Schottky Currents in Dielectric Films

Abstract

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}$${\mathrm{O}}_{5}$ insulating films have been calculated and the parameters needed to fit the data compare well with experimental values. The parameters needed to fit the $I\ensuremath{-}V$ data for Mylar were a work function ($\ensuremath{\Phi}$) of 1.40-1.45 eV, a dielectric constant ($\ensuremath{\epsilon}$) of 2.44, and a mobility-trapping factor product ($\ensuremath{\mu}\ensuremath{\theta}$) of ${10}^{\ensuremath{-}14}$ to ${10}^{\ensuremath{-}18}$ ${\mathrm{m}}^{2}$ \ifmmode\times\else\texttimes\fi{} ${\mathrm{V}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. For ${\mathrm{Ta}}_{2}$${\mathrm{O}}_{5}$, the parameters found were $\ensuremath{\Phi}=0.775$ eV, $\ensuremath{\epsilon}=3.2$, and $\ensuremath{\mu}\ensuremath{\theta}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ ${\mathrm{m}}^{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{V}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. In fitting these SiO data, it was found necessary to employ a temperature-dependent work function which varied from 0.66 eV at 195\ifmmode^\circ\else\textdegree\fi{}K to 0.80 eV at 297\ifmmode^\circ\else\textdegree\fi{}K more or less uniformly with a slope of approximately 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ eV\ifmmode^\circ\else\textdegree\fi{}${\mathrm{K}}^{\ensuremath{-}1}$. 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.