Various methods for determining the critical metallic volume fraction phicat the metal-insulator transition

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Abstract
The metal-insulator transition in composite Al-Ge films has been extensively studied experimentally. Using the superconducting properties of clusters composed of aluminium grains in the presence of a magnetic field, the critical metallic volume fraction phi cgp has been determined for the case of grain percolation (gp). Because the films investigated are composed of extremely small grains of Al partially coated with amorphous Ge, the critical volume fraction phi c takes on a comparably large value. Typically about 56 at.% Al. The low-temperature electrical conductivity data are examined using a number of criteria for phi c. Most of these criteria yield values phi c to within 1% of phi cgp. However, one widely used criterion involving the fitting of the low-temperature conductivity data to a T1/2 dependence, as suggested by the electron-electron interaction theory, was found to yield a significantly smaller value for phi c. Methods based on room-temperature data are also evaluated. These criteria yield phi c values that are within +or-1% of phi cgp.