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CERAMICS INTERNATIONAL
Ceramics International 40 (2014) 13363–13370 www.elsevier.com/locate/ceramint
Structural, ferroelectric, and optical properties of Pb0.60Ca0.20Sr0.20TiO3, Pb0.50Ca0.25Sr0.25TiO3 and Pb0.40Ca0.30Sr0.30TiO3 thin films prepared by the chemical solution deposition technique D.S.L. Pontesa,c, F.M Pontesb,c,n, R.A. Capelib,c, M.L. Garzimb,c, A.J. Chiquitod,c, E. Longoa,c,e a
LIEC—Department of Chemistry, Universidade Federal de São Carlos, Via Washington Luiz, Km 235, PO Box 676, 13565-905 São Carlos, São Paulo, Brazil b Department of Chemistry, Universidade Estadual Paulista—Unesp, PO Box 473, 17033-360 Bauru, São Paulo, Brazil c Instituto de Física de São Carlos, USP, São Carlos 13560-250, São Paulo, Brazil d NanO LaB—Department of Physics, Universidade Federal de São Carlos, Via Washington Luiz, Km 235, PO Box 676, 13565-905 São Carlos, São Paulo, Brazil e Institute of Chemistry, Universidade Estadual Paulista—Unesp, Araraquara, São Paulo, Brazil Received 14 March 2014; received in revised form 7 May 2014; accepted 7 May 2014 Available online 17 May 2014
Abstract Perovskite ferroelectric Pb0.60Ca0.20Sr0.20TiO3, Pb0.50Ca0.25Sr0.25TiO3 and Pb0.40Ca0.30Sr0.30TiO3, thin films were deposited on Pt/Ti/SiO2/Si and (1 0 0) LaAlO3 substrates by a chemical solution deposition method. XRD revealed the formation of pure thin films on both substrates. All thin films have very flat surfaces, and no droplets were found on their surfaces. Raman data showed a gradual phase transition from tetragonal to a pseudocubic perovskite structure in these thin films; a simultaneous increase in Ca and Sr contents at room temperature was also observed. Temperature-dependent dielectric permittivity measurements revealed a decreasing ferroelectric-to-paraelectric phase transition temperature with increasing Ca and Sr contents. At 100 kHz, ferroelectric-to-paraelectric phase transition temperatures were approximately 505, 355 and 290 K for Pb0.60Ca0.20Sr0.20TiO3, Pb0.50Ca0.25Sr0.25TiO3 and Pb0.40Ca0.30Sr0.30TiO3 thin films, respectively. The Eg of the films were estimated from Tauc's law and were found to be inversely dependent on the Ca and Sr content amounts. & 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved. Keywords: Thin films; Optical transmittance; Chemical synthesis; Phase transition
1. Introduction In the last decade, ferroelectric materials technology (FMT) has been motivated from both theoretical and experimental viewpoints [1–3]. Actually, the current focus is on the development of ferroelectric thin film device technology based mainly on the perovskite family [4,5]. This class of materials with the formula ABX3 and a tetragonal P4mm structure continue to attract much attention and PbTiO3 is the archetype due to its rich spectrum of physical properties and its variety of structural phase transitions. In addition, PbTiO3 and PbTiO3-based solid n Corresponding author at: Department of Chemistry, Universidade Estadual Paulista—Unesp, PO Box 473, 17033-360 Bauru, São Paulo, Brazil. Tel.: þ 55 14 3103 6135; fax: þ55 14 3103 6088. E-mail address:
[email protected] (F. Pontes).
http://dx.doi.org/10.1016/j.ceramint.2014.05.052 0272-8842/& 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
solution are now being considered for applications in different kinds of applications such as information storage devices, microand nanoelectronics, optical waveguides, piezoelectric actuators, infrared sensors and ultrasonic transducers in the medical field [6–8]. Physical and chemical properties of these materials are sensitive to extrinsic or/and intrinsic conditions such as temperature, pressure, strain, film thickness, surface energy, thermal expansion coefficients, defects, grain size, external electric and magnetic fields [9–13]. In addition, chemical substitution is another powerful method for tuning properties of perovskite and perovskite-like materials [14]. According to recent experimental and theoretical predictions, a magnetic ion placed on the AO6 octahedral site induces ferromagnetism [15,16]. Physical properties such as ferroelectricity, piezoelectricity, ferromagnetic and dielectric properties, crystal structure and the Curie temperature of the PbTiO3-based solid solution are
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closely related with specific dopants (chemical substitution). Therefore, the formation and stability of the new PbTiO3-based solid solutions are rationalized through the use of adequate chemical elements according with their characteristics such as cations size, charge difference and tolerance factor. When AO12 and/or BO6 sites contain mixtures of two, three or more different chemical elements, control of the cation ordering in a complex perovskite structure is a powerful approach toward to new state with different physical and/or chemical properties; e.g., modifications in the BO6 octahedral site can induce ferroelectricto-relaxor type structural phase transitions in PbTiO3-based perovskite complexes [17,18]. In addition, Kinaci et al. reported that the partial substitution of Ti4 þ by Nb or Ta ions resulted in ntype electrical properties for SrTiO3 compounds [19]. First principles supercell calculations predicted that A-site driven ferroelectricity may occur in disordered (K,Ba,La)ZrO3 [20]. In recent years, much research efforts have been focused on AB1 xBxO3 solid solutions with perovskite-like structures where strong coupling between polarization and magnetization is observed; a good example of this is the multiferroic materials [21,22]. Stoupin et al. [23] reported a reduction of the tetragonal lattice parameter when Mn ions solid solution replaces TiO6 in the octahedral site in PbTiO3. The observed reduction was found to be a function of the Mn amount. Specifically, Mn-K edge XANES and magnetization response measurements revealed that Mn ions actually are in a mixed Mn3 þ /Mn4 þ oxidation state and dilute ferromagnetism, respectively. In an experimental and theoretical study, Paris et al. [24] demonstrated that the amount of Sm in PbTiO3 affects the expected structural and vibrational properties: the O 2p and Ti 3d orbitals were monitored by an ab initio quantum-mechanical method approach and revealed changes closely related to the hybrid orbitals distribution due to Sm. Therefore, for this study, PbTiO3 was chosen as the matrix, and Ca and Sr chemical species were incorporated to replace Pb atoms in the dodecahedra site in order to simultaneously study their effects on structural, optical and dielectric properties. 2. Experimental procedures Our procedure for synthesizing (Pb,Ca,Sr)TiO3 thin films in different compositions such as Pb0.40Ca0.30Sr0.30TiO3 (PCST40), Pb0.50Ca0.25Sr0.25TiO3 (PCST50) and Pb0.60Ca0.20Sr0.20TiO3 (PCST60) consisted in producing a polymeric resin using a soft chemistry method (polymeric precursor route). Starting chemicals were lead acetate trihydrate, calcium carbonate, strontium carbonate and titanium isopropoxide (Alfa Aeasar Co.). Deionized water, citric acid and ethylene glycol were used as the solvent, chelating and polymerizing agents, respectively. First, titanium citrate was formed by the dissolution of titanium isopropoxide in a water solution of citric acid (70–80 1C) under constant stirring to homogenize the titanium citrate aqueous solution. Then the lead acetate trihydrate was dissolved in water, which was added at a stoichiometric quantity to the titanium citrate aqueous solution; CaCO3 was slowly added during a vigorous stirring. After homogenization, SrCO3 was slowly added resulting in a clear solution. In addition, a small amount of citric acid was added to
stabilize the polymeric network structure. After homogenization of the solutions containing Pb2 þ , Ca2 þ , and Sr2 þ cations, ethylene glycol was added to promote mixed citrate polymerization by the polyesterification reaction. Continued heating at 80–90 1C, allows solutions become more viscous but devoid of any visible phase separation. The deposition solution viscosity was adjusted to 12 mPa s. Following the polymeric precursor, the solution was spin-coated on 10 10 mm substrates [Pt/Ti/SiO2/Si] by a commercial spinner operating at 7000 rev./min for 20 s (spin-coater KW-4B, Chemat Technology) via a syringe filter to avoid particulate contamination. A two-stage heat treatment was carried out as follows: initial heating at 400 1C for 4 h at a heating rate of 5 1C/min in air atmosphere to pyrolyze the organic materials, followed by heating at 700 1C for 2 h at a fixed rate of 5 1C/min for crystallization. XRD with Cu-Kα radiation was used to assess the phase purity and possible textural developments of crystallized thin films; diffraction patterns were recorded on a Rigaku D/Max 2400 diffractometer. Typical 2θ angular scans ranging from 201 to 601 in varying steps of 0.021 were used in these experiments. Thin film thicknesses were characterized using a field-emission scanning electron microscopy (FE-SEM) (FEG-VP Zeiss Supra 35) with a secondary electron lens detector on a freshly fractured film/ substrate cross-section. AFM was used to obtain a bi- and tridimensional image reconstruction of the sample surface. These images provided an accurate analysis of the sample surface and parameter quantifications such as roughness and average grain size. A Digital Instruments Multi-Mode Nanoscope IIIa was used in these experiments. The optical transmittance of the PCST60, PCST50 and PCST40 thin films (deposited on (1 0 0) LaAlO3 single crystal substrates under conditions identical described above) was measured from 200 to 1000 nm using a Shimadzu 1240 spectrophotometer. Raman measurements were taken with a T-64000 Jobin-Yvon triple-monochromator coupled to a charge-coupled device (CCD) detector. An optical microscope with a 100 objective was used to focus the 514.5 nm line of a Coherent Innova 90 argon laser onto the sample. The power was maintained at 15 mW. Thin films temperature-dependent capacitances were studied in a metal-ferroelectric-metal configuration and the films were characterized using a Gw Instek LCR 819 m at temperatures ranging from 300 to 600 K for PCST50 and PCST60. For these measurements, circular Au top electrodes with an area of approximately 4.9 10 2 mm2 were deposited (through shadow mask) by thermal evaporation on the heat-treated film surfaces. Temperature-dependent capacitance measurements of PCST40 thin films were taken at temperatures varying from 50 to 300 K using a closed-cycle helium cryostat and a Gw Instek LCR 819 m for capacitance measurements; all measurements were performed at 100 kHz. 3. Results and discussion Fig. 1 shows XRD patterns of (Pb,Ca,Sr)TiO3 thin films on Pt/Ti/SiO2/Si substrates annealed at 700 1C for 2 h in ambient atmosphere (XRD patterns for pure CaTiO3 and SrTiO3 films obtained under the same conditions are also shown in Fig. 1 for
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Fig. 1. XRD patterns of (a) PCST60, (b) PCST50, (c) PCST40, (d) SrTiO3, and (e) CaTiO3 thin films deposited on Pt/Ti/SiO2/Si substrates.
comparison). These results are in agreement with diffraction patterns obtained from powders of the same composition and annealed at the same temperature. All films present a polycrystalline nature of a pure perovskite phase with no secondary phase formation. A gradual evolution related to the increase of the Ca and Sr contents was observed, showing clearly that PCST60 films still exhibits splits of the (0 0 1)/(1 0 0) and (0 0 2)/(2 0 0) diffraction peaks; this behavior indicates that some degree of tetragonality still remains in samples. However, a strong overlapping was observed in PCST50 and PCST40 thin films, indicating that possibly a pseudocubic structure was formed. According to the XRD patterns an increase in Sr and Ca contents co-substituted at the A-site on the (Pb,Ca,Sr)TiO3 composition resulted in decreased tetragonality. Lattice parameter variation as a function of different Sr and Ca contents was estimated from the XRD patterns: the c-axis lattice parameter noticeably decreased while the a-axis lattice parameter slightly decreased as Sr and Ca contents increased (lattice parameters a¼ 3.916 Å, c¼ 3.953 Å; a¼ 3.907 Å, c¼ 3.910 Å; and a¼ 3.904 Å, c¼ 3.909 Å for PCST60, PCST50 and PCST40 thin films, respectively). A similar result was reported by Sun et al. [25] from XRD pattern analysis of Pb0.25BaxSr0.75 xTiO3 system: all used compositions (x¼ 0.05, 0.1, 0.15 and 0.20) revealed a typical cubic perovskite structure. Fig. 2 shows XRD patterns for the PCST60, PCST50 and PCST40 thin films on a (1 0 0) LaAlO3 single crystal substrate. These samples were grown on a (1 0 0) LaAlO3 transparent substrate exhibiting a single perovskite phase; no pyrochlore phase peaks or a deleterious phase were found. The XRD patterns also revealed a much higher intensity for the (1 0 0) and (2 0 0) reflections in thin films, suggesting that they are aligned along the (h 0 0) orientation. Careful inspection of the XRD data also indicates that samples exhibit a reflection occurring at 2θ about 321. Such a peak, with rather low intensity, was identified as belonging to the most intense reflection of the pattern taken in polycrystalline PCST60, PCST50 and PCST40 thin films, as seen in Fig. 1. The cross-sectional image of PCST thin film in Fig. 3 exhibits the formation of a polycrystalline morphology and
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Fig. 2. X-ray diffraction patterns for the (a) PCST60, (b) PCST50, (c) PCST40 thin films deposited on the (1 0 0) LaAlO3 substrate and (d) (1 0 0) LaAlO3 substrate. LAO¼ LaAlO3.
distinctive features in the thin film/substrate interface. PCST60, PCST50 and PCST40 thin films thicknesses were measured to be approximately 520, 560 and 540 nm, respectively. In addition, thin film morphologies of PCST60, PCST50 and PCST40 on Si/SiO2/Si/Pt substrate were also investigated by AFM, see inset in Fig. 3. All samples exhibited a dense and uniform microstructure without any obvious cracks but with spherical-shaped grains. The observed average grain size of films on platinum-coated silicon substrates was approximately 70, 50 and 40 nm for PCST60, PCST50 and PCST40 thin films, respectively. Raman spectroscopy was used to enhance the structural analysis produced by XRD. Raman spectroscopy is a powerful tool to study structural changes and in particular, to detect slight deviations from the tetragonal-to-cubic (or vice-versa) structure that often occur in the class of perovskite-type compounds. Here we investigate the effects of Sr and Ca chemical species acting as lattice modifier elements in the (Pb, Ca,Sr)TiO3 system which in turn, can induce significant modifications in the Raman response of PCST films. Room temperature Raman spectra of PCST60, PCST50 and PCST40 thin films are compared with those obtained for pure CaTiO3 and SrTiO3 films in Fig. 4. An examination of spectrum of the PCST60 film show all Raman active transversal and longitudinal optical modes as it is expected for a tetragonal structure (P4 mm group space) which also is in agreement with the literature [26]. In particular, for PCST60 films, lowest A1(1TO) and E(1TO) phonons (soft mode) are originated from Pb ions vibrating against TiO6 octahedra. Raman peak positions are extremely sensitive to Sr and Ca contents in these samples (see Fig. 4). Furthermore, drastic changes in Raman spectra can be observed in PCST60, PCST50 and PCST40 samples such as diffused, weak and broader peaks. The disappearance and/or displacement of Raman modes for lower wavenumbers indicates that (Pb,Ca, Sr)TiO3 films underwent a dramatic medium- and short-range
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Fig. 3. Cross-sectional FE-SEM micrographs of (Pb,Ca,Sr)TiO3 films with thicknesses of about 520, 560, and 540 nm for (a) PCST60, (b) PCST50 and (c) PCST40, respectively. The inset shows the AFM micrographs of PCST films grown on Pt/Ti/SiO2/Si substrates.
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Fig. 5. Dielectric permittivity–voltage characteristic curves of the (a) PCST60, (b) PCST50 and (c) PCST40 thin films at room temperature and at 100 kHz frequency. Fig. 4. Raman spectra of (a) PCST60, (b) PCST50, (c) PCST40, (d) SrTiO3 and (e) CaTiO3 thin films on Pt/Ti/SiO2/Si substrates.
structural change at room temperature. Similar results has been reported by Wang et al. for (Na1/2Bi1/2)1 xPbxTiO3 thin films [27]. In addition, A1(1TO) and E(1TO) phonon modes (softmodes) are remarkably altered and appear at lower wavenumbers, suggesting clearly a gradual tetragonal phase loss for PCST50 and PCST40 films. For PCST60 and PCST50 samples, the E(1TO) (soft mode) shows a shift toward lower frequencies, at 60 and 49 cm 1, respectively. XRD analysis data for PCST40 films also suggest that the crystal structure appears as cubic while Raman scattering revealed a short-range distortion with A1(1TO), E(2TO), B1 þ E, A1(3TO) and E(3LO)þ A1(3LO) broader phonon modes (indicated by asterisks n in Fig. 4(c)). As a consequence, due to the local disorder, we believe the bands at 114, 191, 272, 553 and 723 cm 1 for PCST40 thin films are more closely associated to the pseudocubic structure than to the cubic structure (common to SrTiO3) as seen in Fig. 4(d). Therefore, it is plausible to assume that PCST40 films exhibit long-range order for a short-range disordered structure according to XRD and Raman analyses, respectively. In summary, Raman spectra agree with the tetragonality gradual loss in the following order: PCST60, PCST50 and PCST40. In principle, these structural changes of PCST films should have a significant impact on optical, dielectric and phase transition properties of these samples, and this phenomenon will be also explored in this study. To establish the structureferroelectric property correlation in our samples, their capacitance–voltage (C–V curves) and polarization-electric field (hysteresis loop) responses were investigated at room temperature. Fig. 5 displays C–V curves obtained from PCST60, PCST50 and PCST40 films grown on a platinum-coated silicon substrate. The butterfly profile of the curves was not visible for PCST40 films which indicates that ferroelectric property domains and the off-center displacement associated with spontaneous polarization in the ferroelectric perovskite structure were very small and/or absent at room temperature.
The PCST60 thin film revealed a larger splitting between sweep up/sweep down measurements which is associated with strong short- and long-range ferroelectric dipolar ordering suggesting that Ti atom shifts inside TiO6 octahedra leading to an intense non-centrosymmetric ferroelectric dipolar order which is expected to show a high value of remnant polarization; i.e., Ti atoms have a larger shift within the octahedron (TiO6 unit) in the c direction (polarization axis) for the PCST60 film than those shifts for PCST50 and PCST40 films. This result is in good agreement with the previous Raman analysis, also resulting in a gradual loss of tetragonality in the following order PCST60 4 PCST50 4 PCST40. Importantly, the lattice parameter reduction also results in an ionic displacement reduction; i.e., Ti atoms have a smaller shift within the oxygen octahedron (TiO6 unit) in the c direction (polarization axis). As a result, small ferroelectric domain shifts occur (i.e., a weakening of long- and short-range ferroelectric dipolar order). Together with this ferroelectricto-paraelectric transition, the relative displacement between the Ti4 þ ion and the O2 octahedron along the c-axis in the tetragonal PCST60 thin films were reduced for PCST50 and PCST40 films. As a result, a more centrosymmetric structure (in our case, the PCST40 films) is obtained. Fig. 6 shows the hysteresis loop response of PCST60, PCST50 and PCST40 thin films. The observed hysteresis loop character is an indication of ferroelectricity in both PCST60 and PCST50 samples and it is consistent with C–V curves. Remnant polarization (Pr) values are estimated to be approximately 12.4, 5.2 and 1.1 μC/cm2 for the PCST60, PCST50 and PCST40 samples on platinum-coated silicon substrates, respectively. Fig. 7 shows the dielectric permittivity temperature dependence of PCST60, PCST50 and PCST40 films at 100 kHz. As Ca and Sr contents increase, the phase transition temperature shifts toward the lower temperature range. In general, this behavior is a feature of reduced tetragonality. As Fig. 8 shows, PCST60 and PCST50 films display a phase transition temperature above room temperature (505 and 355 K, respectively)
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Fig. 6. Polarization hysteresis loops of (a) PCST60, (b) PCST50 and (c) PCST40 thin films at room temperature.
1600 1400 1200 1000 800 600 400 90
180
270
360
450
540
Fig. 7. Temperature dependence of dielectric permittivity for thin films measured at 100 kHz. (a) PCST60, (b) PCST50 and (c) PCST40.
Fig. 8. Optical transmission spectra measured for (a) LaAlO3 substrate, (b) PCST60, (c) PCST50 and (d) PCST40 thin films grown on the (1 0 0) LaAlO3 substrate. The inset shows the plots of (hνα)2 versus hν.
From previous structural analyses, increasing Ca and Sr contents leads to oxygen octahedra shrinkage, decreasing the ionic displacement responsible for inducing a bipolar moment. This behavior allows the observed decrease of the transition temperature for PCST40 samples which is close to room temperature, again in agreement with Raman spectroscopy results. Fig. 7 illustrates the strong tendency to broadening of the dielectric permittivity temperature peak as the Ca and Sr amounts increase in the dodecahedral coordination sites. This is a first indication that the phase transition may be of diffuse type. For PCST60, PCST50 and PCST40 thin films, the dodecahedral coordination sites show a 12-fold oxygen coordination containing three types of PbO12, CaO12 and SrO12 units. The random distribution of these units in the dodecahedral coordination sites produces nanoscale composition heterogeneity and thus it induces a broadening of the phase transition peak; i.e., PCST50 and PCST40 samples exhibit a stronger signature of typical diffuse phase transition behavior. Kumar et al. reported that Ni doping in BaTiO3 shows a diffuse phase transition [28]. Shao et al. [29] studied the influence of strontium content on the phase transition temperature of Pb1 xSrxZr0.52Ti0.48O3 with x¼ 0.2–0.8 thin films where the Tc was observed to linearly decrease with an increase in the strontium content. Fig. 8 shows transmission spectra for 200, 240 and 250 nm thick PCST60, PCST50 and PCST40 thin films annealed at 700 1C for 2 h recorded in the wavelength range of 200–1000 nm on a (1 0 0) LaAlO3 single crystal substrate. The transmittance curves decrease to zero near 330 nm and the films show good transparency in both visible and infrared regions. The optical band gap of the thin films was determined in the high absorption region by using the Tauc relation described as [30,31] αhν ¼ Aðhν E g Þn
ð1Þ
where n is a constant which characterizes different types of transition (n=1/2, 3/2, 2 or 3 for allowed direct, forbidden direct, allowed indirect, and forbidden indirect, respectively), h is the Planck constant, ν is the photon frequency, hν is the incident photon energy, α is the absorption coefficient, A is a constant and Eg is the optical band gap value. Thus, the dependence of (αhν)n versus incident photon energy (hν) yields the Tauc optical band gap Eg value. As depicted in the inset of Fig. 8, the relationship between (αhν)2 plotted against (hν) varies linearly in the high energy region of the absorption edge. Based on the above process, optical band gap energies values were estimated by extrapolating the linear portion of the plot relating (αhν)2 vs. (hν) to (αhν)2 ¼ 0 and considering the direct nature of the transition process to be 3.66, 3.28 and 3.30 eV for PCST60, PCST50 and PCST40 thin films, respectively. It indicates that band gaps of PCST thin films decrease with increasing the Ca and Sr contents. In addition, the band gap of undoped CaTiO3, SrTiO3 and PbTiO3 thin films is around 3.35, 3.25 and 3.45 eV, respectively [6,32–35]. 4. Conclusions
which indicates their ferroelectric nature at room temperature. On the other hand, PCST40 films have a phase transition temperature close to room temperature with a maximum around 290 K which indicates the paraelectric nature at room temperature.
In this study, nanostructured PCST60, and PCST50 and PCST40 thin films were obtained by a chemical solution deposition method on Pt/Ti/SiO2/Si and (1 0 0) LaAlO3 single crystal
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substrates. XRD patterns reveal the formation of thin films without any detectable secondary phase. The microstructural, structural, optical and ferroelectric properties measurements are largely dependent upon Ca and Sr contents. The simultaneous incorporation of isovalent Ca and Sr chemical species in the PbTiO3 lattice structure leads to a gradual loss of the tetragonality and significantly reduces the octahedron distortion. In addition, the A-site cosubstitution in the Pb ion weakens the long-range ferroelectric order parameter and induces the ferroelectric-to-paraelectric transition which is accompanied mainly by hysteresis loop changes; i.e., loops became narrow with an increase in Sr and Ca contents. Temperature-dependent permittivity of the PCST60, PCST50 and PCST40 films shows that the phase transition shifts toward a lower temperature with an increase in Ca and Sr contents. The phase transition temperature was estimated to be about 505, 350 and 290 K for PCST60, PCST50 and PCST40 thin films, respectively. A diffuse phase transition was observed in the PCS T50 and PCST40 thin films because the temperature-dependent permittivity curves show a broad peak. This phenomenon is probably related to order–disordered short-range localization. The band gaps were estimated to be about 3.66, 3.28, and 3.30 eV for the PCST60, PCST50 and PCST40 films deposited on (1 0 0) LaAlO3 single crystal substrate, respectively; additionally, they showed a tendency to the bulk values of SrTiO3 and CaTiO3 (3.22 and 3.35 eV, respectively).
Acknowledgments This work was financially supported by the Brazilian agencies FAPESP, CNPq and CAPES. We thank CEPID/ CDMF/INCTMN. FAPESP process no. 08/57150-6, no. 11/ 20536-7, and no. 13/07296-2.
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