  Electrical conduction mechanisms in the disordered material system is
experimentally studied for p-type amorphous germanium (a-Ge) used for
high-purity Ge detector contacts. The localization length and the hopping
parameters in a-Ge are determined using the surface leakage current measured
from three high-purity planar Ge detectors. The temperature-dependent hopping
distance and hopping energy are obtained for a-Ge fabricated as the electrical
contact materials for high-purity Ge planar detectors. As a result, we find
that the hopping energy in a-Ge increases as temperature increases while the
hopping distance in a-Ge decreases as temperature increases. The localization
length of a-Ge is on the order of $2.13^{-0.05}_{+0.07} A^\circ$ to
$5.07^{-0.83}_{+2.58}A^\circ$, depending on the density of states near the
Fermi energy level within bandgap. Using these parameters, we predict that the
surface leakage current from a Ge detector with a-Ge contacts can be much
smaller than one yocto amp (yA) at helium temperature, suitable for rare-event
physics searches.
