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Contactless measurement of electrical conductance of a thin film of amorphous germanium

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.