Direct Observation of the Double Schottky Barrier in Niobium-Doped Barium Titanate by the Charge-Collection Current Method

Charge-collection (CC) current was measured at a single grain boundary, which exhibited positive temperature coefficient of resistivity (PTCR) effects, in 0.1-mol%-Nb-doped BaTiO₃. The CC current systematically reversed across the grain boundary above the Curie point, which indicated the presence of a double Schottky barrier (DSB) at the grain boundary. In contrast, the CC current was constant across the grain boundary below the Curie temperature. The result obtained from the CC current measurement agrees with the classical DSB model in donor-doped BaTiO₃, indicating the PTCR effects.     

PTCR effect in donor doped barium titanate: review of compositions,microstructures, processing and properties

Abstract

Abstract

Barium titanate is widely used in the fabrication of thermistors with a positive temperature coefficient of resistivity (PTCR). The resistivity can increase by several orders of magnitude near the phase transition temperature T_c for the ferroelectric tetragonal to the paraelectric cubic phase transformation. There is general agreement that the anomaly in the change of electrical resistivity of donor doped BaTiO₃ around T_c is due to the grain boundary effect. The Heywang–Jonker model and other mechanisms involving the nature of the electrical barrier formed across the grain boundaries of polycrystalline BaTiO₃ are reviewed. The compositional effect on BaTiO₃ based PTCR properties is listed and discussed. The influences of manufacturing methods under different stages including the initial doping methods, sample forming methods and final heat treatments on PTCR properties are compared. The complex interrelationships between compositions, microstructures, processing and PTCR characteristics are well discussed.     

Interfacial Segregation in Perovskites: IV, Internal Boundary Layer Devices

A proposed model for interfacial segregation in perovskites, with induced heterogeneous defect distributions, is extended here to account for the formation of internal boundary layer devices, such as positive temperature coefficient of resistance (PTCR) thermistors and internal boundary layer capacitors (IBLC). Boundary layer effects in doped BaTiO₃ are attributed to factors which contribute to the formation of highly resistive boundary layers by a segregation-induced shift in donor incorporation and/or acceptor segregation, and the inhibiting action of segregated donors on boundary mobility and grain growth. The distribution of space charges, formed by electron transfer from conductive grains to resistive boundary layers, leads to the formation of impedance barriers in the grain-boundary vicinity. Depending on the grain size, and on relative size and spatial distribution of the space charge layer and the resistive layer, a transition from semiconducting properties to insulating properties may take place. This model accounts for the observed PTCR and IBLC phenomena.     

BaTiO3系PTCR材料电学性能的复阻抗解析

采用复阻抗解析法研究了ＢａＴｉＯ３系ＰＴＣＲ材料晶粒、晶界的电学性能。结果表明：使用欧姆接触电极的ＰＴＣＲ材料等效电路的复阻抗为：晶粒电阻呈ＮＴＣ特性，而晶界电阻天Ｔ〈Ｔｃ时呈ＮＴＣ特性，Ｔ〉Ｔｃ时呈明显的ＰＴＣ特性；ＰＴＣ效应是一种晶界效应。     

PTCR陶瓷复阻抗图谱拟合结果分析

采用砖形结构模型(brick wall model)分析了PTCR陶瓷的电显微结构,通过公式推导得到复阻抗图谱的宏观拟合结果与陶瓷单个晶粒和晶界电性能的对应关系.     

Grain Orientation Dependence of the PTCR Effect in Niobium-Doped Barium Titanate

The positive temperature coefficient of resistivity (PTCR) effect is directly measured in single grain boundaries in 0.1-mol%-Nb-doped BaTiO₃ with 1 mm coarse grains. The PTCR effect largely depends on grain boundary structure. Random grain boundaries exhibit the PTCR effect as in polycrystalline samples, but the PTCR effect does not appear in highly coherent boundaries such as small-angle boundaries, twin boundaries, and coincidence site lattice (CSL) boundaries with low Σ values. For Σ= 3 boundaries, the resistance increase above the Curie temperature is a function of deviation angle. A small PTCR effect is observed in Σ= 3 boundaries with a deviation angle of about 9° in contrast with ideal Σ= 3 boundaries and boundaries with a deviation of about 4°.     

Characterization of the Firing Schedule for Positive Temperature Coefficient of Resistance BaTiO3

The development of positive temperature coefficient of resistance (PTCR) behavior during the firing procedure of semiconducting BaTiO₃ was characterized. The PTCR properties of BaTiO₃ were shown to be sensitive to the material's microstructure, liquid-phase distribution, and extent of grain-boundary oxidation. The PTCR behavior first became pronounced as the material cooled from the sintering stage at 1350°C to the annealing stage at 1175°C. Within this region, rapid oxidation of the grain boundaries occurred, which resulted in significant formation of charge carrier traps and a potential barrier. The rapid oxidation of the grain boundaries corresponded with the redistribution and solidification of the liquid phases. Once the carrier traps were established, the magnitude and slope of the PTCR jump increased during the annealing and cool-down stages of the firing procedure because of further oxidation of the grain boundaries.     

Effect of PO2 on Bulk and Grain Boundary Resistance of n-Type BaTiO3 at Cryogenic Temperatures

Complex impedance analysis at cryogenic temperatures has revealed that the bulk and grain boundary properties of BaTiO₃ polycrystals are very sensitive to the oxygen partial pressure during sintering. Polycrystals sintered at P _O2 as low as 10⁻¹⁵ atm were already electrically heterogeneous. The activation energy of the bulk conductivity in the rhombohedral phase was found to be close to that of the reduced undoped single crystal (i.e., 0.093 eV). The activation energy of the grain boundary conductivity increases with the temperature of the postsinter oxidation treatment from 0.064 to 0.113 eV. Analysis of polycrystalline BaTiO₃ sintered in reducing atmosphere and then annealed at P _O2= 0.2 atm has shown that the onset of the PTCR effect occurs at much higher temperatures than expected in the framework of the oxygen chemisorption model. The EPR intensity of barium and titanium vacancies increases after oxidation at T > 1000°C. A substantial PTCR effect is achieved only after prolonged annealing of the ceramic in air at temperatures as high as 1200–1250°C. This result suggests that the PTCR effect in polycrystalline BaTiO₃ is associated with interfacial segregation of cation vacancies during oxidation of the grain boundaries.     

PTCR Characteristics and Fabrication of Porous, Sb-Doped BaTiO3 Ceramics

Sb-doped BaTiO₃ ceramics containing corn-starch were prepared by sintering at 1350°C for 1 h in air. In this study, the effect of corn-starch on positive temperature coefficient of resistivity (PTCR) characteristics and microstructures of Sb-doped BaTiO₃ ceramics was investigated. It was found that the porosity and pore size increased and the grain size slightly decreased with increasing corn-starch content. XRD results showed the presence of BaTiO₃ peaks only in the Sb-doped BaTiO₃ ceramics with and without corn-starch. The PTCR jump of the Sb-doped BaTiO₃ ceramics with corn-starch was over 10⁶ and 1–2 orders higher than that of samples without corn-starch. The increase in the room-temperature resistivity with increasing corn-starch content was attributed mainly to the increase in the electrical barrier height of grain boundaries and the porosity as well as the partial decrease in the donor concentration of grains and the grain size. It was also noticed that the grain boundary resistivity contributed largely to the total resistivity of the Sb-doped BaTiO₃—corn-starch ceramics.     

Grain Boundary Oxidation in PTCR Barium Titanate Thermistors

The phenomenon of grain boundary oxidation in PTCR BaTiO₃ thermistors is discussed. In particular, the energy spectra of the surface states were calculated for different samples, and these were related to the nominal composition, the impurity content of the base BaTiO₃ powder used, and the prevalent atmospheric conditions during cooling and/or annealing. It is proposed that the interaction of manganese with oxygen creates deep-lying traps, and, in general, some proof is offered that the majority of the surface states are due to different oxidizing chemisorbed gases. It is believed that the ability of a particular sample to adsorb such gases in adequate amounts, and thus exhibit an appreciable PTCR effect, is related to the presence of acceptor-type dopants perferentially segregated onto the grain surfaces. Notably, the role of 3 d transition metal cations in this process is discussed in some detail.     

Electrically Active and Inactive Single Grain Boundaries in Semiconducting BaTiO3

Bi‐crystal specimens were prepared from Nb and Mn‐doped BaTiO₃ poly‐crystals with giant grains of millimeter order in size, and the resistance (R) versus temperature (T) characteristics of these individual grain boundaries was investigated. The electrically active grain boundaries that show normal positive temperature coefficient resistor (PTCR) behavior had no second phases or they were partially distributed along boundaries. On the other hand, electrically inactive grain boundaries that show flat R‐T characteristics were also observed, where continuous Ti‐rich second phases of Ba₄Ti₁₂O₂₇ could be detected. Different interface state density and its resultant R–T characteristics were observed for each individual active boundary, which indicates the degree of oxidation and the formation of potential barrier can be different depending on the character of the grain‐boundary plane. The resistance of inactive boundaries was determined by that of insulating second phase showing negative temperature coefficient resistor (NTCR) behavior. These results demonstrate that continuous second phase surrounding a grain deactivates the electrical properties of grain boundary, and thus should be distinguished from insulating depletion layer near grain boundary.     

Spontaneous Polarization Screening Effect and Trap-State Density at Grain Boundaries of Semiconducting Barium Titanate Ceramics

The grain-boundary trap-state density and the polarization screening effect were studied for a series of semiconducting PTCR barium titanate ceramic samples with different manganese (Mn) additives and different thermal treatments. The grain-boundary resistance and capacitance data were measured by the ac complex impedance method. The grain-boundary data obtained were analyzed using a simple double-depletion-layer model and an absolute-zero-temperature approach for the Fermi distribution function for the boundary trap states. The energy density distributions of the boundary trap states were found to be V-shaped for the energy range studied, from 0.35 to 1.35 eV, as measured from the conduction band downward. The "neutral" Fermi level at the grain boundary is taken as 1.35 eV and the bulk Fermi level is taken as 0.15 eV from the conduction band. For the samples without the Mn additive, the PTCR effect is controlled by the trap densities located near 0.35 eV. The trap centers are believed to be barium and oxygen vacancies, or chemisorped oxygens. For the samples with Mn additives, the trap densities increase dramatically near 1.35 eV and play a dominant role in the PTCR effect. These trap centers are believed to be Mn⁴⁺ ions at the titanium sites. The charge-compensation effect of spontaneous polarizations on the trap charges was found to be linearly proportional to the total amount of trap charges at that temperature.     

Positive Temperature Coefficient of Resistivity in Ba1-xSrxPb1+yO3-8 Ceramics

The positive temperature coefficient of resistivity (PTCR) effect in Ba_1-xSr_xPb_1+yO_3-s ceramics is systematically studied. The influence of the preparation conditions on the PTCR properties is experimentally tested. The PTCR effect in metallic-conducting BaPb_1+yO₃ is confirmed around 700°C. The temperature where the PTCR effect starts can be shifted to a higher temperature range by substituting strontium for the A-site barium. By the enhancement of the sintering, the magnitude of the PTCR effect was increased and the resisitivity was reduced. In addition to Pb(IV) in the perovskite structure, Pb(II) is detected at the grain boundary in the sintered body.     

Direct Characterization of Grain-Boundary Electrical Activity in Doped (Ba0.6Sr0.4)TiO3 by Combined Imaging of Electron-Beam-Induced Current and Electron-Backscattered Diffraction

Simultaneous measurements of remote electron beam induced current (REBIC) and orientation imaging microscopy (OIM) in a scanning electron microscope (SEM) have been applied to a polycrystalline (Ba_0.6Sr_0.4)TiO₃ with a positive temperature coefficient of resistivity (PTCR) to elucidate a grain-boundary character dependence of the potential barrier formation. The absence of electrical activity in a coherent Σ3 twin boundary is clearly imaged. The resistivity of individual grain boundaries estimated from a resistive contrast image is interpreted in terms of geometrical coherency, which is defined by the degree of coincidence in the reciprocal lattice points.     

Proposed Phenomenological PTCR Model and Accompanying Phenomenological PTCR Chart

The positive temperature coefficient of resistivity (PTCR) behavior of semiconductive BaTiO₃ is well explained by the Heywang model, which predicts the resistivity behavior above the Curie point based on the acceptor state density at the grain boundaries, the charge carrier density, and the energy gap, E _s, between the conduction band and the acceptor levels. However, the relationship between these parameters and the production parameters (sintering time, composition, and cooling rate) is not well understood. Recently, the present authors have found that E _s can be increased by thorough oxidation. This increase is attributed to a change in the oxidation state of the acceptor. Based on this finding and results from the literature, a phenomenological PTCR model and an accompanying PTCR chart for acceptor–donor-codoped BaTiO₃ are proposed to clarify this relationship. The PTCR chart clarifies that acceptor dopant concentrations, oxidation time, and oxygen partial pressure during oxidation or cooling can be optimized simultaneously to obtain optical PTCR properties.     

Formation of Potential Barrier Related to Grain-Boundary Character in Semiconducting Barium Titanate

Resistance–temperature ( R – T ) characteristics were measured directly at single-grain boundaries in 0.1-mol%-niobium-doped barium titanate bicrystals that had been fabricated from polycrystalline sinters, to determine a geometrical grain-boundary character dependence of the positive temperature coefficient of resistivity (PTCR) effect. Both random boundaries and low-Σ boundaries exhibit a similar grain-boundary character dependence of the PTCR effect through a simple geometrical analysis, using the coincidence of reciprocal lattice points. Differences of the R – T characteristics in individual boundaries have been explained in terms of the formation of a potential barrier that is associated with the oxidation of grain boundaries during cooling, after sintering or annealing. The grain-boundary character is likely to affect the diffusivity of O²⁻ ions and, hence, is crucial to the formation of the potential barrier.     

Influence of Stoichiometry on the PTCR Effect in Porous Barium Titanate Ceramics

Porous semiconducting barium titan ate ceramics with small grain sizes (2 to 5 tun) exhibit large PTCR effects (>7 orders of magnitude). The magnitude of PTCR in the ceramic bodies is significantly affected by the grain structure. This study shows the influences of Stoichiometry on both the magnitude of PTCR and resultant grain structures in the sintered bodies .     

Reassessment of the effect of space charge potential on the electrical conductivity of polycrystalline ceramics

The calculation of space charge potential, the difference of the activation energy of grain boundary and grain, and the ratio of conductivity of grain boundary and grain at different temperatures of the polycrystalline ceramics have been reappraised in the present model, in which charge carriers hopping through bulk and grain boundary barriers with different mobility are taken into account. It is evidenced that the present model is valid and more precise than previous models, and thus, it is concluded that the assumption that the mobility of charge carriers hopping through bulk and grain boundary barrier is the same made by the previous studies is unsuitable.     

多晶BaTiO3陶瓷的纳米非均匀性与电性能

发现了多晶ＢａＴｉＯ３陶瓷晶界附近的化学组成具有纳米尺度上的非均匀性，研究了非均匀性对陶瓷电性能的作用。ＰＴＣ热敏电阻器的电阻温度关系可用势垒模型说明：ＢＬ电容器的介电温谱要用壳层模型才能解释，这种差别主要由于晶界区的纳米非均匀性。     

Modification of grain boundary potential barriers by annealing treatments of PTCR ceramics with identical microstructure and room-temperature resistivity

Semiconducting BaTiO₃-based ceramics originating from the same starting powder batch were subjected to different oxidative post-sintering treatments at temperatures between 800 °C and 1200 °C. The annealing profiles were chosen in a way to result in ceramics with same room-temperature and microstructure. However, the different annealing procedures clearly affected the resulting PTCR characteristics above and below the phase transition temperature. Observed changes in electrical properties were investigated by capacitance-voltage measurements and x-ray diffraction. It was found that annealing treatments influence the grain boundary potential barrier height and width by modifying the equilibrium concentration of cation and oxygen vacancies. Moreover, oxidative annealing at 1100 °C appears to influence the temperature development of spontaneous polarization by filling up oxygen vacancies within the grain bulk. These findings not only extent existing knowledge about defect equilibria in barium titanate but also emphasize the strong impact of process parameters on electrical properties of electroceramics.