Flexoelectricity-enhanced photovoltaic effect in flexible LiNbO₃ nanorod array/PVDF nanocomposites

Abstract

Recently, the flexoelectricity-enhanced photovoltaic effect has gained significant scientific attention. In this investigation, we successfully fabricated vertically aligned LiNbO₃ nanorod (LN-NR) arrays and mixed them with a PVDF (polyvinylidene difluoride) solution to produce LN-NR/PVDF nanocomposites. The flexoelectric coefficient measurement results indicate that the LN-NR/PVDF-91 (91% LiNbO₃) nanocomposite has the largest flexoelectric coefficient μ₁₃₃ of 4.95 × 10⁻⁸ C m⁻¹, which is approximately 9-fold that of the pristine PVDF film. The light polarization dependence of the photovoltaic current measurement on an LN-NR/PVDF-91 nanocomposite demonstrated that the increase of photovoltaic (PV) current arises from the flexoelectric effect. Furthermore, the photovoltaic current (I_pv) of the LN-NR/PVDF composites was measured for various nanomaterials. It was revealed that the I_pv of the flat LN-NR/PVDF-67 (0.65 μA cm⁻²) nanocomposite increased by 13.8-fold compared with that of the LN-nanoparticles/PVDF-67 nanocomposites (43.8 nA cm⁻²). Next, the photovoltaic current (I_pv) of the LN-NR/PVDF composites was measured at various curvatures. The data indicate that at a downward bending curvature of 20 m⁻¹, the I_pv of the LN-NR/PVDF-91 composites increases by 88% to 1.88 μA cm⁻² compared to that of the composite under flat conditions. In contrast, the I_pv of the LN-nanosheets/PVDF-67 nanocomposite (71.3 nA cm⁻²) only increased by 21.21% to 86.3 nA cm⁻² at a curvature of 20 m⁻¹ compared with that of the flat state of the LN-nanosheets/PVDF-67. This demonstrated that the shape of LN nanomaterials can strongly influence the photovoltaic current of LN/PVDF nanocomposites, mainly due to the increase of the flexoelectricity of aligned LN-nanoparticles/PVDF nanocomposites. The DFT (density functional theory) calculation results indicate that the bending process can generate a piezoelectric coefficient e₃₅ of 0.038 C m⁻² at a curvature of 20 m⁻¹. Therefore, LN-nanorods/PVDF nanocomposites show great potential application prospects in the non-destructive readout of ferroelectric memory devices.

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Introduction

The flexoelectric effect is a phenomenon in which strain gradients inside a dielectric material can induce relatively large localized polarizations, resulting in an electric polarization field inside the material. The concept of flexoelectricity was first introduced by Mashkevich and Tolpygo in the 1950s.¹ They reported that inhomogeneous strains may induce a polarization response in a crystalline material, resulting in microscopic electrical polarization inside the material. However, the flexoelectric effect in a bulk material was relatively small compared with the piezoelectric effect at that time, so the flexoelectric effect has not been extensively studied over time. In the early 2000s, Ma and Cross investigated the flexoelectricity of bulk ceramic materials. They measured the flexoelectric coefficients of various bulk ceramic materials, including BaTiO₃ and PbMg_2/3Nb_1/3, and reported that their coefficients are on the order of ∼10⁻⁶ C m⁻¹.^2,3 However, in 2006, L. E. Cross theoretically reported that the flexoelectric properties can be greatly improved as ceramic films are scaled down to the nanometer range.⁴ In 2011, Lee et al. investigated flexoelectricity in ferroelectric epitaxial thin films of HoMnO₃ and reported that the flexoelectricity phenomenon shows a quantum-scale photovoltaic property, which is inversely proportional to the thickness of the thin layer of the active material.⁵

In 1970, Fridkin et al. discovered the anomalous photovoltaic (APV) effect in SbSI_0.35Br_0.65 single crystal materials.⁶ Subsequently, the APV effect was continuously observed in ferroelectrics and ferroelastics, such as BiFeO₃,^7,8 BiVO₄,⁹ BaTiO₃,^10,11 AgNbO₃,¹² KNbO₃,¹³ and Pb(Zr,Ti)O₃,¹⁴ single-crystals of LiNbO₃,¹⁵ KNbO₃:Fe¹⁶ and SrTiO₃:Nb.¹⁷ These studies revealed that the electric field generated from piezoelectric polarization can play a critical role in this effect. However, the relatively small photovoltaic current (∼10⁻⁹ A cm⁻²) in piezoelectric single crystal materials greatly limits the application of the APV effect. In 2018, Yang et al. first reported the flexophotovoltaic effect.¹⁸ During their study, they used an atomic force microscopy probe to apply pressure on the SrTiO₃ single crystal and rutile TiO₂ single crystal to produce a strain gradient in the material.¹⁸ They reported that the photovoltaic current of a material can be significantly enhanced by a few orders in a symmetric nonpiezoelectric material. In 2020, Shu et al. investigated the flexophotovoltaic effect in CH₃NH₃PbBr₃ and CH₃NH₃PbCl₃-based perovskite films and reported that strain gradients can increase the photocurrent of the film by several orders of magnitude greater than the dark current.¹⁹

As shown in the schematic in Fig. 1(a), the FPV effect is the modified anomalous photovoltaic effect in ferroelectric materials caused by flexoelectricity. In the FPV effect, if the flexoelectricity generated from strain gradient is in the same direction as the internal electric field (E_bi) of ferroelectrics, it can significantly increase the PV current (I_pv) of ferroelectrics. In contrast, if the flexoelectric polarization is opposite to the internal electric field of ferroelectrics, it can greatly reduce the I_pv of ferroelectrics. For the flexoelectric effect, the magnitude of flexoelectric polarization depends on the flexoelectric coefficient and strain gradient. Although ferroelectric ceramics have relatively large flexoelectric coefficients (∼10⁻⁶ C m⁻¹), their poor flexibility makes generating large flexoelectric polarizations in the material difficult. Typically, polymers have much smaller flexoelectric coefficients (∼10⁻¹¹ C m⁻¹) than ceramics do. However, their ability to withstand high strengths and large curvatures makes it possible for them to generate a large strain gradient.^20–23 In 2018, Chu et al. combined BST (barium strontium titanate) nanofibers with a PVDF (polyvinylidene difluoride) polymer film to improve the flexoelectric coefficients of ferroelectric composites. Compared with the PVDF film, the BST/PVDF composites presented a 10% greater flexoelectric coefficient while maintaining the high flexibility of the polymer.²⁴

Fig. 1 (a) Schematic of the principle of the flexoelectricity-enhanced photovoltaic effect (FPV), which is the modified anomalous photovoltaic effect in ferroelectric materials using flexoelectricity; (b) schematic of the fabrication process of vertically arranged lithium niobate nanorod (LN-NR) arrays and LN-NR/PVDF nanocomposites.

In 2021, C. Wang et al. from Ren's group first discovered the flexoelectricity-enhanced photovoltaic (FPV) effect in potassium sodium niobite/poly(vinylidene fluoride-trifluoroethylene) (KNN/PVDF-TrFE) nanocomposites. In this process, they reported that the flexoelectric coefficient can be greatly improved by adding KNN nanoparticles to the PVDF-TrFE film, which can improve the photovoltaic current by 13.6% at a curvature of 1/20 m⁻¹ compared with the flat state of the KNN/PVDF-TrFE composite film.²⁵ Previously, L. E. Cross reported that varying the shapes of nanomaterials in nanocomposites can largely improve the flexoelectric coefficient of the nanocomposites.⁵ In 2022, B. Zhang et al. compared the FPV performance of PZT-NP/PDMS (Pb(Zr_0.52Ti_0.48)O₃ nanoparticle/polydimethylsiloxane) composites, and PZT-ANW/PDMS (PZT-aligned nanowire/PDMS) composites. They reported that the I_pv of PZT-ANW/PDMS (1.9 vol%) can increase by 27.8% at a curvature of of 34.7 m⁻¹ compared with that of the flat PZT-ANW/PDMS composite. In addition, the I_pv of the PZT-NP/PDMS composites only increased by 10.9% at the same curvature compared with that of the flat PZT-NP/PDMS composites. This finding suggests that polymer composites with vertically aligned nanowires show greater FPV performance.²⁶ Similarly, F. Yu et al. demonstrated that trapezoidal NaNbO₃ nanotube arrays/epoxy (NN-NT/epoxy) composites can increase I_pv by 79.9% to 71.8 nA cm⁻² at a bending curvature of 1/4. These results further demonstrated that the shape of the nanotube arrays has an extremely large effect on the FPV effect of the nanocomposites.²⁷ However, the photovoltaic current of the nanomaterial is still in the ∼nA cm⁻² range, which needs to be greatly improved.

Many researchers have reported the excellent photoelectric properties of ferroelectric LiNbO₃. In the 1970s, Yutaka Ohmori and others reported that a LiNbO₃ single crystal generated a photocurrent of nearly 5 nA cm⁻² under the irradiation of a Xe-arc lamp (1 kW) at 150 Hz without an external electric field.²⁸ In recent years, LiNbO₃ single crystal materials have been widely used in optical modulators because of their high-contrast waveguide ability.²⁹ Jayalakshmy reported the high pyroelectric sensitivity of LiNbO₃/PVDF nanocomposites with increasing concentrations of LiNbO₃ nanoparticles.³⁰ Therefore, as one of the great candidates for ferroelectric materials with large photovoltaic effects, LiNbO₃ shows great potential in the application of flexoelectricity-enhanced photovoltaic (FPV) effects.

In this study, we investigated the FPV effect in lithium niobate nanorod (LN-NR) arrays/PVDF nanocomposites. Among the nanocomposites, LiNbO₃ was designed as the main active material, with PVDF as a substrate. A polarized laser (360 nm) at 20 mW was then used as the illuminating source. By comparing different morphologies, including nanoparticles, nanosheets and nanorod arrays, the FPV effect of the nanocomposites was analyzed. The intrinsic mechanism of the FPV effect in the LN-NR/PVDF nanocomposites was analyzed via density functional theory (DFT) simulations. This study contributes to understanding the influence of the morphology of nanomaterials on the FPV effect with a relatively large photovoltaic effect.

Experimental methods

Preparation of LiNbO₃ nanorod arrays

A schematic of the fabrication process of the LN-NR/PVDF composites is shown in Fig. 1; a hydrothermal method was utilized to fabricate the LN-NR arrays.³¹ Lithium hydroxide (LiOH) and niobium oxide were weighed according to the stoichiometric formula. Next, 0.0631 g of lithium hydroxide and 0.4433 g of potassium hydroxide powder were dissolved in distilled (DI) water. Afterward, 0.2 g of niobium oxide and 0.04 g of polyethylene pyrrolidone were added to the mixed solution. During the reaction process, lithium hydroxide serves as both a lithium source and a mineralizer, whereas polyvinylpyrrolidone (PVP) serves as a surfactant. Potassium hydroxide (KOH) was added to maintain the pH of the solution under alkaline conditions. The mixed solution of the reactant was stirred magnetically for 2 h and then transferred to a 100 ml polytetrafluoroethylene (PTFE)-based inner stainless steel high-pressure reactor. A piece of fluorine-doped tin oxide (FTO)-coated glass (20 × 20 × 2 mm) was placed horizontally into the solution. Afterward, the high-pressure vessel was heated at 240 °C for 6 h in a vacuum drying oven. The obtained sample was rinsed with DI water and alcohol, and then dried in air at 80 °C for 12 h.

To compare the effects of different concentrations of the reactant solutions on the percentage of LN-NR/PVDF composites, the reactant solutions were diluted by 25% and 50% to perform the reaction again. The obtained LN-NR arrays were incorporated into the PVDF film via the same process as that described in Fig. 1.

Fabrication of LN-NR/PVDF nanocomposites

LN-NR/PVDF composites were prepared via a solution casting method. First, 0.344 g of PVDF powder was dissolved in 10 ml of N,N-dimethylformamide (DMF) solvent and stirred via a magnetic stirring method for 30 min. The obtained PVDF solution was poured on top of the LN-NR array, and the mixture was placed in a vacuum drying oven and heated at 60 °C for 6 h to allow the PVDF solution to penetrate into the gaps of the LN-NR arrays to form the LN-NR/PVDF nanocomposite. Second, the LN-NR/PVDF nanocomposite was peeled off from the FTO glass, placed in an oven and annealed at 135 °C for 6 h. Finally, the obtained LN-NR/PVDF nanocomposites were sputter coated with ITO and Au electrodes (15 × 15 mm) at the top and bottom of the composite film, respectively.

Fabrication of LN-NS/PVDF nanocomposites

The preparation process of LiNbO₃ nanosheets (LN-NSs) is similar to that for LN-NRs, and the only difference is that the reaction temperature was changed to 260 °C. After the LiNbO₃ nanomaterials were obtained on the FTO glass, the nanomaterials were removed from the substrate and ground to a fine and homogeneous powder. To compare them with the LN-NRs, the same concentration of LN-NSs was mixed into a PVDF substrate to make the LN-NS/PVDF nanocomposite.

Material characterization

X-ray diffraction (XRD) patterns of the PVDF, LN-NR, and LN-NR/PVDF nanocomposites were analyzed via a PANalytical X'Pert diffractometer (PANalytic Ltd, EA Almelo, The Netherlands), with a Cu Kα radiation source with an operation voltage of 40 kV, and a current of 40 mA at 2θ angles ranging from 10° to 80° with a step size of 0.05°. Field emission scanning electron microscopy (FE-SEM, SU8020, Hitachi Ltd, Japan) was used to characterize the surface morphology of all the samples. The photovoltaic (PV) current of the LN-NR/PVDF nanocomposite was measured via a 360 nm wavelength ultraviolet (UV) laser (Changchun Institute of Optics Ltd, Jilin province, China). Piezoresponse force microscopy (PFM) was conducted via an atomic force microscope (MFP-3D-SA, Oxford Instruments, Santa Barbara, CA, USA) in a PFM mode. Platinum–iridium (Pt–Ir)-coated tips with a force constant of 2.8 N m⁻¹ were applied in the PFM measurements. TGA (thermogravimetric analysis) was performed via TGA/DSC1 (Mettler Toledo LLC, Columbus, OH, USA) to obtain the concentrations of LN-NR in the LN-NR/PVDF nanocomposites at a heating rate of 5 °C min⁻¹ from room temperature to 800 °C. The optical transmission spectrum of the LN-NR/PVDF nanocomposite was investigated via a UV-vis-NIR (UV-visible-near infrared) spectrophotometer (UV 3600, Shimadzu, Japan) in the wavelength range of 200–800 nm with a step size of 0.5 nm.

Results and discussion

Characterization of LN-NR array/PVDF nanocomposites

The fabrication process of the LN-NR/PVDF nanocomposites is shown in Fig. 1(b). The LN-NR array was placed vertically in the PVDF substrate. Fig. 2(a) shows the XRD patterns of the PVDF, LN-NR array, and LN-NR/PVDF nanocomposite films. The XRD results revealed that the phase structure of the sample completely transformed to the polycrystalline structure of the LiNbO₃ material after the hydrothermal reaction at 240 °C. The XRD patterns of the LN-NR/PVDF nanocomposites showed two characteristic peaks at 2θ ≈ 17.8° and 20.0° for PVDF, which correspond to the (100) and (110) crystalline surfaces, respectively, of the α-phase PVDF. This finding indicates that the limited β-phase formed in the PVDF film after high temperature annealing at 135 °C, which is the same as that reported in a previous study.^32,33Fig. 2(b) shows the side view of the LN-NR array, which reveals that the LN arrays were uniformly distributed on the FTO glass along the thickness direction, with a length of 4–5 μm, and a width of 200–300 nm. Fig. 2(c) shows the top surface morphology of the LN-NR array. To compare the effects of different LN-NR concentrations on the PV current of the composite films, LN-NRs were fabricated with 25% and 50% reduced original reactant solutions, and the related SEM images are shown in Fig. 2(d) and (e). SEM images revealed that by adjusting the concentration of the reactants, LN nanorod arrays with different shapes and concentrations were successfully fabricated for LN nanomaterials; this is beneficial for the influence of different concentrations and shapes on the FPV effect of the LN-NR/PVDF composite.

Fig. 2 (a) X-ray diffraction (XRD) patterns of the pristine PVDF film, LN-NR arrays and LN-NR arrays/PVDF nanocomposites; scanning electron microscopy (SEM) image of (b) the side view of the LN-NR array; (c) cross-section of the LN-NR array grown on an ITO substrate; (d) top view of the LN-NR array synthesized by reducing reactant concentration by 25%; and (e) top view of the LN-NR array synthesized by reducing the reactant concentration by 50%.

Next, ITO (indium tin oxide) and Au electrodes (length ∼15 mm) were sputter coated on the top and bottom surfaces of the LN-NR/PVDF samples to measure the electrical output of the LN-NR/PVDF nanocomposites. The atomic force microscopy (AFM) results shown in Fig. S2 (ESI†) indicate that the LN nanorod array exhibits ferroelectricity, which can be reversed by a negative voltage. This is a typical property of ferroelectric materials. However, the data imply that the polarization reversal in Fig. S2(b) (ESI†) is asymmetric. This phenomenon is attributed to the self-poling generated during the fabrication of the LN-NR nanoarray.²⁶

Flexoelectric coefficient measurement

The flexoelectricity of the LN-NR/PVDF nanocomposites was analyzed by measuring the flexoelectric coefficient of the LN-NR/PVDF composites with different LN concentrations. Previously Ma and Cross evaluated the flexoelectric coefficients of various ceramics via a lab-designed experimental setup at room temperature.^3,20,34 Therefore, a similar experimental setup was designed in our laboratory to measure the flexoelectric coefficient of LN-NR/PVDF nanocomposites as shown in previous publications.^26,27 A schematic of the experimental setup is shown in Fig. 3(a). During the flexoelectric measurement, two rectangular Au electrodes (15 mm × 15 mm) were sputter coated on the top and bottom of the LN-NR/PVDF nanocomposites. The top side of the Au electrode was also used as a reflection layer for the displacement measurement via a photon sensor (MTI-2100 Fotonic Sensors, MTI Instruments, Albany, NY, USA). One end of the nanocomposite was fixed on a mechanical holder, while the other end was set free to generate the flexoelectric current. The free end of the sample was driven by a shaker (VT-20, Piezotronics Inc., China) using a sinusoidal signal generated from a lock-in amplifier (model SR830, Stanford Research Systems, Sunnyvale, CA, USA). In addition, the sinusoidal signal was amplified by a power amplifier (Crown XLS202, Harman International Company, Elkhart, IN, USA). Moreover, the generated flexoelectric current was amplified via a low noise current preamplifier (model SR570, Stanford Research Systems, Sunnyvale, CA, USA), and recorded via a digital oscilloscope (TBS 1052B, Tektronix, Beaverton, OR, USA). The flexoelectric coefficient of the nanocomposites was calculated viaeqn (1) and (2) as given below.²¹where μ_xxzz = μ₁₃₃ is the flexoelectric coefficient using Voigt notation; Q is the charge generated from flexoelectricity; f is the vibration frequency of the shaker; b and L are the width and length of the nanocomposite, respectively; x is the distance from the testing point of the tip displacement to the clamped end of the sample; and w(x) is the tip displacement of the nanocomposites. The related parameters used to calculate the flexoelectric coefficient of the LN-NR/PVDF nanocomposites are shown in Table S1.†

Fig. 3 (a) Schematic of the flexoelectric coefficient measurement setup; (b) waveform of the flexoelectric current and tip displacement, and (c) flexoelectric current as a function of tip displacement of the LN-NR/PVDF-91 nanocomposite during the flexoelectric coefficient measurement; and (d) flexoelectric coefficient of the LN/PVDF-based nanocomposites with different LN nanorod concentrations and LN nanosheets/PVDF-67.

The obtained waveform of the flexoelectric current and tip displacement of the nanocomposite film is shown in Fig. 3(b), and the flexoelectric current as a function of tip displacement of the nanocomposite is shown in Fig. 3(c). The flexoelectric coefficient was calculated using eqn (1) and (2). Fig. 3(d) shows the measured flexoelectric coefficients of LN/PVDF nanocomposites with various LN concentrations. In this study, we investigated the effects of different LN-NR concentrations and different shapes of LN nanomaterials on the flexoelectric coefficient of LN/PVDF nanocomposites. Thereafter, the nanocomposites with randomly arranged LN nanosheets and vertically arranged LN nanorod arrays were named LN-NS/PVDF and LN-NR/PVDF, respectively. The nanocomposites with LN-NR concentrations of 91%, 67%, and 36% are denoted as LN-NR/PVDF-91, LN-NR/PVDF-67, and LN-NR/PVDF-36, respectively. The concentration of vertically arranged LN nanorods in LN-NR/PVDF was calculated from the TGA (thermogravimetric analysis) results of the composites, as shown in Fig. S3 (ESI†). To compare the photovoltaic (PV) current of the LN/PVDF composites with different shapes of nanomaterials, the concentration of randomly arranged LN-NSs in the LN/PVDF nanocomposites was the same as that in the LN-NR/PVDF nanocomposites.

From the data shown in Fig. 3(d), the flexoelectric coefficient of the LN-NS/PVDF-67 nanocomposites increased by 47.99% to 8.08 × 10⁻⁹ C m⁻¹ compared with that of the pristine PVDF film (5.46 × 10⁻⁹ C m⁻¹). Compared with that of the pristine PVDF film, the flexoelectric coefficient of LN-NR/PVDF-67 nanocomposites increased by 3.9-fold, reaching 2.68 × 10⁻⁸ C m⁻¹, indicating that a larger strain gradient can be generated along the thickness direction with aligned LiNbO₃ nanorods than with LiNbO₃ nanosheets, in contrast to the randomly disordered LS-NSs. This finding is consistent with our previous conclusion.²⁴ Previously, it was known that varying the concentration of LN arrays has a significant effect on the flexoelectric coefficients of nanocomposites. The measurement results shown in Fig. 3(d) indicate that the flexoelectric coefficient of the LN-NR/PVDF-91 nanocomposite reached 4.95 × 10⁻⁸ C m⁻¹, which was an increase of 84.7% compared with that of the LN-NR/PVDF-67. In contrast, the flexoelectric coefficient of the LN-NS/PVDF-67 nanocomposites is 8.68 × 10⁻⁹ C m⁻¹, which is 67.6% lower than that of LN-NR/PVDF-67 (2.68 × 10⁻⁸ C m⁻¹). The higher concentration of LiNbO₃ nanorods resulted in a higher flexoelectric coefficient, and the aligned LiNbO₃ nanorod arrays were more favorable to generate a large flexoelectric coefficient than the randomly distributed LN nanosheets in PVDF composites.

Flexoelectricity-enhanced photovoltaic effect

Following a previous publication, we designed a flexoelectricity-enhanced photovoltaic measurement setup in the laboratory for photovoltaic current testing. A schematic of the experimental setup is shown in Fig. 4(a). In this setup, a linearly polarized laser (360 nm, 20 mW) and an electronic shutter (GCI-73, Daheng New Epoch Technology, Inc., China) were used to illuminate the sample and control the ON and OFF functions of the light, respectively. During the photovoltaic measurements, the LN-NR/PVDF nanocomposites were sputter coated with ITO and Au as the top and bottom electrodes of the samples, respectively. In addition, the generated photovoltaic currents were amplified via a low noise current preamplifier (SR570, Stanford Research Systems, Sunnyvale, CA, USA) and recorded via a digital oscilloscope (TBS 1052B, Tektronix, Beaverton, OR, USA). A schematic of the upward bending and downward bending states is shown in Fig. 4(b). From the UV-vis-NIR spectra shown in Fig. S4(a)–(h) (ESI†), it is necessary to use lasers with a wavelength less than 365 nm to excite electrons in the LN-NR/PVDF nanocomposites. In contrast, a laser with a wavelength of 280 nm is necessary to excite electrons in pristine PVDF films. Therefore, the laser (360 nm) used in this investigation can mostly excite electrons from LiNbO₃ nanorods, and the LN plays a crucial role in the LN/PVDF nanocomposite for photovoltaic measurements.

Fig. 4 (a) Schematic of the measurement setup for the FPV effect; (b) schematic of the bending state, defined as bending up and bending down; (c) photocurrent and dark current of the flat LN-NR/PVDF-91 nanocomposite as a function of applied voltage (−5 ∼ 5 V); and (d) real-time response of the photovoltaic current (I_pv) and pyroelectric current (I_pyro) of the LN-NR/PVDF-91 nanocomposite.

To compare the photocurrent with the dark current of the flat LN-NR/PVDF-91 nanocomposite, the photo current was measured with an applied voltage between −5 and +5 V, with and without light illumination. From the data shown in Fig. 4(c), the dark current of LN-NR/PVDF is very small (0.8 μA cm⁻²). In contrast, under light illumination (360 nm), the photocurrent of LN-NR/PVDF increased 16-fold, reaching 12.8 μA cm⁻² at 5 V. Based on the data, the small photocurrent without the applied voltage arises from the APV effect in ferroelectrics. From a previous publication, photovoltaic current can be generated under light irradiation (photon energy > the bandgap of the material) even without an applied voltage in ferroelectrics. This mainly arises from the internal electric field in ferroelectric materials.³⁵

For a comparison with the pyroelectric current, the photovoltaic current of the LN-NR/PVDF nanocomposites was measured using the same laser source (360 nm, 20 mW). During the measurement, the laser was turned on for 5 s and off for 10 s in a testing cycle. As shown in Fig. 4(d), the photovoltaic current (I_pv) of the sample rapidly increased after laser illumination and reached a maximum value of 1.43 μA cm⁻². For the measurement of pyroelectric current (I_pyro), thick Au layers were sputter coated on the top and bottom electrodes of the sample to prevent light penetration on the sample. As shown in Fig. 4(d), when the laser illuminates the top Au electrode, the pyroelectric current gradually increases with increasing illumination time and reaches its maximum value of 32.11 nA cm⁻² after 5 s. According to the measurement results, the pyroelectric current contributes only 2.2% of the entire photovoltaic current signal of the sample.

To evaluate whether the polarization in the LN-NR/PVDF nanocomposites is generated from flexoelectric polarization or piezoelectric polarization, the photovoltaic current of the bending LN-NR/PVDF nanocomposite as a function of the polarization direction of the laser light was measured, and the data are shown in Fig. S5 (ESI†). From the data, the curve between the photovoltaic current and the linear polarization direction is similar to a sine function. This trend is consistent with previous publications.²⁶ In principle, flexoelectric polarization is generated from the strain gradient in a material. Therefore, the polarization in the LN-NR/PVDF composites is direction-related, which demonstrates that the photovoltaic effect is due to the flexoelectricity of the LN-NR/PVDF nanocomposites.

Previous publications have shown that the internal electric field in piezoelectric materials can promote the photovoltaic current of the material. In addition, the difference in the Schottky barrier generated by different electrodes on the top and bottom sides of the material can lead to the formation of an internal electric field (E_bi), which may affect the photovoltaic effect. However, the research results of J. F. Scott revealed that the Schottky barrier has the greatest impact on the photovoltaic current when the sample thickness is less than 10 nm.³⁶ When the thickness is greater than 50 μm, the influence of the Schottky barrier can be disregarded.²⁶ In this investigation, the LN nanorod array is approximately 5 μm, and the LN-NR/PVDF nanocomposite is approximately 60 μm. Therefore, it is not necessary to consider the influence of Schottky barriers when we investigate the FPV effect of the films.

To investigate the FPV effect on LN/PVDF-based nanocomposites, the photovoltaic current was measured for nanocomposites with various concentrations of nanorod arrays, nanosheets and nanoparticles. In addition, the photovoltaic current of the LN/PVDF nanocomposites was also measured at different bending curvatures (0: flat state, 1/r: curvature with a radius of r in cm) as the bending state defined in Fig. 4(b).

First, the photovoltaic current of the LN-NR/PVDF nanocomposites with different concentrations of LN-NR arrays was measured using the same laser source (20 mW, 360 nm) with a measurement period of 5 s on and 10 s off at different bending curvatures, and the data are shown in Fig. 5. The I_pv of the flat pristine PVDF film was 8.53 nA cm⁻², and the I_pv values of the LN-NR/PVDF-36, LN-NR/PVDF-67, and LN-NR/PVDF-91 nanocomposites reached 0.45 μA cm⁻², 0.65 μA cm⁻² and 1.03 μA cm⁻², respectively. Compared with that of the flat pristine PVDF film, the I_pv of the flat LN-NR/PVDF-91 nanocomposites increased 121-fold to 1.03 μA cm⁻². This may result from the large photovoltaic current generated from the LiNbO₃ arrays.

Fig. 5 Photovoltaic current (I_pv) of (a) the pristine PVDF, (b) LN-NR/PVDF-36, (c) LN-NR/PVDF-67, (d) LN-NR/PVDF-91 as a function of curvature (downward bending), and I_pv as a function of curvature (upward bending) for (e) the PVDF, (f) LN-NR/PVDF-36, (g) LN-NR/PVDF-67, and (h) LN-NR/PVDF-91 nanocomposites.

Previous publications have shown that the flexoelectric polarization generated from the strain gradient under bending conditions can significantly influence the photovoltaic current of nanocomposites.^25–27Fig. 5(a)–(d) show the photovoltaic current of the LN/PVDF nanocomposites at different bending curvatures. From Fig. 5(a)–(d), the I_pv of the pristine PVDF film increased by 11.72% to 9.53 nA cm⁻² at a curvature of 20 m⁻¹. At the same curvature, the I_pv values of LN-NR/PVDF-91, LN-NR/PVDF-67 and LN-NR/PVDF-36 increased by 88%, 66.15%, and 40% to 1.88 μA cm⁻², 1.08 μA cm⁻² and 0.63 μA cm⁻², respectively; this means that the flexoelectric polarization generated from the downward bending of the LN-NR/PVDF nanocomposite fits in the same direction as the internal electric field in self-poled LiNbO₃ nanorods, which can significantly increase the photovoltaic current of the nanocomposites.

In addition, when the nanocomposites are bent upward, the I_pv of the LN-NR/PVDF nanocomposite was measured with increasing curvature. As shown in Fig. 5(e)–(h), compared with the pristine PVDF film under flat conditions, the I_pv of PVDF film decreased by 13.01%, to 7.42 nA cm⁻² at a curvature of 20 m⁻¹. Similarly, the I_pv values of the LN-NR/PVDF-91, LN-NR/PVDF-67 and LN-NR/PVDF-36 nanocomposites decreased by 53.2%, 43.3%, and 28.3% to 0.468 μA cm⁻², 0.369 μA cm⁻² and 0.323 μA cm⁻², respectively. The mechanism of this effect can be explained as follows. When the LN-NR/PVDF composite is bent down, an additional flexoelectric polarization originating from the strain gradient can be generated, which is along the same direction as the internal electric field (E_bi) generated from self-polarization. Therefore, it can significantly enhance the PV current (I_pv) of PN-NR/PVDF composites. In contrast, if the LN-NR/PVDF composites are bent up, the flexoelectric polarization generated by the strain gradients induces an electric field in the opposite direction as the electric field E_bi generated by self-polarization. This can greatly decrease the I_pv of the composite by the same percentage. However, the asymmetric decrease and increase ratio of the photovoltaic current of the LN-NR/PVDF nanocomposites may arise from the asymmetric structures of the LiNbO₃ nanorod arrays when they are in a bending-down or bending-up position.

The FPV effect of LN/PVDF-based nanocomposites with different LN shapes (nanosheets and nanoparticles) was also investigated further. As shown in Fig. S6 (ESI†), the I_pv values of the flat LN nanoparticle/PVDF-67 and LN nanosheet/PVDF-67 nanocomposites reached 43.8 nA cm⁻² and 71.2 nA cm⁻², respectively, which are 5.13 times and 8.35 times greater, respectively, than those of the flat PVDF film. However, the I_pv values of the flat LN-nanosheet/PVDF-67 and LN-nanoparticle/PVDF-67 composites only show 11% and 6.7% of the I_pv value of the flat LN-NR/PVDF nanocomposite, respectively.

When the nanocomposites were bent downward, as shown in Fig. S6(a) and (b) (ESI†), the I_pv of the LN-nanosheets/PVDF-67 nanocomposites (71.3 nA cm⁻²) increased by 21.21% to 86.3 nA cm⁻² at a curvature of 20 m⁻¹ compared with that of the flat state. The I_pv of the LN-nanoparticle/PVDF-67 increased by only 16.2% to 50.9 nA cm⁻² at the same curvature compared with that of the flat state of the same film. In contrast, when the nanocomposites were bent upward, the I_pv of the LN-nanosheet/PVDF-67 nanocomposites decreased by 16.85%, from 71.2 nA cm⁻² to 59.2 nA cm⁻² at a curvature of 20 m⁻¹. Similarly, the I_pv of the LN-nanoparticle/PVDF-67 nanocomposites decreased by 14.38%, to 37.5 nA cm⁻² at the same curvature (20 m⁻¹). The data demonstrated that the shape of the LN nanomaterials can strongly influence the photovoltaic current of the LN/PVDF nanocomposites, which may result from the increasing flexoelectric coefficients of the LN/PVDF nanocomposites, according to the data shown previously. In particular, in LN-NR/PVDF nanocomposites, the LN-NR array is arranged along the thickness direction (z-direction), which allows LN-nanorods to generate large gradients along the thickness direction during the bending process, which can significantly increase or decrease the photovoltaic current of LN-NR/PVDF nanocomposites, depending on the flexoelectric polarization generated in this process in the same or opposite direction as the internal electric field of the material. On the other hand, compared with the randomly arranged LN-nanosheet/PVDF and LN-nanoparticle/PVDF nanocomposites, the vertically arranged LN-NR/PVDF nanocomposites can exhibit a significant FPV effect.

The data durability of the LN-NR/PVDF-91 nanocomposites was measured, and the data are shown in Fig. 6. During this measurement, the LN-NR/PVDF-91 nanocomposite was measured in a flat state for 90 minutes (360 ON and OFF periods). The I_pv of the nanocomposite decreased from 964.15 to 962.38 nA cm⁻², a decrease of only 0.18% drop in the value of the photovoltaic current. Furthermore, the I_pv of the LN-NR/PVDF-91 nanocomposite was measured every 48 h, and this process was continuously repeated for one month. According to the data shown in Fig. 6(b), the I_pv decreased by approximately 1.2% compared with the data obtained one month before. The reliability of the FPV effect in the LN-NR/PVDF-91 nanocomposites was measured under a curvature of 1/20 and the data are shown in Fig. 6(c). Based on the data, the I_pv of the nanocomposite decreased from 1130.77 to 923.48 nA cm⁻² after a 2000 s measurement. The data demonstrate that the I_pv of the LN-NR/PVDF composites exhibits a relatively stable performance. The decrease in photovoltaic current may be caused by the release of trapped charge from the nanocomposites. In addition, the I_pv of the LN-NR/PVDF-91 nanocomposite was measured for different bending–release cycles to investigate its fatigue strength. As shown in Fig. 6(d), the I_pv of the nanocomposite decreased by 19.3% from 1123.43 to 906.36 nA cm⁻² after 5000 bending–release cycles, which indicates the fatigue strength of LN-NR/PVDF composites. Therefore, LN-NR/PVDF composite films can be utilized in applications of flexible UV detection, nondestructive ferroelectric memory readout, and photovoltaic devices.

Fig. 6 Reliability test of the I_pv for the LN-NR/PVDF-91 nanocomposites in the flat state for (a) 5000 s, (b) a month; reliability test of the FPV effect in the LN-NR/PVDF-91 nanocomposites (c) under a curvature of 1/20, and (d) for 5000 bending–release cycles.

Euler–Bernoulli beam model

The Euler–Bernoulli beam equation for a static deflection of a beam (thin plate) iswhere the beam axis is the x axis and the deflection is along the z direction. The static force acting on the right end of the beam is F, the length of the beam is L (the beam domain is 0 ≤ x ≤ L), E is the elastic modulus, and is the second moment of the area of the cross-section of the beam (b and h are the width and thickness of the beam, respectively). The vertical displacement of the beam centerline is w. The appropriate boundary conditions are as follows:

The solution is

Note that

The general flexoelectric relationship between the change in electric displacement ΔD (or polarization ΔP) due to strain gradients is³⁷

and reduces to, in the present case,

since the strain gradient satisfies

From the Maxwell–Poisson equation,

∇·D = ρ (12)

the induced charge is

From eqn (5) it follows that²¹

and the generated current is

Hence, from the measured current, the flexoelectric coefficient is determined as

We note that eqn (15) and (16) derived here for the photovoltaic current and flexoelectric coefficient μ₁₃₃, respectively, are equivalent to eqn (1) and (2) above. This indicates that the derivation process in this investigation is consistent with previous publications.

Density functional theory (DFT) simulations

The DFT calculations³⁸ on flat and curved LiNbO₃ configurations were conducted via the plane wave-based Vienna Ab initio Simulation Package (VASP)^39,40 to determine the flexoelectric coefficients μ₅₁₁ and μ₅₁₂ and piezoelectric coefficients e₂₅ and e₃₅. During this process, the generalized gradient approximation was employed for the exchange–correlation functional. The calculations were converged in energy to 10⁻⁵ eV per cell and the structures were allowed to relax until the forces were less than 2 × 10⁻² eV Å⁻¹. A vacuum layer of 40 Å was inserted along the z direction to avoid spurious interlayer interactions. Each configuration contains 288 O atoms, 96 Nb atoms, and 96 Li atoms. The size of the flat sheet is 42.09 Å × 9.11 Å × 14.29 Å. The Nb atoms were fixed along the z direction to maintain a curved shape, whereas all the other atoms were completely relaxed. The displacement function is as follows:where A represents the curvature amplitude and H_x is the simulation box length along the x direction.

Then the strain component is

The strain gradient is

The LiNbO₃ nanorod is divided into 8 groups along the x direction to analyze the local polarization.

The polarization in the i-direction is calculated via

where refers to the Born effective charge tensor and ∂r_j is the corresponding displacement, which is defined according to the uncorrugated structure. V is the volume of all the involved atoms. The fitting equations for the calculated polarization of A = 0.5 as well as the obtained piezoelectric and flexoelectric coefficients using DFT are listed in Table S3 of the ESI.† The results of the corresponding DFT calculations are shown in Fig. 7. The calculation results indicate that a flexoelectric coefficient μ₅₁₁ of 0.06 nC m⁻¹ can be generated during the bending process of a LiNbO₃ nanorod, which demonstrates the existence of flexoelectricity during the bending process of LiNbO₃ nanorods. However, this value is a few orders smaller than the flexoelectric coefficient value μ₃₁₁ from the experiment. The discrepancy between the theoretical value and experimental value is always an issue for flexoelectricity, which needs further study.⁴¹ Therefore, the LiNbO₃ lattice is deformed, and a strain gradient is generated along the thickness direction. In this way, an additional field E_dp originating from the strain gradient along the thickness direction can be produced, which is in the opposite direction to the electric field (E_bi) generated by self-polarization. Conversely, if the LN-NR is curved down, the polarization generated from the strain gradients can induce an electric field in the same direction as the field produced by self-polarization. Both the internal electric field and the polarization can affect the free charge generation and recombination. From the DFT simulation result, the polarization generated by the strain gradient in the LN-NR/PVDF can either enhance or reduce the total polarization of the nanocomposites, which can strongly affect the free charge generation. Therefore, the DFT simulation result demonstrated that the bending process can greatly change the photovoltaic current of LN-NR, which is consistent with the experimental results.

Fig. 7 (a) Schematic model used in the DFT calculation for flat and curved LiNbO₃ nanorods (A = 0, 0.5); (b) calculated deformation, strain and strain gradients for the curved LiNbO₃ nanorod with 8 groups along the x directions; (c) calculated polarizations and fitting data for the curved LiNbO₃ nanorod along the x, y, z directions.

Conclusions

In this investigation, the flexoelectricity-enhanced photovoltaic (FPV) effect was investigated in LN-NR/PVDF nanocomposites. First, the flexoelectric coefficient measurement results indicate that the flexoelectric coefficient of the LN-NR/PVDF-91 nanocomposite (4.95 × 10⁻⁸ C m⁻¹) is 4.21 times higher than that of the pristine PVDF. The dependence of light polarization on the photovoltaic current measurement on the LN-NR/PVDF-91 nanocomposite demonstrated that the change in PV current arises from the flexoelectric effect. In addition, it was revealed that the photovoltaic current (I_pv) of the flat LN-NR/PVDF-67 nanocomposite (∼0.65 μA cm⁻²) increased by 8.13-fold and 13.8-fold compared with that of the flat LN-nanosheet/PVDF-67 (71.3 nA cm⁻²) and LN nanoparticle/PVDF-67 nanocomposites (43.8 nA cm⁻²). In addition, the FPV effect of LiNbO₃/PVDF nanocomposites with different shapes of nanomaterials was measured, including LN nanoparticles, random LN nanosheets, and aligned LN-NR arrays. We revealed that at a bending curvature of 20 m⁻¹, the I_pv of the LN-NR/PVDF-91 nanocomposites increased by 88% to 1.88 μA cm⁻² compared with the flat state of the film. In contrast, the I_pv of LN-nanosheets/PVDF-67 nanocomposites (71.3 nA cm⁻²) only increased by 21.21% to 86.3 nA cm⁻² at the same curvature compared with that of the flat state. The data demonstrated that the shape of LN nanomaterials can strongly influence the photovoltaic current of LN/PVDF nanocomposites, which may result from the increasing flexoelectricity in them. Therefore, the LN-nanorod/PVDF nanocomposite shows great potential for non-destructive readout of ferroelectric memory devices.

Data availability

Data supporting this article have been included as part of the ESI.†

Author contributions

Xin Zheng: writing – original draft, methodology, formal analysis, data curation, visualization. Morten Willatzen and Dan Tan: software, visualization. Weidong Wang: investigation. Xiaodan Cao: data curation. Zhong Lin Wang: resources. Kailiang Ren: writing – review & editing, validation, supervision, resources, project administration, investigation, funding acquisition.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

This study was supported in part by The National Key Research and Development from the Ministry of Science and Technology in China under grant no. 2021YFB3200303 and it was supported partially by the National Natural Science Foundation of China under grant no. 52172082.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta06905f

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