Low-temperature Electrical Properties and Correlated Barrier Hopping Conduction Mechanism in CdTiO₃

Arifa Jamil ¹ , M A Rafiq ¹

1 Department of Physics and Applied Mathematics, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, 45650, Pakistan

2 National Institute for Biotechnology and Genetic Engineering (NIBGE), Faisalabad­38000, Pakistan

Abstract

CdTiO₃ nanoparticles were synthesized by solid-state reaction technique. X-ray diffraction (XRD) confirms the formation of rhombohedral CdTiO₃ nanoparticles and scanning electron microscopy (SEM) shows the irregularly shaped nanoparticles. The ac conductivity data was fitted using Jonscher’s power law to find the frequency exponent "s". Correlated barrier hopping (CBH) is found to be prevailing conduction mechanism from 300 K to 160 K. The density of states (DOS) calculated by applying CBH model lie in the range of 2.89 x 10²⁰ eV^-1cm^-3 to 2.96 x 10²¹ eV^-1cm^-3. The calculated minimum hopping distance (R_min) was 2.13 x 10^-9 m. The low values of tangent loss (< 1) at all temperatures suggest CdTiO₃ as a potential material in electrical devices with low energy losses. The shifting of maxima towards higher frequencies with the decrease in temperature in imaginary modulus plots suggests the thermally triggered hopping process in CdTiO₃ nanoparticles. The modulus studies confirm that hopping is the dominant conduction mechanism in CdTiO₃ nanoparticles as suggested by ac conductivity studies.

Keywords

Correlated barrier hopping, Density of states, Energy losses, Electrical modulus, AC conductivity

Introduction

Titanium containing oxides have aroused interest in various industrial disciplines including gas sensing, chemical and biomedical, aerospace, electronics and automotive due to their outstanding characteristics such as high specific strength, low density, good thermal stability, biocompatibility, high melting point and high resistance against corrosion.^1,2 Low cost, chemical stability, non-toxicity and eco-friendly characteristics of titanium containing oxides make them potential members of the research community.³ CdTiO₃ is an utmost significant member of the titanium containing oxides family having excellent? dielectric, optical, electrical, ferroelectric, piezoelectric, photo-resistive and sensing char?acteristics.⁴ The synthesis method and annealing temperature affect the crystal of CdTiO₃. The literature study showed that it crys??tallizes into a rhombohedral ilmenite phase (non-ferroelectric) when sintered less than 1000 °C and? orthorhombic perovskite phase (ferroelectric phase) over1000 °C.?? Both ilmenite and perovskite phases differ slightly in their symmetry, the structure of perovskite is asymmetric in nature having : a = 5.348 Å, b = 7.615 Å and c = 5.417 Å, while the ilmenite structure comprises of threefold axis with a = b = 5.2403 Å and c = 14.838 Å.^5,6

Figure 1: (a) XRD spectrum (b) SEM micrograph of CdTiO₃ nanoparticles.

The wider bandgap of CdTiO₃ makes it suitable for electric, photocatalytic, sensing, and optical applications.^7,8 Investigation of temperature dependent electrical characteristics are fundamentals for electrical device fabrication such as energy storage devices, memory devices, spintronics and actuators. Therefore, we carried out detailed study of frequency and temperature dependent ac conductivities, CBH conduction mechanism, DOS, minimum hopping distance (R_min), calculations and fitting by applying CBH model on experimental data. To our knowledge, these frequency and temperature dependent parameters have not been reported for CdTiO₃ nanoparticles. Therefore, we use solid state reaction method to synthesize CdTiO₃ nanoparticles without any use of surfactant. XRD and SEM confirm the purity, crystallographic structure and physical features of CdTiO₃ nanoparticles. Low temperature (300 K-160 K) ac electrical measurements at varying frequency were performed to investigate electrical and dielectric characteristics, conduction mechanism, density of states and modulus properties in CdTiO₃ nanoparticles.

EXPERIMENTAL SETUP

Solid-state reaction technique was use to prepare CdTiO₃ nanoparticles. Titanium dioxide and cadmium acetate (purity > 99.9% acquired from Sigma-Aldrich, USA) and were used as precursor materials and mixed together in stoichiometric proportions. The mixture was grinded using agate mortar for 1 hour to get homogeneous powder. Annealing of the powder was carried out for 3 hours at 900 °C in a box furnace in air environment. Pellets having diameter 10 mm and thickness 2 mm were formed under a load of 3 tons. Pellets were then sintered for 3 hours at 400°C for the suppression of internal stresses and eradicate crystalline defects on planes. The silver paste contacts separated by about 8mm were formed for electrical measurements. The crystalline structure and purity of synthesized CdTiO₃ were examined by Bruker D8 advance X-ray diffractometer with Cu Kα radiation (λ = 1.5418 Å) functioned at 40 mA and 40 kV. The surface morphology was obtained by scanning electron microscope (JEOL JSM-6360) operated at an accelerating voltage 0.5-30 keV with resolution 4 nm. Agilent E4980A LCR meter was used to perform electrical measurements of CdTiO₃ nanoparticles.

RESULTS AND DISCUSSION

All the diffraction peaks in the XRD spectrum shown in Figure 1(a) were indexed to rhombohedral CdTiO₃ with no impurity peak in accordance with JCPDS card number 00-029-0277. The lattice parameters are a = b = 5.2403 Å, c = 14.8380 Å. The texture coefficient (TC) was calculated for all crystallite planes to determine the preferred orientation along the plane for CdTiO₃ nanoparticles by the relation that is often called Harris formula and modified by Mueller, Chernock and Beck and is given as⁹:

1 TChkl= I(hkl)Ir(hkl) ×                1n ∑nIhklIrhkl-1

Where I(hkl) is peak intensity taken from XRD spectrum of CdTiO₃, I_r(hkl) denotes the reference peak intensity attained from JCPDF 00-029-0277 and n denotes the total reflection number in XRD pattern. TC(hkl) ≤ 1 for randomly oriented planes and TC(hkl) > 1 for materials with preferentially oriented planes ¹⁰. Table 1 shows the computed TC(hkl) for CdTiO₃ planes. For the (122) plane, TC value is 6.46 that is greater than 1 and maximum in the calculated values for CdTiO₃ nanoparticles and hence is preferentially oriented plane. The SEM image in Figure 1(b) shows the irregularly shaped nanoparticles having different diameters.

Table 1: Texture coefficient for rhombohedral CdTiO₃.

Figure 2: Frequency dependent ac conductivity (a) linear scale (b) log-log scale of CdTiO₃ nanoparticles. The inset shows temperature dependent variation of parameter "s".

The frequency dependent variation of ac conductivity from 300 K to 160 K is shown in Figure 2(a) and (b). The ac conductivity of CdTiO₃ increases as temperature increases that is due to rise in drift motion of charge carriers. The rise in electrical conductivity with the increase in temperature shows thermally activated process in CdTiO₃ that specifies the semiconductor behaviour¹¹.

The increase in frequency of ac signal facilitated the transfer of charge carriers among different localized states. Moreover, trapped charges experience higher force at high frequencies and as soon the force go above the trapped energy, confined charges are liberated resulting in increased conductivity. This leads to an increase in ac conductivity with the increase in frequency^12,13.

Figure 3: Variation of N(E_f) with frequency for CdTiO₃ nanoparticles.

Figure 4: Temperature dependent variation of ε' at different frequencies for CdTiO₃ nanoparticles.

The total ac conductivity is:

2 σac'=σ1T+ σ2ω, T

where σ1T represents temperature dependent dc conductivity and σ2ω, T is ac conductivity that is frequency and temperature dependent and follows Jonscher’s power law ¹⁴:

3 σ2ω,T= BTωs(T)

where B is the materials constant define the polarizability of the material having units as that of electrical conductivity and parameter "s" is dimensionless that defines the interaction between lattice and mobile ions in the material¹⁵. The relationship between "s" and temperature can be used to investigate the material’s conduction process. Several theoretical conduction models based on the behaviour of the exponents s have been presented in the literature, including correlated barrier hopping¹⁶, overlapping large polaron tunneling¹⁷, small polaron conduction¹⁸, and quantum mechanical tunneling model¹⁹. The frequency dependent region immediately after frequency independent region in Figure 2(a) was fitted with equation 3 to obtain the power exponent "s" and shown to inset Figure 2 (a). We have to find the appropriate conduction model for CdTiO₃ based on the temperature dependence of parameter s. Accordingly, small polaron conduction model is suggested when s rises with the rise in temperature, conduction mechanism will be OLPT in the material when increasing temperature causes decrease in "s", getting a minimum value after that it increase with the increase in temperature. If there is no change in the value of "s" with the temperature then quantum mechanical tunneling will be the conduction mechanism in the material ²⁰. As these are not the case for the present study of CdTiO₃ nanoparticles so these models are not valid conduction mechanisms for CdTiO₃. Concerning the correlated barrier hopping model, the rise in temperature results a reduction in "s" values that is the case in the present study for CdTiO₃ nanoparticles. Therefore, conduction mechanism in CdTiO₃ nanoparticles is CBH. The CBH model suggests that electron transfer is a thermally triggered process that involves hopping between two sites. As a result, short-range translational type hopping of charge carriers causes electrical conduction in the system ²¹. The binding energy Wm for CBH mechanism is calculated by ²²:

Table 2: Comparison of dielectric and electrical properties of different cadmium titanate structures

Figure 5: Frequency dependent Tanδ from 300 K to 160 K for CdTiO₃ nanoparticles.

4 s=1-β

where

5     β= 6kBT/Wm

The binding energy values obtained from equation (5) are used to calculate R_min ²²:

6            Rmin=2e2/πε0εwm

where ε represents dielectric constant of CdTiO₃ and ε₀ stands for free space permittivity. The R_min values are in the range of 2.13 x 10^-9 m - 1.29 x 10^-7 m.

The density of states at the Fermi level NEf  have calculated (300 K to 160 K) using ac conductivity values for CdTiO₃ by using the relation²³:

7 σacω= π3e2ωkBTNEf2           ×  α-5lnf0ω4

where α is localized wave function (α = 10¹⁰ m^-1) and f₀ is photon frequency ( f₀ = 10¹³ Hz) ^22,24.

Figure 6: Frequency-dependent variation of electric modulus from 300 K to 160 K (a) real part of modulus (b) imaginary part of modulus for CdTiO₃ nanoparticles.

The frequency dependence of N(E_f) is shown in Figure 3 from 300 K to 160 K. The DOS values decreases as frequency increases, then it begins to increase as frequency increases, so, we get minima that moves towards lower frequency side with the decrease in temperature. The DOS decreases as frequency increases because charge carriers get sufficient energy to liberate from different trapping centers with the increase in frequency but they contain insufficient energy to cross grain boundaries and hence accumulate at grain boundaries. Further increase in frequency provide enough energy to charge carriers to cross the grain boundaries that results in the increase in DOS. A similar variation of N(E_f) with frequency was observed in (Bi_0.5Na_0.5)_0.94Ba_0.06TiO₃ ceramic ²³ and ZnO thin films ²⁰.

Figure 4 depicts temperature dependency of dielectric constant (ε') from 300 K to 160 K at different frequencies. At all temperatures, decreasing trend of ε' with the increase in frequency is observed. The decrease in ε' is due to polarization reduction at higher frequencies. All polarizations (electronic, ionic, interfacial etc.) react swiftly to the time-varying electric field at higher frequencies, contributing to the ε'. Rise in frequency of an electric field fasten the periodic reversal as much that complete dipoles cannot form in that short interval, resulting in a drop in total polarization and consequently decrease in ε' ²⁵. Thermally activated dipoles assemble at grain boundaries as temperature increases that results rise in interfacial polarizations and therefore increase in ε' from 160 K to 300 K ²⁶.

The energy losses (tan δ) of CdTiO₃ rises with the rise in temperature especially at lower frequencies as shown in Figure 5. This increase in energy loss is due to more electron exchange through resistive grain boundaries at high temperatures resulting in local electron displacement in the applied field direction ²⁷. Failure of polarization mechanism at higher frequencies due to formation of incomplete dipoles is the probable cause for the drastic increase in tan δ at higher frequencies ²⁸. The low values of tan δ < 1 at all temperatures makes CdTiO₃ a potential material for electrical devices. A comparison of dielectric and electrical properties of different cadmium titanate structures is shown in Table 2.

Complex electrical modulus (M*) is a useful tool for analyzing and visualizing electrode polarization, conductivity relaxation mechanisms and dynamical features of electrical transport mechanisms. It also emphasizes grain boundary conduction that can be difficult to distinguish from complicated impedance plots. It may also be used to distinguish between spectral components of materials with identical resistances but varying capacitances ³³. It examines the effect of grain boundary and grain on the relaxation mechanism. In the present study, the relaxation phenomena in CdTiO₃ have been investigated from 300 K to 160 K as a function of frequency by employing complex electric modulus ³⁴. M* comprises real ( M') and imaginary (M") parts as ³⁴:

8 M*=M'-jM"

9 M'=ε'ε'2+ε"2 , M"=ε"ε'2+ε"2 

where ε' and ε" are real and imaginary parts of permittivity of CdTiO₃.

The M' and M" with applied frequency are presented in Figure 6(a) and (b) from 300 K to 160 K. Figure 6(a) illustrates the frequency dependency curves of M' for CdTiO₃. The M' values approach towards zero at lower frequencies because of the lack of force that governs charge carrier movement under applied electric field. This indicates the negligible electrode polarization contribution in CdTiO₃.³⁵ As the frequency increases, M? increases to a maximum value Mmax' at about 0.25 MHz. Short range mobility is the possible reason of dispersion at higher frequencies ³⁶. Figure 6(b) shows that M" first decreases as frequency increases up to 0.7 MHz after that it raises to acquire maximum value from 300 K to 200 K. For temperatures less than 200 K, M" first increases as frequency increases, get a maximum value after that it decrease and increase again. Therefore, we obtain a peak below 200 K that moves toward higher frequency side as temperature decreases. The shifting of the modulus peak is related with different relaxation time of grains and grain boundaries. As temperature decreases, the peak shifts towards higher frequencies, indicating that dielectric relaxation is a thermally triggered process where hopping is the major conduction mechanism in the material.³³ This confirms that hopping of charge carriers is the dominant conduction mechanism in CdTiO₃ as suggested from ac conductivity data.

CONCLUSIONS

CdTiO₃ nanoparticles were successfully prepared by solid-state reaction technique. XRD verify the rhombohedral structure of prepared CdTiO₃ nanoparticles. SEM image showed the presence of irregularly shaped nanoparticles. The frequency dependent electrical and dielectric properties of CdTiO₃ nanoparticles were investigated from of 300 K to 160 K. The ac conductivity of CdTiO₃ follows Jonschers power law. Frequency exponent s decreased as temperature increases that showed correlate barrier hopping was dominant conduction mechanism in CdTiO₃ from 300 K to 160 K. The minimum hopping distance (R_min) in CdTiO₃ nanoparticles lies in the range of 2.13 x 10^-9 m to1.29 x 10^-7 m. DOS for CdTiO₃ nanoparticles was calculated by the theoretical CBH model and lies in the range of 2.89 x 10²⁰ eV^-1cm^-3 to 2.96 x 10²¹ eV^-1cm^-3. The imaginary part of the complex modulus study of CdTiO₃ nanoparticles showed the appearance of maxima at temperatures less than 200 K at different frequencies that showed different relaxation times at different temperatures.

ACKNOWLEDGMENTS  

Arifa Jamil would like to acknowledge Higher Education Commission for providing IPFP fellowship under the Interim Placement of Fresh PhDs Phase-II Batch-II program at National Institute for Biotechnology and Genetic Engineering (NIBGE), Faisalabad, Pakistan. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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