Ferroelectrics Characterization and Modeling Part 5 docx

Ferroelectrics - Characterization and Modeling 130 using the Nye notation, in which elastic constants and elastic moduli are labeled by replacing the pairs of letters xx, yy, zz, yz, zx, and xy by the number 1, 2, 3, 4, 5, and 6, respectively. This means that the external electric field generates electric displacement, i.e., electric polarization, and strain through the converse piezoelectric effect. However, ceramic materials are multicrystalline structures made up of large numbers of randomly orientated crystal grains. The random orientation of the grains results in a net cancelation of the piezoelectric effect. Thus, the ceramic material must be poled − a dc bias electric field is applied (usually the fired ceramic piece is cooled through the Curie point under the influence of the field) which aligns the ferroelectric domains, resulting in a net piezoelectric effect. As the electrical conductivity of percolative composites strongly increases on approaching the percolation threshold, the feasibility of poling the PZT- Pb 2 Ru 2 O 6.5 samples has been checked. PZT- Pb 2 Ru 2 O 6.5 system has been chosen as its electrical conductivity is much lower than in the PMN-35PT–Pb 2 Ru 2 O 6.5 system or in the KNN–RuO 2 samples which are not treated under vacuum. After poling the PZT-Pb 2 Ru 2 O 6.5 samples with a high dc bias electric field, the piezoelectric coefficient d 33 (strain in the direction of the applied measuring field) has been measured using a small ac voltage. It should be noted that, while various piezoelectric coefficients are usually determined and thus the indication is absolutely necessary, the dielectric constant is almost without exception determined in the direction of the applied field, i.e., ε' without indices in fact denotes the dielectric constant ε 33 . Results of piezoelectric characterization are shown in Fig. 12. While in samples, which are very close to the percolation threshold, the breakdown electric field is below 5 kV/cm, samples with lower Pb 2 Ru 2 O 6.5 content can be poled with the dc bias electric fields higher than 30 kV/cm. It is thus once again revealed that percolative samples with compositions near the percolation threshold are not very suitable for applications, while samples with lower conductive filler concentration, where dielectric constant is still much higher than in the pure ceramic matrix, are very promising for use as high dielectric constant materials. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 10 vol. % of Pb 2 Ru 2 O 6.5 16.5 vol. % 15.5 vol. % 12.5 vol. % d 33 (pC/N) E poling (kV/cm) PZT −Pb 2 Ru 2 O 6.5 Fig. 12. Piezoelectric coefficient d 33 in various PZT-Pb 2 Ru 2 O 6.5 samples, measured with small ac voltage, after poling the sample with a high dc bias electric field (E poling ). All-Ceramic Percolative Composites with a Colossal Dielectric Response 131 5. Conclusion Development of all-ceramic percolative composites i. PZT-Pb 2 Ru 2 O 6.5 ii. PMN-35PT–Pb 2 Ru 2 O 6.5 and iii. KNN–RuO 2 based on the perovskite ferroelectric and ruthenium-based conductive ceramics is reported in this chapter. The structural analysis revealed that there were no chemical reactions between the constituents during processing, which resulted in a perfect structure of composites – conductive ceramic grains are uniformly distributed throughout the ferroelectric ceramic matrix. Thus, in the lead-based PZT-Pb 2 Ru 2 O 6.5 and PMN-35PT– Pb 2 Ru 2 O 6.5 and in the lead-free KNN–RuO 2 systems the dielectric response in fact follows the predictions of the percolation theory. As a result, the dielectric constant strongly increases on the conductive filler increasing content, reaching values near the percolation threshold that are for two orders of magnitude higher than in the pure matrix ceramics. Furthermore, the determined critical exponents and percolation points agree reasonably with the theoretically predicted values. The frequency- and temperature-dependent dielectric response of all developed systems is also presented and discussed. Finally, not only structural and dielectric results, i.e., a successful synthesis of lead-based and lead-free percolative systems exhibiting a stable giant dielectric response, but also electromechanical properties demonstrate the potential of all-ceramic percolative composites for use as high-dielectric-constant materials in various applications. 6. Acknowledgment This work was supported by the Slovenian Research Agency under project J1-9534 and program P2-0105-0106/05 and under European project 6. FP NMP3-CT-2005-515757. We thank to Prof. Horst Beige from the Martin-Luther University in Halle, Germany, for kindly making the experimental facility for the electromechanical characterization of the PZT–Pb 2 Ru 2 O 6.5 system accessible and to Dr. Ralf Steinhausen for help with these measurements. 7. References Bergman, D. J. & Imry, Y. (1977). Critical behavior of the complex dielectric constant near the percolation threshold of a heterogeneous material. Physical Review Letters, Vol. 39, Iss. 19, Nov. 1977, pp. 1222-1225, ISSN 0031-9007. Bobnar, V.; Hrovat, M.; Holc, J. & Kosec, M. (2008). Giant dielectric response in Pb(Zr,Ti)O 3 – Pb 2 Ru 2 O 6.5 all-ceramic percolative composite. Applied Physics Letters, Vol. 92, Iss. 18, May 2008, 182911 3pp., ISSN 0003-6951. Bobnar, V.; Hrovat, M.; Holc, J.; Filipič, C.; Levstik, A. & Kosec, M. (2009a). Colossal dielectric response in all-ceramic percolative composite 0.65Pb(Mg 1/3 Nb 2/3 )O 3 - 0.35PbTiO 3 -Pb 2 Ru 2 O 6.5 . 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Kuščer, D.; Holc, J.; Kosec, M. & Meden, A. (2006). Mechano-synthesis of lead–magnesium– niobate ceramics. Journal of the American Ceramic Society, Vol. 89, Iss. 10, Oct. 2006, pp. 3081-3088, ISSN 1551-2916. Kuščer, D.; Holc, J. & Kosec, M. (2007). Formation of 0.65Pb(Mg 1/3 Nb 2/3 )O 3 –0.35PbTiO 3 using a high-energy milling process. Journal of the American Ceramic Society, Vol. 90, Iss. 1, Jan. 2007, pp. 29-35, ISSN 1551-2916. Li, J F.; Takagi, K.; Terakubo, N. & Watanabe, R. (2001). Electrical and mechanical properties of piezoelectric ceramic/metal composites in the Pb(Zr,Ti)O 3 /Pt system. Applied Physics Letters, Vol. 79, Iss. 15, Oct. 2001, pp. 2441-2443, ISSN 0003-6951. All-Ceramic Percolative Composites with a Colossal Dielectric Response 133 Pecharroman, C. & Moya, J. S. (2000). Experimental evidence of a giant capacitance in insulator-conductor composites at the percolation threshold. Advanced Materials, Vol. 12, Iss. 4, Feb. 2000, pp. 294-297, ISSN 0935-9648. Pecharroman, C.; Esteban-Betegon, F.; Bartolome, J. F.; Lopez-Esteban, S. & Moya, J. S. (2001). New percolative BaTiO 3 -Ni composites with a high and frequency- independent dielectric constant (ε r ≈ 80000). Advanced Materials, Vol. 13, Iss. 20, Oct. 2001, pp. 1541-1544, ISSN 0935-9648. Petzelt, J. & Rychetsky, I. (2005). Effective dielectric function in high-permittivity ceramics and films. Ferroelectrics, Vol. 316, 2005, pp. 89-95, ISSN 0015-0193. Pierce, J. W.; Kuty, D. W. & Larry, J. L. (1982). The chemistry and stability of ruthenium- based resistors. Solid State Technology, Vol. 25, Iss. 10, Oct. 1982, pp. 85-93, ISSN 0038-1101. Priya, S.; Viehland, D. & Uchino, K. (2002). Importance of structural irregularity on dielectric loss in (1–x)Pb(Mg 1/3 Nb 2/3 )O 3 –(x)PbTiO 3 crystals. Applied Physics Letters, Vol. 80, Iss. 22, Jun. 2002, pp. 4217-4219, ISSN 0003-6951. Raymond, M. V. & Smyth, D. M. (1996). Defects and charge transport in perovskite ferroelectrics. 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Physical Review Letters, Vol. 31, No. 24, Dec. 1973, pp. 1463-1465, ISSN 0031-9007. Straley, J. P. (1977). Critical exponents for the conductivity of random resistor lattices. Physical Review B, Vol. 15, Iss. 12, Jun. 1977, pp. 5733-5737, ISSN 1098-0121. Sun, X.; Chen, J.; Yu, R.; Xing, X.; Qiao, L. & Liu, G. (2008). BiFeO 3 -doped (Na 0.5 K 0.5 )NbO 3 lead-free piezoelectric ceramics. Science and Technology of Advanced Materials. Vol. 9, Iss. 2, Jun. 2008, 025004 4 pp., ISSN 1468-6996. Takeshima, Y.; Shiratsuyu, K.; Takagi, H. & Sakabe, H. Y. (1997). Preparation and dielectric properties of the multilayer capacitor with (Ba,Sr)TiO 3 thin layers by metalorganic chemical vapour deposition. Japanese Journal of Applied Physics, Vol. 36, No. 9B, Sep. 1997, pp. 5870-5873, ISSN 0021-4922. van Loan, P. R. (1972). Conductive ternary oxides of ruthenium, and their use in thick film resistor glazes. American Ceramic Society Bulletin, Vol. 51, No. 3, Mar. 1972, pp. 231- 233, ISSN 0002-7812. 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Nature, Vol. 419, Issue 6904, Sep. 2002, pp. 284-287, ISSN 0028-0836. 8 Electrical Processes in Polycrystalline BiFeO 3 Film Yawei Li 1 , Zhigao Hu 1 and Junhao Chu 1,2 1 Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronic Engineering, East China Normal University, Shanghai 2 National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai People’s Republic China 1. Introduction As an oxide with perovskite structure, Bismuth ferrite (BiFeO 3 , BFO) has been studied from 1970s (Teague, et al. 1970; Kaczmarek, et al. 1975). The structure and magnetic properties of BFO were confirmed before 1970s. As reported, the crystal structure of BFO is perovskite with rhombohedral distortion and the space group is R3c. BFO is G-type antiferromagnetic. It was controversial about whether BFO was ferroelectrics until the hysteresis loop of single crystal BFO was measured in 1970 (Teague, et al. 1970). According to Teague’s results, the single crystal BFO was anisotropy. The remnant polarizations (P r ) along the (100) and (111) direction were 3.5μC/cm 2 and 6.1μC/cm 2 at the temperature of liquid nitrogen, respectively. However, because of the higher leakage current in the bulk BFO, it was difficult to measure the ferroelectric properties of BFO at room temperature. The problem of higher leakage blocks not only the studies of the electrical properties of BFO, but also the application of BFO in electrical devices. In 2003, the epitaxial BFO films with higher electrical resistivity and higher remnant polarization was fabricated by pulsed laser deposition (PLD) method (J. Wang, 2003). The value of P r of the epitaxial BFO films is about 50μC/cm 2 . This value is larger than that of the traditional ferroelectrics such as Pb(Zr,Ti)O 3 (PZT), BaTiO 3 (BTO). If the BFO film with larger P r can be used in ferroelectric memory (FeRAM), the size of the storage cell can be reduced and the storage density can be increased (Maruyama, 2007). More studies on BFO films are carried out (Eerenstein, 2005; Zavaliche, 2005; Singh, 2007; Hauser, 2008; Liu, 2008; Yang, 2008). Even though the leakage mechanism in epitaxial BFO film has been studied (Pabst, 2007), the higher leakage current is still an obstacle for the study and application of polycrystalline BFO films. Compared to the epitaxial BFO films grown on perovskite structure substrate, the applications of polycrystalline BFO on silicon wafer are broader in the field of microelectronic devices. In this chapter, polycrystalline BFO films are fabricated by different physical and chemical methods on buffered silicon and perovskite structure substrate. The structural and electrical properties of these polycrystalline BFO films are investigated. Ferroelectrics - Characterization and Modeling 136 2. Experiments Considering the universality of our conclusion for different polycrystalline BFO films, the samples studied in this work are fabricated by two different methods, PLD and chemical solution deposition (CSD) methods. The former is a typical physical method of film deposition. The later is a chemical method. At the same time, different materials are used as substrate. For the samples prepared by PLD, n-type silicon covered by a layer of (La,Sr)CoO 3 (LSCO) is used as substrate. The layer of LSCO acts as bufferlayer for the growth of BFO and bottom electrode for the electrical measurement. For the samples prepared by CSD, the single crystal SrTiO 3 (STO) covered by LaNiO 3 (LNO) is used as substrate. 2.1 The fabrications of BFO films by PLD method For the preparation of polycrystalline BFO films by PLD method, single-side polished silicon wafer is used as substrate. Before the deposition of BFO film, a layer of LSCO is deposited on the surface of silicon wafer by PLD. The component of the LSCO target is (La 0.5 Sr 0.5 )CoO 3 . The component of BFO target is Bi 1.05 FeO 3 . The excess bismuth is used to compensate the evaporation of bismuth at higher temperature during the growth of BFO films. The depositions of LSCO and BFO are carried out in a vacuum chamber with background pressure lower than 10 -4 Pa. A KrF excimer laser with the wavelength of 248 nm is used for the deposition. During the deposition of LSCO layer, the oxygen pressure in the chamber is about 25 Pa. The temperature of the silicon wafer is 650 o C (Li, 2009). Details about the deposition conditions are listed in table 1. The deposition of LSCO layer is carried out for 20 minutes. After the deposition, the oxygen pressure in the chamber increased to 50 Pa and maintained for 30 min. The thickness of the LSCO layer is about 200 nm obtained from the scanning electronic microscope. Target LSCO BFO Frequency of pulse 5Hz 3Hz Oxygen pressure 25Pa 3Pa Substrate temperature 650 o C 700 o C Deposition time 20min 90min Holding temperature 650 o C 495 o C Holding oxygen pressure 50 Pa 3Pa/1.01×10 5 Pa Holding time 30min 30min Table 1. The deposition conditions of LSCO and BFO films grown on silicon wafer by PLD method. The oxygen pressure in the chamber during the deposition of the polycrystalline BFO films is 3 Pa. the temperature of the substrate is kept at 700 o C. Details about the deposition conditions of BFO films are also listed in table 1. The deposition of BFO films is carried out for 90 minutes. After the deposition, the BFO films are cooled to 495 o C slowly and held for 30 min in a certain oxygen pressure. In order to study the effect of oxygen vacancies, two kinds of BFO films are fabricated by PLD. For the BFO film containing less vacancy of oxygen, the oxygen pressure in the chamber is 1.01×10 5 Pa when the sample is held at 495 o C for 30min. For the sample containing more vacancy of oxygen, the oxygen pressure in the chamber is just 3 Pa when the sample is kept at 495 o C for 30min (Li, 2008). Electrical Processes in Polycrystalline BiFeO 3 Film 137 2.2 The fabrications of BFO films by CSD method Regarding the preparation of polycrystalline BFO films by CSD method, single crystal STO is used as substrate. A layer of LNO is fabricated on the surface of STO before the preparation of BFO films. The layer of LNO is also fabricated by CSD method and is used as bottom electrode. Both STO and LNO are perovskite structure and smaller crystal constant than BFO. Therefore, the substrate and the LNO layer can induce the growth of BFO films. The fabrication of LNO layer by CSD method is same to the way has been reported in literature (Meng, 2001). For the synthesizing of LNO precursor, lanthanum nitrate and nickel acetate are used as starting materials. The mixture of acetic acid and water are used as solvent. Lanthanum nitrate and nickel acetate with a stoichiometric molar ratio of 1:1 are dissolved in the solvent. The concentration of the precursor is 0.3mol/L. For the preparation of the LNO layer, the LNO precursor is spin-coated on STO substrate at 3000rpm for 20 s. the wet film is dried at 180 o C for 300s in a rapid thermal process furnace. Then the dried film is calcined at 380 o C for 300s for the organic compound pyrolyzing. Finally, the amorphous film is annealed at 650 o C for 300s for crystallization. The cycle of coating and thermal process are repeated six times to obtain LNO layer with expected thickness. In regard to the synthesizing of BFO precursor, bismuth nitrate and nickel acetate are used as starting materials. Acetic acid is used as solvent (Li, 2005). The fabrication of BFO film is also contained two steps, spin-coating precursor on LNO covered STO substrate and rapid thermal process in furnace. The precursor is spin-coated at 4000rpm for 20 s. The film is dried at 180 o C for 240s, pyrolyzed at 350 o C for 240s, and annealed at 600 o C for 240s. Two kinds of BFO films with different electrical resistivity are fabricated. 2.3 The crystalline and electrical characterizations The crystallinity of BFO, LSCO, and LNO films is characterized by x-ray diffraction (XRD) using Cu Kα as radiation source (D/MAX-2550V, Rigaku Co.). During the XRD measurement, the continuous θ-2θ scanning mode with the interval of 0.02 o is used. All XRD characterizations are carried out at room temperature. For the electrical measurement, platinum is used as top electrode. Platinum dots with the diameter of 2×10 -2 cm are sputtered onto the surface of the polycrystalline BFO films using a shadow mask. The ferroelectric properties are measured using a ferroelectric test system (Permier II, Radiant Technologies, Inc.). During the measurement, the frequency of the alternating current (ac) signal is 1 kHz. Two triangle waves with different polarity are used as the applied voltage. Before each measurement of hysteresis loop, a pre-polar voltage is applied on the film. The dielectric properties of the polycrystalline BFO films are measured using an impedance analyzer (Hewlett-Packard 4194A). The voltage of the small ac signal is 0.05V. The frequency dependence of the permittivity and dielectric loss is measured in the frequency range from 100 Hz to 1 MHz. The voltage dependence of the permittivity is measured at 1 MHz. The leakage current behaviour of the polycrystalline BFO films under dc voltage bias is measured using an electrometer (Keithley 6517A). Besides the electrical measurements carried out at room temperature, the temperature dependence permittivity and leakage current measurements are carried out at different temperatue and the temperature is controlled with an accuracy of ±0.5K using a variable temperature micro-probe stage (K-20, MMR technologies, Inc.). Ferroelectrics - Characterization and Modeling 138 3. Crystalline structures Because the impurity has great effects on the electrical properties of the BFO films, it is important that the studied polycrystalline BFO films do not contain any impurity or parasitical phase. The structure of the polycrystalline BFO films fabricated by PLD and CSD on different substrates is investigated firstly. 3.1 The crystalline structure of BFO films fabricated by PLD method Figure 1 shows the XRD curves of the polycrystalline BFO films grown on LSCO covered silicon substrate and thermal treated at different oxygen pressure. The XRD curve of LSCO film grown on silicon wafer by PLD method is also exhibited in the figure. The indexes of each diffractive peak are labelled in the figure. The indexes of pseudo-cubic structure are used for BFO films. 20 30 40 50 60 (211) ∗ (200) ∗ (111) ∗ (110) ∗ (121) (120) (200) (111) (110) (100) ∗ (La 0.5 Sr 0.5 )CoO 3 BiFeO 3 treated at 3 Pa Intensity (a.u.) 2θ (Degree) BiFeO 3 treated at 1.01∗10 5 Pa (100) Fig. 1. The XRD patterns of (La 0.5 Sr 0.5 )CoO 3 film and BiFeO 3 films fabricated by PLD method and thermal treated at different oxygen pressure. The labels contained a star (*) indicate the diffractive peaks of LSCO. The indexes of pseudo-cubic structure are used to label the diffractive peaks of BFO films. There is no any trace of impure phase in the XRD curves of the polycrystalline BFO films thermal treated at 1.01×10 5 Pa or 3 Pa. Neither LSCO nor BFO films exhibit (100) preferential orientation even the (100) silicon wafer is used as substrate. The position of the diffractive peak does not show perceptible shift for the two kinds of BFO films thermal treated at different oxygen pressure. It indicates that the thermal process at different oxygen pressure does not affect the crystalline structure of the polycrystalline BFO films. The pseudo-cubic crystal constant calculated from the XRD curve is about 3.96Å. This value is close to the value of bulk BFO (JCPDS: 74-2016). Therefore, even the crystal constant of LSCO is smaller than that of BFO, the mismatch between BFO and LSCO has no effect on the crystalline structure of the polycrystalline BFO films. Moreover, the full width at half maximum (FWHM) of the diffractive peak has no obvious variety. It indicates that the size of the crystal grain in the two kinds of BFO films is not influenced by the difference of the thermal process. [...]... fabricated by PLD and CSD methods are shown in figure 3 and figure 4, respectively 140 Ferroelectrics - Characterization and Modeling 1.0 treated at 1.01∗10 Pa treated at 3 Pa 0.8 100 0.6 0.4 50 tanδ Capacitance (pF) 150 5 0.2 0 10 2 10 3 10 4 Frequency (Hz) 10 0.0 5 10 6 Fig 3 The frequency dependence of capacitance and loss tangent of BFO films prepared by PLD method and thermal treated at 1.01×1 05 Pa (black)... 19 95) Thus, the mechanism of the dielectric transition is likely to involve hopping of the copper ions among two or more positions Two phase transitions have been observed at 155 K and 190 K by dielectric measurement and differential scanning calorimetry (DSC) The crystal is antiferroelectric below 155 K and paraelectric above 190 K For the intermediate phase between 155 and 190 K, a quasi- 154 Ferroelectrics. .. 0003-6 951 Yun K Y ; Noda M ; Okuyama M (2003) Prominent ferroelectricity of BiFeO3 thin films prepared by pulsed-laser deposition Appl Phys Lett., 83, 3981 ISSN : 00036 951  152 Ferroelectrics - Characterization and Modeling Zavaliche, F ; Shafer P ; Ramesh R ; Cruz M P ; Das R R ; Kim D M ; Eom C B (20 05) Polarization switching in epitaxial BiFeO3 films Appl Phys Lett., 87, 252 902 ISSN : 0003-6 951 Zhang... dues to the nature of ferroelectrics that dielectric constant changes with the applied dc voltage It is indicated that the dielectric response contributed by interfacial polarization between the BFO film and electrode can be ignored in our sample 61.6 Capacitance (pF) 200 60.9 150 60.2 9.5x10 4 10 5 1.05x10 5 100 dc Voltage = 0.0V dc Voltage = 3.0V 50 10 2 10 3 10 4 10 Frequency (Hz) 5 10 6 Fig 6 The frequency... 146 Ferroelectrics - Characterization and Modeling Measured at 70K 2 Polarization (μC/cm ) 100 50 Capacitance (pF) 0 -50 -100 -20 -10 0 Voltage (V) 50 45 40 -14 -7 0 7 14 Voltage (V) 10 20 Fig 9 The hysteresis loops under different applied voltages for the polycrystalline BFO film fabricated by CSD method The inset displays the voltage dependence of the capacitance Both ferroelectric hysteresis and. .. dielectric dispersion also occurs in Ag0.1Cu0.9InP2S6 and in CuIn1+δP2S6 at low temperatures Such dielectric dispersion is typical of dipolar glasses (Figs 4 and 5) (Macutkevic et al 2008) Fig 4 Temperature dependence of the complex dielectric permittivity of CuInP2S6 crystals Low temperature region  158 Ferroelectrics - Characterization and Modeling Fig 5 Frequency dependence of the complex dielectric... ISSN : 00036 951 Kaczmarek W., Pajak Z & Polomska M.(19 75) Differential thermal analysis of phase transitions in (Bi1-xLax)FeO3 solid solution Solid State Comm., 17, 807 ISSN : 00381098 Li Y W ; Sun J L ; Chen J ; Meng X J ; Chu J H (20 05) Preparation and characterization of BiFeO3 thin films grown on LaNiO3-coated SrTiO3 substrate by chemical solution deposition J Cryst Growth, 2 85, 59 5 ISSN : 0022-0248... Debye-type relaxation and can be represented by universal dielectric response (UDR) model In this model, the real part and imaginary part of complex dielectric constant can be described respectively as (Lunkenhjeimer et al.,2002; Tselev et al., 2004) 1 π  σ 0 tan  s  ω s − 1 ε0 2  σ σ ε "T = dc + 0 ω s − 1 ωε 0 ε 0 ε rT = (2) where εrT and ε”T are the real part and imaginary part of complex dielectric... 87, 252 902 ISSN : 0003-6 951 Zhang L (20 05) Electrode and grain-boundary effects on the conductivity of CaCu3Ti4O12 Appl Phys Lett., 87, 022907 ISSN : 0003-6 951 9 Phase Transitions in Layered Semiconductor - Ferroelectrics Andrius Dziaugys1, Juras Banys1, Vytautas Samulionis1, Jan Macutkevic2, Yulian Vysochanskii3, Vladimir Shvartsman4 and Wolfgang Kleemann5 1Department of Radiophysics, Faculty of Physics,... term 142 Ferroelectrics - Characterization and Modeling and s is a parameter with the value between 0 and 1 Considering the dielectric response related to the oxygen vacancies and all the other dielectric response processes, the frequency dependence of complex dielectric constant of the BFO films with lower electrical resistivity should following a model which is constituted by Cole-Cole’s model and UDR . constant materials. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 10 vol. % of Pb 2 Ru 2 O 6 .5 16 .5 vol. % 15. 5 vol. % 12 .5 vol. % d 33 (pC/N) E poling (kV/cm) PZT −Pb 2 Ru 2 O 6 .5 Fig. 12. Piezoelectric. supported by the Slovenian Research Agency under project J1- 953 4 and program P2-01 05- 0106/ 05 and under European project 6. FP NMP3-CT-20 05- 5 157 57. We thank to Prof. Horst Beige from the Martin-Luther. 154 1- 154 4, ISSN 09 35- 9648. Petzelt, J. & Rychetsky, I. (20 05) . Effective dielectric function in high-permittivity ceramics and films. Ferroelectrics, Vol. 316, 20 05, pp. 89- 95, ISSN 00 15- 0193.