Electron Concentration Dependence of the Coulomb Gap in AlGaAs:Si

Abstract

The Efros-Shklovskii (ES) ${T}_{1/2}$ and Mott ${T}_{1/4}$ parameters and the width of the soft Coulomb gap in ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{A}\mathrm{s}:\mathrm{S}\mathrm{i}$ have been determined for electron concentration $n$ ranging from $1.2\ifmmode\times\else\texttimes\fi{}{10}^{16}$ to $14\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{cm}}^{\ensuremath{-}3}$. The gap width presents a maximum at an $n$ value corresponding to a compensation ratio $K$ between 0.94 and 0.97. The ${T}_{1/2}$ and ${T}_{1/4}$ parameters decrease exponentially with $n$ and provide the simple relation ${e}^{2}{g}_{0}{\ensuremath{\xi}}^{2}/\ensuremath{\kappa}\ensuremath{\propto}n$, between the localization length $\ensuremath{\xi}$ and the dielectric constant $\ensuremath{\kappa}$. This is compatible with scaling theory. Our data also suggest that the validity limits for the Mott and ES regimes should be estimated, respectively, by $2.5({T}_{1/2}{)}^{2}/{T}_{1/4}$ and $({T}_{1/2}{)}^{2}/{T}_{1/4}$.