D.c. electrical conductivity of evaporated amorphous germanium—the low-temperature behaviour

Abstract

Measurements have been made of the d.c. electrical conductivity σ of amorphous germanium (a-Ge) films. These films were prepared by evaporation under a standard vacuum pressure of ∼ 10⁻⁷ Torr and were then exposed to air before being measured at ∼ 10⁻⁸ Torr. The temperature dependence of the logarithm of the conductivity σ(T) is roughly linear with T ^−1/4, exhibiting in all cases a bend at around 110 K. In addition, for the first time, a systematic deviation from linearity is observed for the films of the present work at low temperatures (T < 40 K). An attempt to account for this deviation by considering electron-electron correlation (Mott 1976, Pollak 1971, Knotek and Pollak 1974, Fleishman, Licciardello and Anderson 1978, Fleishman and Anderson 1980) is shown to be unsuccessful. It is suggested that the correct magnitude for σ(T), as well as the detailed shape of the experimental curves cannot be accounted for by current variable-range hopping models (originally proposed by Mott (1969) for electron hopping in some disordered systems) and might be most properly calculated by employing the non-adiabatic multiphonon hopping transition rate for a strongly localized carrier in a deformable lattice (Gorham-Bergeronand Emin 1977), which is valid for all strengths of electronphonon coupling and includes both acoustic and optical phonon modes. The variable-range hopping aspects of the conduction process play a minor role in explaining the experimental data.