The disorder-induced superconductor-to-insulator transition in amorphous ${\mathrm{Nb}}_x{\mathrm{Si}}_{1-x}$ two-dimensional thin films is studied for different niobium compositions $x$ through a variation of the sample thickness $d$. We show that the critical thickness $d_c$, separating a superconducting regime from an insulating one, increases strongly with diminishing $x$, thus attaining values of over 100 Å. The corresponding phase diagram in the $(d,x)$ plane is inferred and related to the three-dimensional situation. The two-dimensional superconductor-to-insulator transition well connects with the three-dimensional superconductor-to-metal transition.

• Received 21 October 2013
• Revised 5 August 2014

DOI:https://doi.org/10.1103/PhysRevB.90.060203