  Unusual transport properties of superconducting (SC) materials, such as the
under doped cuprates, low dimensional superconductors in strong magnetic
fields, and insulating films near the Insulator Superconductor Transition
(IST), have been attributed to the formation of inhomogeneous phases.
Difficulty correlating the behaviors with observations of the inhomogeneities
make these connections uncertain. Of primary interest here are proposals that
insulating films near the IST, which show an activated resistance and giant
positive magnetoresistance, contain islands of Cooper Pairs (CPs). Here we
present evidence that these types of inhomogeneities are essential to such an
insulating phase in amorphous Bi (a-Bi) films deposited on substrates patterned
with nanometer-sized holes. The patterning induces film thickness variations,
and corresponding coupling constant variations, that transform the composition
of the insulator from localized electrons to CPs. Analyses near the
thickness-tuned ISTs of films on nine different substrates show that weak links
between SC islands dominate the transport. In particular, the ISTs all occur
when the link resistance approaches the resistance quantum for pairs. These
observations lead to a detailed picture of CPs localized by spatial variations
of the superconducting coupling constant.
