  Based on the Efros-Shklovskii behavior observed in electron transport and
tunneling, we have determined, independently and up to a constant on the order
of unity, the localization length and the dielectric constant for
quench-condensed ultrathin amorphous beryllium films. As the normal-state sheet
resistance of the films at 20 K is reduced with increasing film thickness, the
localization length increases exponentially. The superconductor-insulator
transition occurs when the localization length crosses the Ginzburg-Landau
coherence length. We discuss the implication of these results on a number of
issues regarding superconductivity in the strongly disordered regime.
