The temperature and volume fraction dependence of the resistivity of granular Al-Ge near the percolation threshold

Extensive measurements of the temperature and of the Al volume fraction dependence of the resistivity of granular Al-Ge have been made near the percolation threshold phi _c. The results at 295 K are analysed using the percolation equations, as modified by Efros and Shklovskii, and by Straley, for systems where the two components have finite conductivity ratios, and by fitting the results to the general effective media (GEM) equation, which also takes into account the finite conductivities of both components. The parameters of these equations are the conductivities (resistivities) of the two components, the critical conductivity exponents s and t, and the critical (percolation) volume fraction phi _c. The experimental value of phi _c, obtained from resistivity and magnetoresistivity measurements at and below the superconducting transition temperature for Al, agrees remarkably well with the values obtained from the percolation and GEM equations. The observed exponents are found to be high, and the width of the critical region surprisingly large. Attempts to extend this type of analysis to lower temperatures proved unsuccessful, and it is concluded that the resistivity of the more insulating component, namely of the amorphous Al-doped Ge, depends on the total Al content of the sample. It is shown that phi _c cannot be identified from the resistivity versus temperature curves between 5 and 295 K, nor from temperature derivatives of these curves. Graphs of the resistivity versus temperature of the amorphous Al-doped Ge for individual samples are extracted using the GEM equation.