  We present a contactless method for measuring charge in a thin film of
amorphous germanium (a-Ge) with a nanoscale silicon MOSFET charge sensor. This
method enables the measurement of conductance of the a-Ge film even in the
presence of blocking contacts. At high bias voltage, the resistance of the
contacts becomes negligible and a direct measurement of current gives a
conductance that agrees with that from the measurement of charge. This
charge-sensing technique is used to measure the temperature- and
field-dependence of the conductance, and they both agree with a model of Mott
variable-range hopping. From the model, we obtain a density of states at the
Fermi energy of 1.6 x 10^18 eV^-1 cm^-3 and a localization length of 1.06 nm.
This technique enables the measurement of conductance as low as 10^-19 S.
