Electric and Dielectric Properties of Polycrystalline Yttrium Iron Garnet: Space-Charge-Limited Currents in an Inhomogeneous Solid

The dc conductivity of n-type polycrystalline yttrium iron garnet has been measured at temperatures near room temperature as a function of the applied voltage. At voltages below a critical value an Ohmic behavior is observed, while above this value we find i∝V^α, with α=1.2-5.1. ac conductivity and dielectric permittivity both show a large dispersion in the 10^-3-10⁵-Hz frequency range, e.g., a static value of the relative permittivity εₛ≈4000 and a high-frequency value ε_∞=18. The results are interpreted in terms of a two-layer model with well-conducting grains (e.g., σ300 K≈7.2×10^-8 Ω^-1 cm^-1) measuring 4 {μ}m separated from each other by poorly conducting boundary layers (e.g., σ300 K≈1.8×10^-15 Ω^-1 cm^-1) of thickness 0.02 {μ}m. At low voltages, conduction is determined by the boundary layer. At higher voltages, the current in the boundary layers is space-charge limited. A model is developed for space-charge-limited currents in an inhomogeneous solid of this kind. All experimental results can be explained qualitatively by this model. For one sample the measurements have been quantitatively analyzed. Good agreement with theory is found if we assume an exponential distribution of the density of states of the trapping centers in the boundary layers of the form Nₜ(E)=NₜkTₜe^(E-Ec)kTₜ, with Nₜ=3.3×10²⁰ cm^-3 and Tₜ=1110 K. At 300 K, in the region of Ohmic conduction in the grain boundary layer ($V<10$ V), the Fermi level of this layer is situated 0.88 eV below the conduction band; upon charge injection its position rises, for an externally applied voltage of 500 V, to about 0.63 eV below the conduction band. Annealing experiments at different oxygen pressures show that the poorly conducting boundary layers are regions which are reoxidized during cooling from the sintering temperature of 1430 ^∘{}C to room temperature.