates up to several tens of hertz can be used to maintain a small but stable cation off-stoichiometry throughout the electrode growth. A deviation from the ideal stoichiometry therefore allows growing perfectly lattice matched strain-free “single crystal” films. In order to backup this model, we have investigated the stoichiometry of the SrMoO3 films. The Sr 3d, Mo 3d, and O 1s core photoelectron spectra were measured for 20 regions of four films (see Fig. 3). The positions and shapes of the peaks in Fig. 3 for all the emissions correspond to the previously reported data for SrMoO3 thin films.26 In particular, the observed Mo 3d spectra originate from the superposition of the emission lines from the Mo4+ and Mo6+ final states [Fig. 3(b)]. Here, the Mo4+ emissions are split into a screened and an unscreened component due to screening effects originating from electron correlations and charge transfer in the electrically conducting transition metal oxides.31 The Mo 3d emission from the Mo6+ states was observed as the films were exposed to air prior to the XPS measurements, which indicates that the surface of SrMoO3 oxidizes to the scheelite structure SrMoO4 with Mo6+.

FIG. 3.

Core level XPS spectra for (a) Sr3d, (b) Mo3d, (c) O1s, and (d) relative atomic concentration of Sr and Mo measured for 20 regions of 4 SrMoO3 thin films grown by PLD. The threefold standard deviation of 3σ ≈ 1.0 is shown for every measured region. Prior to the XPS measurements, the films were exposed to ambient atmosphere for 10 min.

FIG. 3.

Core level XPS spectra for (a) Sr3d, (b) Mo3d, (c) O1s, and (d) relative atomic concentration of Sr and Mo measured for 20 regions of 4 SrMoO3 thin films grown by PLD. The threefold standard deviation of 3σ ≈ 1.0 is shown for every measured region. Prior to the XPS measurements, the films were exposed to ambient atmosphere for 10 min.

Close modal

Figure 3(d) shows relative atomic concentrations of Sr and Mo in 20 studied regions. The obtained mean atomic concentrations of Sr (51.6%) and Mo (48.4%) with the threefold standard deviation of 3σ ≈ 1.0 indicate Sr excess in the grown SrMoO3 films. This is consistent with the experimentally observed increased out-of-plane lattice constant as compared to the expected value calculated taking into account a Poisson ratio of 0.271.32 Note that the off-stoichiometry is associated with antisite defects acting as additional scattering centers, reducing the conductivity of our SrMoO3 thin films as compared to single crystals. It is important to note that the method of intentional cation off-stoichiometry can be only used to grow micrometer-thick perovskite-oxide films in a limited range of small lattice mismatch, in particular when PLD is chosen as thin film growth method. However, due to the availability of a broad range of perovskite substrates with (pseudo) cubic lattice constants between 0.37 and 0.42 nm, the suggested method can be transferred to other material systems as well. This widens the scope of oxide electronics to include functional layers of various thicknesses, as is routinely available in semiconductor technology.

Similar as in the case of mobility in a two-dimensional electron gas, varactor performance parameters such as tunability and quality factor sensitively relate to materials properties. Due to the described breaking of the critical thickness limit for ultra-thick SrMoO3 electrodes, it became possible to fabricate high-performance varactors using only a 50 or 100 nm thick layer of dielectric.

Figure 4(a) shows the effective relative permittivity εr,eff (including all dielectric layers) and tunability, n, of the varactors with 50 nm (black) and 100 nm (red) thick BST50 layers at 1 GHz vs bias voltage. Due to the thin functional layer, we were able to focus on the so far inaccessible application range of an energy-efficient varactor tunable with Li-ion battery voltage of 3.7 V, corresponding to a maximum electric field of 74 V/μm (740 kV/cm) for a 50 nm thick BST50 layer. Despite this extremely thin film thickness for a varactor application, the BST50 shows a rather high εr,eff of about 350. This effective value already includes the effect of the non-tunable low permittivity of the SrTiO3 interlayer and possible dead layers. Assuming a SrTiO3 permittivity between 100 and 150, yields a BST50 permittivity for 50 nm BST between 440 and 395 when applying a simple model of a stacked dielectric capacitor. Due to the compressively stressed state and high defect concentration of the ten-unit-cells-thick SrTiO3, one would assume even lower permittivity values, which would suggest an even higher intrinsic crystalline quality of the BST50. At the relevant value of 1 GHz, the varactor with 50 nm BST50 has a high tunability of n (3.7 V) = 3.1 defined as n(Vb) = C(0)/C(Vb). Note that within 100 cycles no change of device parameters has been observed. Thus, despite the presence of the SrTiO3 interlayer which reduces the real electric field across the BST50 layer, this oxide electronics device forges ahead into the so far unachievable region of direct application at low voltages in the range of today’s batteries without additional electronics for voltage amplification.

FIG. 4.

(a) Dependences of effective relative permittivity εr,eff and tunability n from the applied bias voltage Vb, (b) frequency dependence of the Q-factor, and (c) leakage current as a function of the applied electric field of the Au/Pt/BST50/SrTiO3/SrMoO3/SrTiO3/GdScO3 MIM varactors with 50 nm (black) and 100 nm (red) thick BST50 layers. Comparison of (d) commutation quality factor (CQF) and (e) voltage performance factor (VPF) of the varactors to literature values of BST-based MIM7,33,34 varactors and, for more completeness, tunable IDCs.10,11,35 Note that IDC intrinsically need considerably higher operating voltages as compared to MIM varactors.

FIG. 4.

(a) Dependences of effective relative permittivity εr,eff and tunability n from the applied bias voltage Vb, (b) frequency dependence of the Q-factor, and (c) leakage current as a function of the applied electric field of the Au/Pt/BST50/SrTiO3/SrMoO3/SrTiO3/GdScO3 MIM varactors with 50 nm (black) and 100 nm (red) thick BST50 layers. Comparison of (d) commutation quality factor (CQF) and (e) voltage performance factor (VPF) of the varactors to literature values of BST-based MIM7,33,34 varactors and, for more completeness, tunable IDCs.10,11,35 Note that IDC intrinsically need considerably higher operating voltages as compared to MIM varactors.

Close modal

The quality factor (Q) of the varactors measured at frequencies up to 3 GHz is shown in Fig. 4(b). Without bias, the zero-bias Q factor at 1 GHz (3 GHz) is 76 (41) for the sample with 50 nm BST50. For the sample with 100 nm BST50, the zero-bias Q factor at 1 GHz (3 GHz) is 72 (40). Note that for frequencies above a few gigahertz, the Q factor is dominated by the electrode losses, leading to an inverse proportionality with frequency, while at lower frequencies, it is determined by the frequency-independent part of the losses in BST,1,36 becoming more prominent, as the impedance of the capacitance increases. For the varactor with 100 nm thick BST50, the Q factor reaches values well above 102 at 50 MHz [see red line in Fig. 4(b)] where the dielectric properties dominate, showing the high crystallinity and low losses of the BST50. The zero-bias Q factor as a function of frequency for the varactor with 50 nm BST50 merges with Q(f) of the varactor with 100 nm BST50 from 700 MHz to the highest measured frequency of 3 GHz. The decrease of Q at 4 V of the 50 nm BST50 varactor below 500 GHz is due to the increased leakage current in the thinner layer which occurs due to residual oxygen vacancies as a larger part of the layer was grown at low oxygen pressure to avoid undesired oxidation of the SrMoO3 electrode [see Fig. 4(c)].26 Overall, these observations mean that in the most relevant frequency range of application, the higher tunability of the thinner dielectric layer can be used without compromising the Q factor.

An aggregate performance of varactors is commonly evaluated using a commutation quality factor (CQF) which takes into account both tunability and losses, defined as2,37

CQFVb,f=QVb,fQ(0,f)(nVb1)2n(Vb).
(1)

For the investigated Au/Pt/BST50/SrTiO3/SrMoO3/SrTiO3/GdScO3 MIM varactors, the combination of excellent tunability and, at the same time, high Q factor leads to a high CQF of 3700 (1200) at 1 GHz (3 GHz) at the small bias voltage of 3.7 V [see Fig. 4(d)]. Thus, for the investigated varactors, the general demand for RF applications of CQF >2000 is fulfilled up to 2.3 GHz.38 

Although the CQF was suggested for comparison of the varactor performances, it was mainly defined for switches operating at two defined states with emphasis on the quality factor.37 In order to take into account the low-voltage applicability, we remind the originally discussed figure of merit of varactors and tunable components, treating quality factor and tunability on equal level. It was defined as the product of tunability n and Q factor both changing usually within one order of magnitude (typical values are n ≈ 1–10 and Q ≈ 10–100) at tuning voltages Vb ≈ 3–30 V for film thicknesses ranging from 50 to 500 nm. We therefore define a voltage performance factor (VPF),

VPF(Vb,f)=nVbVbQ(0V,f),
(2)

and compare available literature values of CQF and VPF to the here described MIM varactors as plotted in Fig. 4(e). Using the VPF representation, it becomes obvious that the here described SrMoO3 based varactors stand out in the frequency range of interest due to their unique operability at low voltage, and compare to the best results obtained at lower frequencies.

This fundamental growth study shows that perovskite oxide materials have the potential to enter into the realm of electronic devices by extending their available thickness range into the micrometer scale whilst maintaining the previously demonstrated atomic control in layer-by-layer mode. In particular, the highly conducting perovskite SrMoO3, having the highest conductivity among all perovskites and even higher than Pt metal, can be used as a (thick) electrode material in all-oxide devices by controlling the cation ratio. In a ferroelectric varactor with a five-micrometers-thick low-resistive SrMoO3 bottom electrode and a 50 nm thin tunable dielectric BST50 layer, we have achieved a tunability above three at a battery voltage of 3.7 V. The here suggested approach has the unique advantage that it allows significant and sufficient tunability at the battery voltage level. Upon further material and device optimization, SrMoO3 based varactors have the potential to drive all-oxide varactors in the emerging “5th generation (5G)” frequency range of 3–10 GHz.

See supplementary material for a technical description of the varactor device geometry, measurement setup, and its modeling.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG) within Nos. KO 4093/1-1 and JA 921/31-1, as well as the BMBF VIP+ Project No. 03VP01150. A.Z. and L.M.L. acknowledge financial support from DFG Grant No. MO 3010/3-1 and the European Research Council (ERC) “Horizon 2020” Program under Grant No. 805359—FOXON. The JEOL JEM ARM 200F transmission electron microscope used in this work was partially funded by the German Research Foundation (No. DFG/INST163/2951).

1.
A. K.
Tagantsev
,
V. O.
Sherman
,
K. F.
Astafiev
,
J.
Venkatesh
, and
N.
Setter
,
J. Electroceram.
11
,
5
(
2003
).
2.
S.
Gevorgian
,
Ferroelectrics in Microwave Devices, Circuits and Systems
(
Springer-Verlag
,
London
,
2009
).
3.
G.
Subramanyam
,
M. W.
Cole
,
N. X.
Sun
,
T. S.
Kalkur
,
N. M.
Sbrockey
,
G. S.
Tompa
,
X. M.
Guo
,
C. L.
Chen
,
S. P.
Alpay
,
G. A.
Rossetti
,
K.
Dayal
,
L. Q.
Chen
, and
D. G.
Schlom
,
J. Appl. Phys.
114
,
191301
(
2013
).
4.
T.
Jackson
and
I.
Jones
,
J. Mater. Sci.
44
,
5288
(
2009
).
5.
K.
Khamchane
,
A.
Vorobiev
,
T.
Claeson
, and
S.
Gevorgian
,
J. Appl. Phys.
99
,
034103
(
2006
).
6.
E.
Mikheev
,
A. P.
Kajdos
,
A. J.
Hauser
, and
S.
Stemmer
,
Appl. Phys. Lett.
101
,
252906
(
2012
).
7.
C. R.
Freeze
and
S.
Stemmer
,
Appl. Phys. Lett.
109
,
192904
(
2016
).
8.
H. J.
Nam
,
D. K.
Choi
, and
W. J.
Lee
,
Thin Solid Films
371
,
264
(
2000
).
9.
C. H.
Lee
,
N. D.
Orloff
,
T.
Birol
,
Y.
Zhu
,
V.
Goian
,
E.
Rocas
,
R.
Haislmaier
,
E.
Vlahos
,
J. A.
Mundy
,
L. F.
Kourkoutis
,
Y. F.
Nie
,
M. D.
Biegalski
,
J. S.
Zhang
,
M.
Bernhagen
,
N. A.
Benedek
,
Y.
Kim
,
J. D.
Brock
,
R.
Uecker
,
X. X.
Xi
,
V.
Gopalan
,
D.
Nuzhnyy
,
S.
Kamba
,
D. A.
Muller
,
I.
Takeuchi
,
J. C.
Booth
,
C. J.
Fennie
, and
D. G.
Schlom
,
Nature
502
,
532
(
2013
).
10.
C. J. G.
Meyers
,
C. R.
Freeze
,
S.
Stemmer
, and
R. A.
York
,
Appl. Phys. Lett.
109
,
112902
(
2016
).
11.
C. J. G.
Meyers
,
C. R.
Freeze
,
S.
Stemmer
, and
R. A.
York
,
Appl. Phys. Lett.
111
,
262903
(
2017
).
12.
I.
Nagai
,
N.
Shirakawa
,
S.
Ikeda
,
R.
Iwasaki
,
H.
Nishimura
, and
M.
Kosaka
,
Appl. Phys. Lett.
87
,
024105
(
2005
).
13.
A.
Radetinac
,
K. S.
Takahashi
,
L.
Alff
,
M.
Kawasaki
, and
Y.
Tokura
,
Appl. Phys. Express
3
,
073003
(
2010
).
14.
A.
Radetinac
,
A.
Mani
,
S.
Melnyk
,
M.
Nikfalazar
,
J.
Ziegler
,
Y.
Zheng
,
R.
Jakoby
,
L.
Alff
, and
P.
Komissinskiy
,
Appl. Phys. Lett.
105
,
114108
(
2014
).
15.
L.
Alff
,
P.
Komissinskiy
,
A.
Radetinac
,
T.
Sirman
, and
M.
Vafaee
,
J. Phys. D: Appl. Phys.
47
,
034012
(
2014
).
16.
H.
Boschker
,
M.
Huijben
,
A.
Vailionis
,
J.
Verbeeck
,
S.
van Aert
,
M.
Luysberg
,
S.
Bals
,
G.
van Tendeloo
,
E. P.
Houwman
,
G.
Koster
,
D. H. A.
Blank
, and
G.
Rijnders
,
J. Phys. D: Appl. Phys.
44
,
205001
(
2011
).
17.
M. W.
Zhu
,
P.
Komissinskiy
,
A.
Radetinac
,
M.
Vafaee
,
Z. J.
Wang
, and
L.
Alff
,
Appl. Phys. Lett.
103
,
141902
(
2013
).
18.
S.
Madhukar
,
S.
Aggarwal
,
A. M.
Dhote
,
R.
Ramesh
,
A.
Krishnan
,
D.
Keeble
, and
E.
Poindexter
,
J. Appl. Phys.
81
,
3543
(
1997
).
19.
J. A.
Moyer
,
C.
Eaton
, and
R.
Engel-Herbert
,
Adv. Mater.
25
,
3578
(
2013
).
20.
D.
Oka
,
Y.
Hirose
,
S.
Nakao
,
T.
Fukumura
, and
T.
Hasegawa
,
Phys. Rev. B
92
,
205102
(
2015
).
21.
Y. S.
Lee
,
J. S.
Lee
,
T. W.
Noh
,
D. Y.
Byun
,
K. S.
Yoo
,
K.
Yamaura
, and
E.
Takayama-Muromachi
,
Phys. Rev. B
67
,
113101
(
2003
).
22.
B. H.
Smith
and
M. D.
Gross
,
Electrochem. Solid-State Lett.
14
,
B1
(
2011
).
23.
A.
Radetinac
,
J.
Zimmermann
,
K.
Hoyer
,
H. B.
Zhang
,
P.
Komissinskiy
, and
L.
Alff
,
J. Appl. Phys.
119
,
055302
(
2016
).
24.
L.
Zhang
,
Y.
Zhou
,
L.
Guo
,
W.
Zhao
,
A.
Barnes
,
H.-T.
Zhang
,
C.
Eaton
,
Y.
Zheng
,
M.
Brahlek
,
H. F.
Haneef
,
N. J.
Podraza
,
M. H. W.
Chan
,
V.
Gopalan
,
K. M.
Rabe
, and
R.
Engel-Herbert
,
Nat. Mater.
15
,
204
(
2015
).
25.
M. P.
Wells
,
B.
Zou
,
B. G.
Doiron
,
R.
Kilmurray
,
A. P.
Mihai
,
R. F. M.
Oulton
,
P.
Gubeljak
,
K. L.
Ormandy
,
G.
Mallia
,
N. M.
Harrison
,
L. F.
Cohen
,
S. A.
Maier
,
N. McN.
Alford
, and
P. K.
Petrov
,
Adv. Opt. Mater.
5
,
1700622
(
2017
).
26.
A.
Radetinac
,
J.
Ziegler
,
M.
Vafaee
,
L.
Alff
, and
P.
Komissinskiy
,
J. Cryst. Growth
463
,
134
(
2017
).
27.
D. A.
Muller
,
N.
Nakagawa
,
A.
Ohtomo
,
J. L.
Grazul
, and
H. Y.
Hwang
,
Nature
430
,
657
(
2004
).
28.
Y.
Kozuka
,
H.
Seki
,
T. C.
Fujita
,
S.
Chakraverty
,
K.
Yoshimatsu
,
H.
Kumigashira
,
M.
Oshima
,
M. S.
Bahramy
,
R.
Arita
, and
M.
Kawasaki
,
Chem. Mater.
24
,
3746
(
2012
).
29.
M.
Ito
,
M.
Uchida
,
Y.
Kozuka
,
K. S.
Takahashi
, and
M.
Kawasaki
,
Phys. Rev. B
93
,
045139
(
2016
).
31.
D. O.
Scanlon
,
G. W.
Watson
,
D. J.
Payne
,
G. R.
Atkinson
,
R. G.
Egdell
, and
D. S. L.
Law
,
J. Phys. Chem. C
114
,
4636
(
2010
).
32.
N.
Kaur
,
R.
Mohan
,
N. K.
Gaur
, and
R. K.
Singh
,
J. Alloys Compd.
509
,
6077
(
2011
).
33.
A.
Vorobiev
,
P.
Rundqvist
,
K.
Khamchane
, and
S.
Gevorgian
,
Appl. Phys. Lett.
83
,
3144
(
2003
).
34.
A.
Tombak
,
J.
Maria
,
F.
Ayguavives
,
J.
Zhang
,
G. T.
Stauf
,
A. I.
Kingon
, and
A.
Mortazawi
,
IEEE Microwave Wireless Compon. Lett.
12
,
3
(
2002
).
35.
Y.
Liu
,
A. S.
Nagra
,
E. G.
Erker
,
P.
Periaswamy
,
T. R.
Taylor
,
J.
Speck
, and
R. A.
York
,
IEEE Microwave Guided Wave Lett.
10
,
448
(
2000
).
36.
A.
Vorobiev
,
P.
Rundqvist
,
K.
Khamchane
, and
S.
Gevorgian
,
J. Appl. Phys.
96
,
4642
(
2004
).
37.
I. B.
Vendik
,
O. G.
Vendik
, and
E. L.
Kollberg
,
IEEE Trans. Microwave Theory Tech.
48
,
802
(
2000
).
38.
S. V.
Razumov
,
A. V.
Tumarkin
,
M. M.
Gaidukov
,
A. G.
Gagarin
,
A. B.
Kozyrev
,
O. G.
Vendik
,
A. V.
Ivanov
,
O. U.
Buslov
,
V. N.
Keys
,
L. C.
Sengupta
, and
X.
Zhang
,
Appl. Phys. Lett.
81
,
1675
(
2002
).

Supplementary Material