  Disorder in a proximitizing bulk superconductor can scatter quasiparticles in
a putative topological superconductor and eventually destroy the topological
superconducting state. We use a scattering approach and a random-matrix
calculation to estimate the disorder scattering time in a topological Josephson
junction. We find that the disorder scattering rate from the bulk of the
superconductor, even in the strong coupling limit, is suppressed in the ratio
of Fermi momenta between the semiconductor and superconductor. This suppression
of disorder scattering is accompanied by near perfect Andreev reflection at
such semiconductor/superconductor interfaces, which can be used as a signature
of such clean proximity effect. We also find that these results can be
understood by a semiclassical estimate of scattering. We discuss limits in
other systems such as the semiconductor nanowire where disorder scattering is
suppressed according to similar classical estimates.
