  We study the superconducting proximity effect between a conventional
semiconductor and a disordered s-wave superconductor. We calculate the
effective momentum relaxation rate in the semiconductor due to processes
involving electron tunneling into a disordered superconductor and scattering
off impurities. The magnitude of the effective disorder scattering rate is
important for understanding the stability of the topological (chiral p-wave)
superconducting state that emerges in the semiconductor, since disorder
scattering has a detrimental effect and can drive the system into a
non-topological state. We find that the effective impurity scattering rate
involves higher-order tunneling processes and is suppressed due to the
destructive quantum interference of quasi-particle and quasi-hole trajectories.
We show that, despite the fact that both the proximity-induced gap and the
effective impurity scattering rate depend on interface transparency, there is a
large parameter regime where the topological superconducting phase is robust
against disorder in the superconductor. Thus, we establish that the static
disorder in the superconductor does not suppress the proximity induced
topological superconductivity in the semiconductor.
