Thickness Dependence of Hopping Transport in Amorphous-Ge Films

Abstract

The conductivity of gas-free thin films of amorphous germanium was measured as a function of temperature and film thickness. Existing theories of hopping conduction have been modified to apply to very thin films. The results are consistent with experiment, indicating that hopping conduction near the Fermi energy is the mechanism responsible for the conductivity below room temperature. The radius $a$ of the localized wave functions and the density of states ${N}_{\mathrm{F}}$ at the Fermi energy found are $a=10$ \AA{} and ${N}_{\mathrm{F}}=1.5\ifmmode\times\else\texttimes\fi{}{10}^{18}$ ${\mathrm{eV}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}3}$.