  Coupling a normal metal wire to a superconductor induces an excitation gap in
the normal metal. In the absence of disorder, the induced excitation gap is
strongly suppressed by finite-size effects if the thickness of the
superconductor is much smaller than the thickness of the normal metal and the
superconducting coherence length. We show that the presence of disorder, either
in the bulk or at the exposed surface of the superconductor, significantly
enhances the magnitude of the induced gap, such that it approaches the
superconducting gap 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.
