  We have studied the insulator-superconductor transition (IST) by tuning the
thickness in quench-condensed $Bi$ films. The resistive transitions of the
superconducting films are smooth and can be considered to represent
"homogeneous" films. The observation of an IST very close to the quantum
resistance for pairs, $R_{\Box}^N \sim h/4e^2$ on several substrates supports
this idea. The relevant length scales here are the localization length, and the
coherence length. However, at the transition, the localization length is much
higher than the superconducting coherence length, contrary to expectation for a
"homogeneous" transition. This suggests the invalidity of a purely fermionic
model for the transition. Furthermore, the current-voltage characteristics of
the superconducting films are hysteretic, and show the films to be granular.
The relevant energy scales here are the Josephson coupling energy and the
charging energy. However, Josephson coupling energies ($E_J$) and the charging
energies ($E_c$) at the IST, they are found to obey the relation $E_J < E_c$.
This is again contrary to expectation, for the IST in a granular or
inhomogeneous, system. Hence, a purely bosonic picture of the transition is
also inconsistent with our observations. We conclude that the IST observed in
our experiments may be either an intermediate case between the fermioinc and
bosonic mechanisms, or in a regime of charge and vortex dynamics for which a
quantitative analysis has not yet been done.

Superconductivity