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Surface modification of grains with silver nano-clusters: a new route to great enhancement of photoluminescence in Eu3+-doped ferroelectric polycrystalline oxide thin films

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Abstract

We report on a new route to greatly enhance the photoluminescence of Eu3+ doped ferroelectric polycrystalline oxide thin films: surface modification of grains with silver nanoclusters (NCs). The Ag doped Bi3.6Eu0.4Ti3O12 (BET) thin films were prepared by a chemical solution deposition method. According to the XRD, TEM and XPS analysis, partially oxidated Ag NCs have been formed on the surfaces of the BET grains. A greatly enhanced photoluminescence was obtained in a wide range of Ag doping level. Role of the Ag NCs in the photoluminescence enhancement was investigated by means of absorption, emission and excitation spectra, as well as decay lifetime measurement. The results indicate that the intra-4f transition of Eu3+ can be intensively activated by the coupling of the charge transfer band of BET with the 5D0 state of Eu3+ ions, and the enhancement of Eu3+ ions emission in the present thin films was attributed to the surface modification of BET crystalline grains by Ag NCs. In addition, the influences of Ag NCs on the dielectric and ferroelectric properties of these materials were discussed as well.

© 2013 Optical Society of America

1. Introduction

The rare-earth ions substituted bismuth titanate, namely Bi4-xRexTi3O12 (Re = La, Sm, Nd, Eu, etc.; 0<x<1), have attracted much attention because of their excellent ferroelectric properties [1]. The trivalent Re ions substitute for Bi3+ in the A site of the layered perovskite structure of Bi4Ti3O12 and act as structural modifiers [2]. The photoluminescence (PL) of rare-earth ions in ferroelectric oxides is another interesting issue to be specified. Although the luminescent efficiencies of rare-earth ions in oxide matrix are usually low compared with those in sulfides, fluorides and halides due to their relatively large phonon energy, the stability of oxide compounds is especially favorite for the applications in luminescent host matrix. Ferroelectric oxides were recently proposed as a promising host for the rare earth luminance, in an attempt to modify the luminescence characteristics of the rare earth ions by controlling the electric poling direction and the symmetry of the host lattice [3, 4]. It has been demonstrated that the Eu3+ substituted Bi4Ti3O12 ferroelectric thin films possess not only excellent ferroelectric properties but also characteristic red emissions of Eu3+ ions [5]. However, because of the small absorption cross section arising from the formally forbidden intra-4f transition of Eu3+, further enhancement of the excitation efficiency of Bi4-xEuxTi3O12 is desirable.

Doping with noble metals such as Ag and Au has been proved an effective method to improve the luminescent properties of rare earth ions in various host matrix [68]. The PL enhancement through such approach was attributed by many authors to the local-field surface plasmon resonance (SPR) effect of noble metal nanoparticles [912]. Theories based on energy transfer from Ag related centers to rare earth ions was also developed to explain the influence of non-plasmonic silver nanoclusters [1315]. The term “nanoclusters” refers to small aggregates of several to ~100 metal atoms. Since the size of NCs (10 nm) is comparable to the Fermi wavelength of electrons (the de Broglie wavelength of the electrons at the Fermi level: 0.5 nm for Ag), the Ag NCs modified lanthanide-doped compounds do not exhibit the SPR effect because of their relatively low density of states for endowing them with SPR features [15]. In contrast to the SPR absorption band of Ag nanocrystals around 420 nm, the absorption band of Ag NCs in glasses that associate with the pairs of silver ions/atoms locates in the spectral region between 300 and 450 nm, opening the possibility of energy transfer towards rare earth ions [13]. More evidences for the energy transfer enhancement have been reported by other authors, e.g. Tikhomirov et al. [16] on the Ag-Yb co-doped oxyfluoride glasses and Guo et al. [17] on the Ag-Eu co-doped oxyfluoride glasses. However, since the absorptance of Ag NCs at the most efficient excitation wavelength is usually Reweak and often undetectable, the specific enhancement mechanism of Ag NCs remains controversial.

In this work, the Ag doped Bi4-xEuxTi3O12 ferroelectric thin films have been studied. A systematic research on the effect of Eu content has revealed that both PL and FE properties are optimized at a specific concentration Bi3.6Eu0.4Ti3O12, though there was no evidence of direct correlation between the two phenomena [5]. Therefore, the content of Eu3+ was set at x = 0.4, while the ratio of Ag to Bi3.6Eu0.4Ti3O12 was varied from 0 to 0.4. The microstructural features, the PL properties, and the spectroscopic characteristics was comprehensively investigated. A model based on surface modification of BET grains with Ag NCs is proposed to interpret the possible mechanism that has led to the improved emission efficiency of the Ag-BET nanocomposite.

2. Experimental

The Ag doped Bi3.6Eu0.4Ti3O12 (Ag-BET) thin films were fabricated by a chemical solution deposition method using Bi(NO3)3∙5H2O, Eu(NO3)3∙5H2O, Ti(OC4H9)4 and AgNO3 powders as the Bi, Eu, Ti and Ag sources. The mole ratio of Ag to BET was selected at 0:1, 0.1:1, 0.2:1, 0.3:1 and 0.4:1, which were denoted by BET0, BET1, BET2, BET3, BET4, respectively. The Bi(NO3)3∙5H2O, Eu(NO3)3∙5H2O and Ti(OC4H9)4 powders were weighed and resolved in the mixed solvents containing 67% 2-Methoxyethanol, 33% acetic acid and a small amount of acetyl acetone. Bi(NO3)3∙5H2O was 10% excess in the solution to compensate for the Bi loss during the thermal annealing. The concentration of BET was adjusted to 0.06 mol/L. Then, different amounts of AgNO3 were added in. Spin coating of the mixed solution was performed on fused silica and Pt/Ti/SiO2/Si substrates at a spinning rate of 3000 rpm for 30 s, followed by baking on a hotplate at 300 °C for 5 min. The spin coating and baking processes were repeated for several times until the desired film thickness was attained. In the end, the samples were annealed at 700 °C for 1 h in air.

The crystal structure of the nanocomposite thin films was analyzed by X-ray diffraction (XRD) (Rigaku, D/MAX 2200 VPC) with Cu Kα radiation operated at the working voltage and current of 40 kV and 30 mA, respectively. X-Ray photoelectron spectroscopy (XPS) (ESCALAB 250) was undertaken on the surface of the thin films with a monochromized Al Kα radiation (1486.6 eV). All the XPS peaks were corrected by the C 1s (284.6 eV) as the internal reference. The composition and chemical state were investigated on the basis of the areas and binding energies of Ag 3d. The transmission electron microscope (TEM) is used to image particles and perform electron diffraction patterns (FEI, Tecnai G2 Spirit). Photoluminescence spectra were measured at room temperature using a spectro-fluorophotometer (Shimadzu, RF5301). The decay lifetime spectra were obtained by the use of fluorescence system (Edinburgh FLSP 920) and the UV-Vis spectra were recorded with a spectrophotometer (Shimadzu UV-3150) in the transmittance mode. To measure the electrical properties, Pt top electrodes were deposited on the surface of the films through a shadow mask. The dielectric properties were measured using 4284a LCR meter (Agilent, CA, USA). The polarization-electric field (P-E) hysteresis loops of the thin films were measured at 1 kHz by a precision workstation ferroelectric tester (Radiant Technologies, Inc. NM, USA).

3. Results and discussion

According to the XRD patterns presented in Fig. 1(a), all the investigated Ag-BET thin films with different Ag-BET molar ratio have crystallized in a layered perovskite structure without any detectable secondary phase. Although no distinctive diffraction peaks of metallic silver or its compounds were detected in the whole investigated Ag constitution range, the position of diffraction peaks of the BET matrix did not change with the varied Ag content, implying little solubility of Ag atoms in the lattice of BET. Since the strongest diffraction peak of Ag polycrystals is close to the (0014) diffraction of Bi4Ti3O12, it is hard to monitor the phase structure of Ag by XRD technique. Therefore, XPS analysis was employed to determine the oxidation state of the Ag atoms. As illustrated in Fig. 1(b) for BET4 (molar ratio Ag:BET = 0.4:1), the Ag 3d5/2 and Ag 3d3/2 binding energies appeared at 368.1 eV and 374.1 eV in good agreement with the literature values for bulk metallic silver [18, 19]. This, however, cannot be taken as an evidence of the existence of metallic silver. It has been demonstrated that the XPS core levels of Ag 3d can be influenced by the grain size and the oxidation states of silver. In particular, the XPS peaks shift right in Ag NCs and shift left in Ag2O. As a combination of these two opposite trends in oxidated silver NCs, the deviation of XPS binding energy from the metallic Ag 3d may be very small. It should be noted that the XPS signal of Ag is quite weak compared with those of Bi and Ti in spite of the high doping level of Ag. The reason might be that silver atoms aggregate on the grain boundaries rather than on the thin-film surfaces. Since XPS is a surface-sensitive technique and only the signal from the top 0 to 10 nm of the films is detectable, the signal for the embedded Ag can be very weak.

 figure: Fig. 1

Fig. 1 (a) XRD patterns of the pure and the Ag-doped Bi3.6Eu0.4Ti3O12 thin films with different molar ratio Ag:BET = 0:1, 0.1:1, 0.2:1, 0.3:1 and 0.4:1, which are denoted by BET0, BET1, BET2, BET3 and BET4, respectively. (b) XPS spectrum of the Ag 3d narrow-scan for BET4 with the highest Ag concentration.

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Clear evidences of the co-existence of metallic and oxidated Ag NCs in the Ag-BET thin films were obtained by TEM technique. The thin films for TEM analysis were peeled from the fused silica substrate and dispersed in ethanol by magnetic stirring. It is evident in Fig. 2(a) that the BET matrix has been crystallized in rod-like grains with diameters ~64 nm and lengths 200-300 nm. The magnified images from two selected areas, denoted by A and B in Fig. 2(a), are presented in Figs. 2(b) and 2(d), respectively. The dark area (A) contains dark round particles with diameters around 2-4 nm. The electron diffraction pattern collected from this area can be identified to be metallic Ag polycrystals. As for the gray area (B) that consists of even lighter particles, only diffused rings of a semi-crystalline state were observed, as shown in Figs. 2(c) and 2(e), respectively. The interplanar spacings (d) are determined from the radii (R) of diffraction rings using Bragg law,

d=1(R/x)×5
where, x is the measured length of the scale. The results of Figs. 2(c) and 2(e) are listed in Table 1 and Table 2, respectively, in comparison with the literature values of Ag and Ag2O polycrystals determined by powder XRD. It can be claimed that the results obtained from SAED are in good agreement with the references. It comes out that the incorporated Ag atoms precipitated at the surface of BET grains in a form of nanoclusters and were partially oxidated during the thin film deposition process.

 figure: Fig. 2

Fig. 2 (a) TEM image of BET4 thin films peeled from the fused silica substrate. (b) and (d) are the amplified TEM images of the selected areas A and B in (a), of which the selected area electron diffraction patterns are presented as (c) poly-crystalline Ag and (e) semi-crystalline Ag2O nanoclusters.

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Tables Icon

Table 1. Comparison of interplanar spacings determined by SAED from the selected area in Fig. 2(b) of the Ag-doped Bi3.6Eu0.4Ti3O12 thin films with the reference values obtained by XRD analysis on Ag polycrystals.

Tables Icon

Table 2. Comparison of interplanar spacings determined by SAED from the selected area in Fig. 2 (d) of the Ag-doped Bi3.6Eu0.4Ti3O12 thin films with the reference values obtained by XRD analysis on Ag2O polycrystals.

The influence of Ag NCs on the photoluminescence properties of Eu3+ in BET were investigated by means of absorption/transmittance, excitation and emission spectroscopy. According to the transmittance spectra in Fig. 3(a) of the Ag-BET thin films, a steep charge transfer absorption edge appeared at 360 nm, and the wavelength kept almost unchanged against the variation of Ag content. The inset in Fig. 3(a) shows that the optical band gap of pure BET is about 3.6 eV, in agreement with the literature value [20] for charge transfer from the top of the valence band to the bottom of the conduction band. In order to distinguish the contribution of Ag NCs to the total absorptance, the absorption spectrum of pure Ag NCs was also measured. The thin film of pure Ag NCs was deposited on fused silica by the same process for preparing Ag-BET and exhibited a similar morphology, as illustrated in the inset in Fig. 3(b). As shown in Fig. 3(b), the absorption edge of Ag NCs appeared at 250-350 nm in the UV region. The absorbance of the Ag-BET thin films did not show obvious change with the Ag content in the range from BET0 to BET3. It should be noted that the classic SPR absorption band (~420 nm) of Ag nano-particles did not appear in this case. Therefore, the SPR enhancing effect should be excluded from the possible mechanisms that have contributed to the photoluminescence of Ag-BET. This opinion is also supported by the luminescence decay monitoring the 617 nm emission at 360 nm excitation in Fig. 4. The decay curves of all the investigated thin films can be approximately fitted by a single exponential function. The values are listed in the inset of Fig. 4, and the estimated lifetimes around 0.88 ms are similar for all the examined samples. Since the lifetime of Eu3+ emission is known to decrease under the SPR enhancement [21], nearly no change of lifetime appears as a disproof of this mechanism.

 figure: Fig. 3

Fig. 3 (a) The optical transmission spectra of the pure and the Ag doped Bi3.6Eu0.4Ti3O12 thin films. Inset: Plot of (αE)2 versus (E) for the pure BET thin film near the optical band gap edge; linear extrapolation is performed to determine the optical band gap. (b) The UV–visible absorption spectra of pure Ag NCs and Ag doped BET thin films on fused silica substrate . Inset: TEM image of the Ag NCs thin film peeled from the substrate. (c) Excitation spectra of the Ag-BET samples monitored at 617 nm. (d) Emission spectra under the excitation wavelength of 360 nm. Inset: plot of PL intensities versus Ag:BET molar ratio.

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 figure: Fig. 4

Fig. 4 Luminescence decay transients measured for the pure and the Ag-doped Bi3.6Eu0.4Ti3O12 thin films. Inset: a list of the estimated lift times.

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The excitation spectra of the Ag-BET thin films were obtained by monitoring the emission intensity caused by the 5D07F2 transition (at 617 nm) of Eu3+ ions. As shown in Fig. 3(c), the excitation spectra of our samples consist of three parts: one broad band at 300-390 nm and two sharp peaks at 394 and 465 nm. The two sharp peaks are related to the intra-4f transitions (7F05L6 and 7F05D2) of Eu3+ ions. The position of the broad band is consistent with the optical absorption energy of BET (~360 nm), which is associated with a charge transfer from the top of the valence band to the bottom of the conduction band. The excitation in this wavelength range indicates a strong coupling of photo-electrons with the 5D0 state of Eu3+ ions, and all the photo-electrons relax directly to the meta-stable 5D0 state when the UV bands are excited. In contrast, the emission intensities of Eu3+ are neglectable at a pumping wavelength near the UV absorption edge of Ag NCs (250-350 nm). Consequently, the possibility of energy transfer from Ag NCs towards Eu3+ is definitely ruled out. As is evident in Fig. 3(c), the emission intensities of Eu3+ increase with the increasing Ag content and reach a maximum in BET3 (molar ratio Ag:BET = 0.3:1). Meanwhile, the peak positions of the spectra (~360 nm) shift slightly to longer wavelength.

The PL enhancing effect of Ag NCs is more evident in Fig. 3(d). A 360 nm excitation source was used to activate the charge transfer band of BET matrix. Since Eu3+ ions substitute for Bi3+ in the A sites without inversion symmetry, the hypersensitive forced electric-dipole 5D07F2 transition with the emission wavelength of 610-620 nm comes in sight with a strong intensity, while the allowed magnetic-dipole 5D07F1 transition of Eu3+ appears at 590-600 nm as normal [22]. The intensities of both emissions are plotted as functions of Ag content in the inset of Fig. 3(d). Maximums as high as 7 times of those in the Ag-free samples are obtained at a molar ratio Ag:BET = 0.3:1.

As we already concluded, neither the local-field SPR effect of Ag particles nor the sensitizer effect of Ag related centers can be employed to explain the PL enhancement in Ag co-doped BET thin films. Moreover, the surfaces of all the thin films fluctuate in the same orders of magnitude of several nanometers, implying a neglectable influence of roughness on the spectroscopic properties of these samples. Considering the strong coupling of the charge transfer band with the characteristic emissions of Eu3+, we suggest that the surface modification by Ag NCs might be crucial to the PL enhancement of BET. The mechanism will be described as follows, generally on the basis of the energy level schemes shown in Fig. 5.

 figure: Fig. 5

Fig. 5 Schematics of energy levels and the carrier transfer process in (a) the bare grains and (b) the Ag NCs-coated grains of Bi3.6Eu0.4Ti3O12.

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Unlike glassy host, the crystalline grains of oxide compounds contain much less defects, which usually concentrate on grain boundaries to minimize the surface energy. Luminescence quenching by defects may occur if the Forster or Dexter energy transfer are enabled. In fact, reducing the amount of surface quenching centers by surface modification has been found to be an effective method to improve the PL efficiency of various materials, including organic phosphor [23], semiconductor [24], up-conversion [25], and down-conversion [26] photoluminescent materials. On the other hand, the crystalline oxide semiconductors have separated continuous energy bands to sustain rapid migration of electrons and holes over a long distance. Surface states may exist at the surface of the semiconductors due to the termination of lattice periodicity. For a semiconductor with higher Fermi level on the surface, the electrons will transfer from the surface to the bulk, resulting in downward band bending in the space charge region, as illustrated in Fig. 5(a). When the semiconductor contacts with a metal of lower Fermi level, charge will flow to the metal, causing upward band bending toward the interface, as illustrated in Fig. 5(b). Although the actual energy band bending in the BET grains has not been measured, a high density of the surface states for electrons can be expected due additionally to the deficiency of Bi atoms on the grain surfaces caused by thermal evaporation.

One can envision the charge transfer in the Ag-free BET grains by trailing the migration of a single pair of photo-excitons. First, the electron in the valence band is pumped to the conduction band, leaving a hole in the valence band. Instead of being captured by a Eu3+ center, the photo-excited carriers are attracted to grain boundaries along the downward-bended energy band and recombined nonradiatively in a defect quenching center. By this approach, the possibility of radiative recombination via Eu3+ centers can be reduced. In the Ag NCs coated BET grains, however, the flowing of charge carriers are constrained inside the grains by the potential barrier at the interface. The opportunities of excitons or free electrons and holes being captured by the radiative Eu3+ centers are sequentially improved, leading to the luminescence enhancement.

Such a model may explain the red shift of the excitation band near 360 nm in Fig. 3(c). When the photo-electrons are activated and start traveling in the energy bands, those at higher energy levels are more capable to escape from the grain boundaries and approach the Eu3+ centers. As for the Ag NCs coated BET grains, the electrons are likely to be repelled by the potential walls at the interface. That means less motivation energy is needed for transferring the excited electrons to Eu3+ centers. If the model is true, it will be useful in material design to control the energy band bending and consequently the luminescent properties of Re-doped semiconductors by grain surface modification. Metals with large Fermi energy levels, such as platinum, gold, silver and copper, are expected to work as surface modifiers. More experimental evidences are needed to check the feasibility of this model.

At the end of this section, the dielectric properties of the Ag-BET thin films are presented. As shown in Fig. 6(a), the dielectric characteristics of all these samples are relatively frequency stable up to 105 Hz. The relative dielectric constant varied from 250 to 450 and reached a maximum in BET2 (molar ratio Ag:BET = 0.2:1). The dielectric loss (<0.2) are reasonably low for dielectric applications. The dependence of dielectric properties on the molar ratio of Ag NCs can be interpreted by the percolation theory for a metal-insulator mixture [27]. In general, by the percolation theory, the effective dielectric constant of a metal-insulator mixture could be much larger than that of a single component dielectric in several orders of magnitude [28]. Even though the Ag NCs have been partially oxidated, the amount of metallic Ag tends to increase with the increasing Ag content. In consistence with the qualitative prediction of the percolation theory, the apparent dielectric constant of the Ag-BET composites increase gradually with the increasing Ag content and finally changed to a conductive state at a threshold concentration, but the amplitude of increase in dielectric constant is smaller than expected, since the relative dielectric constant of Ag2O (εr = 8.8) [29] is much lower than that of BET. The polarization-electric field (P-E) hysteresis loops of the Ag-BET thin films are shown in Fig. 6(b). The BET0, BET1, BET2, and BET3 thin films exhibit well-saturated hysteresis loops that are indicative of favorable ferroelectric properties, while the ferroelectric property of BET4 was apparently destroyed due to the large leakage current. All the Ag-BET samples except for BET4 have similar remnant polarization around 20 µC/cm2 and coercive field of 128 kV/cm, which are close to literature values [30] of pure BET.

 figure: Fig. 6

Fig. 6 (a) Dielectric spectra and (b) P-E hysteresis loops of the pure and the Ag doped Bi3.6Eu0.4Ti3O12 thin films.

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4. Conclusion

In summary, incorporation of Ag nanoclusters in the Bi3.6Eu0.4Ti3O12 ferroelectric thin films is an effective method to improve the photoluminescence of Eu3+ ions. The intra-4f transition of Eu3+ can be intensively activated by the coupling of the charge transfer from the valence band to the conduction band with the 5D0 state of Eu3+. Silver nanocrystals act neither as origin of an enhanced local field nor as absorption centers for a subsequent energy transfer.

A surface modification model rather than the classic local-field SPR effect and energy transfer mechanism is employed to explain the PL enhancement of Ag-BET. In this model, the energy bands of the host BET crystals bend in different directions depending on the state of the grain surface with or without Ag NCs. The flowing direction of the charge carriers can be influenced by the bending of energy band. In the bare BET grains, the photo-excitons are attracted to the grain surface and thus improve the nonradiative recombination via surface defect quenching centers. In contrast, the photo-excitons in Ag NCs coated BET grains are repelled from the interface, resulting in enhanced radiative recombination via Eu3+ centers.

In addition, the dielectric and ferroelectric properties of BET thin films were maintained, in a wide range of Ag content. These results suggest that Ag-BET thin films might be considered as a promising multifunctional material for applications in new integrated photoluminescence ferroelectric thin film devices.

Acknowledgments

This study was funded by National Natural Science Foundation of China (Nos. 51172289 and 51202298), National Basic Research Program (973 Program) of China (No. 2012CB619302), Natural Science Foundation of Guangdong Province, China (No. 10251027501000007), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Nos. 20110171130004 and 20110171120030).

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Figures (6)

Fig. 1
Fig. 1 (a) XRD patterns of the pure and the Ag-doped Bi3.6Eu0.4Ti3O12 thin films with different molar ratio Ag:BET = 0:1, 0.1:1, 0.2:1, 0.3:1 and 0.4:1, which are denoted by BET0, BET1, BET2, BET3 and BET4, respectively. (b) XPS spectrum of the Ag 3d narrow-scan for BET4 with the highest Ag concentration.
Fig. 2
Fig. 2 (a) TEM image of BET4 thin films peeled from the fused silica substrate. (b) and (d) are the amplified TEM images of the selected areas A and B in (a), of which the selected area electron diffraction patterns are presented as (c) poly-crystalline Ag and (e) semi-crystalline Ag2O nanoclusters.
Fig. 3
Fig. 3 (a) The optical transmission spectra of the pure and the Ag doped Bi3.6Eu0.4Ti3O12 thin films. Inset: Plot of (αE)2 versus (E) for the pure BET thin film near the optical band gap edge; linear extrapolation is performed to determine the optical band gap. (b) The UV–visible absorption spectra of pure Ag NCs and Ag doped BET thin films on fused silica substrate . Inset: TEM image of the Ag NCs thin film peeled from the substrate. (c) Excitation spectra of the Ag-BET samples monitored at 617 nm. (d) Emission spectra under the excitation wavelength of 360 nm. Inset: plot of PL intensities versus Ag:BET molar ratio.
Fig. 4
Fig. 4 Luminescence decay transients measured for the pure and the Ag-doped Bi3.6Eu0.4Ti3O12 thin films. Inset: a list of the estimated lift times.
Fig. 5
Fig. 5 Schematics of energy levels and the carrier transfer process in (a) the bare grains and (b) the Ag NCs-coated grains of Bi3.6Eu0.4Ti3O12.
Fig. 6
Fig. 6 (a) Dielectric spectra and (b) P-E hysteresis loops of the pure and the Ag doped Bi3.6Eu0.4Ti3O12 thin films.

Tables (2)

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Table 1 Comparison of interplanar spacings determined by SAED from the selected area in Fig. 2(b) of the Ag-doped Bi3.6Eu0.4Ti3O12 thin films with the reference values obtained by XRD analysis on Ag polycrystals.

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Table 2 Comparison of interplanar spacings determined by SAED from the selected area in Fig. 2 (d) of the Ag-doped Bi3.6Eu0.4Ti3O12 thin films with the reference values obtained by XRD analysis on Ag2O polycrystals.

Equations (1)

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d= 1 (R/x)×5
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