Complex impedance and electrical conduction analysis of Ho2O3 doped CaCu3Ti4O12 NTC ceramics

ABSTRACT The structure and electrical properties of CaCu3Ti4O12 (CCTO) ceramics doped with xHo2O3 synthesized by solid-phase reaction method were systematically studied. Insights from X-ray diffraction (XRD) measurements indicate the existence of a primary phase of CCTO in all samples. Ho2O3 dopant was found to inhibit grain growth and thus leading to a reduced grain size of ceramics. Moreover, the distribution of resistivity with temperature revealed the manifestation of a negative temperature coefficient (NTC) effect in the samples. More specifically, the resistivity (ρ 20) values of obtained ceramics configurations decreased from 8.54 × 106 to 1.76 × 105 Ω cm with increasing Ho2O3 doping content. In addition, thermal constant (B 20/75) of all samples was higher than 4000 K. Electrical properties analysis disclosed that electron hopping process is main conduction mechanism within CCTO-based ceramics. In addition, insights from complex impedance spectra revealed the existence of grain boundaries with resistance higher than grains resistance. This effect is strongly connected with the manifestation of electrical relaxation procedures within grain boundaries. Our outcomes verify that both the structural configuration and the electrical performance of the CCTO-based ceramics can be tuned directly and effectively by incorporating Ho2O3 dopant.


Introduction
NTC thermistor is a type of important electronic component due to its functional characteristic since its resistivity reduced by elevating the temperature. Such types of materials are widely used in temperature control and in-situ measurement of mechanical devices. Traditional NTC thermistors exhibit the spineltype (AB 2 O 4 ) structure that mainly consists of transition metal elements (such as Mn, Co, and Ni et al.) [1][2][3].
The performance of NTC thermistors is determined by two quite important parameters: the electrical resistivity (ρ) and the thermal constant (B). However, spinel-type NTC thermistors display relative high B values that are always coupled with higher ρ and vice versa, which is detrimental for their applications [4]. Additionally, they exhibit poor electrical stability due to the decomposition-related processes of the spinel structure, which induced serious problems during the device operation at temperatures above 300°C [5]. The abovementioned issues render imperative the need to explore new NTC thermistor configurations with good stability and suitability for a wide temperature range. Along these lines, ceramics with perovskite structure (ABO 3 ) arise as a promising solution since they exhibit good structural stability due to the reduced cations interchange rates at high temperatures [6]. Such types of materials with perovskite structure including Bi 0.2 Sr 0.5 La 0.3 TiO 3 [6], YCr 0.5 Mn 0.5 O 3 [7], BaBiO 3 [8], Bi 0.5 Ba 0.5 FeO 3 [9], CCTO [10] exhibit also distinct NTC characteristics and as a result have been extensively studied in recent years.
As far as the CCTO-based ceramics are concerned, the inherent colossal dielectric permittivity ε′ values (approximately 10 4 -10 5 ), as well as the excellent nonohmic properties, render them promising candidates for capacitors with high dielectric constant and protection against overvoltage events [11]. In general, the internal barrier layer capacitor approach is suitable for interpreting the anomalous dielectric behavior of the CCTO-based ceramics [12][13][14]. Although CCTO ceramics exhibit huge ε′ values, the high loss tangent (tanδ) limits their widespread applications. Moreover, numerous synthesis processes have been considered in order to optimize the dielectric characteristics of CCTO-based ceramics, such as sol-gel deposition [15] and spark-plasma sintering [16]. Additionally, high dielectric constant and low loss were obtained in similar material configurations by doping single Zn 2+ ion or (Y 3+ , Mg 2+ ) and (Zr 4+ , Nb 5+ ) ion pair [17][18][19]. Thus, the local microstructures and electrical properties of CCTObased ceramics can be significantly regulated by the doping approach.
Meanwhile, the semiconducting and the impedance performance of CCTO ceramics have been also preliminarily studied. The impedance spectrum for CCTO ceramics reveals that the grain exhibits a semiconductivity pattern, while the grain boundary possesses insulating properties [20]. This implies this type of material displays a certain conductivity pattern within a specific temperature range. The established conduction mechanism model of CCTO-based ceramics stems from the cation-related non-stoichiometry theoretical approach, proposed by Li et al. [21]. Considering that CCTO ceramics behave as n-type semiconductors by assembling a big amount of available free electrons in the conduction band, renders them attractive for active material within the NTC thermistors. In addition, the electrical performance of CCTO ceramics can be tuned directly by following a doping strategy with Zr, La, Y and Mn, as was reported by B. Zhang et al. [22][23][24].
Although the implementation of the NTC effect by employing CCTO ceramics has been previously reported, a detailed study of the underlying conduction mechanisms is still missing. In this work, we present a thorough study on the doping effect of CCTObased ceramics with Ho 2 O 3 and the concomitant impact on the local microstructure and electrical properties. In addition, fruitful insights are attained by elaborating on the physical conduction mechanisms, whereas the impedance spectroscopy studies divulged the role of the electrical relaxation effects on the total conduction pattern.

Experimental procedures
In order to fabricate the xHo 2 O 3 -(1-x)CCTO (x= 0, 0.01, 0.03, 0.05) ceramics through the solid-phase method the following starting powders were used: CaCO 3 (99%, Sinopharm), TiO 2 (98%, Sinopharm), CuO (99%, Sinopharm), Ho 2 O 3 (99%, Aladdin). The starting powders were weighed stoichiometrically and subsequently ball-milled for 16 h by using alcohol as grinding media. Afterward they were dried and calcined at 850°C for 6 h. The calcined mixtures were ballmixed for 16 h and powders were pressed into disks of 15 mm in diameter with PVA. Subsequently, the disks were sintered at 1100°C for 2 h after removing the binder at 610°C. Finally, the silver paste coated on the surface of the polished samples was thermal annealed at 620°C for 20 min.
The phase structure of the Ho-CCTO ceramics was characterized by performing 2θ scanning from 20° to 70° by using an X-ray diffractometer (Ultima IV, Rigaku Co., LTD, Japan). Field-emission scanning electron microscopy (SEM, Zeiss, merlin compact, Germany) was employed to perform the morphology of the surface and fracture, while the elemental distribution was detected by carrying out energy-dispersive X-ray spectroscopy (EDS, IE250X-Max50, Oxford, UK). X-ray photoelectron spectroscopy (XPS, K-Alpha+, Thermo fisher Scientific, USA) measurements were carried out to determine the valence state of the elements. Electrical resistance measurements were conducted within the temperature from 20°C to 300°C by a multimeter (Keithley Instruments Inc., USA) with a heat source. In addition, the dielectric characteristics, modulus and complex impedance distributions of all samples were examined by employing the Broadband Dielectric/Impedance Spectrometer (Concept80, Novocontrol Inc., Germany).  Figure 1(a) can be matched with the standard CCTO configuration (JCPDS 75-2188), indicating that all samples possess a pure perovskite structure with a space group of Im-3 [25]. As it is depicted in Figure 1(b), the (220) diffraction peak of the xHo 2 O 3 -(1-x)CCTO ceramics shift toward to higher angles with increasing Ho 2 O 3 addition, indicating that the occupation of Ca 2+ (0.99 Å) by Ho 3+ (0.901 Å). The extracted analysis reveals that Ho 3+ ions have fully entered the CCTO lattice as x ≤ 0.03; however, the (220) diffraction angle is not increasing further more for the xHo 2 O 3 -(1-x)CCTO ceramics as x > 0.03. This result indicates that the doping amount of Ho 2 O 3 is not larger than 0.03. Figure 2 depicts the SEM micrographs for the xHo 2 O 3 -(1-x)CCTO ceramics. The results signify that the microstructures of the pure CCTO and Ho 2 O 3 doped samples are significantly different. Moreover, it can be observed that coarse grains are embedded within smaller grains matrix in the pure CCTO ceramic, which could be related to its liquid phase sintering mechanism at high temperatures [26]. In addition, the inhibitory effect of the Ho 2 O 3 -based doping on the abnormal grain growth effect of the host ceramic can be also observed. A declined trend of the average grain size and a more uniform distribution can be detected by increasing the Ho 2 O 3 concentration, which could originate from the implementation of the solute drag mechanism [27]. Zn/Al doping has a similar effect on CCTO-based ceramics [28]. A detailed analysis of the elemental distribution of 0.03Ho 2 O 3 -0.97CCTO samples is presented in Figure 3, where the samples' fracture section was taken into account. Additionally, the relevant intensity profile shows the characteristic peaks of Cu, Ca, Ti and Ho detected with no additional peak as an impurity phase. The EDS analysis results of section profiles revealed the homogeneous distribution of the following elements: Ca, Ti, Cu, O and Ho, which confirm the stoichiometric nature of the sintered sample. Figure 4 reveals the DC resistivity vs. temperature plot of the xHo 2 O 3 -(1-x)CCTO ceramics. Table 1 lists the detailed resistivity values at 20°C (ρ 20 ) and 75°C (ρ 75 ). An exponential decrease of resistivity as a function of the temperature can be confirmed, indicating the manifestation of the typical NTC response. As can be ascertained from Table 1, the resistivity values ρ 20 decreased from the value of 8.54 × 10 6 to 1.76 × 10 5 Ω cm by enhancing the doping amount of Ho 2 O 3 . The resistivity distribution pattern of the NTC ceramics can be interpreted by considering the impact of both grain size and carrier concentration [9]. More specifically, from the SEM analysis, it can be concluded that elevating the Ho 2 O 3 doping concentrations makes the grain size distribution more uniform. The grain size in pure CCTO presents a bimodal distribution, with large grains surrounded by small grains. Simultaneously, smallsized grains occupy a larger proportion of the number. The inhomogeneous microstructure in the pure CCTO ceramic could accelerate the electron scattering events in the grain boundary area, resulting thus in a higher resistivity value [29]. Furthermore, Ho 2 O 3 could also play the role of donor dopant and introduce electrons into the system through the following reaction:

Results and discussion
Ho � Ca þ e 0 . As a result, an elevated carrier concentration will be attained which lowers the energy barrier height for electron hopping and induce the resistance to decrease. Similar results have been reported regarding the modification of the electrical properties in CCTO-based ceramics with Y 3+ doping [22]. Figure 5 shows the distribution between ln ρ and 1000/T for the xHo 2 O 3 -(1-x)CCTO ceramics. The linear relationship between them indicates the manifestation of a thermally activated conduction process of carriers that can be well fitted by Arrhenius expression: where ρ 0 , k and T represent the inherent factor of material, the Boltzmann constant and the absolute temperature, respectively. doped CCTO-based ceramics from 0.5346 to 0.3845 eV by increasing the doping content, which probably originates from the elevated concentration of charge carriers. As far as the NTC thermistors are concerned, the B value is also a quite important parameter that reflects their sensitivity within a certain temperature range. B 20/75 can be obtained according to the equation: As can be ascertained from  Figure 5, indicate that Ho 2 O 3 modified CCTO ceramics is a great candidate for temperature control applications within a wide-temperature range.   XPS was used in order to clarify the valence states of various elements in the ceramics, and the XPS spectra of Cu 2p, O 1s and Ti 2p of xHo 2 O 3 -(1-x)CCTO ceramics illustrated in Figure 6(a-c). Figure 6(a) depict the highresolution XPS spectra of Cu 2p, while by employing Gaussian-Lorentzian profile fitting, the peak of Cu 2p 3/2 can be individually resolved into two components and attributed to the existence of Cu 2+ and Cu + [31]. Moreover, as can be observed from Figure 6(c), the Ti 2p 3/2 signal can be well fitted by considering the manifestation of two peaks, which signify the existence of Ti 4+ and Ti 3+ [15]. More importantly, the peak fitting results show that the concentration percentages of Cu + and Ti 3+ increase with the increase of Ho 2 O 3 doping content. The increase of electron carriers promotes the conversion of Cu 2+ to Cu + and Ti 4+ to Ti 3+ . By considering the chemical environment of the detected signal of O 1s (Figure 6(b)), the fitting peaks are assigned to both lattice oxygen with low binding energy and oxygen vacancy with high binding energy. Similar to other perovskite structure compounds, the creation mechanism of oxygen vacancies in CCTO ceramics is associated with the oxygen deficiency in making ceramics [32]. Additionally, it can be observed that the oxygen vacancy concentration decreases when x = 0.05, which may be due to excessive Ho 2 O 3 doping inhibiting oxygen deficiency.
According to the literature [4], the conduction mechanisms of thermistors are closely associated with electron hopping processes between different valence states that are induced by the cations' formation. The coexistence of the following cations: Cu 2 + /Cu + , Ti 4+ /Ti 3+ in XPS analysis verifies this assumption, which are prerequisites for the hopping-based electron transport. Li et al. [21] reported that in terms of CCTO-based ceramics with semi-conducting characteristics, double-charged Cu 2+ cations will be reduced to single charged Cu + during the sintering process, while the loss of charge is compensated by Ti 4+ occupying Cu site, which resulting in the creation of the following formula: On the other hand, the electrons in the Cu + state will hop to the Ti 3d orbit and reduce part of Ti 4+ to Ti 3+ as the cooling process occurs, which can be described by: Cu + +Ti 4 + →Cu 2+ +Ti 3+ . Due to Ho 2 O 3 doping will induce the creation of more electrons, which can trigger the subsequent reactions: Cu 2+ + e′ → Cu + , Ti 4+ + e′ → Ti 3+ . XPS results show that Ho 2 O 3 doping increases the Cu + and Ti 3+ concentration, thus an enhanced concentration of heterovalent ion pairs is anticipated to take place that could significantly influence the electrical conduction process. This assumption is consistent with the observed result that the monotonous decrease of the measured resistivity values by increasing the concentration of Ho 2 O 3 . Figure 7(a-d) shows the frequency dependent dielectric constant (ε′) of the xHo 2 O 3 -(1-x)CCTO ceramics measured at various temperatures. The slight decreases of ε′ value with the increase of frequency can be ascertained. The space charge polarization effect causes dielectric dispersion in the low frequency zone (< 10 3 Hz), which could lead to a relatively high value of ε′. However, the step-like decrease of ε′ by elevating the temperature indicates the thermally activated dielectric relaxation process [31]. The presence of the dielectric relaxation phenomenon within the measured frequency range (1-10 6 Hz) can be interpreted by considering the Maxwell-Wagner polarization effect [33], which is caused by the electrical inhomogeneity of the charge carriers of xHo 2 O 3 -(1-x)CCTO ceramics. Furthermore, the ε′ value in the low-frequency zone (< 10 3 Hz) slightly decreases by elevating the temperature, which could be assigned to the weak electrical inhomogeneity caused by the grain boundary resistance (R gb ) being comparable to the grain resistance (R g ) [34].
The ε′ and tan δ as functions of frequency of xHo 2 O 3 -(1-x)CCTO ceramics measured at 20°C are presented in Figure 7(e). It is interesting to notice that all samples possess a giant ε′ value within the measured frequency range. Additionally, the ε′ and tan δ increase by enhancing the Ho 2 O 3 doping content, which could be correlated with the generation of free electrons that are induced by Ho doping. These electrons can be subsequently confined by the related clusters to enhance the dielectric response [35].
The Nyquist plots of the xHo 2 O 3 -(1-x)CCTO ceramics at selected temperatures are shown in Figure 8. It is wellestablished that CCTO ceramics possess various electrically inhomogeneous phases. For the Nyquist plots, the grain boundary-related electrical behavior is represented by the low frequency arc while the grain-related electrical response is manifested by the high frequency arc. Furthermore, the observed single recessed semicircle shapes suggest that the grain as well as grain boundary in the ceramics may possess similar relaxation times [36]. Additionally, the contribution of the grains to the electrical response becomes more pronounced as the Ho 2 O 3 content increases. The semicircle's centers lie below the x-axis, indicating the manifestation of non-Debye relaxation [34]. Moreover, it can be ascertained that the intercept of the semicircle (R total ) at the low-frequency range decreases as the temperature rises, which is a typical response of the NTC effect.
In order to further examine the contribution of both grain boundaries and grains to the total resistance, the Zview software was employed to fit the complex impedance spectrum of xHo 2 O 3 -(1-x)CCTO ceramics at the temperature value of 20°C. The equivalent circuit is composed of two in series connected subcircuits that include a resistor and constant phase element (CPE), which are parallelly connected (Figure 9 inset) [37]. CPE has previously been used to describe the non-ideal relaxation of ceramic materials explained by the expression [38]: where ω is the angular frequency of the alternating current. Use the R g /CPE 1 and R gb /CPE 2 components to fit the left and right sides of the frequencies marked by the arrow in Figure 8 respectively, and finally perform a full-spectrum fitting over the entire frequency range. Figure 8 shows that the impedance spectra experimental data (black symbol) of xHo 2 O 3 -(1-x)CCTO ceramics at 20°C is in good agreement with the fitting results (orange line), and the error rates of the R g and R gb values are less than 5%. Figure 9 depicts the R g and R gb fitted values as functions of Ho 2 O 3 doping concentration, where a clear decrease in both the R gb value (from 840 kΩ to 14 kΩ) and the R g value (from 82 kΩ to 5.3 kΩ) by increasing Ho 2 O 3 concentration can be observed. Besides, the values of both fitting parameters R total and R gb are in the same order of magnitude, while R g is much smaller than R gb . From these results, we can draw the conclusion that the electrical response of CCTO ceramics can be directly tuned by adjusting the content of Ho 2 O 3 . Additionally, the different contribution of R gb and R g on the resistance distribution are captured by the IBLC model and play an important impact on dielectric properties [39]. It needs to be emphasized that the presence of electrical heterogeneous phases within composite dielectrics will cause interface polarization, which leads to the implementation of the Maxwell-Wagner relaxation [40,41]. Figure 10 shows the frequency dependences of the real part of the impedance (Z′) obtained at selected temperatures. Due to the accumulation effect of space charges, the Z′ value at the temperature of 20°C is very high and stable in the lowfrequency range (<10 1 Hz), while it decreases rapidly as the frequency shifts toward higher values.  Moreover, the magnitude of Z′ of each component decreases with increasing the temperature, suggesting an enhancement of the AC conductivity. Additionally, the shift of the Z′ plateau in the lowfrequency region to a higher value by increasing the temperature provides a piece of strong evidence in the manifestation of frequencydependent relaxation [42]. Finally, the Z′ responses at all temperature ranges are merged to a line in the higher frequency zone, which could originate from the reduction of the potential barrier induced by the release of space charges [43]. Furthermore, the Z′ value decreases by enhancing the content of Ho 2 O 3 , probably due to the elevated electron concentration. Figure 11 illustrates the frequency-dependent imaginary part of the impedance (Z′′) at selected temperatures. The Z′′ curve at each temperature will reach its maximum value (Z′′ max ) at the relaxation frequency (f r ). The existence of a sole peak for all curves at a lower frequency represents that the materials are governed by a single relaxation process, which is closely related to the grain boundary effect [20]. In addition, Z′′ decreases by increasing the temperature and shift toward higher frequencies, indicating the decrease of the relaxation time (τ). Moreover, from the extracted data it is concluded that the Z′′ max signal also decreases by increasing the Ho 2 O 3 content, suggesting a clear reduction in R gb (Z′′ max = R gb /2) [44], which is similar to the fitting result presented in Figure 9.
The electrical modulus analysis is an effective method for investigating the electrode polarization effects as well as identifying the bulk (grain and grain boundary) conduction properties. The M′′ spectra for the xHo 2 O 3 -(1-x)CCTO ceramics within the temperature range of 20-100°C are presented in Figure 12. For all samples, a discernible broadened peak (M′′ max ) can be observed in the measured spectra for all the studied temperatures, indicating the expansion of the relaxation time for non-Debye response. M′′ max shifts to high-frequency zone implying the manifestation of a temperature dependent-relaxation mechanism. From these results, it's apparent that the carriers hopping triggers the thermally activated relaxation process [45].
In order to further reveal the relaxation nature for the xHo 2 O 3 -(1-x)CCTO ceramics, the relationship between ln(τ) and 1000/T is plotted in Figure 13. The activation energy for the relaxation process (E relax ) can be expressed from the Arrhenius law: where τ 0 denotes the pre-exponential factor, while τ is determined from f r at different temperatures by using the following relation: τ = 1/2πf r . Table 1 lists the E relax values in the range of 0.5755-0.6200 eV, which are consistent with the Maxwell-Wagner polarization phenomenon that is caused by the activation of oxygen vacancies [46]. CCTO-based ceramics can inevitably produce oxygen vacancies during the sintering process, as described by the following defect equation The values of E relax are also closely associated with the energies required for the second ionization of oxygen vacancies (V �� o ). Generally, since the long-range migration of oxygen vacancies is easily inhibited by the presence of grain boundaries, the respective relaxation processes are dominated by space charge-related mechanisms [47].

Conclusions
The microstructure, NTC effect as well as relaxation behavior of xHo 2 O 3 -(1-x)CCTO ceramics were investigated. XRD analysis proves that Ho 3+ dissolve into the CCTO lattice and maintains the cubic perovskite structure. The average grain size of the samples was reduced by considering the impact of Ho 3+ ions. Furthermore, all samples exhibit excellent NTC effect, while the incorporation of a small amount of Ho 2 O 3 yield in a clear reduction of the ρ 20 values of CCTO from 8.54 × 10 6 to 1.76 × 10 5 Ω cm, whereas  the B 20/75 values ranged from 4258-5954 K. The electrons hopping between various oxidation energy states, induced by the formation of cation, was proposed as the prevailing conduction mechanism for the sintered sample. Significant insights were gained by analyzing the impedance spectra, confirming the grain boundary resistances were higher than the respective grain resistances. Moreover, the electrical relaxation behavior was induced by the presence of space charges at the interface of ceramics. From our analysis, we can draw the conclusion that the electrical properties for CCTO NTC ceramics could be significantly regulated by varying the Ho 2 O 3 content.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
This work was supported by the National Natural Science