Σac Values Research Articles

Dielectric, modulus and conductivity studies of Au/PVP/n-Si (MPS) structure in the wide range of frequency and voltage at room temperature

Both the real-imaginary components of complex dielectric permittivity and electric modulus, and ac conductivity of Au/PVP/n-Si (MPS) structures were analyzed by admittance spectroscopy technique between 1 and 500 kHz, − 3 and 5 V. The polyvinylpyrrolidone (PVP) polymer layer was deposited on n-Si wafer by spin-coating technique. The e′, e″, M′, M″ and σac values were calculated from the admittance measurements and they are quite function of frequency and voltage due to a special distribution of surface states at PVP/n-Si interface, interfacial/dipole polarizations at low frequencies. While the e′ and e″ values decrease as frequency increases, the σac, M′ and M″ increase. The ln(σac) vs ln(ω) plot for 3V has two linear region between 1 and 20 kHz, 30 and 500 kHz frequencies, respectively. The obtained 0.033 slope value for low-frequencies which corresponding to dc conductivity and it is almost independent of frequency, but it obtained 0.46 for high-frequencies which corresponding ac conductivity and is strong function of frequency due to the increase eddy current. As a result, the prepared MPS structure can be used as charges/energy storage device due to the dielectric property of the PVP polymer layer.

Effect of sintering temperature on the developed crystalline phases, optical and electrical properties of 5ZnO-2TiO2- 3P2O5 glass

Glass of the composition 5ZnO-2TiO2- 3P2O5 was prepared by the melt-quenching technique. The prepared samples were heat-treated at the nucleation (625 °C) and crystallization (875 °C) temperatures for different soaking times. SEM, XRD, UV–Vis, DSC and electrical measurements were used. Ti(PO4) and Zn3(PO4)2 phases were formed at the nucleation temperature; while, Ti5O4(PO4)4 and α-Zn2P2O7 phases were observed at the crystallization temperature. Long soaking time caused color fading or formation of opaque white samples due to the decrease of Ti3+ ions or increase of Ti4+ ions, respectively. The formation of Ti3+ ions causes a development of violet color with absorption bands in the range 400–800 nm. SEM suggested that prolonged heating at the crystallization temperature caused disintegration of the formed phases. The electrical conductivities of the studied samples at the low and high measuring temperatures occur via electrons revealing their suitability to be applied as semiconductors. The values of σac and dielectric constant ε′ increase with rising the sintering temperature. The ε′ of the as-prepared sample (19.23) is increased to 152.45 or 189.11 when heat-treated at the nucleation temperature for 4 h and at crystallization temperature for 15 min, respectively. Samples of high ε′ values represent promising candidates for energy storage in electronic devices.

Dielectric properties of ferromagnetic Ni nanoparticles added (Cu0.5Tl0.5)Ba2Ca2Cu3O10-δ superconducting phase

Ferromagnetic nickel (Ni) nanoparticles were added in (Cu0.5Tl0.5)Ba2Ca2Cu3O10–δ (CuTl-1223) superconducting matrix to get Nix/CuTl-1223; x = 0–1.00 wt% nanoparticles-superconductor composites. Temperature- and frequency-dependent dielectric properties of CuTl-1223 superconducting phase with different contents of Ni nanoparticles were studied. Different dielectric parameters such as dielectric constant (εr′, εr′′), dielectric tangent loss (tan δ) and ac conductivity (σac) were determined from experimentally measured capacitance and conductance at different frequencies from 10 kHz to 10 MHz and at different operating temperatures from 78 to 290 K. The values of εr′ and εr′′ were found maximal at smaller frequencies and started to decrease at higher frequencies. The value of σac is high at high frequency unlike to εr′ and εr′′, which is due to release of space charges at high frequencies. Peaks in tan δ graphs represent the resonance phenomenon at certain frequencies in these samples. Non-monotonic behavior in variation of dielectric parameters with temperature of Nix/CuTl-1223 samples was observed particularly at high temperatures which was due to thermal instability of the system at high temperatures.

Determining electrical and dielectric parameters of Al/ZnS-PVA/p-Si (MPS) structures in wide range of temperature and voltage

In this study zinc sulphide (ZnS) nanostructures have been prepared by microwave-assisted method in presence of polyvinyl alcohol (PVA) as a capping agent. The structural and morphological properties of prepared sample have been investigated by X-ray diffraction (XRD) and scanning electron microscopy (SEM). These analyses confirm that the sample has nano structure. They have been used this sample to fabrication of Al/ZnS-PVA/p-Si structure. The effect of temperature and voltage on the electrical and dielectric parameters of the Al/ZnS-PVA/p-Si (MPS) structures has been investigated in the wide range of temperature (140–340 K) and voltage (− 2 V to + 4 V) using capacitance/conductance-voltage (C/G–V) measurements at 500 kHz. Experimental measurements revealed that the values of C/G–V increase with increasing temperature but the values of series resistance (Rs) increase with decreasing temperature. As well as the dielectric parameters such as the values of real and imaginary parts of the dielectric constants (e′ and e″) and electric modules (M′ and M″), loss tangent (tanδ), and ac electrical conductivity (σac) were obtained using C and G/ω data. These parameters are found out as strong functions of temperature and voltage. While the values of e′, e″ and tanδ increase with increasing temperature, the values of σac, M′ and M″ decrease. The Arrhenius plot (ln(σac) vs q/kT) shows two distinct linear ranges with different slopes or activation energies (Ea) at low (140–230 K) and high (260–340 K) temperatures. Both values of Rs and (ZnS-PVA) interfacial layers are also very effective parameters on the electric and dielectric properties.

Effect of the type of metal on the electrical conductivity and thermal properties of metal complexes: The relation between ionic radius of metal complexes and electrical conductivity

Co(II) complexes (1–4) and Ni(II) complexes (5–8) were prepared and characterized by elemental analysis, IR spectra and thermal analysis data. Thermal decomposition of all complexes was discussed using thermogravimetric analysis. The dielectric properties and alternating current conductivity were investigated in the frequency range 0.1–100 kHz and temperature range 300–660 K. The thermal activation energies of electrical conductivity (ΔE1 and ΔE2) values for complexes were calculated and discussed. The values of ΔE1 and ΔE2 for complexes (1–8) were found to decrease with increasing the frequency. Ac electrical conductivity (σac) values increases with increasing temperatures and the values of σac for Co(II) complexes are greater than Ni(II) complexes. Co(II) complexes showed a higher conductivity than other Ni(II) complexes due to the higher crystallinity as confirmed by X-ray diffraction analysis.

Preparation and characterization of polymer nanocomposites based on PVDF/PVC doped with graphene nanoparticles

Novel nanocomposites based on PVDF/PVC blend containing graphene oxide nanoparticles (GO) were prepare using sonicator. IR analysis revealed that the addition of GO prompts a crystal transformation of α-phase of PVDF. The change of the structural before and after adding GO to PVDF/PVC were studied by X-ray diffraction. A decrease in activation energy gap from UV data was observed with increasing GO content, implying a variation of reactivity as a result of reaction extent. The variation of ε′ with frequency is nearly the same as that of ε″. At higher frequencies, the decrease of both ε′ and ε″ becomes nearly constant. The dispersion at lower frequencies ε′ of ε′ polarization is of Maxwell–Wagner interfacial polarization but at higher frequencies, it levels off. The behavior of conductivity (σAC) tends to acquire constant values approaching it DC values. The values of σAC was increased after doped GO with exponential increase after the critical value of frequency. All nanocomposites behaved the same fashion revealing that a higher number of polarons were getting added to conducting pool in composites as graphene content was increased. Conduction mechanism appeared to be getting expedited with increasing frequency due to fact that increase in frequency enhances polaron hopping frequency.

Investigation of AC conductivity, dielectric and thermodynamics properties of Se Te Pb glassy system

The AC conductivity and dielectric properties of amorphous Se90Te10-xPbx (x = 2, 6 at%) films have been studied in the frequency range (0.01–100 kHz)and in the temperature range (303–338 K). It is found that AC conductivity σAC(ω), dielectric constant ε1 and dielectric loss ε2 depend on frequency and temperature. The temperature dependence of both σAC(ω) and the frequency exponent s is reasonably well interpreted on the basis of correlated barrier hopping model (CBH). Values of σAC(ω) is found to increase with increasing frequency and Pb content, while values of ε1and ε2 are found to increase with temperature and decrease with frequency. The frequency exponent and dielectric loss have been analyzed to determine the maximum barrier height Wm. The two estimated values of Wm are in a good agreement with the theory of charge carriers. The relationship between the experimental measured σAC(ω), ε1, ε2 and other related parameters and chemical composition of the Se90Te10-xPbx (x = 2, 6 at%) is also discussed in terms of the average coordination number Nc and the average heat of atomization Hs for better understanding of the role of Pb addition.

Frequency and Voltage-Dependent Dielectric Properties and AC Electrical Conductivity of (Au/Ti)/Al2O3/n-GaAs with Thin Al2O3Interfacial Layer at Room Temperature

An (Au/Ti)/Al2O3/n-GaAs structure with thin (30 A) interfacial oxide layer (Al2O3), formed by atomic layer deposition technique is fabricated to investigate both frequency and applied bias voltage dependences of real and imaginary parts of dielectric constant (e′ and e′′) and electric modulus (M ′ and M ′′), loss tangent tan δ and ac electrical conductivity σAC in a wide frequency range from 1000 Hz to 1 MHz at room temperature. The dielectric properties of the (Au/Ti)/Al2O3/n-GaAs metal-insulator-semiconductor structure are obtained using the forward and reverse bias capacitance-voltage (C-V ) and conductance-voltage (G/ω-V ) measurements in the applied bias voltage range from –4 V to +4 V, at room temperature. Experimental results show that the dielectric parameters were strongly frequency and voltage dependent. For each frequency the (C-V ) plots show a peak and the change in frequency has effect on both the intensity and position of the peak. e′, e′′ and tan δ decrease with increasing frequency, whereas σAC increases with increasing frequency at applied bias voltage. M ′ increases with the increasing frequency and reaches a maximum. M ′′ shows a peak and peak position shifts to higher frequency with increasing applied voltage. It can be concluded that the e′, e′′, tan δ, M ′, M ′′ and σAC values of the (Au/Ti)/Al2O3/ n-GaAs structure are strongly dependent on both the frequency and applied bias voltage especially in the depletion and accumulation region. Also, the results can be deduced to imply that the interfacial polarization is easier at low frequencies, therefore contributing to the deviation of dielectric properties and AC electrical conductivity of (Au/Ti)/Al2O3/n-GaAs structure.

Conducting Polymers. VII. Effect of Doping with Iodine on the Dielectrical and Electrical Conduction Properties of Polyaniline

The oxidative chemical polymerization of aniline monomer in acidic aqueous media by using potassium dichromate as unconventional initiator was carried out at room temperature based on two different comparative methods. In the first method, in situ polymerization of polyaniline, polymerization was carried out in the presence of iodine solution (PANI/I2-In). In the second method, ex situ polymerization, after complete polymerization polyaniline was doped with iodine (PANI/I2-Ex). FTIR, UV measurements, and TGA analysis for undoped polyaniline (PANI), iodine doped polyaniline (PANI/I2-Ex), and iodine doped polyaniline (PANI/I2-In) show that iodine doping process occurred at the quinoid units in the polyaniline backbone of (PANI/I2-Ex) while iodine doping occurred at benzenoid units in polyaniline, in addition the iodination occurred at the rings of polyaniline backbone of (PANI/I2-In.). The data extracted from the XRD patterns shows the crystalline nature of synthesized samples and particles sizes are in the range 37–42 nm. The activation energies of thermal degradation of polyaniline or iodine doped polyaniline were determined from the TGA thermogram for PANI, (PANI/I2-In), and (PANI/I2-Ex) are 24.1, 43.4, and 44.19 KJ/mol, respectively. Doping of PANI with iodine enhances the ac conductivity of PANI whatever the method of doping, The room temperature values of σac measured under test frequency 100 kHz are found to be 6×10−5, 2.5×10−4, and 1×10−3 Ω−1.m−1 for PANI, (PANI/I2-In), and (PANI/I2-Ex), respectively.

Frequency and voltage dependent profile of dielectric properties, electric modulus and ac electrical conductivity in the PrBaCoO nanofiber capacitors

In this study, praseodymium barium cobalt oxide nanofiber interfacial layer was sandwiched between Au and n-Si. Frequency and voltage dependence of ε′, ε′, tanδ, electric modulus (M′ and M″) and σac of PrBaCoO nanofiber capacitor have been investigated by using impedance spectroscopy method. The obtained experimental results show that the values of ε′, ε′, tanδ, M′, M″ and σac of the PrBaCoO nanofiber capacitor are strongly dependent on frequency of applied bias voltage. The values of ε′, ε″ and tanδ show a steep decrease with increasing frequency for each forward bias voltage, whereas the values of σac and the electric modulus increase with increasing frequency. The high dispersion in ε′ and ε″ values at low frequencies may be attributed to the Maxwell–Wagner and space charge polarization. The high values of ε′ may be due to the interfacial effects within the material, PrBaCoO nanofibers interfacial layer and electron effect. The values of M′ and M″ reach a maximum constant value corresponding to M∞≈1/ε∞ due to the relaxation process at high frequencies, but both the values of M′ and M″ approach almost to zero at low frequencies. The changes in the dielectric and electrical properties with frequency can be also attributed to the existence of Nss and Rs of the capacitors. As a result, the change in the ε′, ε″, tanδ, M′, M″ and ac electric conductivity (σac) is a result of restructuring and reordering of charges at the PrBaCoO/n-Si interface under an external electric field or voltage and interface polarization.

Temperature and voltage dependences of dielectric properties and ac electrical conductivity in Au/PVC+TCNQ/p-Si structures

Dielectric properties and ac conductivity (σac) of Au/PVC+TCNQ/p-Si structures have been investigated in the wide temperature range of 80–420K using capacitance–voltage (C–V) and conductance–voltage (G/ω–V) measurements at 1MHz. It has been found that the forward bias C–V plots exhibit a distinct peak especially at a high temperature. Effects of the series resistance (Rs), interfacial PVC+TCNQ layer and the density distribution of interfaces׳ traps (Dit) on the electrical peak and the dielectric properties were investigated in detail. All of the dielectric properties such as the real and imaginary parts of dielectric constants (ε′,ε″), electric moduli (M′ and M″), loss tangent (tanδ), and σac values were found to be strong functions of temperature and applied bias voltage. These changes become considerably high especially in the depletion region. In addition, the voltage dependent Rs values were obtained and they increased with decreasing temperature C–V–T and G/ω–V–T measurements confirmed that Rs, Dit, and PVC+TCNQ layers are very important parameters that strongly influence both dielectric properties and σac of structures.

Dielectrical, conduction mechanism and thermal properties of rhodanine azodyes

In this paper, we report on the differential scanning calorimetry analysis (DSC) and thermogravimetric analysis (TGA) performed for 5-(4'-derivatives phenylazo)-2-thioxothiazolidin-4-one (HLn) (n=1, R=OCH3; n=2, R=CH3; n=3, R=H; and n=4, R=NO2) in the temperature range 46–800°C. The values of the thermal activation energies of decomposition of HL1, HL3 and HL4 are found in the range 59.10–299.72kJ/mol. The molecular and electronic structures of the investigated compounds (HLn) were also studied using quantum chemical calculations. The alternating current conductivity (σac) and dielectrical properties of HLn were investigated in the frequency range 0.1–100kHz and temperature range 303–500K. The temperature and frequency dependence of the real and the imaginary dielectrical constants are studied. The values of the thermal activation energy for derivatives under investigation were calculated at different frequencies. The values of thermal activation energies of electrical conductivity ΔE1 and ΔE2 for all ligands decrease with increasing the test frequency. The activation energies, ΔE1 and ΔE2, increase according to the following order p-(NO2>H>CH3>OCH3). This is in accordance with that expected from Hammett's substituent coefficients (σR). The conductivities are found to be dependent on the structure of the compounds. The values of σac are related to the frequency as σacα ωS where the behavior of the exponent S determines the operating conduction mechanism. The correlated barrier hopping (CBH) is the dominant conduction mechanism for HLn. The values of maximum barrier height (Wm) were calculated.

Multifunctional antistatic and scratch resistant UV-cured acrylic coatings

Organic–inorganic antistatic hybrid acrylic coatings were prepared. Trialkoxy-silyl ammonium salt was added to the photocurable formulations in order to introduce an antistatic additive which could be covalently linked to the hybrid network through a co-condensation reaction involving the alkoxy groups. The influence of the antistatic additive on the radical photopolymerization reaction of the acrylic resin was evaluated by real time FTIR, keeping the inorganic precursor content constant at 20phr and increasing the trialkoxy-silyl ammonium salt in the range between 5 and 15phr. When the samples were cured under nitrogen atmosphere, a complete conversion of acrylic double bonds was achieved after 90s of irradiation both for the acrylic resin and the formulations containing the ammonium salt. The scratch behavior of coatings was investigated by carrying out of progressive load scratch test. The penetration depth (Pd) and the residual depth patterns were investigated for all the hybrid films. A consistent improvement of penetration resistance by increasing alkoxy-ammonium salt content was noted in terms of Pd. Inorganic component and antistatic additives increase ε′ and σAC values of the hybrid coatings and decrease the resistivity ones, showing their efficiency for increasing antistatic properties of coatings, improved with respect to the pure acrylic resin.

Frequency- and voltage-dependent dielectric properties and electrical conductivity of Au/PVA (Bi-doped)/n-Si Schottky barrier diodes at room temperature

In this study, frequency and voltage dependence of dielectric constant (e′), dielectric loss (e″), loss tangent (tanδ), the real and imaginary parts of electric modulus (M′ and M″) and ac electrical conductivity (σac) of an Au/PVA (Bi-doped)/n-Si Schottky barrier diode have been investigated in detail by using experimental C–V and G–V measurements in the wide frequency range of 5 kHz–10 MHz and the voltage range of ±2 V at room temperature. Experimental results indicate that the values of e′,e″, tanδ and σac are strongly frequency and voltage dependent. It has found that the values of e′,e″ and tanδ decrease while the values of σac, M′ and M″ increase. It is clear that the values of M″ show a distinctive peak with a U-shape and its position shifts towards the positive-bias region with increasing frequency. Such behavior of the peak can be attributed to the particular distribution of interface states located at the Si/PVA interface and interfacial polarization. It can be concluded that the interfacial polarization and the charge at the interface can easily follow the ac signal at low frequencies.

On the Voltage and Frequency Distribution of Dielectric Properties and ac Electrical Conductivity in Al/SiO2/p-Si (MOS) Capacitors

An Al/SiO2/p-Si (MOS) capacitor with a thick (826 Å) interfacial oxide layer (SiO2) which is formed by using the thermal oxidation method is fabricated to investigate both frequency and applied bias voltage dependences of real and imaginary parts of dielectric constant (ε′ and ε″) and electric modulus (M′ and M″), loss tangent (tan δ) and ac electrical conductivity (σac) in a wide frequency range from 1 kHz to 1 MHz at room temperature. The dielectric properties of the MOS capacitor are obtained using the forward and reverse bias capacitance-voltage (C—V) and conductance-voltage (G/ω—V) measurements in the applied bias voltage range 1.4–5.6 V. The values of ε′, ε″, tanδ, M′, M″ and σac are found to be strong functions of frequency and applied bias voltage in the depletion region due to excess capacitance Cex and conductance Gex/ω especially at low frequencies. The experimental results show that the interfacial polarization can occur at low frequencies more easily, consequently contributing to the dispersion in ε′, ε″, tanδ, M′, M″ and σac values of the MOS capacitor. The other reason for dispersion in the dielectric properties may be attributed to a particular density distribution of interface states (Nss) localized at the Si/SiO2 interface, as well as space charge carriers and inhomogeneity of interfacial oxide layer. The increase in conductivity with increasing frequency can be attributed to the hopping type conduction mechanism. It can be concluded that the ε′, ε″, tanδ, M′, M″ and σac values of the Al/SiO2/p-Si (MOS) capacitor are strongly dependent on both the frequency and applied bias voltage especially in the depletion region.

Dielectric Properties of Au/PVA (Cobalt-Doped)/n-Si Photoconductive Diodes

The voltage (V) and frequency (f) dependence of dielectric parameters such as the dielectric constant (e′), dielectric loss (e″), dielectric loss tangent (tan δ), real and imaginary parts of electrical modulus (M′ and M″), and alternating-current (AC) electrical conductivity (σAC) of Au/PVA (cobalt-doped)/n-Si structures have been investigated by using experimental admittance measurements conducted at room temperature. The values of e′, e″, and tan δ were found to be strong functions of voltage and frequency, especially at low frequencies in the positive voltage region. It was observed that the values of e′ and e″ increase as the frequency decreases. The M′ values increase with increasing frequency due to increasing dielectric relaxation, while M″ values, in general, remain stable as frequency is changed. The σAC values at each bias voltage increase with increasing frequency.

Structure refinement and dielectric relaxation of M-type Ba, Sr, Ba-Sr, and Ba-Pb hexaferrites

M-type hexaferrites with compositions BaFe12O19 (BFO), SrFe12O19 (SFO), Ba0.5Sr0.5Fe12O19 (BSFO), and Ba0.5Pb0.5Fe12O19 (BPFO) were synthesized by commercial solid state reaction method. The Rietveld refinement of x-ray powder diffraction revealed a single hexagonal phase with space group P63/mmc for BFO, SFO, and BSFO samples, whereas BPFO sample contains hematite (α-Fe2O3) phase with space group R3c along with the M-type main phase. All the samples show dispersion in dielectric constant (ɛ′) and dielectric loss (tan δ) values with frequency. The values of ɛ′ and tan δ increase with increase in temperature due to increase in the number of charge carriers and their mobilities, which are thermally activated. The reciprocal temperature dependence of conductivity (σac) and the most probable relaxation time (τM″) satisfies the Arrhenius relation. A perfect overlapping of the normalized plots of modulus isotherms on a single “super curve” for all the studied temperatures reveals a temperature independence of dynamic processes involved in conduction and for relaxation. Further, the complex plots of M* (M″ vs M′) indicate that dc conductivity dominates in the region below the M″max point. Above M″max, the variations follow Jonscher power law (σ = Aωs) implying that ac conductivity is dominating in this region. Among the prepared samples, SFO hexaferrite has lowest values of σac, ɛ′, and tan δ making it suitable for use in microwave devices.

Mineralogy, Mössbauer spectroscopy and electrical conductivity of heterosite (Fe3+, Mn3+)PO4

Mineralogical analysis, electrical conductivity and thermopower are reported for monocrystalline heterosite (Fe3+, Mn3+)PO4 with the orthorhombic olivine-type structure. The 57Fe Mossbauer spectrum could be adequately described using two Fe3+ doublets. By impedance spectroscopy (20 Hz–1 MHz) the electrical DC conductivity σDC and AC conductivity σAC were determined parallel (∥) and perpendicular to the [001] direction (space group Pnma) in the range ∼160–440 K. The graph log σDC−1/T shows a slightly bent curve in both directions with activation energies of E A ∼0.30 and ∼0.15 eV in the high and low temperature ranges, respectively. The reduced E A is associated with electronic conduction; σDC ∥ [001] follows Mott’s T 1/4 variable range hopping law at lower temperatures with hopping between localized levels. The values of σAC are increased relative to σDC at high frequencies and low temperatures, obeying Jonscher’s universal dynamic response law; for σAC ∥ [001], the variation with temperature of the frequency exponent is in fair agreement with the model of small polaron hopping. The absolute thermopower Θ is negative and low between ∼295 and ∼440 K, Θ does hardly vary with temperatures in both directions; the temperature independency of Θ ∥ [001] is consistent with the small polaron hopping model.

Effect of Ag on the electrical properties of a-Ge20Se80 glasses

This article reports the effect of Ag impurity (low ~4 and ~6 at.% and high ~10 at.%) on the ac conductivity (σac) of a-Ge20Se80 glass. Frequency (ω)-dependent ac conductance and capacitance of the samples over a frequency range ~100 Hz to 50 kHz was taken in the temperature range ~268–358 K. At frequency 2 kHz and temperature 298 K, the value of σac increases at low as well as at higher concentration of Ag. The σac is proportional to ωs for undoped and doped samples. The value of frequency exponent (s) decreases as the temperature increases.

Dielectric Relaxations in the Ce1-xYbxO2-δ System

The dielectric properties of Yb-doped CeO2 (Ce1-xYbxO2-δ) which is an oxide-ion conductor were investigated. Numerical analysis of the frequency dependences of dielectric constants (ε') and dielectric loss factors (ε'') revealed that the dielectric characteristics can be successfully explained by the superimposition of both Debye-type polarization due to dopant-vacancy associates and electrolyte–electrode interfacial polarization. The temperature response of the dielectric properties was less active than that of the Sm- or Nd-doped CeO2 systems, which have higher oxide-ion conductivity than the present system. Three types of Debye-type polarizations were observed. The first polarization at the highest-frequency region was ascribed to a long-range migration of oxygen vacancies. The second and third polarizations at the lower-frequency region were ascribed to the dopant-vacancy associates. The observed values of σac and tan δ were also successfully explained using the dielectric parameters that were obtained from the numerical analysis of dielectric constant.