Hole localization and interaction in 2-d heavily doped p-type germanium

We have measured conductivity and magnetoconductivity as a function of temperature and magnetic field (T from 1.3 to 4.2 K, H from 0 to 1.25 T) on two-dimensional heavily doped p-type germanium thin films,. The films were semicontinuous, aluminum doped with carrier concentrations up to around 10²⁰holes/cm and sheet resistances from 350 to 1200 ohm/square at 4.2 K. The resistance depends on temperature as a In T in the range studied, with a between 0.81 and 1.50 e²/2ॠ²\hbar. The magnetoconductivity at low fields and low temperatures is mainly due to localization, positive in the most heavily doped samples and negative in the others. At fields higher than approximately 0.4 T interaction effects become dominant and the magnetoconductivity is negative.