Design of a bilayer ceramic capacitor with low temperature coefficient of capacitance.

We show how a simple bilayer system that combines a layer of undoped BaTiO3 (BT) with a second layer of Ba0.975Na0.025Ti0.975Nb0.025O3 (2.5NNBT) can be used to improve the temperature coefficient of capacitance (TCC) of BaTiO3-based materials for capacitor applications. The bilayer system emulates the volume ratio between a conventional core and shell phase microstructure allowing a simple resource efficient approach to optimise the system for low TCC. Optimisation was achieved with a volume ratio of 0.67 2.5NNBT with 0.33 BT and results in a TCC of ±6% over the temperature range ∼25 to 125 °C whilst maintaining a permittivity of εr ∼ 3000 and low dielectric loss

The analysis of impedance spectra for core–shell microstructures : why a multiformalism approach is essential

The impedance response of a core–shell microstructure with 80% core volume fraction has been simulated using finite‐element modeling and compared to two equivalent circuits for a wide range of shell permittivity and conductivity values. Different equivalent circuits, corresponding to different variants of the well‐known brick layer model, are applicable for different combinations of material properties in the microstructure. When the shell has a similar conductivity or permittivity to the core, adding a parallel pathway increases the accuracy of the fit by ≈±10%. When both the conductivity and permittivity values of the core and shell regions are different the series circuit is a better fit. This is confirmed by multiformalism impedance analysis, which reveals features in the data that are not apparent using a single formalism. Finally, the conductivity and permittivity values for both the shell and core are extracted from the simulated spectra using all formalisms and compared to the original input values. The accuracy of the extracted values often depends on the impedance formalism used. It is concluded that impedance spectroscopy data must be analyzed using multiple formalisms when considering core–shell microstructures

Finite element modeling of resistive surface layers by micro‐contact impedance spectroscopy

Micro‐contact impedance spectroscopy (MCIS) is potentially a powerful tool for the exploration of resistive surface layers on top of a conductive bulk or substrate material. MCIS employs micro‐contacts in contrast to conventional IS where macroscopic electrodes are used. To extract the conductivity of each region accurately using MCIS requires the data to be corrected for geometry. Using finite element modeling on a system where the resistivity of the surface layer is at least a factor of ten greater than the bulk/substrate, we show how current flows through the two layers using two typical micro‐contact configurations. This allows us to establish if and what is the most accurate and reliable method for extracting conductivity values for both regions. For a top circular micro‐contact and a full bottom counter electrode, the surface layer conductivity (σs) can be accurately extracted using a spreading resistance equation if the thickness is ~10 times the micro‐contact radius; however, bulk conductivity (σb) values can not be accurately determined. If the contact radius is 10 times the thickness of the resistive surface, a geometrical factor using the micro‐contact area provides accurate σs values. In this case, a spreading resistance equation also provides a good approximation for σb. For two top circular micro‐contacts on thin resistive surface layers, the MCIS response from the surface layer is independent of the contact separation; however, the bulk response is dependent on the contact separation and at small separations contact interference occurs. As a consequence, there is not a single ideal experimental setup that works; to obtain accurate σs and σb values the micro‐contact radius, surface layer thickness and the contact separation must all be considered together. Here we provide scenarios where accurate σs and σb values can be obtained that highlight the importance of experimental design and where appropriate equations can be employed for thin and thick resistive surface layers

Using metadynamics to obtain the free energy landscape for cation diffusion in functional ceramics : dopant distribution control in rare earth-doped BaTiO3

Barium titanate is the dielectric material of choice in most multilayer ceramic capacitors (MLCCs) and thus in the production of ≈3 trillion devices every year, with an estimated global market of ≈$8330 million per year. Rare earth dopants are regularly used to reduce leakage currents and improve the MLCC lifetime. Simulations are used to investigate the ability of yttrium, dysprosium, and gadolinium to reduce leakage currents by trapping mobile oxygen defects. All the rare earths investigated trap oxygen vacancies, however, dopant pairs are more effective traps than isolated dopants. The number of trapping sites increases with the ion size of the dopant, suggesting that gadolinium should be more effective than dysprosium, which contradicts experimental data. Additional simulations on diffusion of rare earths through the lattice during sintering show that dysprosium diffuses significantly faster than the other rare earths considered. As a consequence, its greater ability to reduce oxygen migration is a combination of thermodynamics (a strong ability to trap oxygen vacancies) and kinetics (sufficient distribution of the rare earth in the lattice to intercept the migrating defects)

Electric field enhancement in ceramic capacitors due to interface amplitude roughness

The electrical behaviour of the interface between the ceramic and electrode layers in multi layer ceramic capacitors has been studied using finite element modelling. Interface models were produced with varying amplitudes of roughness based upon analysis of micrographs both captured in-house and from the literature. The impedance responses, direct current electric field and current density distributions of the different interfaces were compared. Increasing the root-mean-squared amplitude roughness from 0 to 0.16 μm increased the maximum field strength by over a factor of four. The electric field distribution showed that fluctuations in the increase of field strength were due to local interface morphology. Sharp intrusions of the electrode into the ceramic layer resulted in particularly large field enhancements and should be avoided to reduce the likelihood of device breakdown

Predicting the energy storage density in poly(methyl methacrylate)/methyl ammonium lead iodide composites

In high-energy density pulsed power capacitors, high permittivity particles are dispersed within a high breakdown strength polymer matrix. In theory, such composites should be able to achieve higher volumetric energy densities than is possible with either of the individual constituents. CH3NH3PbI3 (MALI) has a perovskite structure and may be fabricated at room temperature using a mechanosynthesis route in ethanol. In this study, MALI is used to form a dielectric composite with poly(methyl methacrylate) (PMMA) used as the matrix. Theoretical models are used to predict composite permittivity values that are compared to experimental values. Finite element modeling is used to simulate their effective permittivity and, beyond what the theoretical models can achieve, predicts their energy storage capabilities by analyzing electric field intensification. The simulations show increasing energy storage capability with penetration of MALI, but this is limited experimentally by their mixing capability

High quality factor cold sintered Li2MoO4BaFe12O19 composites for microwave applications

Ceramics-ceramic composites in series (1-x)Li2MoO4-xBaFe12O19 (LMO-BF12, 0.00 ≤ x ≤ 0.15) have been cold sintered at 120 °C and their structure and properties characterized. X-ray diffraction, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) confirmed that compositions were dual phase and had a dense microstructure. Composites in the xBF12-(1-x)LMO (0.0 ≤ x ≤ 0.15) series resonated at MW frequencies (∼6 GHz) with 5.6≤εr ≤ 5.8 and Qf = 16,000–22,000 GHz, despite the black colour of compositions with x > 0. The permeability of the composites was measured in the X band (∼8 GHz) and showed an increase from 0.94 (x = 0.05) to 1.02 (x = 0.15). Finite element modelling revealed that the volume fraction of BF12 dictates the conductivity of the material, with a percolation threshold at 10 vol% BF12 but changes in εr as a function of x were readily explained using a series mixing model. In summary, these composites are considered suitable for the fabrication of dual mode or enhanced bandwidth microstrip patch antennas

How to extract reliable core-volume fractions from core-shell polycrystalline microstructures using cross sectional TEM micrographs

A reliable method of extracting core-volume fraction from TEM micrographs of core-shell polycrystalline microstructures is presented. Three commonly used averaging methods based on a simple spherical model are shown to consistently underestimate the core-volume fraction due to the interpretation of a 3D structure from a 2D slice. The same trend is also revealed using Voronoi tessellated structures to mimic polycrystalline ceramics. In some cases the underestimate is less than half the true core-volume fraction. We show that using a new maximum core-volume fraction methodology can improve the extracted value to a consistent error of less than 5%. This approach uses a value taken from the largest core-volume fraction measured from 10 grains that exhibit a core-shell microstructure. This provides increasing accuracy and improvements in the confidence of the measurement when extracting core-volume fractions of polycrystalline ceramics from 2D TEM micrographs

Application of Johnson's approximation in finite element modeling for electric field‐dependent materials

Johnson's approximation is implemented in a finite element code to simulate the electric field dependence of a core–shell microstructure material. We show how the microstructure, based here on a 50:50 volume fraction, influences the measured effective permittivity as a function of applied voltage. Using a Johnson's parameter of β = 1.0 × 1010 Vm5/C3, verified from commercial BaTiO3-based multilayer ceramic capacitors (MLCC), we show how the microstructure and the difference in core and shell conductivities alter the local fields generated and how this influences the voltage dependence of the effective permittivity. Systems that comprise a conductive core-like material surrounded by a resistive shell experience little or modest voltage dependence due to the shell material providing shielding to large electric fields within the cores. Conversely, if the core material is more resistive than the shell material, substantial voltage dependence occurs with simulations showing over a 50% decrease in the effective permittivity. These simulations give improved understanding of voltage dependence and provide a method to help guide the design of future materials for MLCCs with improved performance

Field theoretic description of charge regulation interaction

In order to find the exact form of the electrostatic interaction between two proteins with dissociable charge groups in aqueous solution, we have studied a model system composed of two macroscopic surfaces with charge dissociation sites immersed in a counterion-only ionic solution. Field-theoretic representation of the grand canonical partition function is derived and evaluated within the mean-field approximation, giving the Poisson-Boltzmann theory with the Ninham-Parsegian boundary condition. Gaussian fluctuations around the mean-field are then analyzed in the lowest order correction that we calculate analytically and exactly, using the path integral representation for the partition function of a harmonic oscillator with time-dependent frequency. The first order (one loop) free energy correction gives the interaction free energy that reduces to the zero-frequency van der Waals form in the appropriate limit but in general gives rise to a mono-polar fluctuation term due to charge fluctuation at the dissociation sites. Our formulation opens up the possibility to investigate the Kirkwood-Shumaker interaction in more general contexts where their original derivation fails.Comment: 12 pages, 9 figures, submitted to EPJ