A new model based on a linear diffusion equation is proposed to explain the current-voltage characteristics of blocking grain boundaries in Y-doped CeO2 in particular. One can also expect that the model can be applicable to the ionic conductors with blocking grain boundaries, in general. The model considers an infinitely long chain of identical grains separated by grain boundaries, which are treated as regions in which depletion layers of mobile ions are formed due to trapping of immobile charges that do not depend on the applied voltage as well as temperature. The model assumes that (1) the grain boundaries do not represent physical blocking layers, which implies that if there is a second phase at the grain boundaries, then it is too thin to impede ion diffusion and (2) the ions follow Boltzmann distribution throughout the materials. Despite its simplicity, the model successfully reproduces the "power law": current proportional to voltage power n and illustrated with the experimental example of Y-doped ceria. The model also correctly predicts that the product nT, where T is the temperature in K, is constant and is proportional to the grain boundary potential as long as the charge at the grain boundaries remains trapped. The latter allows its direct determination from the current-voltage characteristics and promises considerable simplification in the analysis of the electrical characteristics of the grain boundaries with respect to the models currently in use.

The validity and limitations of two quantitative approaches for estimating the height of the potential barrier at grain boundaries, Ψgb, in polycrystalline ionic conductors are examined both theoretically and experimentally. The linear diffusion model recently proposed by Kim and Lubomirsky determines Ψgb from the value of the power exponent of the current (Igb)-voltage (Ugb) relationship at the grain boundary, dln(Igb)/dln(Ugb), while the conventional approach calculates Ψgb from the ratio of the grain boundary resistivity to the grain core resistivity. The results of our theoretical analysis demonstrate that both approaches should yield consistent values for Ψgb if the ionic current through the grain boundary is limited exclusively by space charge. While the value of Ψgb obtained by the power law procedure is relatively insensitive to other causes of current obstruction, e.g. current constriction and/or local structural disorder, the resistivity ratio method, if not explicitly corrected for these additional limitations, results in a considerable overestimate of the grain boundary potential barrier. Hence, it is possible to distinguish between grain boundary resistance due to the presence of space charge and that due to additional sources by comparing the values of Ψgb determined using each of the two methods. Our theoretical analysis is confirmed experimentally with 3 mol% Gd-doped ceria with and without an additional source of current constriction across the grain boundary.

We demonstrate the applicability of the linear diffusion model recently proposed for the current-voltage, Igb-Ugb, characteristics of blocking grain boundaries in solid electrolytes to various oxygen-ion and proton conductors: the model precisely reproduces the Igb-Ugb characteristics of La-, Sm-, Gd-, and Y-doped ceria as well as Y-doped barium zirconate to provide accurate explanations to the "power law" behavior of the Igb-Ugb relationship, i.e. Igb ∝ Ugb(n), experimentally observed. The model also predicts that the grain-boundary potential, Ψgb, in doped ceria weakly depends on temperature, if the trapped charge remains constant, and that the value of Ψgb can be determined from the value of the power n. Furthermore, the model provides a plausible explanation for the increase in the Ψgb with temperature observed for the proton conductor in which the concentration of the charge carrier decreases with temperature. Hence, it is evident that the linear diffusion model is robust and applicable to grain boundaries in a large variety of practically important solid electrolytes.

The impact of electron injection, using 10 keV beam of a Scanning Electron Microscope, on minority carrier transport in Si-doped β-Ga2O3 was studied for temperatures ranging from room to 120°C. In-situ Electron Beam-Induced Current technique was employed to determine the diffusion length of minority holes as a function of temperature and duration of electron injection. The experiments revealed a pronounced elongation of hole diffusion length with increasing duration of injection. The activation energy, associated with the electron injection-induced elongation of the diffusion length, was determined at ∼ 74 meV and matches the previous independent studies. It was additionally discovered that an increase of the diffusion length in the regions affected by electron injection is accompanied by a simultaneous decrease of cathodoluminescence intensity. Both effects were attributed to increasing non-equilibrium hole lifetime in the valence band of β-Ga2O3 semiconductor.

The effect of electron injection on minority carrier transport in Si-doped β-Ga2O3 Schottky rectifiers with 18 MeV alpha particle exposure (fluences of 1012–1013 cm−2) was studied from room temperature to 120°C. Electron Beam-Induced Current technique in-situ in Scanning Electron Microscope was used to find the diffusion length of holes as a function of duration of electron injection and temperature for alpha-particle irradiated rectifiers and compared with non-irradiated reference devices. The activation energy for electron injection-induced effect on diffusion length for the alpha-particle irradiated sample was determined to be ∼ 49 meV as compared to ∼74 meV for the reference sample. The decrease in activation energy of the electron injection effect on diffusion length for irradiated sample is attributed to radiation-induced generation of additional shallow recombination centers closer to the conduction band edge.