Coupling a normal-metal wire to a superconductor induces an excitation gap Δind in the normal metal. In the absence of disorder, the induced excitation gap is strongly suppressed by finite-size effects if the thickness DS of the superconductor is much smaller than the thickness DN of the normal metal and the superconducting coherence length ξ. We show that the presence of disorder, either in the bulk or at the exposed surface of the superconductor, significantly enhances the magnitude of Δind, such that Δind approaches the superconducting gap Δ in the limit of strong disorder. We also discuss the shift of energy bands inside the normal-metal wire as a result of the coupling to the superconducting shell.
