  We incorporate quantum size effect to investigate the extrinsic spin-Hall
effect in ultrathin metal films. A Lippmann-Schwinger formalism based
theoretical method, accounting for quantum confinement and surface roughness
scattering, is developed to calculate both spin-Hall and longitudinal
resistivities and spin-Hall angle. The presence of quantum confinement gives
rise to a linear relation $\rho_{sH}=\alpha \rho+\beta$ between the extrinsic
spin-Hall resistivity $\rho_{sH}$ and longitudinal charge resistivity $\rho$.
The linear term $\alpha\rho$ originates from side jump, and the constant
$\beta$ is due to skew scattering. This deviates significantly from the
commonly accepted scaling law $\rho_{sH}=a\rho^2+b\rho$ in a bulk conductor.
Thus we call for cautious interpretation of experimental data when applying the
scaling law.
