  The superconductor-insulator transition of ultrathin films of bismuth, grown
on liquid helium cooled substrates, has been studied. The transition was tuned
by changing both film thickness and perpendicular magnetic field. Assuming that
the transition is controlled by a T=0 critical point, a finite size scaling
analysis was carried out to determine the correlation length exponent v and the
dynamical critical exponent z. The phase diagram and the critical resistance
have been studied as a function of film thickness and magnetic field. The
results are discussed in terms of bosonic models of the
superconductor-insulator transition, as well as the percolation models which
predict finite dissipation at T=0.
