Effect of rare-earth (RE) ionic radius on the dielectric properties of Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals

Abstract

High-performance dielectric materials are essential components of electronic devices. In this work, RE-doped SrTiO₃ (RE = La, Nd, Yb) single crystals with excellent dielectric properties were prepared by the Verneuil method. For La-STO and Nd-STO, the RE ions are substituted for Sr²⁺ only, and the excellent dielectric properties are mainly caused by defect dipoles associated with oxygen vacancies including and defect dipole clusters. For Yb-STO, Yb³⁺ partially replaces Ti⁴⁺, forming an additional defect dipole , resulting in the best dielectric properties (ε′ = 3.6 × 10⁴, tan δ = 0.0036 under 1 kHz). In addition, N₂ atmosphere treatment promotes the production of oxygen vacancies and Ti³⁺ and the formation of more defect dipoles, thus further optimizing the dielectric properties of Yb-STO (ε′ = 4.9 × 10⁴, tan δ = 0.004 under 1 kHz). This work suggests that the dielectric properties of RE-doped SrTiO₃ materials are closely related to oxygen vacancies, and the simultaneous substitution of Sr²⁺ and Ti⁴⁺ should enable obtaining dielectric properties superior to those of the substitution of Sr²⁺ only. The present work provides a clearer understanding of the origin of SrTiO₃ dielectric properties, which is of great significance to the development of SrTiO₃-based dielectric materials.

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1. Introduction

With the rapid development of information technology, especially in the electronics and microelectronics industries, higher requirements are put forward for the performance of dielectric materials.^1,2 How to obtain materials with high dielectric constant, low dielectric loss, good temperature and frequency stability has become an important research direction of dielectric materials.³ Many dielectric materials with colossal permittivity (CP) have been studied, including CaCu₃Ti₄O₁₂ (CCTO),⁴ A_2/3Cu₃Ti₄O₁₂ (A = trivalent rare earth or Bi),^5–7 doped-BaTiO₃,^8–10 doped NiO,^11,12 doped TiO₂^13–16 and doped SrTiO₃.^17–19 However, there are still some specific problems with these materials that limit their practical application. For example, doped BaTiO₃ shows a strong temperature-dependent behavior of the dielectric response,²⁰ while CCTO and NiO are limited in capacitor applications due to high dielectric loss.^21,22

In addition, the exact mechanism and explanation of CP generation are still unclear, which makes it impossible to have a good control of the dielectric properties of materials. Initially, it was thought that a new intrinsic polarization mechanism caused by charge order and/or crystal structure might be related to CP performance.^23,24 Subsequently, a large number of studies have shown that a well-known extrinsic excitation of Maxwell–Wagner (MW) polarization, which is associated with inhomogeneous electrical properties between grains and grain boundaries, can produce CP in some cases.^25–27 More recently, a model of electron-pinned defect dipoles (EPDDs) was proposed in Nb + In co-doped TiO₂ ceramic material.^28–30 According to the EPDD theory, several modified TiO₂ materials do have higher dielectric constant and lower dielectric loss than materials in other systems.^{23,25,28–30} It is well known that the EPDD mechanism is also used in other materials and that the choice of the matrix material has an important influence on the dielectric properties. In addition, defect chemical design has always been an effective method to improve material properties, and an appropriate defect concentration often leads to excellent dielectric properties.

SrTiO₃ (STO) is a favourable dielectric material with low dielectric loss (<0.01). Moreover, STO has better structure stability and dielectric stability than TiO₂.³¹ In the past decades, a number of isovalent ion substitutions in STO ceramics, such as Sr²⁺ in the A-site replaced by Ba²⁺, Ca²⁺ or Pb²⁺, and Ti⁴⁺ in the B-site replaced by Zr⁴⁺, have been widely studied and reported as having preferable enhanced dielectric properties.^32–36 In addition, rare earth oxide (Pr₂O₃, Gd₂O₃, La₂O₃, Nd₂O₃, Y₂O₃, Ce₂O₃, Sm₂O₃) doped STO ceramics have attracted the extensive attention of researchers in recent years due to their unique dielectric properties.^37–43 Although the dielectric properties have been significantly improved, their origin remains unclear. The Maxwell–Wagner polarization initiates the CP behavior of Y-modified STO ceramics.³⁹ Sm-doped STO ceramics sintered in N₂ atmosphere obtained colossal permittivity and low dielectric loss, interpreted as a result of the production of the electron-pinned defect dipoles.⁴⁰ The EPDD effect leads to the improvement of the dielectric properties of Nd-doped STO ceramics.⁴² Sr vacancies and Ti vacancies are considered to be the origin of the CP properties of La-doped STO ceramics.⁴³ The main factors resulting in CP behavior are defect dipoles that come in contact with O vacancies for Ho-doped STO ceramics.⁴⁴ Previous studies have mostly focused on STO ceramics, which contain defects such as grain boundaries and porosity, so their dielectric properties are particularly sensitive to the preparation process, and there are few studies on STO single crystals, especially STO single crystals doped with rare earth elements of different sizes. The influence of doping rare earth atoms on dielectric properties is not well understood due to the existence of inhomogeneous microstructures such as grain boundaries and pores in ceramics. To better explore the origin of dielectric properties of STO materials and the effect of rare earth element doping, it is increasingly significant to study the dielectric properties of rare earth-doped STO single crystals. In addition, fewer defects in crystals result in lower dielectric loss.⁴⁵

In this work, Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals were prepared by the Verneuil method and their dielectric properties were studied. Doping with different sizes of rare earth elements can produce different types of defects, resulting in different dielectric properties. Understanding the relationship between the sizes of the doped rare earth elements and the dielectric properties, while excluding the interference of grain boundaries and porosity, is important for the development and design of STO-based CP materials.

2. Experimental

Previously, we have prepared La_xSr_1−xTiO₃ (x = 1%, 3%, 5%, 8%) single crystals by the Verneuil method. It was found that when the doping amount reached 8%, it was difficult to obtain a stable solid–liquid interface. When the doping amount was 5%, although crystal growth could be achieved, serious crystal cracking occurred. When the doping amount was 3%, slight cracking was found. Thus, in the present experiment, a doping amount of 1% was chosen. SrTiO₃ and Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) powder was prepared by the traditional solid-state method using rutile TiO₂ (Aladdin, 99.99%), SrCO₃ (Aladdin, 99.99%), Nd₂O₃ (Aladdin, 99.99%), Yb₂O₃ (Aladdin, 99.99%) and La₂O₃ (Aladdin, 99.99%) as the starting materials. Subsequently, crystals with different compositions were grown by the Verneuil method. The schematic diagram of the device is shown in Fig. 1a. The crystal growth was carried out by using a two-channel burner, in which the central hole is O₂ and the outer ring is H₂. A 3 mm × 3 mm × 10 mm crystal column with the (200) crystal face as the growth plane was used as seed crystal. The crystal was grown at a rate of 14 mm h⁻¹. The process is shown in Fig. 1b. First, the furnace was ignited using the parameters H₂ 16 L min⁻¹ and O₂ 6.4 L min⁻¹. After the chamber was preheated, a seed crystal was placed and gradually raised to the observation hole position. Second, the O₂ flow rate was gradually increased until the top of the seed crystal melted, then the feeding system and crystal dropping device were turned on. Third, the powder melt fell on the seed crystal, and when a clear solid–liquid interface appeared, the H₂ and O₂ flow rates were increased simultaneously and the crystal started to expand its shoulder. Fourth, after the crystal grew to the desired size, the H₂ and O₂ flow rates were kept constant to maintain the crystal isometric growth. Finally, when the crystal grew to the ideal length, the gas valve and feeding system were closed, and the furnace was insulated to prevent cracking of the crystal caused by rapid cooling. During the whole process, the feed rate and crystal drop rate need to be controlled to keep the crystal dropping slowly, and the horizontal position of the crystals needs to be adjusted at all times to maintain a stable solid–liquid interface (see Fig. S1†). The grown crystals were annealed for a long time in a muffle furnace to eliminate the thermal stress formed during growth, and the specific annealing process is shown in Fig. S2.† The annealed crystals were cut into 10 mm × 10 mm × 2 mm slices using a diamond wire (STX-202A) after orientation determination. The cut wafers were defined as STO, La-STO, Nd-STO and Yb-STO. Subsequently, Yb-STO was annealed under N₂ atmosphere at 1400 °C for 4 h, and it was recorded as N₂-Yb-STO.

Fig. 1 (a) Schematic diagram of the equipment. (b) Diagram of the growth process. (c) STO crystal after long annealing.

The phase composition and crystal structure were examined by X-ray diffraction (XRD, Rigaku SmartLab, CuK_α) and Raman spectroscopy (Horiba Jobin Yvon). The co-doped crystals were observed by scanning electron microscopy (SEM, Ultra Plus, ZEISS) combined with EDS after thermal etching at 1300 °C for 2 h. Transmission electron microscopy (TEM, JEOL JEM-2100F TEM) was used to characterize the detailed microstructure of the sample. X-ray photoelectron spectroscopy (XPS, Shimadzu Kratos Analytical, UK) was adopted to detect the valence states of elements. A layer of Ag was coated on the specimens by screen printing and sintered at 700 °C for 10 minutes. The dielectric behaviors and the impedance spectra at room temperature and high temperatures were measured using an electrochemical impedance spectrometer (TH 2839) equipped with a heating device.

3. Results and discussion

The annealed doped crystals are all similar to that shown in Fig. 1c. Even after a long time of annealing, the crystals remain black, indicating that they still contain oxygen vacancies and Ti³⁺. Fig. S3a† shows the XRD pattern of SrTiO₃ and Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) powders synthesized by the solid phase method. All samples show the pure perovskite structure and no secondary impurity phases can be detected, indicating that the RE elements have successfully entered the perovskite lattice. Fig. S3b† presents a detailed view of the (110) diffraction peak. It can be seen that the change in peak position is easily observed relative to pure STO. The (110) diffraction peak shifts to a larger angle with the addition of La³⁺ and Nd³⁺ ions because the ionic radii of La³⁺ (1.36 Å, C.N. = 12)⁴⁶ and Nd³⁺ (1.27 Å, C.N. = 12)⁴⁷ are smaller than that of Sr²⁺(1.44 Å, C.N. = 12),⁴⁸ demonstrating that La³⁺ and Nd³⁺ have substituted for Sr²⁺ ions. In contrast, the smallest Yb³⁺ ions instead make the (110) diffraction peak shift to a lower angle. This indicates that the substitution of Yb³⁺ for Ti⁴⁺ occurs in Yb-STO. This phenomenon has been previously reported^49,50 due to the fact that the ionic radius of Yb³⁺ (0.868 Å) is smaller than that of Sr²⁺ (1.44 Å) but larger than that of Ti⁴⁺ (0.605 Å) and closer to Ti⁴⁺.

Fig. 2a shows the XRD patterns of SrTiO₃ and Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals. They all maintain a (200) crystal orientation, which proves that we successfully obtained high-quality crystals. In order to obtain the crystal lattice constants, the block crystals were ground into powder, and the XRD patterns of the powder were tested. Fig. 2b and c show the Rietveld refinement results for La-STO and Nd-STO with pure STO cubic structure. The lattice parameters calculated from Rietveld refinement profile fits are 3.902 Å and 3.898 Å, respectively, slightly lower than the standard value of STO (3.904 Å) (ICSD-94573). The decrease of the lattice size could be attributed to the smaller ionic radii of La³⁺ and Nd³⁺ that occupy the position of Sr²⁺. Fig. 2d shows the Rietveld refinement result of Yb-STO, and its lattice constant was calculated to be 3.907 Å, which again confirms that some of the Yb³⁺ replace Ti⁴⁺, resulting in a larger lattice constant.

Fig. 2 (a) XRD patterns of STO crystals. (b)–(d) Rietveld refinement results for Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals, respectively.

Fig. S4† shows the SEM images of Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals. All the samples show a smooth surface, and energy-dispersive X-ray spectroscopy shows that the elements are evenly distributed and there is no element segregation, indicating that we have obtained high-quality crystals, thus excluding the influence of grain boundaries, pores and second-phase structures on subsequent dielectric properties. In order to better determine the integrity of the crystals, high-resolution images of Nd-STO under TEM were observed as an example. Fig. S5† shows the HRTEM images of the Nd-STO single crystals, indicating that the crystals are relatively perfect. Selected area electron diffraction (SAED) patterns also confirm the good crystallinity of the Nd-STO single crystal. The EDS elemental distribution maps of the low-magnification TEM images indicate that the composition of the Nd-STO crystals is homogeneous.

Raman spectroscopy is an effective method to study the local structure symmetry and chemical bond changes of materials. As shown in Fig. 3, the Raman spectra of crystals before and after doping show the same trend, indicating that they belong to the same crystal space group.⁵¹ SrTiO₃ crystals with ideal cubic structure will not generate first-order Raman modes at room temperature, but due to the existence of defects, the symmetry is relaxed and these prohibited first-order scattering modes will be activated. In our case, all samples have two strong scattering bands in the range of 220–400 cm⁻¹ and 600–750 cm⁻¹, which is a classical cubic second-order Raman mode,⁵² and the Raman peak at about 300 cm⁻¹ is an in-plane vibrational mode of the oxygen sublattice (B₁ mode).⁵³ Compared with the Raman peak of the SrTiO₃ crystal (303.2 cm⁻¹), the Raman peaks of the La, Nd, and Yb doped crystals are shifted to 309.5 cm⁻¹, 308.4 cm⁻¹ and 306.3 cm⁻¹, respectively. The change in Raman peak position is related to the non-centrosymmetric Jahn–Teller distortion due to the accumulation of oxygen ions.^54,55 Larger shifts correspond to larger distortion, and it can be seen that Yb doping causes the largest distortion. In addition, two weak scattering peaks of the doped crystal near 538 cm⁻¹ and 793 cm⁻¹ can be assigned to the TO₄ mode and LO₄ mode, respectively, which are caused by surface oxygen vacancies or higher polarity defects.⁵⁶ Moreover, a weak scattering peak (873.2 cm⁻¹) sensitive to the B site is observed in Yb-STO, indicating that the Ti⁴⁺ ion shares the B site with Yb³⁺ and causes a change in the Ti–O structure, confirming that Yb³⁺ may replace some Ti⁴⁺.⁵⁷

Fig. 3 Room-temperature Raman spectra of the STO single crystals with different doping.

The dielectric properties of STO single crystals before and after doping are shown in Fig. 4a. All crystals exhibit frequency-independent dielectric properties. The dielectric constant of doped crystals is more than 2 × 10⁴, which is two orders of magnitude higher than that of undoped STO crystal, and the dielectric constant increases with the decrease of doped ion radius. Although the dielectric loss of doped crystals is slightly higher than that of the undoped STO crystal, it is still less than 0.015. The best dielectric properties are obtained in Yb-STO, with a dielectric constant of 3.6 × 10⁴ and dielectric loss of 0.0036 at 1 kHz. Fig. 4b shows the temperature dependence of the dielectric constant and dielectric loss of doped crystals at 1 kHz. The dielectric properties of all samples show good thermal stability over a wide temperature range (25–310 °C). The dielectric constant of all samples decreases slowly with the increase of temperature and begins to increase rapidly at about 350 °C, while the dielectric loss increases slowly at first and then sharply with the increase of temperature. In brief, the dielectric properties of the doped crystals have been significantly improved. However, there are still differences among these samples, indicating that the difference of doping ions has an important influence on the dielectric properties of STO single crystals.

Fig. 4 (a) Frequency dependence and (b) temperature dependence (1 kHz) of permittivity and dielectric loss for STO single crystals with different doping.

In order to explore the effect of different doping ions on the dielectric properties of STO single crystals, we use complex impedance analysis to establish the relationship between the micro-structure and the electrical properties.⁵⁸Fig. 5 shows the impedance spectra of Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals at various temperatures. The presence of non-zero intercepts at high frequencies is not observed in any of the samples, again confirming that no grain boundary effects are responsible for the excellent dielectric properties. Considering the possible influence of weak electrode effects, the circuit diagram shown in Fig. 5d is used for fitting,⁵⁹ where R_b, R_e, C_b and C_e represent bulk resistance, electrode contact resistance, bulk capacitance and electrode contact capacitance, respectively. The fitted results show that Yb-STO has the largest resistance value. This is because the replacement of Sr²⁺ by trivalent rare earth dopant ions introduces excess electrons, while Yb³⁺ doping partially replaces Ti⁴⁺ and reduces the number of free electrons. R_b decreases with increasing temperature for all samples, indicating that this is a thermally activated process, and E_a can be calculated by the Arrhenius law:⁶⁰

where σ₀ is a pre-exponential term, E_a is the activation energy, k_B is the Boltzmann constant, and T is absolute temperature (K). The activation energies of La-STO, Nd-STO and Yb-STO single crystals are 0.073 eV, 0.075 eV and 0.087 eV, respectively, which are comparable to the activation energies of conductivity caused by bound electrons, again excluding the effect of grain boundary effects.⁶¹ La-STO and Nd-STO single crystals exhibit similar activation energies, which is due to the same doping concentration and close number of free electrons. However, the activation energy of the Nd-STO single crystal is slightly larger due to the greater distortion caused by the substitution of Nd³⁺ for Sr²⁺, which has a greater effect on electron binding. The Yb-STO single crystal exhibits the maximum activation energy which, on the one hand, is due to the partial substitution of Yb³⁺ for Ti⁴⁺ that reduces the number of free electrons, and on the other hand, is due to the substitution of Yb³⁺ doping for both Sr²⁺ and Ti⁴⁺, which form more complex defects, and has a stronger effect on free electron binding.

Fig. 5 Impedance spectra of Sr_99%RE_1%TiO₃ single crystals at various temperatures: (a) La-STO, (b) Nd-STO and (c) Yb-STO. Insets are dc conductivity activation energy fitted by the Arrhenius equation. (d) Equivalent circuit diagram.

After excluding the effect of grain boundaries on the dielectric properties, considering that the interfacial polarization associated with the electrodes may be responsible for the improvement of the dielectric properties, the dielectric constants of Sr_99%RE_1%TiO₃ single crystals were tested at different voltages. If the interfacial effects associated with the electrodes have an effect on the dielectric properties, the dielectric constant will increase sharply at low frequencies with increasing DC bias because the barrier height between the heterogeneous interfaces becomes asymmetric.⁶² As shown in Fig. 6, the dielectric constants of all samples remained stable under different voltages, indicating that the interfacial effects associated with the electrodes is not the main cause of the improved dielectric properties.⁶³

Fig. 6 Frequency-dependent dielectric properties measured under different DC bias voltages for Sr_99%RE_1%TiO₃ single crystals: (a) La-STO crystal, (b) Nd-STO crystal and (c) Yb-STO crystal.

Another reason for the improved dielectric properties is the defect associated with oxygen vacancies. In order to investigate the structure of defects associated with oxygen vacancies, Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals were analyzed using XPS. The XPS spectra and corresponding fitting results of Ti 2p and O 1s are displayed in Fig. 7. The presence of Ti³⁺ and oxygen vacancies is detected in all samples. The peaks at about 458.0 eV and 463.8 eV represent Ti⁴⁺, and the peaks at about 456.2 eV and 462.3 eV represent Ti³⁺.⁴² Additionally, the peaks at about 529.2 eV represents the Ti–O bond, the peak at about 529.8 eV represents the oxygen vacancy, and the peak at about 531.2 eV represents the H₂O of the adsorbed surface.^64,65 It was obvious that the content of Ti³⁺ and oxygen vacancies increases as the radius of doped ions decreases. For La-STO and Nd-STO single crystals, the trivalent Re atoms mainly replace Sr²⁺, introducing an extra electron which is responsible for the charge transfer from Ti⁴⁺ to Ti³⁺, as shown in the following equations:

The Nd-STO single crystal can cause greater lattice distortion and thus increase the number of defects, resulting in a slightly higher Ti³⁺ and oxygen vacancy content. As for the Yb-STO single crystal, on the one hand, the trivalent Yb³⁺ atom replaces Sr²⁺ and introduces excess electrons, making Ti⁴⁺ convert to Ti³⁺, and on the other hand, the trivalent Yb³⁺ replaces Ti⁴⁺, requiring oxygen vacancies to compensate for the charge. In addition, lattice oxygen will overflow to form oxygen vacancies at high temperature, as shown in the following equations:

Ti⁴⁺ + e⁻ → Ti³⁺ (6)

The greater difference in ionic radii between Yb³⁺ and Sr²⁺ will cause greater lattice distortion, resulting in more Ti³⁺ and oxygen vacancies. In addition, as some Yb³⁺ replaces Ti⁴⁺, some Sr vacancies will be formed. In La-STO and Nd-STO single crystals, point defects such as , and are present, and in the Yb-STO single crystal, the point defects should be , , , and . These differences cause the different polarizations and thus the difference in dielectric properties.

Fig. 7 XPS results of Ti and O in Sr_99%RE_1%TiO₃ single crystals: (a) and (d) La-STO crystal, (b) and (e) Nd-STO crystal, and (c) and (f) Yb-STO crystal.

By studying the dielectric properties at different temperatures, the polarization process can be clearly understood. The temperature-dependent dielectric spectra are shown in Fig. 8. The dielectric constant of all samples show a similar response with temperature, decreasing and then increasing with increasing temperature over the measurement range. The dielectric loss of all samples remained below 0.1 in the range of room temperature to about 280 °C over the measured frequency range. A set of relaxation peaks can be observed for all samples in the range of 70 °C to 250 °C, and the peaks move towards high frequencies with increasing temperature, indicating a thermally activated process. The activation energy can be calculated by the Arrhenius-type equation:

where E_a is the activation energy, f₀ is a constant, k_B is the Boltzmann constant, T is absolute temperature (K). f can be obtained at the relaxation peak of tan δ. The relaxation activation energies of 0.73 eV and 0.72 eV for La-STO and Nd-STO single crystals, respectively, are close to the second-order ionization energy of V˙˙, indicating that this relaxation behavior is due to defects associated with oxygen vacancies.^38,66 Considering the type of point defects present in the samples, this relaxation may be related to the defect dipole clusters and defect dipole clusters. The Yb-STO single crystal exhibits a larger activation energy of 0.89 eV, which is caused by the coupling of and to form a new defect dipole cluster in addition to and defect dipole clusters. Meanwhile, the presence of the defect dipole cluster enables the Yb-STO single crystal to obtain better dielectric properties.

Fig. 8 Temperature dependence of dielectric properties and plot of ln f versus 1000/T for Sr_99%RE_1%TiO₃ single crystals with RE = La (a–c), RE = Nd (d–f), and RE = Yb (g–i).

The Yb-STO single crystal with better dielectric properties was selected to study the dielectric properties after N₂ annealing. As shown in Fig. 9, the dielectric constant of N₂-Yb-STO has improved significantly, increasing by 34% compared to Yb-STO, and lower dielectric loss was obtained in the high frequency. At the same time, good frequency stability and temperature stability are maintained. The XPS spectra of Ti 2p and O 1s of N₂-Yb-STO and their fitting results are shown in Fig. 10. The presence of Ti³⁺ and oxygen vacancies can be clearly observed, and their content has increased significantly compared to that before N₂ annealing.⁶⁷ This indicates that the enhancement of dielectric properties of the N₂-Yb-STO single crystal is closely related to the oxygen vacancy concentration. The N₂-Yb-STO crystal contains more oxygen vacancies, Ti³⁺ and other point defects, and they couple with each other to form defect complexes or clusters, which can greatly increase the dielectric constant. At the same time, these defect clusters can better localize the electrons, thus obtaining a lower dielectric loss.

Fig. 9 (a) Frequency dependence and (b) temperature dependence (1 kHz) of permittivity and dielectric loss for N₂-Yb-STO and Yb-STO single crystals.

Fig. 10 XPS results of (a) Ti and (b) O in the N₂-Yb-STO single crystal.

Fig. 11 illustrates the mechanism of obtaining excellent dielectric properties of RE-doped STO single crystals. For La-STO and Nd-STO, the excellent dielectric properties are mainly caused by defects associated with oxygen vacancies including defect dipole clusters and defect dipole clusters. These defects generate an electron pinning effect, which localizes free electrons and hinders their long-range transition. For the Yb-STO crystal, in addition to these defect dipoles, new defect dipoles are formed, and these defect dipoles work together to obtain superior dielectric properties. In addition, annealing under N₂ atmosphere promotes the production of oxygen vacancies and Ti³⁺, forming more defect dipoles, thus further optimizing the dielectric properties.

Fig. 11 Mechanism of obtaining excellent dielectric properties:(a) La-STO crystal, (b) Nd-STO crystal and (c) Yb-STO crystal.

4. Conclusions

Sr_99%RE_1%TiO₃ (RE = La, Nd, Yb) single crystals were prepared by the Verneuil method and their dielectric properties were studied. For the La-STO and Nd-STO crystals, the RE ions are substituted for Sr²⁺ only, and the excellent dielectric properties are mainly caused by defect dipole associated with oxygen vacancies, including and defect dipole clusters. Lattice distortion of the Nd-STO crystal is larger than that of the La-STO crystal, and thus the amount of defects is larger, resulting in better dielectric properties. For the Yb-STO crystal, some Yb³⁺ replaced Ti⁴⁺, forming an additional defect dipole , resulting in the best dielectric properties (ε′ = 3.6 × 10⁴, tan δ = 0.0036 under 1 kHz). In addition, annealing under N₂ atmosphere promotes the production of oxygen vacancies and Ti³⁺, forming more defect dipoles, thus further improving the dielectric properties. This work suggests that the dielectric properties of RE-doped SrTiO₃ materials are closely related to oxygen vacancies and that the simultaneous substitution of Sr²⁺ and Ti⁴⁺ may be able to obtain superior dielectric properties compared to the substitution of Sr²⁺ only. This is of great significance to the development of SrTiO₃-based dielectric materials.

Author contributions

W. L. designed and performed the experiment with the help of S. X. D. and M. Z. X. B. X. G. and L. X. D. provided help with crystal growth. Z. M. and L. J. S. provided help with property testing. W. L. wrote the manuscript with the help of S. X. D and C. J. L. S. X. D., C. J. L. and L. J. S. provided financial support for the whole experiment. All authors have approved the final version of the manuscript.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the Projects of the National Natural Science Foundation of China (No. 51872033 and No. 51732007), the Project of the Natural Science Foundation of Liaoning Province (No. 2019-ZD-0572), the Natural Science Foundation of Hebei Province (Grant No. E2021501017), the Young Talents Program of Hebei Province (Grant No. BJ2020202), and the Fund of the State Key Laboratory of Advanced Technologies for Comprehensive Utilization of Platinum Metals (SKL-SPM-202016 and SKL-SPM-202019).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2ce01278b

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