Schottky Currents in Dielectric Films

The Frank-Simmons theory of emission-limited conduction in insulators has been extensively explored. The current-voltage data for Mylar, SiO, and ${\mathrm{Ta}}_2$ ${\mathrm{O}}_5$ insulating films have been calculated and the parameters needed to fit the data compare well with experimental values. The parameters needed to fit the $I-V$ data for Mylar were a work function ($\Phi$) of 1.40-1.45 eV, a dielectric constant ($\epsilon$) of 2.44, and a mobility-trapping factor product ($\mu \theta$) of ${10}^{-14\mathrm{}}$ to ${10}^{-18\mathrm{}}$ ${\mathrm{m}}^2$ × ${\mathrm{V}}^{-1\mathrm{}}$ ${\sec }^{-1\mathrm{}}$. For ${\mathrm{Ta}}_2$ ${\mathrm{O}}_5$, the parameters found were $\Phi =0.775\mathrm{}$ eV, $\epsilon =3.2\mathrm{}$, and $\mu \theta =1\mathrm{}\times {10}^{-13\mathrm{}}$ ${\mathrm{m}}^2$×${\mathrm{V}}^{-1\mathrm{}}$ ${\sec }^{-1\mathrm{}}$. In fitting these SiO data, it was found necessary to employ a temperature-dependent work function which varied from 0.66 eV at 195°K to 0.80 eV at 297°K more or less uniformly with a slope of approximately 1.4×${10}^{-3\mathrm{}}$ eV°${\mathrm{K}}^{-1\mathrm{}}$. The model of Frank and Simmons is analyzed in terms of both the Poole-Frenkel effect and hot-electron effects, and equations containing both terms are presented.