DC conductivity of amorphous germanium

A critical review of the phonon-assisted hopping theory of the dc conductivity σ is given. It is argued that the current theories either contain uncontrollable approximations, or they yield the result of the same order of magnitude as the approximations used or they may also lead to temperature dependence of σ other than that described by the Mott law. For the simplest usually accepted model of amorphous Ge (a-Ge), the low-temperature asymptote of σ is obtained in the form of a power law. In the experimental part of the work, careful measurements from 300 down to 8 K are reported, both for the pure and the gold-doped a-Ge films. Since the results of such measurements yield a straight line in a wide interval of temperature both in the log σ versus $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ and log σ versus log T scale, the power law appears to be equally well justified as the Mott law, both from the point of view of theory and that of experiment.