The superconductor-insulator transition in ultrathin films of amorphous Bi was tuned by changing the film thickness, with and without an applied magnetic field. The first experimentally obtained phase diagram is mapped as a function of thickness and magnetic field in the T=0 limit. A finite size scaling analysis has been carried out to determine the critical exponent product vz, which was found to be 1.2 for the zero field transition, and 1.4 for the finite field transition. Both results are different from the exponents found for the magnetic field tuned transition in the same system, 0.7.
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