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 aluminum volume fraction dependence of the resistivity of granular Al--Ge have been made near the percolation threshold phi sub c . The results at 295K are analysed using the percolation equations, as modified by Efros and Shklovskii, and by Straley. 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 sub c . The experimental value of phi sub 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 unsucessful, 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 sub c cannot be identified from the resistivity vs. temperature curves between 5 and 295K, nor from temperature derivatives of these curves. Graphs of the resistivity vs. temperature of the amorphous Al-doped Ge for individual samples are extracted using the GEM equation.