Thin Films with Excellent Dielectric Properties over a Wide Range of Frequencies

All-Inorganic Flexible Ba

_0.67

Sr

_0.33

TiO

₃

Thin Films with Excellent Dielectric Properties over a Wide Range of Frequencies

Dong Gao,

^†,‡,⊥

Zhengwei Tan,

^†,‡,⊥

Zhen Fan,*

^,†,‡

Min Guo,

^†

Zhipeng Hou,

^†

Deyang Chen,

^†

Minghui Qin,

^†

Min Zeng,

^†

Guofu Zhou,

^‡,§

Xingsen Gao,

^†

Xubing Lu,*

^,†,‡

and Jun-Ming Liu

^†,∥

†Institute for Advanced Materials, South China Academy of Advanced Optoelectronics,^‡Guangdong Provincial Key Laboratory of Optical Information Materials and Technology, South China Academy of Advanced Optoelectronics, and^§National Center for International Research on Green Optoelectronics, South China Normal University, Guangzhou 510006, China

∥Laboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

*^S Supporting Information

ABSTRACT: With rapid advances in flexible electronics and communication devices, flexible dielectric capacitors exhibiting high permittivity, low loss, and large electric-field tunability over a wide frequency range have attracted increasing attention. Here, a large-scale Ba_0.67Sr_0.33TiO₃ (BST) dielectric thin film sandwiched between SrRuO₃ (SRO) bottom electrode and Pt top electrode is fabricated on a flexible mica substrate. The mica/SRO/BST/Pt capacitor exhibits a dielectric constant (εr′) of more than 1200, a loss tangent [tan(δ)] as low as 0.16, and a tunability of 67% at low frequencies around 10 kHz. Simultaneously, the capacitor can retain

anεr′of 540 and a tan(δ) of 0.07 at microwave frequencies, e.g., 18.6 GHz. Moreover, even when the capacitor is bent to a small radius of 5 mm or undergoes 12 000 bending cycles (at 5 mm radius), almost no deterioration inεr′, tan(δ), and tunability is observed. The excellent dielectricity and mechanicalflexibility and durability endow the mica/SRO/BST/Pt capacitor with huge potential forflexible electronic and microwave applications.

KEYWORDS: flexible capacitor, (Ba,Sr)TiO₃, mica, dielectricity, microwave frequencies

1. INTRODUCTION

The new era of Internet of things promises a widespread use of flexible electronic devices, such as paperlike displays,¹⁻³ bendable smartphones,^4,5 and electronic skins.⁶⁻⁸ Notably, almost all of theseflexible devices need the integration of a key component, namely, dielectric capacitors, to function properly.

Therefore, flexible, lightweight, and scalable dielectric capacitors have been subjected to extensive research over the past few years. So far, a variety offlexible capacitors based on polymers,⁹⁻¹¹ inorganic/polymer nanocomposites,¹² and in- organic/flexible substrate heterostructures¹³⁻¹⁶have been well developed, and their low-frequency (frequency below 1 MHz) dielectric properties, particularly energy density and charge/

discharge efficiency, were greatly concerned. However, the dielectric properties in the microwave region (frequency on the order of gigahertz) remain almost unexplored for theseflexible capacitors. Indeed, the capacitors exhibiting tunable dielectric constant at microwave frequencies canfind wide applications in the field of communication, such as waveguide phase shifters,¹⁷ frequency agile filters,¹⁸ and tunable oscillators.¹⁹ Hence, developing flexible capacitors with good dielectric properties over a wide frequency range (extending to the microwave region) is quite appealing.

While polymer-based capacitors are flexible enough, they typically exhibit limited thermal and operational stabilities, as well as poor compatibility with conventional inorganic electronic circuits. These drawbacks may be circumvented in all-inorganic flexible capacitors, which consist of the stack of inorganic dielectric layers on flexible substrates. For the inorganic dielectric layers, barium strontium titanate (Ba_xSr_1−xTiO₃; BST) appears to be the best choice because it is among the lead-free materials with the highest dielectric constant (εr′) at room temperature.²⁰ More specifically, the BST possesses a distribution of εr′ ranging from several hundred to more than one thousand depending on the Ba/Sr ratio. The maximumεr′at room temperature is achieved when the molar fraction of Ba approaches 0.7 because BST at this composition has a Curie temperature around room temper- ature.²¹ At the Curie temperature, the transition between ferroelectric and paraelectric phases occurs, giving rise to a very high dielectric constant. Besides, the BST also has low dielectric loss [tan(δ)], high breakdown voltage, and large electric-field tunability of εr′, which makes BST a promising

Received: May 20, 2019 Accepted: July 8, 2019 Published: July 8, 2019

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candidate dielectric for dynamic random access memory and tunable microwave devices.²²⁻²⁴

However, the integration of BST onflexible substrates is still challenging because the growth of high-quality BST thinfilms typically requires high temperatures (>600°C), which limits the selection of flexible substrates. Commercially available flexible polymer substrates, e.g., polyimide (PI),²⁵ polyester [poly(ethylene terephthalate)],²⁶ poly(dimethylsiloxane),²⁷ and polyethylene naphthalate (PEN),²⁸ have relatively low melting temperatures (T_M < 350 °C). Some inorganic substrates can beflexible when made ultrathin, e.g., ultrathin glass and silicon (∼50 μm), but they are fragile and expensive.^29,30Alternatively, one mayfirst grow thin films on rigid substrates and then transfer the free-standingfilms onto flexible substrates.^14,31However, this“grow-transfer”technique involves a tedious multistep process, and it can hardly produce large-scale films. Recently, mica has emerged as a popular flexible substrate for the van der Waals growth of two- dimensional materials and oxide thin films.³² Mica has mechanicalflexibility, chemical inertness, high thermal stability (T_M> 700°C), and high transparency. Additionally, the mica owns a layered structure, enabling it to be exfoliated down to

∼10 μm with an atomically smooth cleavage surface and enhancedflexibility. Therefore, mica has been widely used as a flexible substrate for the development of all-inorganicflexible electronics with novel functionalities. For example, Jiang et al.³³ developed flexible ferroelectric memories consisting of lead zirconium titanate (PZT) thin films on mica substrates, which exhibited a large polarization of 60μC/cm²and almost no polarization degradation after being bent to 2.5 mm radius for 1000 cycles. In addition, Yang et al.¹³ prepared flexible

mica/SrRuO₃ (SRO)/BaTi_0.95Co_0.05O₃ (BTCO)/Au resistive switching memories with an ON/OFF ratio of more than 50, which could withstand a bending radius down to 1.4 mm and 10 000 bending cycles. Because BST has a similar perovskite structure as PZT and BTCO, it is therefore expected that the high-quality BSTfilms with desired dielectric properties [high εr′, low tan(δ), and large tunability] can be well integrated with theflexible mica substrates.

In this work, polycrystalline BST dielectric thin films sandwiched between SRO bottom electrodes and Pt top electrodes have been successfully fabricated on mica substrates (Figure 1a). The composition of Ba/Sr = 0.67/0.33 is chosen for BST because this composition is near the optimal one, which shows the highest room-temperatureεr′, as introduced earlier. The mica/SRO/BST/Pt capacitors exhibit excellent dielectric properties in both low-frequency and microwave regions [εr′= 1200 and tan(δ) = 0.16 @ 10 kHz, andεr′= 540 and tan(δ) = 0.07 @ 18.6 GHz], and their dielectric performances show almost no deterioration after being bent to a small radius of 5 mm or repeatedly bending for 12 000 cycles (at 5 mm radius). The mechanisms for the performance degradation are also investigated.

2. EXPERIMENTAL PROCEDURE

2.1. Fabrication of Thin Films.Aflexible mica substrate of 15× 15 mm²in area and∼10μm in thickness was prepared by stripping a thin layer from a thickfluorophlogopite mica plate [KMg₃(AlSi₃O₁₀)- F₂] (Changchun Taiyuan Co.) in clean water with the aid of a polyimide tape. Then, SRO/BST/Pt heterostructures were sequen- tially grown on the mica substrate using pulsed laser deposition (PLD) (Shenyang Kecheng Vacuum Tech Co.) with a KrF excimer laser (λ = 248 nm) operated at a laser energy of 90 mJ and a Figure 1.(a) Schematic diagram of the mica/SRO/BST/Ptflexible capacitor (left panel) and a photograph of the capacitor under bending (right panel). (b) Photographs (upper panel) and transmission spectra (bottom panel) of the mica substrate, mica/BSTfilm, and mica/SRO/BSTfilm.

(c) X-ray diffraction (XRD)θ−2θscan patterns of the mica/SRO/BSTfilm, mica/SROfilm, and mica substrate. (d) Atomic force microscope (AFM) topography image of the BSTfilm grown on the SRO-buffered mica substrate. (e) Cross-sectional transmission electron microscopy (TEM) image of the SRO/BST heterostructure (the mica substrate was unintentionally removed during the preparation of the TEM sample).

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repetition rate of 5 Hz. Both SRO and BSTfilms were grown at 680

°C and under 15 Pa oxygen pressure. After it, the SRO/BSTfilms were cooled to room temperature at a rate of 5°C/min under 10⁴Pa oxygen pressure. Then, Pt top electrodes with a diameter of 200μm were grown on the SRO/BSTfilms at room temperature and in high vacuum (10⁻⁴Pa) through a shadow mask.

2.2. Characterizations.The transmission spectra were recorded using UV−vis spectroscopy (UV1800Pc). The crystal structures were characterized by X-ray diffraction (XRD) (Bruker D8). The characterizations of surface morphology and piezoresponse force microscopy (PFM) were performed using a commercial atomic force microscope (AFM) (Cypher Asylum Research). The cross section of the sample was characterized by transmission electron microscopy (TEM) (Tecnai G2-F20). The TEM sample was prepared following the steps: cutting, grinding, polishing, and ion milling. The polarization−electric field (P−E) hysteresis loops were measured with a ferroelectric workstation (Radiant Precision Multiferroic). The direct current (DC) current−voltage (I−V) characteristics were measured with a source meter (Keithley 6430). The dielectric properties in the frequency range of 500−10⁶ Hz were measured using an inductance−capacitance−resistance meter (Agilent E4980A) with an alternating current (AC) voltage of 0.1 V. The microwave dielectric measurements were made with a network analyzer (Agilent N5244A) in a shielded resonant cavity (seeFigure S1and ref34for details). The tests under bending were performed when theflexible capacitor was taped on homemade semicircular iron molds with different radii. The repeated bending cycles were applied by a homemade uniaxial stretching machine.

3. RESULTS AND DISCUSSION

Figure 1a shows the photograph of an actual mica/SRO/BST/

Ptflexible capacitor with a lateral size of 15×15 mm², where the mica substrate has been peeled offto∼10μm thick. The capacitor is capable of being bent to millimeter-scale radii, demonstrating the good mechanicalflexibility. In addition, the mica/SRO/BST film is seen to be semitransparent by eyes, whereas the mica substrate and the mica/BSTfilm are quite transparent (Figure 1b). The transparencies of mica, mica/

BST, and mica/SRO/BST samples were comparatively studied using UV−vis spectroscopy. As shown in Figure 1b, the

transmittances of both the mica substrate and mica/BSTfilm are above 50% in the wavelength range of 400−900 nm. By contrast, the transmittance of the mica/SRO/BSTfilm drops to below 20% in the same wavelength range. These results suggest that the BST layer itself exhibits good transparency, and it may be used inflexible screens if it is able to be grown on a transparent electrode like indium-tin oxide.

Figure 1c displays the XRDθ−2θscan patterns (2θ= 20− 50°) of a mica/SRO/BST bilayer film together with two control samples, i.e., a mica/SROfilm and a mica substrate.

The characteristic (00l) peaks from the mica substrate can be easily identified. Besides, the (001), (110), and (111) peaks from BST and SRO are also observed, suggesting the polycrystalline nature of BST and SRO films. While the (001) and (110) peaks from BST and SRO may overlap, the presence of the (111) peak only in the BST film unambiguously confirms that a perovskite phase of BST (either ferroelectric or paraelectric or a mixture of both) exists.

The average lattice constants of BST are estimated to bea= 3.95 Å and c = 3.96 Å, consistent with those reported previously.^35,36

Figure 1d shows a typical topography image for a 3×3μm² area of the mica/SRO/BST film. The film surface exhibits a granular feature, and it is relatively flat with a roughness of

∼3.9 nm. As can be seen in the cross-sectional TEM image (Figure 1e), the BST layer is tightly adhered to the SRO layer, and their interface is sharp. In addition, the BST layer exhibits densely packed columnar grains, which are∼300 nm in height and∼50 nm in diameter. These results demonstrate the good crystalline qualities of the BST and SROfilms grown on the mica substrate.

For BST at the composition of Ba/Sr = 0.67/0.33, the ferroelectric and paraelectric phases may coexist. The ferro- electric properties of the BSTfilm grown on the mica substrate were therefore studied via the P−E hysteresis loop measure- ment and PFM.Figure 2a shows typicalP−Ehysteresis loops measured at 10 kHz with different applied voltages for the mica/SRO/BST/Pt capacitor. The loops are quite slim with Figure 2.(a) Typical polarization−electricfield (P−E) hysteresis loops of the mica/SRO/BST/Pt capacitor (frequency: 10 kHz) with different applied voltages. PFM (b) amplitude and (c) phase images of the BSTfilm after box-in-box writing, where the outer box (2×2μm²) was written by−8 V, whereas the inner box (1×1μm²) was written by +8 V. (d) PFM amplitude and phase hysteresis loops.

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noticeable nonlinearity. As the applied voltage increases, the loop nonlinearity increases, indicating the gradual saturation of BST’s polarization. At the applied voltage of 6 V, a small remanent polarization (P_r) of∼2μC/cm²and a coercivefield (E_c) of ∼20 kV/cm can be observed. Similar loops with comparableP_randE_cvalues were observed for the BSTfilms grown on rigid substrates, which indeed suggests the mixed ferroelectric−paraelectric behavior.^37,38 Figure 2b,c presents the PFM amplitude and phase images of the mica/SRO/BST film after a box-in-box writing. The outer 2×2μm²region was first written with a tip bias of−8 V, followed by another tip bias of +8 V applied to the inner 1×1μm². As seen in the phase image (Figure 2c), only a partial of the −8 V-written region shows white color, whereas the as-grown and +8 V- written regions exhibit mainly brown color. This phase contrast indicates that there are some switchable domains existing in the BST film. However, due to the coexistence of the paraelectric phase, a full switching of domains cannot be realized in the −8 V-written region. Additionally, as seen in Figure 2d, the PFM phase loop shows a sharp ∼180° switching, whereas the amplitude loop shows a butterfly-like shape. These PFM results demonstrate that the BST film grown on the mica substrate contains a ferroelectric phase and thus it can exhibit ferroelectric switching behavior.

Now, let us focus on the dielectric properties of theflexible mica/SRO/BST/Pt capacitor.Figure 3b,c shows the typicalεr′

and tan(δ) as a function of frequency inflat and bending states.

Only the data in the frequency range of 500−(1×10⁶) Hz are shown because the dielectric behaviors at frequencies below 500 Hz and above 1×10⁶Hz are significantly influenced by space charge polarization and stray inductance, respec- tively.^39,40 In the initial flat state, the εr′ decreases monotonously with frequency (Figure 3b), consistent with the fact that fewer dipoles are able to follow the ACfield with

higher frequencies. At the frequency of 10 kHz, the εr′ can reach up to ∼1210, whereas the tan(δ) is as low as ∼0.16 (Figure 3b,c). These dielectric properties are as good as those of BST and other dielectricfilms grown on rigid substrates,^38,41 which can be attributed to the good quality of our BSTfilm.

The growth of a high-quality BSTfilm on the mica substrate is enabled by the SRO buffer layer, which is flat and highly conductive (Figure S2). If the SRO buffer layer is replaced with the Pt buffer layer, the BST film exhibits much poorer electrical properties (Figure S3).

After the measurement in the initialflat state, the capacitor was sequentially bent to the radii (R) of 20, 15, 10, and 5 mm in theflex-out bending mode, and the corresponding dielectric spectra were recorded. As shown in Figure 3b,c, theεr′ and tan(δ) in these bending states remain almost unchanged compared with those in the initialflat state. After the bending withR= 5 mm, the capacitor wasflattened again and theεr′ and tan(δ) could be fully recovered. These results demonstrate the good mechanical flexibility of our mica/SRO/BST/Pt capacitor. However, when the capacitor was further bent toR

= 2 mm, the spectrum ofεr′shifts downward, whereas that of tan(δ) shifts upward (purple lines in Figure 3b,c). More specifically, at the frequency of 10 kHz, theεr′drops to∼930 and the tan(δ) increases to ∼0.47. The degradation of dielectric properties seems to be persistent because the εr′ and tan(δ) cannot be recovered after re-flattening the capacitor (orange lines inFigure 3b,c). Therefore, it is deduced that the BSTfilm undergoes permanent damage after being bent toR= 2 mm.

Besides theεr′ and tan(δ) spectra, the characteristics ofεr′ (@ 10 kHz) versus applied electric field (E) were also measured for theflexible BST capacitor in theflat and bending states. As shown inFigure 3d, in the initialflat state, theεr′at E ≈ 0 exhibits a maximum value of ∼1210, but it decreases nonlinearly to ∼420 as E increases to 133 kV/cm. The decrease of εr′ with increasing E is due to the polarization gradually getting saturated at high electric fields, typical for nonlinear dielectrics like BST. In addition, the observation of twoεr′maxima located very close toE= 0 implies the mixed ferroelectric−paraelectric behavior in the BSTfilm, consistent with the results ofP−E loops.^42,43The ratio of electric-field- induced change inεr′ can be defined as a tunability

ε ε

= ′ ε− ′

′ tunability (%) (0) ( )E

(0)

r r

r (1)

whereεr′(0) andεr′(E) are theεr′values at zero-DCfield and E(here,E = 133 kV/cm), respectively. The tunability of our mica/SRO/BST/Pt capacitor is calculated to be∼67%, which is comparable to those achieved in BST and other dielectric films grown on rigid substrates.^44,45

Figure 3d also illustrates that the εr′−E characteristics almost do not change even when the capacitor is bent toR= 5 mm. However, when a further bending with R = 2 mm is performed, the εr′−E curve exhibits a noticeable downward shift and the value ofεr′(0)−εr′(E) decreases. These changes are persisted after re-flattening the capacitor, indicating that the capacitor undergoes permanent degradations of both zero- DCfield dielectric properties and tunable dielectric perform- ance after being bent toR= 2 mm.

To demonstrate that the flexible mica/SRO/BST/Pt capacitor is sufficiently reliable to fulfill the requirement of flexible electronic applications, the capacitor was bent (R= 5 Figure 3. (a) Photography of the mica/SRO/BST/Pt capacitor

pasted onto a mold in the flex-out bending mode. (b) Dielectric constant (εr′) and (c) loss tangent [tan(δ)] as a function of frequency, and (d) dielectric constant vs electric field (εr′−E) characteristics (frequency: 10 kHz) in the bending states with different radii. The bending radii are indicated in (c), and “flat-1”,

“flat-2”, and“flat-3”denote the initialflat state, secondflat state after being bent toR= 5 mm, and thirdflat state after being bent toR= 2 mm. The inset in (b) illustrates that a smaller bending radius corresponds to a larger extent of bending.

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mm)/flattened repeatedly, and its dielectric properties were measured after various bending cycles.Figure 4a displays the

schematic diagram of an automatic apparatus, which was used to perform the multiple bends for our flexible capacitor. As shown inFigure 4b−d, theεr′and tan(δ) spectra as well as the εr′−Echaracteristics remain roughly identical after being bent for 12 000 cycles, suggesting that the dielectric properties of theflexible BST capacitor are immune to up to 12 000 bending cycles. As the bending cycle increases to 16 000, the dielectric properties degrade slightly, and the degradation becomes more significant after another 4000 bending cycles. Nevertheless, an εr′of∼940, a tan(δ) of∼1.75, and a tunability of∼63% can be retained after the total bending cycles of 20 000.

For our flexible mica/SRO/BST/Pt capacitor, good mechanicalflexibility and durability are observed not only in the flex-out bending mode but also in the flex-in bending mode. As shown inFigures S4 and S5,flex-in bending withR= 5 mm or bending repeatedly for 12 000 cycles does not degrade the dielectric performance. However, further decreas- ingR or increasing bending cycles leads to the degradation.

These results are similar to those obtained in the flex-out bending mode, suggesting that the degradation of dielectric

performance in the mica/SRO/BST/Pt capacitor depends on the magnitude of strain (or accumulated strains) rather than the type of strain (tensile or compressive).

Figure 5a depicts a schematic setup for measuring microwave dielectric properties, which mainly consists of a shielded resonant cavity and a network analyzer. Theεr′ and tan(δ) at 18.6 GHz of the mica/SRO/BST/Pt capacitor after various bending cycles are shown inFigure 5b. In the initialflat state, the εr′ and tan(δ) are ∼540 and ∼0.07, respectively.

Such a value of εr′ at a microwave frequency is indeed quite high, comparable to those obtained in rigid BST capaci- tors.^46,47Moreover, the εr′ almost does not change after the capacitor is bent for 10 000 cycles (@ R = 5 mm), but it decreases to ∼460 after 20 000 bending cycles. Nevertheless, the tan(δ) remains below 0.1 even after 20 000 bending cycles.

Therefore, similar to those at low frequencies, the dielectric properties at microwave frequencies of our mica/SRO/BST/Pt capacitor are also very stable against mechanical bending.

To show the up-to-date research progress in flexible capacitors, the comprehensive dielectric and mechanical performances of some representative mica- and polymer- based capacitors are compared, as shown inTable 1. Notably, our mica/SRO/BST/Pt capacitor emerges as thefirst flexible capacitor ever reported, which can exhibit an εr′higher than 500 and simultaneously a tan(δ) lower than 0.1 at a microwave frequency. In addition, the mica/SRO/BST/Pt capacitor can also exhibit anεr′of more than 1200 and a tan(δ) of below 0.2 at low frequencies (e.g., 10 kHz), which are comparable to or even superior to those of other capacitors. Moreover, the tunability of ∼67% achieved in our mica/SRO/BST/Pt capacitor is the highest among all of the capacitors listed in Table 1. Last but not the least, the mica/SRO/BST/Pt capacitor can be bent toR= 5 mm and endure 12 000 bending cycles (@R= 5 mm), which are among the best mechanical properties of the reported capacitors. In a word, our mica/

SRO/BST/Pt capacitors have excellent dielectricity in a wide frequency range as well as good mechanical flexibility and durability.

Below, we proceed to analyze the degradation mechanism of the mica/SRO/BST/Pt capacitor in theflex-out bending tests (because the results of flex-out and flex-in bending tests are similar, only the former are analyzed in detail to reveal the mechanism). Two capacitors, the one after being bent toR= 2 mm (denoted“cap-1”) and the other after undertaking 20 000 bending cycles at R = 5 mm (denoted “cap-2”), were systematically compared with their respective initialflat states, in terms of morphology, impedance, and DC conductivity.

First, the AFM topography images of cap-1 and cap-2 after the Figure 4. (a) Schematic diagram of the setup for measuring the

bending endurance of the mica/SRO/BST/Pt capacitor in theflex- out bending mode. The two ends of the sample were clamped by two holders. One holder wasfixed, whereas another one was movable and its movement was controlled by a computer. (b)εr′and (c) tan(δ) as a function of frequency, and (d)εr′−Echaracteristics (frequency: 10 kHz) after different bending cycles. The bending cycles are indicated in (c).

Figure 5.(a) Schematic illustration of the shielded resonant cavity method for the measurement of microwave dielectric properties. (b)εr′and tan(δ) as a function of bending cycle (frequency: 18.6 GHz).

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bending tests show the presence of microcracks (Figure S6).

The microcracks often act as leakage paths,^55,56which may be the origin for the increase in dielectric loss.

Next, the complex impedance data of cap-1 and cap-2 were analyzed to gain deeper insights into the degradation of dielectric properties, using the Nyquist plot of the imaginary component of impedance (Z″) versus real component of impedance (Z′). Typically, the Nyquist plot would be composed of two semicircles, each semicircle representing a distinct process whose time constant is sufficiently separated from the other. The semicircle at higher frequencies represents the bulk (grains) contribution, whereas that at lower frequencies represents grain boundary and film/electrode interface contributions.⁵⁷ As shown in Figure 6, only one

semicircular arc is observed in each Nyquist plot for cap-1 and cap-2 in the initial flat state and after bending. This semicircular arc can be assigned to the BST bulk, allowing for the fact that the BST bulk contributes mainly to the dielectric response in the frequency range of 500−(1× 10⁵) Hz.⁵⁸ Therefore, the mica/SRO/BST/Pt capacitor may be modeled using an equivalent circuit, which combines a series resistance (R_s) and an RC circuit consisting of a constant phase element (CPE) and a parallel resistance (R_p). The R_s represents the contact resistance between the BST film and the electrode. The RC circuit represents the BST bulk, where the leakage contribution is reflected by R_p and the nonideal

Debye-like dielectric behavior is described by CPE.⁵⁹ The impedance of a CPE is defined by

ω ω

* = [ ]⁻

Z_CPE( ) A j( )^{n 1} (2)

whereAis the pseudocapacitance andnis a quantity between 0 and 1 describing the deviation from an ideal capacitor. Forn

= 1, the CPE becomes an ideal capacitor with capacitance equaling A, whereas, for n = 0, the CPE represents an ideal resistor with resistance equaling 1/A.

As shown inFigure 6, the complex impedance data of both cap-1 and cap-2 can be wellfitted using the equivalent circuit model. Thefitting parameters are summarized inTable 2. For cap-1, the values of CPE-related parameters (Aandn) remain almost unchanged after being bent toR= 2 mm, whereas the R_pdecreases dramatically from 1.1×10⁷to 2.9×10⁵Ω and the R_s increases from 1.1 × 10³ to 7.0 × 10³ Ω. The small changes in CPE-related parameters suggest that the BST bulk is nearly unaffected by the bending. The decrease inR_pis well correlated with the microcracks formed after a large extent of bending, which increases the leakage current. The enhance- ment inR_smay be due to thefilm/electrode contact becoming poor owing to the bending. Likewise, for cap-2, the variation trends of CPE-related parameters, R_p, and R_s are similar to those for cap-1 (Table 2). It is therefore deduced that the cyclical bending leads to similar degradation behavior as the large extent of bending, i.e., the formation of microcracks increasing the leakage current and the deterioration of film/

electrode contact.

The enhanced leakage current due to microcracks is responsible not only for the degradation of zero-DC field dielectric properties (as discussed above) but also for the degradation of tunable dielectric performance. It is known that the tunable dielectric constant results from the polarization increasing nonlinearly with the electricfield. For the capacitor after bending, the enhanced leakage current can reduce the effectivefield used for inducing the polarization. Therefore, the dielectric constant variation [εr′(0)−εr′(E)] is smaller in the capacitors after bending than in those before bending (Figures 3d and4d).

Table 1. Comparison of Dielectric Properties between our Flexible BST Capacitor and Other Flexible and Rigid Capacitors

mica/BST mica/PZT mica/BLT mica/BZT PVDF/BCZT silicon/PZT Ag/nanopaper LaAlO₃/BST^a

εr′ 1200 540 1950 460 500 80 90 540 700 1660 1057

@f(Hz) 10k 18.6G 1k 1M 10k 10k 10k 1.1G 10k 10G

tan(δ) 0.16 0.07 0.005 0.025 0.25 0.05 0.172

@f(Hz) 10k 18.6G 10k 10k 1.1G 10k 10G

tunability (%)^b 67 11 43 42 18 56

R_min(mm) 5 2.2 2.5 1.4 4 5 5

N_bending 12 000 10 000 1000 10 000 10 000 1000 1000

@R(mm) 5 mm 2.2 mm 5 mm 1.4 mm 4.5 mm 5 mm

reference this work ref48 ref33 ref49 ref50 ref51 ref52 ref53 ref44 ref54

aThis is a reference rigid capacitor.^bA benchmark for the evaluation of tunability was adopted: only the values ofεr′(0) andεr′(E= 133 kV/cm) were used ineq 1to calculate the tunability for all of the capacitors.

Figure 6.Nyquist plots of complex impedances for (a) cap-1 and (b) cap-2. The equivalent circuit is indicated in (a).

Table 2. Parameters Obtained after Fitting the Complex Impedance Data Using the Equivalent Circuit Model

state R_s R_p A n

cap-1 initial 1.1×10³ 1.1×10⁷ 3.7×10⁻¹⁰ 0.94

R= 2 mm 7.0×10³ 2.9×10⁵ 3.7×10⁻¹⁰ 0.92

cap-2 initial 6.9×10² 5.8×10⁶ 3.0×10⁻¹⁰ 0.96

20 000 cycles 3.0×10³ 3.1×10⁵ 3.2×10⁻¹⁰ 0.94

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To further understand the enhanced leakage current arising from microcracks, the DC current−voltage (I−V) character- istics were measured for cap-1 and cap-2. As shown inFigure 7a, the leakage current in cap-1 increases significantly, from

∼149.8μA (@ 6 V) in the initialflat state to∼873.7μA (@ 6 V) after the bending withR= 2 mm. Similar enhancement in leakage current is observed in cap-2, which undertakes 20 000 bending cycles (Figure 7d).

The conduction mechanisms at low and intermediate voltages (|V| < 3 V) were first analyzed. The I−V character- istics in this voltage range are replotted in the log−log scale for both cap-1 and cap-2, as shown inFigures 7b,e andS7a,c. The log(I)−log(V) curves show three characteristic linear regions, in accordance with a space-charge-limited current (SCLC) model. Region (i) at |V| < ∼0.4 V exhibits a slope of ∼1, indicating typical Ohmic conduction behavior

= μ J qn V

d

e

(3) where J is the leakage current density, q is the charge of an electron, n_e is the electron density, μ is the mobility of the electrons (0.001 cm²/(V s) for BST⁶⁰), V is the applied voltage, anddis the sample thickness. The n_eof cap-1 in the initial state is calculated to be 5.6×10¹⁴cm⁻³, which increases to 2.2×10¹⁵cm⁻³in the bending state withR= 2 mm. For cap-2, then_eincreases from 1.1×10¹⁴cm⁻³in the initial state to 2.1×10¹⁵cm⁻³after 20 000 bending cycles. The increase in n_e may be caused by the defects in the microcracks contributing more free electrons.

In region (ii) at∼0.4 V <|V|<∼2 V, the number of injected electrons is greater than that of thermally stimulated free electrons, thus leading to the SCLC behavior with a slope of

∼2. The current density from SCLC follows the modified Child’s law, which can be expressed as⁶¹

ε ε θμ

= ′

J V

d 9

8 ^{r 0}

2

3 (4)

whereε0is the permittivity of free space andθis the ratio of free-to-trapped electrons.

As the applied voltage enters region (iii) (∼2 V <|V|< 3 V), the log(I)−log(V) slope abruptly increases to much greater than 2, indicating a trap-filling process. The voltage where the slope increases abruptly is called the trap-filled limit voltage (V_TFL), which can be used to calculate the trap density (N_t)⁶²

= ε ε′

N q

V d 9

t 8 r 0 TFL

2 (5)

where an average value ofV_TFL is taken if theV_TFL values in positive and negative voltage regions are different. For cap-1, the average N_t value increases from 3.9 × 10¹⁷ cm⁻³ in the initialflat state to 4.4×10¹⁷cm⁻³after being bent toR= 2 mm. Similarly, the cap-2 also exhibits an increase in averageN_t value, from 4.0×10¹⁷cm⁻³in the initialflat state to 4.4×10¹⁷ cm⁻³after 20 000 bending cycles. The increase inN_tcan also be attributed to the formation of microcracks after bending because the dangling bonds in microcracks may create a large number of trap states.^55,56

At high voltages (|V|> 3 V), the Fowler−Nordheim (FN) tunneling often occurs, manifesting itself as the tunneling of electrons through the triangular-shaped interface potential barrier (Φt) into the conduction band of the dielectric. The current for the FN tunneling is given by

i kjjjjj j

y {zzzzz z

= − π Φ

I BE m

exp 8 2hqE 3

2 eff t

3/2

(6) whereBis a constant, Eis the electricfield (i.e.,V/d),m_effis the effective electron mass,⁶³ and h is the Planck constant.

According toeq 6, a linear relationship between Ln(I/V²) and 1/Vexists for the FN tunneling. To check it, we have plotted theI−Vcurves of cap-1 and cap-2 in the voltage range of 3 V <

|V|< 6 V as Ln(I/V²) versus 1/V, as presented inFigures 7c,f andS7b,d. The Ln(I/V²)−1/Vcurves exhibit good linearity at high voltages, indicating that the FN tunneling is the dominant conduction mechanism. Through thefittings, theΦtvalues of both cap-1 and cap-2 are found to decrease after bending, which may be attributed to the microcracks that can lower the local potential barrier for electron tunneling.

From the above analyses, it is inferred that suppressing the formation of microcracks is critical to address the bending- Figure 7.Typical current−voltage (I−V) characteristics of (a) cap-1 and (d) cap-2. Replots ofI−Vcharacteristics (voltage range: 0 to−3 V) for (b) cap-1 and (e) cap-2 in log−log scale. Replots ofI−Vcharacteristics (voltage range:−3 to−6 V) for (c) cap-1 and (f) cap-2 as Ln(I/V²) vs 1/V.

The dotted lines are thefitting lines.

ACS Applied Materials & Interfaces

induced degradation of dielectric properties. A viable approach may be reducing the thickness of the mica substrate. This is because as the mica thickness becomes smaller, the bending- induced strain on the BSTfilm is reduced (note: the strain can be estimated with d_sub/2R, where d_sub and R are the mica thickness and bending radius, respectively, and the thicknesses of BST and SRO layers are neglected because they are too small compared withd_sub). The reduced strain may give rise to a smaller amount of microcracks formed during the bending.

4. CONCLUSIONS

In summary, large-scale and high-quality SRO/BST/Pt capacitors were fabricated onflexible mica substrates through PLD. The polycrystalline BSTfilm shows an average grain size of∼50 nm, a roughness of∼3.9 nm, and a high transparency of∼50% in the 400−900 nm wavelength range. The BSTfilm also exhibits ferroelectricity with a small polarization of ∼2 μC/cm². Then, we focused on the investigation of the dielectric properties of the flexible mica/SRO/BST/Pt capacitor in both low-frequency and microwave regions. The capacitor exhibits an εr′ exceeding 1200, a tan(δ) as low as

∼0.16, and a tunability of 67% at low frequencies (e.g., 10 kHz). Meanwhile, a highεr′of∼540 and a low tan(δ) of∼0.07 are retained at microwave frequencies (e.g., 18.6 GHz). More importantly, the capacitor can endure a small bending radius of 5 mm and 12 000 bending cycles (@R= 5 mm) with almost no decays inεr′, tan(δ), and tunability. Further decreasing the bending radius or increasing bending cycles leads to the dielectric performance degradation, which may be caused by the formation of microcracks increasing the leakage current.

Nevertheless, the dielectricity of the BST bulk (grains) is sufficiently robust against the bending. Given the excellent dielectric and mechanical properties, theflexible mica/SRO/

BST/Pt capacitor is promising for wide applications inflexible electronic and microwave devices.

■

ASSOCIATED CONTENT

*^S Supporting Information

The Supporting Information is available free of charge on the ACS Publications websiteat DOI:10.1021/acsami.9b08712.

Details of the method for measuring microwave dielectric properties, morphology, and electrical con- ductivity of the SROfilm; characterizations of the BST film grown on the Pt-buffered mica substrate; dielectric properties in theflex-in bending mode; observation of microcracks using AFM; and fittings ofI−Vcharacter- istics in the positive voltage region (PDF)

■

AUTHOR INFORMATION Corresponding Authors

*E-mail:fanzhen@m.scnu.edu.cn (Z.F.).

*E-mail:luxubing@m.scnu.edu.cn(X.L.).

ORCID

Zhen Fan:0000-0002-1756-641X

Deyang Chen:0000-0002-8370-6409

Min Zeng: 0000-0003-3594-7619

Guofu Zhou:0000-0003-1101-1947

Xingsen Gao:0000-0002-2725-0785

Xubing Lu: 0000-0002-2552-9571

Jun-Ming Liu:0000-0001-8988-8429

Author Contributions

⊥D.G. and Z.T. contributed equally to this work.

Notes

The authors declare no competingfinancial interest.

■

ACKNOWLEDGMENTS

The authors would like to thank the National Key Research Program of China (No. 2016YFA0201002), the State Key Program for Basic Researches of China (No. 2015CB921202), the National Natural Science Foundation of China (Nos.

51602110, 11674108, 51431006, and 51561135014), the Guangdong Innovative Research Team Program (No.

2013C102), the Science and Technology Project of G u a n g d o n g P r o v i n c e ( N o s . 2 0 1 6 B 0 9 0 9 1 8 0 8 3 , 2017B030301007, and 2015B090927006), the Natural Science Foundation of Guangdong Province (No. 2016A030308019), and the Science and Technology Project of Shenzhen Municipal Science and Technology Innovation Committee (GQYCZZ20150721150406). X.L. and Z.F. acknowledge the Project for Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme 2016 and 2018, respectively. D.G. and Z.T. acknowledge the support from the Innovation Project of Graduate School of South China Normal University.

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