Tuning enhanced dielectric properties of (Sc³⁺–Ta⁵⁺) substituted TiO₂ via insulating surface layers

Abstract

In this study, we achieved significantly enhanced giant dielectric properties (EG-DPs) in Sc³⁺–Ta⁵⁺ co-doped rutile-TiO₂ (STTO) ceramics with a low loss tangent (tanδ ≈ 0.05) and high dielectric permittivity (ε′ ≈ 2.4 × 10⁴ at 1 kHz). We focused on investigating the influence of insulating surface layers on the nonlinear electrical properties and the giant dielectric response. Our experimental observations revealed that these properties are not directly correlated with the grain size of the ceramics. Furthermore, first-principles calculations indicated the preferred formation of complex defects, specifically 2Ta diamond and 2ScV_o triangular-shaped complexes, within the rutile structure of STTO; however, these too showed no correlation. Consequently, the non-Ohmic properties and EG-DPs of STTO ceramics cannot be predominantly attributed to the grain boundary barrier layer capacitor model or to electron-pinned defect-dipole effects. We also found that the semiconducting grains in STTO ceramics primarily arise from Ta⁵⁺, while Sc₃₊ plays a crucial role in forming a highly resistive outer surface layer. Notably, a significant impact of grain boundary resistance on the nonlinear electrical properties was observed only at lower co-dopant concentrations in STTO ceramics (1 at%). The combination of low tanδ values and high ε′ in these ceramics is primarily associated with a highly resistive, thin outer-surface layer, which substantially influences their non-Ohmic characteristics.

Introduction

Recently, there has been a growing research interest in TiO₂-based materials due to their enhanced giant dielectric properties (EG-DPs). These properties include high dielectric permittivity (ε′ > 10⁴), low loss tangent (tanδ < 0.1), and a low temperature coefficient of ε′ at temperatures above 150 °C^{1,2,3,4,5,6,7,8,9}. Materials with enhanced giant dielectric properties (EG-DPs) possess great potential for applications in high-energy density storage devices and ceramic capacitors⁵.

Although CaCu₃Ti₄O₁₂ and related ACu₃Ti₄O₁₂ ceramics are the classic giant dielectric ceramics, exhibiting ε′ values of more than 10⁴ and low tanδ < 0.05, their ε′ values are usually temperature dependent at above 100 °C^{10,11,12,13,14}. EG-DPs cannot be obtained from this material group. Greatly enhanced ε′ ≈ 6 × 10⁴ with low tanδ values of ≈ 0.02 for rutile-TiO₂ ceramics was accomplished by partial co-substitution of In³⁺–Nb⁵⁺ ions (InNbTO)¹. The ε′ and tanδ values of the InNbTO ceramics are dependent on the co-dopant In³⁺–Nb⁵⁺ concentration, which continuously increases as the doping concentration was enhanced from 0.05 to 10%, while tanδ decreased. Interestingly, it was reported that ε′ of InNbTO ceramics is independent of temperature and frequency over wide ranges. The complete details of the investigations of the EG-DPs of TiO₂ ceramics, which were co-doped by other ion pairs such as Ga³⁺–Nb⁵⁺, Sm³⁺–Ta⁵⁺, Sc³⁺–Nb⁵⁺, Al³⁺–Nb⁵⁺, Al³⁺–Ta⁵⁺, and Ga³⁺–Ta⁵⁺, have been reported^{3,15,16,17,18,19}. These ceramics exhibited EG-DPs. It is believed that co-doped TiO₂ ceramics are a promising material group with high potential for use in energy-storage devices with high-energy density and capacitors. Furthermore, TiO₂-based materials are widely utilized in various applications due to their low cost, abundance, non-toxic nature, and excellent chemical stability^20,21,22,23.

The temperature stability of ε′ (i.e., temperature coefficient, Δε′(%)) of InNbTO ceramics and other co-doped TiO₂ ceramics may be one of most serious problems inhibiting their practical use²⁴. Improvement of the Δε′(%) value is an important research issue. Another important topic that has been extensively studied is the origination of EG-DPs of TiO₂-based materials. Complex defect dipoles inside the grains or polarization at the interfaces of grain boundaries (GBs) and resistive outer-surface layers were proposed as the leading causes of EG-DPs^{1,2,15,16,17,25,26,27}. Each proposed model is reasonable from different points of view. Thus, the actual origin of the EG-DPs of all TiO₂ ceramics remains unclear.

The search a new co-doped TiO₂ system that exhibits EG-DPs and/or possesses attractive electrical properties is one of the most important activities to increase the available ceramic choices for use in future applications⁵. Although the giant dielectric properties (ε′ ≈ 1.9 × 10⁴–1.4 × 10⁵) of (A³⁺_1/2Ta_1/2)_0.1Ti_0.9O₂ ceramic systems (ATTO, A = In, Ga, Yb, Sm, Al, Fe, Bi, Dy, Sc, or Gd) have been presented by Li et al.¹⁸, comprehensive details of experimental results and their discussion focused only on the (Al_1/2Ta_1/2)_xTi_1−xO₂ system with x = 0–0.15. EG-DPs were obtained in the (Al_1/2Ta_1/2)_xTi_1−xO₂ system with x = 0.125 (tanδ ~ 0.054 and ε′ ~ 3.76 × 10⁴ at 1 kHz). Recently, we found that the EG-DPs of the ATTO family were formed in Ga³⁺–Ta⁵⁺ co-doped TiO₂ (GaTaTO) materials by optimizing the sintering conditions and co-dopant concentrations¹⁷. Besides GaTaTO and AlTaTO ceramics, the EG-DPs of various ceramics in the ATTO family may be achieved.

Nonlinear current density–electric field (J–E) characteristics have been widely studied in giant-dielectric oxides, especially for CaCu₃Ti₄O₁₂ and related ACu₃Ti₄O₁₂ ceramics, due to their attractiveness for varistor applications^28,29. However, the giant dielectric and nonlinear J–E characteristics of co-doped TiO₂ in the ATaTO family have rarely been reported³⁰. The nonlinear electrical properties in polycrystalline materials typically arise from the interface between the semiconducting and insulating components^31,32. The observation of nonlinear J–E characteristics suggests the presence of at least one type of insulating layer, which can influence the EG-DPs of these materials. The objective of this research is to explore the EG-DPs of co-doped TiO₂ oxides, with a particular focus on their potential use in ceramic capacitors. Additionally, the study aims to investigate the impact of the introduced insulating surface layer on the EG-DPs.

It was reported that the EG-DPs of co-doped TiO₂ ceramics were primarily influenced by multiple factors, depending on the ionic radii of the acceptor dopants used²⁶. In the InNbTO system^1,2,26, the electron-pinned defect-dipole (EPDD) was produced, attributed to the relatively larger ionic radius of In³⁺ (r₆ = 80 pm) compared to Ti⁴⁺ (r₆ = 60.5 pm)³³. Therefore, the predominant origin of the EG-DPs in InNbTO was ascribed to the EPDD effect. Contrarily, in GaTaTO ceramics¹⁷, theoretical calculations have demonstrated the absence of EPDD formation. The EG-DPs in GaTaTO ceramics were explained by extrinsic effects, such as interfacial polarization at the insulating GBs and resistive outer-surface layers, as opposed to the intrinsic EPDD effect. However, the existence of resistive outer-surface layers has yet to be proved. Furthermore, theoretical studies on the formation of EPDD have only focused on In³⁺ and G³⁺ ions. The effect of an acceptor dopant with an ionic radius intermediary to these ions, such as Sc³⁺ (r₆ = 74.5 pm), has not been theoretically investigated.

Therefore, in this study, we successfully synthesized a novel Sc³⁺–Ta⁵⁺ co-doped TiO₂ system employing a conventional solid–state reaction (SSR) method. This process resulted in EG-DPs characterized by exceptionally high ε′ of ~ 2.4 × 10⁴ and low tanδ ~ 0.05 values. First-principle calculations were employed to predict the presence of EPDDs. Additionally, we measured the nonlinear J–E properties to confirm the existence of resistive outer-surface layers. Impedance spectroscopy played a key role in revealing the formation of distinct semiconducting and insulating regions. The underlying mechanisms of the EG-DPs were comprehensively elucidated through a synergy of theoretical insights and experimental findings.

Experimental details

An SSR technique was employed to prepare (Sc_0.5Ta_0.5)_xTi_1-xO₂ (x = 0.01, 0.025, and 0.05) powders. These ceramics are referred to as the 1%STTO, 2.5%STTO, and 5%STTO ceramics, respectively. Single-doped Sc_0.025Ti_0.975O₂ (2.5%STO) and Ta_0.025Ti_0.975O₂ (2.5%TTO) ceramics were also synthesized via the SSR method. The starting raw oxides, purchased from Sigma–Aldrich, consisted of Sc₂O₃ (99.9% purity), rutile-TiO₂ (> 99.9%), and Ta₂O₅ (99.99%). Details of the SSR method for preparing co-doped TiO₂ ceramics are given elsewhere¹⁷. First, the starting powders were mixed using a wet-ball milling method in ethanol for 24 h. ZrO₂ balls, each with a diameter of 2 mm, served as the grinding media. Second, the ethanol was evaporated by heating in an oven at 90 °C for 6 h. Third, the resulting dried powders were compressed into pellets at a uniaxial pressure of 250 MPa without prior calcination or the addition of a binder. Extending the findings of our previous research¹⁷, which demonstrated high ε′ values exceeding 5.0 × 10³ in TiO₂ co-doped with 2.5% and 5.0% (Ga³⁺–Ta⁵⁺), the pellets were sintered at 1500 °C for a duration of 5 h. In this work, the STTO pellets were similarly sintered at 1500 °C for 5 h.

A UV–vis Raman spectrometer (Horiba Jobin–Yvon T64000), scanning electron microscope (SEM) (SEC, SNE4500M), X-ray diffraction (XRD, PANalytical, EMPYREAN), field-emission scanning electron microscopy (FE-SEM) with energy-dispersive X-ray analysis (EDS) (HITACHI SU8030, Japan), and X-ray photoelectron spectroscopy (XPS) were employed to systematically examine the sintered STTO specimens. Comprehensive details of each technique are provided in our previous published work¹⁷. The sintered samples were first polished and then thermally etched at 1200 °C for 30 min. To calculate the mean grain size, the following procedure was employed: First, six different diameters were measured for each grain using the relative scale bars. Next, the average size of each individual grain was determined. Finally, the overall mean grain size for the sample was calculated, based on measurements from approximately 100 grains. The nonlinear J–E properties of as-sintered specimens were tested at ~ 25 °C (Keithley Model 247). The α value was calculated using the following formula:

$${\upalpha } = \frac{{\log \left( {{\text{J}}_{2} /{\text{J}}_{1} } \right)}}{{\log \left( {{\text{E}}_{2} /{\text{E}}_{1} } \right)}},$$

(1)

where E₁ and E₂ represent the electric fields, at which J₁ = 1 and J₂ = 10 mA cm⁻², respectively. E_b was defined as equal to being E₁^31,32,34,35. Capacitance (C_p) and tanδ values of as-sintered specimens were determined as a function of frequency (40–10⁷ Hz) and temperature (− 60 to 210 °C) by employing a KEYSIGHT E4990A Impedance Analyzer. The ε′ value was calculated by the equation,

$${\upvarepsilon }^{\prime } = \frac{{{\text{C}}_{{\text{p}}} {\text{d}}}}{{{\upvarepsilon }_{0} {\text{A}}}},$$

(2)

where A and d represent the electrode area and sample thickness, respectively. ε₀ = 8.854 × 10^–12 F/m. The complex dielectric constant (ε^*) and complex impedance (Z^*) were calculated from the equations,

$${\upvarepsilon }^{*} = {\upvarepsilon }^{\prime } - i{\upvarepsilon }^{\prime \prime } = \left( {i\omega C_{0} Z^{*} } \right)^{ - 1} = \left[ {i\omega C_{0} \left( {{\text{Z}}^{\prime } - i{\text{Z}}^{\prime \prime } } \right)} \right]^{ - 1} ,$$

(3)

where ε′ and ε′′ represent the real and imaginary parts of ${\upvarepsilon }^{*}$ (ε′′ = ε′tanδ), while Z′ and Z′′ represent the real part and imaginary parts of Z*, respectively. ${{\text{C}}}_{0}={\upvarepsilon }_{0}{\text{A}}/{\text{d}}$ is the empty cell capacitance. The most preferred configuration for STTO ceramics was determined for the DFT calculations. Details of our computational calculations are given elsewhere¹⁷.

Results and discussion

Figure 1a gives XRD patterns of single as well as co-doped specimens, confirming that the main phase of rutile-TiO₂ (JCPDS 21-1276) contains no impurity phases. Both the ionic radii Sc³⁺ (r₆ = 0.745 Å) and Ta⁵⁺ (r₆ = 0.64 Å) dopants are larger than the host Ti⁴⁺ ion (r₆ = 0.605 Å)³³. Thus, cell parameters of the rutile-structure may be changed by doping with Sc³⁺ and/or Ta⁵⁺ ions. Consequently, the lattice parameters (a and c values) were obtained from Rietveld refinement method. TiO₂, 2.5%STO, 2.5%TTO, 1%STTO, 2.5%STTO and 5%STTO ceramics showed respective a values of 4.593, 4.595, 4.595, 4.598, 4.598 and 4.601 Å, while c values were 2.959, 2.960, 2.962, 2.965, 2.965 and 2.969 Å, respectively. The unit cell volumes were 62.44, 62.50, 62.54, 62.68, and 62.68 Å, respectively. Single and co-doped ceramic a and c values are slightly greater than for a pure TiO₂ ceramic. Therefore, both Sc³⁺ and Ta⁵⁺ dopant ions could be substituted into the rutile-TiO₂ structure.

Figure 1

(a) XRD patterns of sintered 2.5%STO, 2.5%TTO, 1.0%STTO, 2.5%STTO, and 5.0%STTO ceramics. (b) Raman spectra of TiO₂, 1.0%STTO, 2.5%STTO, and 5.0%STTO ceramics.

Figure 1b shows Raman spectra of STTO specimens compared to that of a pure TiO₂ material. Overall, the Raman spectra are similar to co-doped TiO₂ systems reported in literature^{17,19,30,36,37}. Here, we focused on the strongest E_g and A_1g peaks. These affect the giant dielectric response of TiO₂-based oxides. These two main peaks are usually associated with oxygen vacancies and O–Ti–O bonds, respectively³⁷. E_g mode Raman peaks for TiO₂, 1%STTO, 2.5%STTO and 5%STTO ceramics are, respectively, at 447.9, 447.1, 446.3, and 443.3 cm⁻¹, while the A_1g peaks are at 611.3, 610.1, 611.2, and 610.2 cm⁻¹, respectively. The E_g peak of the STTO specimens shifted to lower wave numbers as the Sc³⁺ and Ta⁵⁺ co-dopant concentrations increased from 0 to 5 at.%, whereas the A_1g peak is not changed significantly. Generally, substitution of an acceptor dopant, such as Sc³⁺, into the TiO₂ structure requires oxygen vacancies for charge compensation, following Eq. (1). According to this equation, the nominal composition of the 5%STTO ceramic with an E_g peak appeared at 443.33 cm⁻¹, the theoretical ratio of [O]/[Ti] in the 5%STTO ceramic should be 1.987. This result is in agreement with Parker et al.³⁸. They reported that the TiO_2−x E_g peak decreased from 447 to 443 cm⁻¹ as the [O]/[Ti] ratio in a rutile-TiO₂ was reduced, from 2.0 to 1.99. The E_g peak shifting to lower a wave number confirms that the presence of oxygen vacancies in STTO materials, which increased with the Sc³⁺ concentration. Oxygen vacancies detected using Raman analysis confirms the origin of the enlarged grain size of the co-doped 5.0%STTO ceramic was due to diffusion of oxygen vacancies when compared to that of the 2.5%TTO ceramic, since the average grain size of the 2.5%TTO specimen enlarged with addition of 2.5 at% Sc³⁺ ions (5.0%STTO).

The XPS technique was used to further analyze the possible effects of the dopants on the presence of defects in co-doped STTO materials. As illustrated in Fig. S1a (supplementary Information), the fitted XPS peaks of O1s confirmed the oxygen lattices, oxygen vacancies, and surface hydroxyl (OH) groups in the 5.0%STTO ceramic^1,16,36. Therefore, it can be confirmed that substitution of Sc³⁺ can contribute to promoting oxygen vacancies, following Eq. (1). Furthermore, the presence of Ti⁴⁺ and Ti³⁺ was confirmed^1,39, Fig. S1b. Furthermore, the XPS results also showed Ta⁵⁺ (Fig. S1c)^39,40 and Sc³⁺ (Fig. S1d)¹⁵. The Ti³⁺/Ti⁴⁺ ratio of the 5.0%STTO material was found 4.84%, which was larger than the expected ratio calculated from the nominal composition of the 5.0%STTO ceramic (2.63%), following:

$$2{\text{TiO}}_{2} + {\text{Ta}}_{2} {\text{O}}_{5} \mathop{\longrightarrow}\limits^{{4{\text{TiO}}_{2} }}2{\text{Ti}}_{{{\text{Ti}}}}^{\prime } + 2{\text{Ta}}_{{{\text{Ti}}}}^{ \cdot } + 8{\text{O}}_{O} + 1/2{\text{O}}_{2} ,$$

(4)

$${\text{Ti}}^{4 + } + e \to {\text{Ti}}^{3 + } .$$

(5)

A higher Ti³⁺/Ti⁴⁺ ratio is generally due to the oxygen loss during sintering, following the relationship.

$${\text{O}}_{{\text{O}}}^{x} \to \frac{1}{2}{\text{O}}_{2} + V_{{\text{O}}}^{ \cdot \cdot } + 2e^{\prime } .$$

(6)

Figure 2a–f reveal the effects of Sc³⁺ and Ta⁵⁺ dopants upon the microstructural evolution of TiO₂ specimens. Highly dense materials with no porosity are achieved in these sintered materials. Average grain sizes of the un-doped TiO₂, single-doped 2.5%TTO, and 2.5%STO are about 42.9 ± 16.0, 12.6 ± 4.1, and 85.6 ± 33.6 µm, respectively. Only doping TiO₂ with Sc³⁺ ions causes a great increase in an average grain size, by ~ 2 times. This result is likely attributed to diffusion of oxygen vacancies ($V_{{\text{O}}}^{ \cdot \cdot }$), which are produced as part of the Sc³⁺-doped TiO₂ structure owing to charge compensation, following:

$${\text{Sc}}_{2} {\text{O}}_{3} \mathop{\longrightarrow}\limits^{{2{\text{TiO}}_{2} }}2{\text{Sc}}_{{{\text{Ti}}}}^{\prime } + V_{{\text{O}}}^{ \cdot \cdot } + 3{\text{O}}_{{\text{O}}} .$$

(7)

Figure 2

SEM images of surface morphologies of (a) TiO₂, (b) 2.5%STO, (c) 2.5%TTO, (d) 1.0%STTO, (e) 2.5%STTO, and (f) 5.0%STTO ceramics. Elemental mapping of the 5%STTO ceramic, (g) Sc and (h) Ta.

A highly enlarged grain size of the 2.5%STO ceramic is similar to that described by Tuichai et al.¹⁷ for a Ga³⁺-doped TiO₂ ceramic. Doping TiO₂ with a pentavalent cation, such as Ta⁵⁺, resulted in a remarkable reduction in a grain size. The primary contribution of the Ta⁵⁺ dopant is to suppress the GB mobility¹⁷.

The roles of Sc³⁺ and Ta⁵⁺ ions on the microstructural evolution of TiO₂ ceramics are totally different. The combination effect of co-doped Sc³⁺–Ta⁵⁺ ions was therefore studied to determine the dominant effect of Sc³⁺ or Ta⁵⁺. Mean grain sizes of co-doped 1%STTO, 2.5%STTO, and 5%STTO specimens are about 27.3 ± 10.5, 20.2 ± 5.1, and 17.8 ± 6.9 µm, respectively. Although these grain sizes are between those of the 2.5%STO and 2.5%TTO specimens, they are closer to a single-doped 2.5%TTO material than that of the 2.5%STO ceramic. These indicate that the restorative force inhibiting GB migration caused by the Ta⁵⁺ dopant is more dominant than that of the driving force for promoting grain growth that primarily resulted from the Sc³⁺ dopant¹⁷.

Dopant dispersion in STTO ceramics is revealed in the elemental images shown in Fig. 2g, h. The Ta and Sc dopants are observed to homogeneously disperse throughout the microstructure with no segregation towards any specific region.

It was suggested that the EPDDs in co-doped TiO₂ ceramics is determined by the ionic size of the acceptor dopant^26,37. Ga³⁺–Nb⁵⁺ and Ga³⁺–Ta⁵⁺ co-dopants in TiO₂ ceramics cannot create EPDDs owing to the lower ionic radius of Ga³⁺ (r₆ = 62.0 pm) compared to that of an In³⁺ dopant (r₆ = 80.0 pm)³³. Considering that the ionic radius of Sc³⁺ (r₆ = 74.5 pm) is between that of Ga³⁺ and In³⁺ ions³³, EPDDs could be formed in the current study. Thus, the possible formation of EPDDs in Sc³⁺–Ta⁵⁺ co-doped TiO₂ ceramics is theoretically predicted using first-principles calculations. An oxygen vacancy was shown to exist the XPS and Raman results. Thus, for the first step of the calculation, one oxygen atom was removed from the rutile structure, and two Sc atoms were substitute into the positions of two Ti atoms_. Such a defect cluster is referred to (Ti–2Sc–V_o)O₂. Various characteristics of the defect cluster were tested. For each characteristic, all atoms were allowed to relax completely with no symmetrical constraints. As presented in Fig. 3, by considering the total energy, the (Ti–2Sc–V_o)O₂ characteristic with a triangular shape was the most stable. According to our previous work ¹⁷, with substitution of two Ta atoms in the rutile TiO₂ structure, the most preferable structure of a (Ti–2Ta)O₂ defect cluster was diamond shaped. Finally, the lowest energy configuration, which indicates the most stable among the diamond-shaped (Ti–2Ta)O₂ and triangular–shaped (Ti–2Sc–V_o)O₂ defect clusters, was then was calculated. The result showed that these two types of defect clusters are preferentially separated from each other, as illustrated in Fig. 3. Thus, EPDDs are not created in Sc³⁺–Ta⁵⁺ co-doped TiO₂ ceramics.

Figure 3

The lowest energy configurations of (Ti–2Sc–V_o)O₂ triangular shaped complex, (Ti–2Ta)O₂ diamond shaped defect, and triangular and diamond shaped defects of Sc³⁺–Ta⁵⁺ co-doped TiO₂ ceramics.

Influences of Sc³⁺ and Ta⁵⁺ dopants on the dielectric response in TiO₂ materials was explored at ~ 25 °C from 10² to 10⁶ Hz. As displayed in Fig. 4, the ε′ of the 2.5%TTO was very high (10⁴–10⁵), while its tanδ was also very large. Thus, EG-DPs cannot be obtained in the 2.5%TTO ceramic. This result is usually seen in Nb⁵⁺ and Ta⁵⁺ doped TiO₂ ceramics^1,17,26. Alternatively, both the ε′ and tanδ values of the 2.5%STO ceramic were very low, ~ 150 and 0.03, respectively. The dielectric characteristics of the single-doped 2.5%STO ceramic are similar to those reported for acceptor doped TiO₂ ceramics, such as Al³⁺–, In³⁺–, and Ga³⁺-doped TiO₂ ceramics^1,16,17,30. Therefore, the EG-DPs of TiO₂ cannot be accomplished in single-doped Ta⁵⁺ or Sc³⁺. Nevertheless, EG-DPs can be accomplished by co-doping with Sc³⁺–Ta⁵⁺. A high ε′ of 2.4 × 10⁴ with a low tanδ ~ 0.06 was obtained, as shown in the inset of Fig. 4a. According to the first principles calculations, the EG-DPs of Sc³⁺–Ta⁵⁺ co-doped TiO₂ materials are not likely attributable to the EPDDs. The defect clusters associated with the Ta⁵⁺ and Sc³⁺ dopants are not correlated. Therefore, these EG-DPs should be attributed to extrinsic factors such the internal and/or surface barrier layer capacitor (IBLC/SBLC) effects.

Figure 4

(a) Dielectric permittivity (ε′) as a function of frequency at 30 °C for single − doped TiO₂ ceramics (2.5%STO and 2.5%TTO) and co–doped TiO₂ (2.5%STTO) ceramic; inset reveals the ε′ and tanδ values (1 kHz and 30 °C). (b) tanδ as a function of frequency at 30 °C.

To further describe the primary cause of EG-DPs, the effect of co-dopant content on the dielectric characteristics of Sc³⁺–Ta⁵⁺ co-doped TiO₂ materials was further studied. As demonstrated in Fig. 5 and its inset, the ε′ of the Ta⁵⁺–Sc³⁺ co-doped TiO₂ materials increases with the Ta⁵⁺–Sc³⁺ content from 1.0 to 5.0% over a measured frequency range. From frequencies of 10²–10⁵ Hz, the tanδ of the 1.0%STTO material was the largest. Values of tanδ at 1 kHz for the 1.0%SSTO, 2.5%SSTO, and 5.0%SSTO ceramics were 0.22, 0.05, and 0.07, respectively. EG-DPs of the Sc³⁺–Ta⁵⁺ co-doped TiO₂ materials are similar to that found in the (Zn²⁺–Nb⁵⁺)⁴, (Ga³⁺–Ta⁵⁺)¹⁷, (In³⁺–Nb⁵⁺)^1,24,25, (Sc³⁺–Nb⁵⁺)¹⁵, (Al³⁺–Nb⁵⁺)³⁷, and (Ga³⁺–Nb⁵⁺)²⁶ co-doped TiO₂ systems. The IBLC and SBLC models⁴¹ indicated that the giant dielectric response is dependent on the charge carrier density inside the semiconducting portion (semi-P), the C value at the internal interface between the (semi-Ps) and insulating regions (in-Ps). Conductivity and tanδ are dependent on the resistivity of the in-Ps. According to Eq. (2), the free charge concentration in Sc³⁺–Ta⁵⁺ co-doped TiO₂ materials is increased with the Ta⁵⁺ content. Thus, more charge carriers inside the in-Ps trapped at the internal interface of the in-Ps gives rise to significantly increased ε′ value.

Figure 5

Frequency dependence of tanδ at 30 °C for Sc³⁺/Ta⁵⁺ co–doped TiO₂ ceramics with different co–dopant concentrations; inset shows the frequency dependence of dielectric permittivity (ε′) at 30 °C.

Impedance spectroscopy was carried out to further confirm the presence of semi-Ps and in-Ps in Sc³⁺–Ta⁵⁺ co–doped TiO₂ materials. Figure 6a and its inset show impedance complex plane (Z*) plots at ~ 25° and nonzero intercept on the Z′-axis at high-frequencies for Sc³⁺–Ta⁵⁺ co-doped TiO₂ materials compared to that of Ta⁵⁺ single-doped TiO₂. A full semicircular arc was not observed at ~ 25 °C for any of the samples. Only portions of a large semicircular arc are appeared in the Z* plot. The observed large arcs and nonzero intercepts in the Sc³⁺–Ta⁵⁺ co-doped TiO₂ materials indicates the electrical responses of the in-Ps and semi-Ps, respectively⁴². Resistance of the semi-Ps significantly decreased with increasing co-dopant content, from 1.0 to 2.5%, following Eqs. (2) and (3). However, a nonzero intercept was observed in the single-doped 2.5%TTO ceramic. Clearly, a small semicircular arc is observed in this ceramic (inset of Fig. 6b) with relatively large semicircular arcs of the GB and electrode responses. Formation of semi-Ps (grains) in TiO₂ is usually caused by substitution of pentavalent ions, following Eqs. (2) and (3). Alternatively, substitution of Sc³⁺ cannot create semi-Ps, as displayed in Fig. 6c and its inset. Only parts of a large arc are observed with no nonzero intercept. This can be explained by Eq. (1), where $V_{{\text{O}}}^{ \cdot \cdot }$ was created in the single-doped 2.5%STO ceramic, rather than free electrons. A complete large arc can be observed at high temperatures for all co-doped ceramics, as demonstrated in Fig. 6d for the 5.0%STTO material. This result indicates that the resistance of the in-Ps decreases with increasing temperature. According to the impedance spectroscopy, the EG-DPs of the STTO materials should primarily be attributed to extrinsic factors such as the IBLC/SBLC effect.

Figure 6

(a) Z* plots at RT for Ta single–doped and (Sc³⁺–Ta⁵⁺) co–doped TiO₂ ceramics; inset shows an expanded view near the origin. (b) Z* plot of 2.5%TTO ceramics; the blue solid curve is the estimated R_gb value. Inset of (b) illustrates Z* plot close to the origin, showing the electrical response of the semiconducting grains of the 2.5%TTO ceramic. (c) Z* plot of 2.5%STO ceramic at RT; inset demonstrates an expanded view close to the origin, showing zero intercept on Z′ axis. (d) Z* plots at various temperatures for the 2.5%STTO ceramic.

The nonlinear J–E characteristics of the single and co-doped TiO₂ ceramics were investigated at ~ 25 °C. As shown in Fig. 7a, all as-sintered ceramics exhibit nonlinear J–E properties. Their E_b and α values significantly increased with decreasing co-dopant concentration. Surprisingly, the α value of the 1.0%STTO ceramic was very, ~ 1459 V/cm, calculated in the J range of 1–10 mA/cm². The α value of the 2.5%STTO ceramic was also very large, ~ 37.0 V/cm, compared to that of CaCu₃Ti₄O₁₂-based ceramics¹³. Nevertheless, as shown in the inset of Fig. 7a, the E_b and α values of the single-doped 2.5%TTO ceramic were very low (~ 2 V/cm) since there was no acceptor Sc³⁺ dopant in the sample. This result clearly shows the essential role of acceptor-Sc³⁺ dopant ions to form the in-Ps. It is noteworthy that both the E_b and α values of the 2.5%STTO and 5.0%STTO materials were lower than that of the 1.0%STTO ceramic. According to the impedance spectroscopy results, the resistance of the semi-Ps for the 2.5%STTO and 5.0%STTO ceramics was smaller than that of the 1.0%STTO ceramic, indicating that the free charge concentration (N_s) in these two samples is higher than that of the 1.0%STTO ceramic. According to the double Schottky barrier models in polycrystalline ceramics⁴², the potential barrier height at the internal insulating interface (Φ_b) is reduced with increasing N_s in the semi-Ps. The significantly decreased Φ_b values of the 2.5%STTO and 5.0%STTO ceramics may be the primary cause of the decreased E_b values, even though their GB densities were larger than that of the 1.0%STTO ceramic (due to larger average grain sizes).

Figure 7

(a) Nonlinear J–E properties of the 2.5%TTO ceramic and all Sc³⁺/Ta⁵⁺ co–doped TiO₂ ceramics at RT; inset shows J–E characteristics of the 2.5%TTO ceramic before (as-fired sample) and after polishing outer surfaces (polished sample). (b, c) J–E characteristics of the co-doped 1.0%STTO and 2.5%STTO ceramics before and after polishing the outer surface.

According to our previous work²⁷, the E_b value of as-fired InNbTO materials was much larger than that of polished samples. This result indicates that the outer surface layer (or SBLC) of the InNbTO materials had a remarkable impact on its J–E characteristics. Therefore, the effect of the surface layer was studied. We first examined the 2.5%TTO ceramic. These results are shown in the inset of Fig. 7a. The outer surface layer (or SBLC) has an effect on the J–E character of the single-doped 2.5%TTO ceramic. Both the E_b and α values of the as-fired and polished specimens are nearly the same. In other words, an SBLC was not formed on the surface of the as-fired 2.5%TTO ceramic due to the absence of an acceptor dopant. The weak nonlinear J–E properties of the 2.5%TTO ceramic result from the weak effect of the IBLC at the GBs. As illustrated in Fig. 7b and c, after removing the outer surface layer, strong nonlinear J–E properties of the polished 1.0%STTO ceramic were found, with an extremely high α value, ~ 615. However, strong nonlinear J–E properties of the polished 2.5%STTO ceramic were not obtained with a low α value, ~ 2.6. This result clearly shows that the SBLC effect was dominant in the 2.5%STTO and 5.0%STTO ceramics. Unfortunately, it should be emphasized that the nonlinear J–E characteristic of the 1.0% STTO ceramic did not exhibit reversibility following the measurement. While the nonlinear J–E characteristic of the 1.0% STTO ceramic precludes its application in varistor devices, this experiment highlighted the significant role of the outer surface layer in the EG-DPs. Therefore, the EG-DPs (high ε′ and low tanδ) of STTO ceramics are attributed to the SBLC effect. However, if we consider only a high ε′ neglecting a low tanδ, such a high ε′ is caused by the IBLC and sample-electrode interface effects. When the outer surface was removed, a high ε′ could be obtained, while tanδ was also very large. This research provides comprehensive guidance for achieving high-performance giant-dielectric response in co-doped TiO₂ ceramics by inhibiting the formation of non-Ohmic sample-electrode contact via creation of a highly resistive outer surface layer.

Conclusions

Excellent giant dielectric properties with very high ε′ ≈ 2.4 × 10⁴ and low tanδ ≈ 0.05 coupled with strong non-Ohmic properties with high E_b and α were observed in as-fired STTO ceramics. Based on microstructural analysis and first-principles calculations, these two interesting electrical properties were not primarily caused by the IBLC or EPDD effects. Systematically investigated results clearly show that free charges inside a semiconducting inner core or grain interiors of STTO ceramics were induced by Ta⁵⁺ dopant ions. A highly resistive outer surface layer of STTO ceramics, associated with Sc³⁺ dopant ions, was the key factor contributing to the strong non-Ohmic properties and low tanδ values. The GB contribution to the non-Ohmic properties was only observed in the STTO ceramic that was co-doped with 1%(Sc + Ta).