Electric and Dielectric Properties of Polycrystalline Yttrium Iron Garnet: Space-Charge-Limited Currents in an Inhomogeneous Solid
Electric and Dielectric Properties of Polycrystalline Yttrium Iron Garnet: Space-Charge-Limited Currents in an Inhomogeneous Solid
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DOI：
10.1103/physrevb.8.2016
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发表时间：
1973-09
影响因子：
3.7
通讯作者：
P. Larsen;R. Metselaar
中科院分区：
文献类型：
--
作者：
P. Larsen;R. Metselaar
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 $i\ensuremath{\propto}{V}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}=1.2\ensuremath{-}5.1$. ac conductivity and dielectric permittivity both show a large dispersion in the ${10}^{\ensuremath{-}3}$-${10}^{5}$-Hz frequency range, e.g., a static value of the relative permittivity ${\ensuremath{\epsilon}}_{s}\ensuremath{\approx}4000$ and a high-frequency value ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}=18$. The results are interpreted in terms of a two-layer model with well-conducting grains (e.g., ${\ensuremath{\sigma}}_{300 \mathrm{K}}\ensuremath{\approx}7.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$) measuring 4 \ensuremath{\mu}m separated from each other by poorly conducting boundary layers (e.g., ${\ensuremath{\sigma}}_{300 \mathrm{K}}\ensuremath{\approx}1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$) of thickness 0.02 \ensuremath{\mu}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 ${\mathfrak{N}}_{t}(E)=\frac{{N}_{t}}{k{T}_{t}}{e}^{\frac{(E\ensuremath{-}{E}_{c})}{k{T}_{t}}}$, with ${N}_{t}=3.3\ifmmode\times\else\texttimes\fi{}{10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and ${T}_{t}=1110$ K. At 300 K, in the region of Ohmic conduction in the grain boundary layer ($Vl10$ 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 \ifmmode^\circ\else\textdegree\fi{}C to room temperature.
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 $i\ensuremath{\propto}{V}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}=1.2\ensuremath{-}5.1$. ac conductivity and dielectric permittivity both show a large dispersion in the ${10}^{\ensuremath{-}3}$-${10}^{5}$-Hz frequency range, e.g., a static value of the relative permittivity ${\ensuremath{\epsilon}}_{s}\ensuremath{\approx}4000$ and a high-frequency value ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}=18$. The results are interpreted in terms of a two-layer model with well-conducting grains (e.g., ${\ensuremath{\sigma}}_{300 \mathrm{K}}\ensuremath{\approx}7.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$) measuring 4 \ensuremath{\mu}m separated from each other by poorly conducting boundary layers (e.g., ${\ensuremath{\sigma}}_{300 \mathrm{K}}\ensuremath{\approx}1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$) of thickness 0.02 \ensuremath{\mu}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 ${\mathfrak{N}}_{t}(E)=\frac{{N}_{t}}{k{T}_{t}}{e}^{\frac{(E\ensuremath{-}{E}_{c})}{k{T}_{t}}}$, with ${N}_{t}=3.3\ifmmode\times\else\texttimes\fi{}{10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and ${T}_{t}=1110$ K. At 300 K, in the region of Ohmic conduction in the grain boundary layer ($Vl10$ 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 \ifmmode^\circ\else\textdegree\fi{}C to room temperature.