  Based on the Kubo formula approach, the spin Hall conductivity (SHC) of a
two-dimensional (2D) Rashba s-wave superconductor in the presence of
nonmagnetic impurities is calculated. We will show that by increasing the
superconducting gap, the SHC decreases monotonically to zero, while by
decreasing the concentration of impurities at zero gap, the SHC closes to the
clean limit universal value . As a function of the impurity relaxation rate at
and (is the spin-orbit coupling in unit of), we will show that in the dirty
limit () the SHC vanishes, and by increasing the relaxation time () the SHC
depends on the value of superconducting gap (), is changed from zero for full
gap to in zero gap. At low temperatures, the SHC goes to zero exponentially and
near the critical temperature depending on the concentration of the scattering
centers, the SHC will tend to the value of normal state. We will also show that
the SHC is independent of spin-orbit coupling () in the clean limit.
