Modeling of transport properties of interfacially controlled electroceramics: Application to n-conducting barium titanate

Grain boundary regions in n-conducting barium titanate (BaTiO₃) are re-oxidized during the cooling process after sintering the ceramics in air. The kinetics of this re-oxidation process is determined by rapid transport of oxygen along the grain boundaries and slow (rate-determining) diffusion of cation vacancies from the grain boundaries into the grains until the diffusion process is frozen-in. Based on numerical calculations of frozen-in diffusion profiles of cation vacancies at grain boundary regions for various cooling rates, a modified Schottky-barrier model is introduced in order to calculate the grain boundary resistivity as a function of temperature from the Curie-point up to 900°C. A change of the activation energy at approximately 500°C is predicted owing to an enrichment of holes in the space charge layers at elevated temperatures. The modeling results are compared with experimental data for BaTiO₃-based positive temperature coefficient resistors (PTCRs).     

PTCR Effect in BaTiO3: Structural Aspects and Grain Boundary Potentials

Extensive microstructural and structure-property studies on donor doped barium titanate have revealed that the PTCR phenomenon is strongly controlled by the density, number of grain boundaries available to conduction, domain orientation and grain boundary domain coherence. Structural heterogeneities lead to a wide range of grain boundary structures, potential barriers and, therefore, depletion widths. Conduction thus occurs primarily by percolation of electrons through favorably aligned domain pathways and low potential barrier grain boundaries. At the Curie point, the increase in the potential barriers along these pathways is likely to dominate the PTCR effect. To improve theoretical understanding a model needs to take heed of local values of parameters and also incorporate the fact that the bulk of the current flow is only through a certain percentage of grain boundaries. The specific structural factors that have led to an improved qualitative understanding of overall PTCR phenomenon are discussed.     

Microstructures of Impurity Precipitates in Sintered Alumina used as a Crucible to Anneal Lead Titanate

Impurity precipitates at grain boundaries in sintered alumina were characterized with a scanning electron microscope (SEM) and a transmission electron microscope(TEM) and by energy dispersion analysis of X-ray (EDX). Spherical and cylindrical impurity precipitates were found at grain boundaries in the alumina obtained after annealing 1700°C-sintered alumina at 1000°C. On the other hand, filmy precipitates of an amorphous phase about 2.5 nm in thickness were found at grain boundaries in the alumina quenched to room temperature from 1700°C. The EDX data indicated that the elements of impurity precipitates contained Na, Ca, Al, and Si. The formation mechanisms of the spherical and cylindrical precipitates and the reaction between the precipitates and PbTiO₃ were briefly discussed.     

Nonuniformity of electrical Characteristics in microstructures of ZnO surge varistors

The nonuniformity of electrical characteristics of grain boundaries in ZnO varistors was systematically analyzed. The high nonuniformity exists in barrier voltages and nonlinearity coefficients in different grain boundaries. The barrier voltages have normal distributions, only a few grain boundaries were electrically active, and the grain boundaries can be simply classified into good, bad, and ohmic ones according to the electrical characteristics of grain boundaries. The average barrier voltage is equal to 3.3 V by the direct method, but it is only 2.3 V by the indirect method. There is a high difference between the barrier voltages by direct and indirect measurement methods. These few good grain boundaries are responsible for the good varistor effect, and control the leakage current of ZnO varistor at low values of applied voltage. The Al/sub 2/O/sub 3/ dopants affect the electrical characteristics of grain boundaries by changing the electron status in grain boundary and intragrain.     

Complex impedance analysis of Ba0.65Sr0.35TiO3 ceramics

Complex impedance spectra of BST ceramics were measured at different temperatures, and the results reveal that all the centers of the semicircles lie below the real axis, and the area of the semicircles decreases with the increasing temperature. Activation energy of grains and grain boundaries was obtained from a classical Arrhenius relation. The results show that the activation energy of grains and grain boundaries of undoped BST ceramics is 0.98 and 0.97 eV, respectively. After doping B₂O₃–SiO₂, the activation energy of grain increased to 1.12 eV, which was due to B₂O₃–SiO₂ redistribution to the grain boundary during the cooling process. The activation energy of grains increased to 1.16 eV after 1 mol% MgO doping, which was caused by the decrease of the oxygen vacancy concentration and the increase of the potential barrier of the grain boundary.     

Electrochemical properties of doped ceria electrolyte under reducing atmosphere: Bulk and grain boundary

The electrochemical behavior of a symmetrical cell, Pt/Ce_0.8Sm_0.2O_1.9?δ/Pt, under reducing conditions and wide temperature range (250 – 600 °C) is detailed. In terms of the charge carriers transport through the electrolyte microstructure, AC impedance spectroscopy has been applied to address useful concerns about the transport properties over electrolytic and mixed conduction regimes. The impedance spectra at lower temperature and oxygen partial pressure show the electrochemical response of separated bulk and grain boundary contributions. The increase in the electronic conductivity from 250 to 400 °C shows that the electrochemical reduction Ce⁴⁺/Ce³⁺ is as kinetic as thermodynamically favorable in the experimental conditions. In a typical Nyquist plot of an impedance diagram, until temperatures as low as 400 °C, the high and low frequency arcs can be accessed and the influence of reducing atmosphere over both the components is presented. The apparent activation energy for the electronic process (ΔE) extracted from the total conductivity is 2.54 eV. Distinguished bulk (2.34 eV) and grain boundary (2.63 eV) activation energies point the latter as an energetic barrier in the redox reaction. The oxygen partial pressure dependence of individual capacitances suggests storage of electrical charge along grain boundaries which can potentially behave as a chemical capacitor.     

ZnO Grain Boundaries: Electrical Activity and Diffusion

The operation and performance of electroceramics are commonly dependent on the characteristics of electrically active grain boundaries. To date, our understanding of the role of specified additives and heat treatments on the grain boundary properties remains underdeveloped. We describe efforts directed towards improving our understanding by (a) fabrication and analysis of individual boundaries, (b) improved control and simplification of boundary chemistry (c) systematic investigation of properties (e.g., I-V, DLTS, D_O and D_M) as a function of boundary structure and chemistry and (d) development of appropriate energy band, defect and diffusion models. Following this approach, preliminary results suggest that lattice defects play critical roles in controlling both the electrical and diffusive properties of the boundaries while the additives appear to act in supportive manner by activating the key lattice defects particularly with respect to the electrical activity of the boundaries.     

Interface mediated transport properties in n-type SrTiO3 : Induced dipole alignment at oxide grain boundaries

Low temperature potentiometry and capacitance measurements based on noncontact atomic force microscopy were used to quantify local properties due to grain boundaries at a 0.05 wt.% Nb-doped SrTiO₃ [001] surface. Local I-V curves were constructed by combining potential steps and transport currents measured at individual grain boundaries (GBs) under different lateral biases. The GBs exhibit a positive temperature coefficient of resistivity (PTCR) effect. A comparison of transport properties and calculations suggest that SrTiO₃ grain boundaries undergo a non-polar to polar state phase transition induced by the large electric field associated with the boundary charge. This is supported by the temperature dependence of the barrier height and the boundary charge obtained by numerical simulation of I-V curves using a double Schottky barrier model. The built-in potential associated with the boundary was directly imaged with frequency-modulated Kelvin probe force microscopy at different temperatures and the results support the previous conclusion.     

Interface Defect Chemistry and Effective Conductivity in Polycrystalline Cerium Oxide

Polycrystalline cerium oxide exhibits increasing electronic and decreasing ionic conductivity upon reduction of the grain size. In the present study, the origin of this effect was examined. Temperature-programmed reduction (TPR) and oxygen titration measurements on nanocrystalline cerium oxide revealed a large excess oxygen deficiency associated with the surface. Using a two-phase model for the combined system of the bulk phase in equilibrium with a surface layer, this enhanced oxygen deficiency could be explained by a reduced binding energy of surface oxygen ions in agreement with results from atomistic computer simulations. The model also revealed that this segregation of oxygen vacancies is the origin of an intrinsic space charge potential. Translating this effect to polycrystalline cerium oxide and taking into account the segregation of dopants and the accumulation/depletion of charge carriers, it was possible to model the grain size dependence of electrical conductivity and thermopower of polycrystalline cerium oxide. A straightforward 1-dimensional numerical model and a change from Boltzmann to Fermi-Dirac statistics allowed to calculate the conductivity of heavily doped polycrystalline cerium oxide for grain sizes in the range of 5–10,000 nm and acceptor concentrations up to 20%. Using this approximation, the effect of grain size on mixed ionic/electronic conductivity and the electrolytic domain boundary was investigated.     

MoO3和CaCO3掺杂对MnZn铁氧体磁特性的影响

用普通陶瓷工艺制备了高磁导率MnZn铁氧体材料,研究了MoO3和CaCO3掺杂对材料的磁特性的影响。发现添加MoO3能够促进晶粒长大,从而提高材料的磁导率,但添加过量会增大铁氧体材料的气孔率。添加CaCO3使得晶界明显,晶粒均匀,起始磁导率增高,同时形成了高电阻的晶界层,降低了材料的比损耗因子。     

Influences of grain structure on thermally induced stresses in 3D IC inter-wafer vias

We discuss the development of a grain-continuum model to examine the effects of thermally induced stress in 3D IC inter-wafer vias. We demonstrate the approach using stress-driven grain boundary migration in polycrystalline copper films, assuming that migration is due to vacancy migration. The anisotropic elastic constants of single crystal Cu are used for each grain, after aligning them with each grain’s orientation. Stresses are thermally induced in a series of films, including one with a dominant <111> texture surrounding a single <100> grain. Grain boundary velocities are calculated from the fluxes of vacancies to grain boundaries. The computed velocities are then used to update the level sets that represent the grain boundaries using the PLENTE software.     

Study of fluctuations in advanced MOSFETs using a 3D finite element parallel simulator

Two important new sources of fluctuations in nanoscaled MOSFETs are the polysilicon gates and the introduction of high-κ gate dielectrics. Using a 3D parallel drift-diffusion device simulator, we study the influence of the polycrystal grains in polysilicon and in the high-κ dielectric on the device threshold for MOSFETs with gate lengths of 80 and 25 nm. We model the surface potential pinning at the grain boundaries in polysilicon through the inclusion of an interfacial charge between the grains. The grains in the high-κ gate dielectric are distinguished by different dielectric constants. We have found that the largest impact of the polysilicon grain boundary in the 80 nm gate length MOSFET occurs when it is positioned perpendicular to the current flow. At low drain voltage the maximum impact occurs when the grain boundary is close to the middle of the gate. At high drain voltage the impact is stronger when the boundary is moved toward the source end of the channel. Similar behaviour is observed in the 25 nm gate length MOSFET.     

Fractal Approach to ac Impedance Spectroscopy Studies of Ceramic Materials

A novel fractal model for grain boundary regions of ceramic materials was developed. The model considers laterally inhomogeneous distribution of charge carriers in the vicinity of grain boundaries as the main cause of the non-Debye behaviour and distribution of relaxation times in ceramic materials. Considering the equivalent circuit the impedance of the grain boundary region was expressed. It was shown that the impedance of the grain boundary region has the form of the Davidson–Cole equation. The fractal dimension of the inhomogeneous distribution of charge carriers in the region close to the grain boundaries could be calculated based on the relation d _s = 1 + , where is the constant from the Davidson–Cole equation.     

MODEL FOR GRAIN SIZE EFFECT ON DIELECTRIC NONLINEARITY OF FERROELECTRICS

ABSTRACT

Dielectric nonlinearity is an important characteristic of ferroelectrics. It is assumed that in ferroelectrics the grains are all uniform, in order and cubic-shaped. Moreover, the dielectric constant of the grain boundary does not vary with direct current bias. And then the grains and the grain boundaries were modeled in terms of capacitors and resistors. Based on these analyses, a model for grain size effect on dielectric nonlinearity of ferroelectrics was established. In this model there are some parameters such as the grain size and the grain boundary width, which intensively influence on the dielectric properties of ferroelectric ceramics and thin films. The accuracy of the model prediction was quantitatively verified by our experimental data. The results proved that the above model can describe the grain size effect on dielectric nonlinearity of ferroelectrics.     

Electrochemical Characterization of Thin Films for a Micro-Solid Oxide Fuel Cell

One of the first technological benchmarks towards the realization of a micro solid oxide fuel cell is the production of thin film structures with adequate electrochemical properties. This paper describes the deposition of thin film yttria-stabilized zirconia electrolytes and lithographically patterned platinum and gold electrodes. By using conventional, ultraviolet lithography, electrode patterns were produced with features sizes as fine as 15 m, enabling a more direct investigation into the role of the triple phase boundary. Impedance spectroscopy measurements show three arcs, ascribed to the grain, grain boundary and electrode processes, and an offset on the real axis due to the leads. The high frequency arc, ascribed to the ohmic resistance of the YSZ electrolyte, exhibited an activation energy of 1.0 eV, while the intermediate frequency arc, attributed to blocking grain boundaries, exhibited an activation energy of 0.69 eV. The low frequency, non-ohmic arc was found to be highly dependent upon the electrode material and exhibited activation energies of 0.91 eV for gold electrodes and 0.77 eV for platinum electrodes. The electrode impedances for different sample geometries were similar when normalized to the triple phase boundary length.     

Theoretical analysis of the impedance spectra of electroceramics Part 2: isotropic grain boundaries

The grain-size dependence of impedance spectra of electroceramics is simulated, based on a brick layer model with explicit consideration of parallel boundaries. A constant grain interior conductivity is assumed and the grain boundary (gb) conductivity is varied. Parallel and series gb are assumed isotropic, i.e. charge transport along and across gb is supposed identical. Various grain sizes between 500 and 0.5 nm are studied and impedance spectra are shown in complex plane and Bode representations.     

Giant Piezoresistive Effects in Single Grain Boundaries of Semiconducting Barium Titanate Ceramics*

Extremely large piezoresistive effects with a gage factor (elastoresistance) of > 1 × 10⁶ in single grain boundaries of thin ceramic bars of semiconducting barium titanate have been observed at room temperature. Thin barium titanate ceramic bars with a diameter in the range of 10 to 20 μm were prepared to consist of single grains joined together in series. Large piezoresistive effects were observed for some of the single grain boundaries in the present samples under compressive stresses, but no distinct piezoresistance was observed in the grain bulk. A giant piezoresistive effect with a gage factor of 3 × 10⁷ was observed for a single grain boundary which exhibited a saw-tooth type PTCR (positive temperature coefficient of resistivity) characteristic with a significantly large bias dependence of it. This demonstrates that the piezoresistive phenomenon may be interpreted in terms of the change of the potential barrier height due to the change of ferroelectric domain morphologies in the vicinity of grain boundaries under mechanical and electric stresses.     

Grain Boundary Defect Chemistry of Acceptor-Doped Titanates: High Field Effects

The field enhanced average conductivity in grain boundary space charge depletion layers in acceptor-doped SrTiO₃ ceramics was investigated by impedance analysis in the time domain. The dependence of the grain boundary conductivity on the acceptor concentration, the temperature and the field dependence are discussed and interpreted in terms of a Schottky diffusion model combined with the influence of accumulated oxygen vacancies at the GB interface.     

The Influence of Excess Precipitate on the Non-Ohmic Properties of SnO2-Based Varistors

Based on our background in the field of nonlinear electrical properties of SnO₂-based varistors, we have been observing the influence of microstructural heterogeneities, e.g., the precipitate phase at triple points of the grain boundary region. In this study, we have prepared a SnO₂-based varistor system with excess precipitates at triple points in the grain boundary region in order to discuss their influence on the system's non-ohmic properties, including thermal treatment at oxidizing atmospheres. Our results indicate that an excessive amount of such precipitates may be deleterious to the non-ohmic properties because they may create adjacent regions at grain boundaries with lower concentrations of segregated metal atoms, thus increasing the presence of a non-active potential barrier and increasing leakage current paths. Under these circumstances, the effect of thermal treatment in oxidizing atmospheres is to decrease the leakage current density instead of increasing the nonlinear coefficient.     

Pt/TiN electrodes for stacked memory with polysilicon plug utilizing PZT films

Abstract

The mechanism of TiN barrier metal oxidation of Pt/TiN electrodes are investigated for planarized stacked memory utilizing lead zirconate titanate (PZT). Thinner (<100 nm) and highly oriented platinum films are required in gigabit scale ferroelectric nonvolatile memories whose capacitor size is comparable to PZT grain size. Oxygen diffusivity to oxidize TiN is found to depend on the Pt film thickness. In cross-sectional TEM images of PZT/Pt/TiN/Si, titanium oxide is observed beneath the Pt grain boundary. The oxygen is diffused through the Pt grain boundary under heat treatment in an oxygen atmosphere for crystallization of PZT films, and oxidizes the underlying TiN barrier metal.