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

The metal-insulator transition in composite Al-Ge films has been extensively studied experimentally. Using the superconducting properties of percolating clusters composed of small aluminum grains in the presence of a magnetic field, the critical metallic volume fraction φ_c(sc) for the metal-insulator transition has been uniquely determined. The low temperature electrical conductivity data are examined using a number of criteria for φ_c. Some of these criteria are quite successful, yielding φ_c's to within one percent of φ_c(sc), the definitive value. However, one widely used criterion involving the fitting of the low temperature conductivity data to a T ^{1 2} dependence, which results from the electron-electron interaction theory, was found to yield a very different value of φ_c. Other methods and/or criteria, using room temperature conductivity data to determine φ_c, are evaluated. These also yield φ_c values that are within 1% of φ_c(sc).