Observing the twinkling fractal nature of the glass transition

A fundamental understanding of the nature and structure of the glass transition in amorphous materials is currently seen as a major unsolved problem in solid-state physics. A new conceptual approach to understanding the glass transition temperature (T_g) of glass-forming liquids called the twinkling fractal theory (TFT) has been proposed in order to solve this problem. The main idea underlying the TFT is the development of dynamic rigid percolating solid fractal structures near T_g, which are said to be in dynamic equilibrium with the surrounding liquid. This idea is coupled with the concept of the Boltzmann population of excited vibrational states in the anharmonic intermolecular potential between atoms in the energy landscape. Solid and liquid clusters interchange or “twinkle” at a cluster size dependent frequency ω_TF, which is controlled by the population of intermolecular oscillators in excited energy levels. The solid-to-liquid cluster transitions are in accord with the Orbach vibrational density of states for a particular fractal cluster g(ω) ~ ω^df − 1, where the fracton dimension d_f = 4/3. To an observer, these clusters would appear to be “twinkling.” In this paper, experimental evidence supporting the TFT is presented. The twinkling fractal characteristics of amorphous, atactic polystyrene have been captured via atomic force microscopy (AFM). Successive two-dimensional height AFM images reveal that the percolated solid fractal clusters exist for longer time scales at lower temperatures and have lifetimes that are cluster size dependent. The computed fractal dimensions, ≈ 1.88, are shown to be in excellent agreement with the theory of the fractal nature of percolating clusters in accord with the TFT. The twinkling dynamics of polystyrene within its glass transition region are captured with time-lapse one-dimensional AFM phase images. The autocorrelation cluster relaxation function was found to behave as C(t) ~ t^− 4/3 and the cluster lifetimes τ versus width R were found to be in excellent agreement with the TFT via τ ~ R^1.42. This paper provides compelling new experimental evidence for the twinkling fractal nature of the glass transition.     

High frequency acoustic attenuation of vitreous silica: New insight from inelastic x-ray scattering

We present new experimental results on the propagation and damping of the high frequency acoustic-like modes in vitreous silica. The new data are measured by means of the inelastic x-ray scattering technique down to an exchanged wavevector Q ∼ 0.9 nm ^− 1, at the limit of the instrument capabilities. Thanks to the continuous development of the technique, the new spectra are characterized by a very high signal to noise ratio when compared to previous experiments. The higher data quality finally allows for a reliable determination of the position and width of the inelastic excitations. The new data show that the sound damping Γ is marked by a frequency dependence compatible with the Rayleigh law, Γ ∼ ν⁴, for frequencies below the position of the excess vibrational modes at the boson peak. We show that the new data are in good agreement with estimates of the acoustic mean free path from the thermal conductivity, which take into account the peculiar plateau at a few Kelvin. The connection between the boson peak and the Rayleigh law is further confirmed by a comparison of the present data with literature data for the sound attenuation in a permanently densified silica sample.     

Optical and spectroscopic properties of germanotellurite glasses

In this work, new glass compositions in the TeO₂-GeO₂-Nb₂O₅-K₂O system have been prepared and studied. The germanotellurite glasses were prepared by melt-quenching and their density, refractive index and characteristic temperatures have been determined. The structure of these glasses has been studied by infrared and Raman spectroscopies.The progressive replacement of TeO₂ by GeO₂ led to an increase of the glass transition and crystallisation temperatures of the glasses and a simultaneous decrease of their density and refractive index. Typical density and refractive index values of these glasses ranged from 4.98 to 3.85 g cm^− 3 and 2.08 to 1.79, respectively, with increasing GeO₂ content. The infrared spectra are dominated by a band ~ 640 cm^− 1 in the tellurite glass and ~ 800 cm^− 1 in the germanate glass. The Raman spectra of the germanotellurite glasses present an intense boson peak between ~ 34 and 47 cm^− 1, together with high frequency peaks at ~ 670 cm^− 1 and ~ 470 cm^− 1 for high tellurite and high germanate glass compositions, respectively. The vibrational spectra of these germanotellurite glasses indicate that the glass network consists basically of TeO₄ and [TeO₃]/[TeO_3 + 1] units, mixed with GeO₄ and NbO₆ polyhedra.     

Study on the influence of isotope exchange of hydrogen with deuterium on the vibrational spectrum of lysozyme by inelastic neutron scattering

The influence of isotope exchange of hydrogen with deuterium on the lysozyme dynamics was studied by incoherent inelastic neutron scattering. The generalized vibrational densities of states G(ω) were constructed from experimental results for protonated and deuterated protein samples at 200, 280, and 311 K. The major isotope effect was observed in G(ω) in the frequency region higher than 100 cm^?1. At all temperatures, both the Debye mode and the region of G(ω), whose spectral dimension corresponds to the fracton mode, are observed in the low-frequency region of the densities of states of both protonated and deuterated lysozyme. The influence of the hydrogen isotope exchange on the low-frequency region of G(ω) is insignificant.     

High-resolution inelastic X-ray scattering measurements of an Al72Pd20Mn8 alloy above the melting point

The dynamic structure factor S(Q, ω) of the melt of an icosahedral quasicrystal, Al₇₂Pd₂₀Mn₈, was measured at 1223 K near the melting point, T_m = 1140 K, for momentum transfers, Q, from 1.5 nm⁻¹ to 5.55 nm⁻¹ by means of inelastic X-ray scattering technique using synchrotron radiation at SPring-8. The composition of Al₇₂Pd₂₀Mn₈ is a special one in AlPdMn ternary alloys, since icosahedral AlPdMn quasicrystal is formed directly from the melt. The acoustic mode was observed in the low Q region, and a sound velocity was estimated to be 4170 ± 100 m/s.     

Synthesis and characterization of potassium, rubidium, and cesium thiogermanate glasses

Glass-forming regions were investigated for the binary xM₂S + (1 − x)GeS₂ (M=K, Rb, Cs) systems. Glasses were prepared from 0?x?0.20 mole fraction alkali sulfide using a novel preparation route involving the decomposition of the alkali hydrosulfides in situ. At higher alkali concentrations near x=0.33, the glass-forming regions are limited by the readily formed adamantane-like M₄Ge₄S₁₀ crystals. Structural characterization of the glasses and polycrystals for x?0.33 were performed using Raman scattering and IR absorption. Terminal Ge-S⁻ vibrational modes, observed between 473 and 479 cm⁻¹, increased in intensity and decreased in frequency with increasing alkali modifier content. Glass transition temperatures decreased with increasing alkali modifier, ranging from 250 to 215 °C. Corresponding crystallization onset temperatures were between 340 and 385 °C. DC conductivity values of the glasses ranged from 10⁻¹⁰ to 10⁻⁷ (Ω cm)⁻¹ with activation energies between 0.54 and 0.93 eV for the temperature range of ∼100-250 °C. Higher ionic conductivities were observed with increasing alkali concentration and decreasing alkali radii. Additionally, an increase in the activation energy was observed above the glass transition temperature.     

Dielectric study and ac conductivity of iron sodium silicate glasses

A series of glasses with formula (SiO₂)_0.7−x(Na₂O)_0.3(Fe₂O₃)_x with ( 0.0 ≤ x ≤ 0.20) were prepared and studied by means of AC measurements in the frequency range 20 kHz to 13 MHz at room temperature. The study of frequency dependence of both dielectric constant ε' and dielectric loss ε" showed a decrease of both quantities with increasing frequency. The results have been explained on the basis of frequency assistance of electron hopping besides electron polarization. From the Cole-Cole diagram the values of the static dielectric constant ε_s, infinity dielectric constant ε_∞, macroscopic time constant τ, and molecular time constant τ_m are calculated for the studied amorphous samples. The frequency dependence of the ac conductivity obeys a power relation, that is σ_ac (ω) = Α ω^s. The obtained values of the constant s lie in the range of 0.7 ≤ s ≤ 1 in agreement with the theoretical value which confirms the simple quantum mechanical tunneling (QMT) model. The increase in ac conductivity with iron concentration is likely to arise due to structural changes occurring in the glass network. The structure of a glass with similar composition was published and showed clustering of Fe²⁺ and Fe³⁺ ions which favor electron hopping and provide pathways for charge transport.     

Non-Debye excess heat capacity and boson peak of binary lithium borate glasses

The non-Debye excess heat capacities of binary lithium borate glasses with different Li₂O compositions of x = 8, 14 and 22 (mol%) are investigated to understand origin of the boson peak. The low-temperature heat capacities are measured between 2 and 50 K by a relaxation calorimeter. The experimental non-Debye heat capacities with x = 14 is successfully reproduced using the excess vibrational density of states measured by inelastic neutron scattering. This finding indicates that the non-Debye heat capacities of lithium borate glasses originate from the excess vibrational density of states measureable by inelastic neutron scattering. Moreover, it is demonstrated that all of the excess heat capacity spectra lie on a single master curve by the scaling using boson peak temperature and intensity.     

Low-temperature/high-temperature AlN superlattice buffer layers for high-quality AlxGa1−xN on Si (1 1 1)

We present MOVPE-grown, high-quality Al_xGa_1−x N layers with Al content up to x=0.65 on Si (1 1 1) substrates. Crack-free layers with smooth surface and low defect density are obtained with optimized AlN-based seeding and buffer layers. High-temperature AlN seeding layers and (low temperature (LT)/high temperature (HT)) AlN-based superlattices (SLs) as buffer layers are efficient in reducing the dislocation density and in-plane residual strain. The crystalline quality of Al_xGa_1−xN was characterized by high-resolution X-ray diffraction (XRD). With optimized AlN-based seeding and SL buffer layers, best ω-FWHMs of the (0 0 0 2) reflection of 540 and 1400 arcsec for the (1 0 1¯ 0) reflection were achieved for a ∼1-μm-thick Al_0.1Ga_0.9N layer and 1010 and 1560 arcsec for the (0 0 0 2) and (1 0 1¯ 0) reflection of a ∼500-nm-thick Al_0.65Ga_0.35N layer. AFM and FE-SEM measurements were used to study the surface morphology and TEM cross-section measurements to determine the dislocation behaviour. With a high crystalline quality and good optical properties, Al_xGa_1−x N layers can be applied to grow electronic and optoelectronic device structures on silicon substrates in further investigations.     

Characterization of the structure of calcium alumino-silicate and calcium fluoro-alumino-silicate glasses by magic angle spinning nuclear magnetic resonance (MAS-NMR)

Calcium aluminosilicate and calcium fluoro-aluminosilicate glasses have been characterized by ²⁹Si, ²⁷Al and ¹⁹F MAS-NMR. The two calcium aluminosilicate glasses examined were based on the composition 2SiO₂ · Al₂O₃ · 2CaO (ART1) and the mineral anorthite 2SiO₂ · Al₂O₃ · CaO (ART2). The observed chemical shifts for ²⁹Si and ²⁷Al agreed with previous studies. The fluorine containing glasses were based on 2SiO₂ · Al₂O₃ · (2−X)CaO · XCaF₂. The ²⁹Si chemical shift moved in a negative direction with increase fluorine content indicating a progressive reduction in the average number of non-bridging oxygens, NBO, attached to a silicon. The ²⁷Al spectra indicated the presence of four coordinate aluminium in the glasses with X=0.0-0.75, but aluminium was present in Al(IV), Al(V) and Al(VI) coordination states in the highest fluorine content glass with X=1.0. The ¹⁹F spectra indicated the presence of F-Ca(n) in low fluorine content glasses and both F-Ca(n) and Al-F-Ca(n) in high fluorine content glasses. We speculate here that the Al-F-Ca(n) species are oxyfluorides [AlO_xF_y]ⁿ⁻, where x=1-6, y=1-6 and n is the charge on the total complex when aluminium is in Al(IV), Al(V) and Al(VI) coordinate states. The reduction in the average number of NBO per silicon with increasing fluorine content is explained by fluorine converting Ca²⁺ to F-Ca(n).     

Effect of Bi2O3 proportion on physical, structural and electrical properties of zinc bismuth phosphate glasses

The variation in physical, structural and electrical properties has been studied as a function of Bi₂O₃ content in 20ZnF₂-(10 + x) Bi₂O₃-(70-x) P₂O₅, 0 ≤ x ≤ 10 mol% glasses, which were prepared by melt quenching technique and characterized by differential thermal analysis (DTA). Colorless samples, which have no absorption peaks, are obtained for 10 and 12 mol% of Bi₂O₃ and the glasses are slowly becoming brownish from 15 to 20 mol% of Bi₂O₃ which exhibit two absorption peaks at ~ 370 nm, ~ 450 nm correspond to Bi° transitions ⁴S_3/2 → ²P_3/2 and ⁴S_3/2 → ²P_1/2 respectively. The decrease in ³P₁ → ¹S₀ transition of Bi³⁺ photo luminescence emission for 18 and 20 mol% of Bi₂O₃ and increase in optical absorption area shows the reduction of Bi³⁺ to Bi°. From FTIR studies it is observed that an addition of Bi₂O₃ decreases the P―O―P covalent bond by forming P―O―Bi bonds due to high polarizing nature of Bi³⁺ ions. Dielectric parameters like ε', tan δ and a.c. conductivity σ_ac are found to increase and activation energy for a.c. conduction is found to decrease with the increase in the concentration of Bi₂O₃. Density of defect energy states is found to increase for higher concentration of Bi₂O₃ and is discussed according to quantum mechanical tunneling (QMT) model.     

Preparation of single-crystalline ZnO films on ZnO-buffered a-plane sapphire by chemical bath deposition

High-quality zinc oxide (ZnO) films were successfully grown on ZnO-buffered a-plane sapphire (Al₂O₃ (1 1 2¯ 0)) substrates by controlling temperature for lateral growth using chemical bath deposition (CBD) at a low temperature of 60 °C. X-ray diffraction analysis and transmission electron microscopy micrographs showed that the ZnO films had a single-crystalline wurtzite structure with c-axis orientation. Rocking curves (ω-scans) of the (0 0 0 2) reflections showed a narrow peak with full width at half maximum value of 0.50° for the ZnO film. A reciprocal space map indicated that the lattice parameters of the ZnO film (a=0.3250 nm and c=0.5207 nm) were very close to those of the wurtzite-type ZnO. The ZnO film on the ZnO-buffered Al₂O₃ (1 1 2¯ 0) substrate exhibited n-type conduction, with a carrier concentration of 1.9×10¹⁹ cm⁻³ and high carrier mobility of 22.6 cm² V⁻¹ s⁻¹.     

Underlying reverse current mechanisms in a-Si:H p-i-n solar cell and compact SPICE modeling

The defect states in bulk of i-layer and at p⁺/i interface have been studied by using dark reverse current-voltage (J-V) measurements. The dark reverse current as a function of voltage has been analyzed on the basis of thermal generation of the carriers from mid-gap states in i-layer. Based on its behavior the thermal generation mechanism has been divided into two types. Thermal generation at lower bias (<5 V) shows V^1/2 behavior, whereas at higher bias follows an exponential dependence of voltage (>5 V). This was explained using a thermal generation zone at lower bias, which is a source of reverse currents, and its evolution towards p⁺/i interface with increasing voltage. The analytical result has shown that at lower reverse bias (V < 5 V) the defect states in the bulk of i-layer and at higher bias (V ∼ 25 V) the defect states at p⁺/i interface are contributing to the reverse currents. Reverse bias annealing (RBA) treatment which has been performed on these cells shows that a reduction of defect states more in the i-region near to the p⁺-layer and at p⁺/i interface as compared to the deep regions in bulk of i-layer. The calculated defect state density (DOS) is varying from its intrinsic value of 2.4 × 10¹⁷ cm⁻³ in the bulk of the i-layer up to 2.1 × 10¹⁹ cm⁻³ near and at p⁺/i interface. These values decrease to 7.1 × 10¹⁶ cm⁻³ and 2.7 × 10¹⁷ cm⁻³, respectively, in the samples annealed under reverse bias at 2 V. The bias dependent leakage current behavior has been modeled and implemented in simulation program with integrated circuit emphasis (SPICE) using simple circuit elements based on voltage controlled current sources (VCCS). Simulated and measured reverse leakage current characteristics are in reasonable agreement.     

On the analysis of the vibrational Boson peak and low-energy excitations in glasses

Implications of reduction procedures applied to the low energy part of the vibrational density of states in glasses and supercooled liquids are considered by advancing a detailed comparison between the excess – over the Debye limit – vibrational density of states g(ω) and the frequency-reduced representation g(ω)/ω² usually referred to as the Boson peak. Analyzing representative experimental data from inelastic neutron and Raman scattering, we show that reduction procedures distort to a great extent the otherwise symmetric excess density of states. The frequency of the maximum and the intensity of the excess experience dramatic changes; the former is reduced while the latter increases. The frequency and the intensity of the Boson peak are also sensitive to the distribution of the excess. In the light of the critical appraisal between the two forms of the density of states (i.e. the excess and the frequency-reduced one) we discuss changes of the Boson peak spectral features that are induced under the presence of external stimuli such as temperature (quenching rate, annealing), pressure, and irradiation. The majority of the Boson peak changes induced by the presence of those stimuli can be reasonably traced back to simple and expected modifications of the excess density of states and can be quite satisfactorily accounted for by the Euclidean random matrix theory. Parallels to the heat capacity ‘Boson peak’ are also briefly discussed.     

Theoretical studies of the spin Hamiltonian parameters and the local structures for the tetragonal Cu centers in the LKB glasses

The spin Hamiltonian parameters (g factors g_∥, g_⊥ and the hyperfine structure constants A_∥, A_⊥) for the Cu²⁺ centers in the lithium potassium borate (LKB) glasses xLi₂O·(30 − x)·K₂O·70B₂O₃ (0 ≤ x ≤ 25) were theoretically studied using the high-order perturbation formulas of these parameters for a 3d⁹ ion in a tetragonally elongated octahedron. The [CuO₆]¹⁰⁻ clusters in the LKB glasses are found to suffer the relative elongations of about 3% along the tetragonal axis due to the Jahn-Teller effect. The concentration dependences of the g factors are illustrated by the approximately linear decrease of the cubic field parameter Dq as well as the increases of the covalency factor N and the relative elongation ratio ρ due to the slight expansion of the cell volume or bond lengths with increasing the Li₂O concentration x. Meanwhile, the slow non-linear increases of the hyperfine structure constants are described as the rough exponential increase of the core polarization constant κ with x due to the increase of the tetragonality of the systems. The theoretical spin Hamiltonian parameters and their concentration dependences show good agreement with the experimental data. To evaluate validity and applicability of the present theoretical model and formulas, the EPR results of the Cu²⁺ centers in similar lithium sodium borate (LNB) xLi₂O·(30 − x)·Na₂O·70B₂O₃ (5 ≤ x ≤ 25 mol%) glasses are also analyzed and compared with those in the LKB systems using the uniform model and formulas.     

Longitudinal acoustic compliance and tagged particle susceptibility in liquid and supercooled glycerol

Brillouin spectra of glycerol measured in the visible, ultraviolet and X-ray frequency regions allow us to reckon the imaginary part of acoustic compliance, J″(ω), over a broad frequency range from fraction of GHz to tens of THz. We observe that J″(ω) suitably mimic the shape of the tagged particle susceptibility, χ″_INS(ω), measured by incoherent neutron spectra for both the liquid and supercooled states. The proportionality between these two quantities suggests a strict relationship between acoustic dissipation and generalized density of states.     

Thermal, chemical, optical properties and structure of Er-doped and Er/Yb-codoped P2O5-Al2O3-ZnO glasses

This study was explored in series of the optical, thermal, and structure properties based on 60P₂O₅-10Al₂O₃-30ZnO (PAZ) glasses system that doped with varied rare-earth (RE) elements Yb₂O₃/Er₂O₃. The glass transition temperature, softening temperature and chemical durability were increased with RE-doping concentrations increasing, whereas thermal expansion coefficient was decreased. In the optical properties, the absorption and emission intensities also increase with RE-doping concentrations increasing, When Er₂O₃ and Yb₂O₃ concentrations are over than 3 mol% in the Er³⁺-doped PAZ system and Yb³⁺-doped concentration is over than 3 mol% for Er³⁺/Yb³⁺-codoped PAZ system, the emission intensity significantly decreases presumably due to concentration quenching, formation of the ions clustering, and OH⁻ groups in the glasses network. It is suggested that the maximum emission cross-section (σ_e) is 7.64 × 10^− 21 cm² at 1535 nm is observed for 3 mol% Er³⁺-doped PAZ glasses. Moreover, the maximum σ_e × full-width-at-half-maximum is 327.8 for 5 mol% Er³⁺-doped PAZ glasses.     

All-chalcogenide middle infrared dielectric reflector and filter

We have fabricated a dielectric reflector and a passband filter, both with first order photonic bandgaps in the middle-infrared region around λ = 4 μm. The devices were made from alternating amorphous Ge₂₅S₇₅ and Ge₁₅Te₈₅ chalcogenide films with high transparency in the middle infrared region stacked in multilayers. Due to high thickness accuracy and periodicity of prepared multilayers we also observed second order photonic bandgaps at λ ~ 1.4 μm. The experimental data were in good agreement with theoretical predictions. The work focused on investigation of compositional homogeneity, surface roughness, thermal and optical properties of individual amorphous Ge₂₅S₇₅ and Ge₁₅Te₈₅ films. We confirmed chalcogenide materials as being of suitable choice for designing middle-infrared quarter wave stack devices. FT-IR reflectance spectra confirmed occurrence of 99.4% stopband near λ = 4 μm for fabricated reflector and narrow ~ 50% passband of prepared filter near λ = 3.934 μm.     

Structural investigations of magnesium silicate glasses by Si 2D Magic-Angle Flipping NMR

The two-dimensional Magic Angle Flipping Nuclear Magnetic Resonance (2D MAF NMR) experiment on ²⁹Si nuclei is used to determine the distribution of Q⁽ⁿ⁾ sites in two ²⁹Si-enriched magnesium silicate glasses with compositions 2MgO·SiO₂ and MgO·SiO₂. A significant degree of polymerization is observed in the 2MgO·SiO₂ glass, supporting previous studies using Raman and ²⁹Si NMR spectroscopy. Relative abundances of 0.629 ± 0.001 for Q⁽⁰⁾ and 0.371 ± 0.001 for Q⁽¹⁾ were obtained from spectral fits of the 2D MAF spectrum of the 2MgO·SiO₂ glass. Mole fractions for the free oxygen anion and each Q⁽ⁿ⁾-species were calculated and used in a thermodynamic model of Q⁽ⁿ⁾ disproportionation to calculate an equilibrium constant of k₀ = 0.04 ± 0.02 in 2MgO·SiO₂. In the MgO·SiO₂ glass relative abundance of 0.014 ± 0.001 for Q⁽⁰⁾, 0.191 ± 0.003 for Q⁽¹⁾, 0.530 ± 0.004 for Q⁽²⁾, 0.252 ± 0.003 for Q⁽³⁾, and 0.014 ± 0.001 for Q⁽⁴⁾ were measured. The mole fractions for the free oxygen anion and each Q⁽ⁿ⁾-species in MgO·SiO₂ were used to calculate corresponding disproportionation equilibrium constants of k₁ = 0.19 ± 0.02, k₂ = 0.174 ± 0.009, and k₃ = 0.11 ± 0.01. A comparison of k₃ values from previous MAF studies of various alkali and alkaline earth silicate glasses indicate an exponential increase in k₃ with the increasing modifying cation potential. Using the van't Hoff relation, we show that differences in both thermal history and modifier cation potential contribute to this spread in k₃ values. Nuclear shielding tensor anisotropy, ζ, and asymmetry, η, values of ζ = 0.0 ppm and η = 0.0 for Q⁽⁰⁾ and ζ = 33.0 ± 0.1 ppm, and η = 0.4 ± 0.1 for Q⁽¹⁾ in 2MgO·SiO₂ glass were determined from its 2D MAF spectrum. These values were used in obtaining the remaining values of ζ = − 36.0 ± 0.5 ppm and η = 0.99 ± 0.01 for Q⁽²⁾, and ζ = − 27.5 ± 0.5 ppm and η = 0.45 ± 0.11 for Q⁽³⁾, ζ = 0.0 ppm and η = 0.0 for Q⁽⁴⁾ in the MgO·SiO₂ glass from its 2D MAF spectrum. The magnitude of ζ values observed are lower than those reported in previous MAF studies of alkali and alkaline earth silicate glasses containing different modifier cations, consistent with previously reported trends in ζ versus modifying cation potential.     

Studies on electrical and the dielectric properties in MS structures

In this study, we investigated frequency dependent electrical and dielectric properties of metal-semiconductor (MS) structures using capacitance-voltage (C-V) and conductance-voltage (G/ω-V) characteristics in the frequency range 100 kHz-10 MHz in the room temperature. The dielectric constant (ε′), dielectric loss (ε″), dielectric loss tangent (tan δ) and ac electrical conductivity (σ_ac) were calculated from the C-V and G/ω-V measurements and plotted as a function of frequency. In general, ε′, ε″ and tan δ values decreased with increasing the frequency, while σ_ac increased with increasing frequency. Furthermore, the voltage and frequency dependence of series resistance were calculated from the C-V and G/ω-V measurements and plotted as functions of voltage and frequency. The distribution profile of R_S-V gives a peak in the depletion region at low frequencies and disappears with increasing frequencies. Also, series resistance values decreased with increasing frequency. The experimental results show that both frequency dependent electrical and dielectric parameters were strongly frequency and voltage dependent.