  The spin-Hall effect has recently attracted a lot of attention and a central
question is whether the effect is due to the intrinsic spin-orbit interaction
or due to spin-asymmetric scattering by extrinsic impurities. The objective of
this paper is to shed light on this question using a new approach based on the
non-equilibrium Green function (NEGF) formalism, which allows us to go
continuously from the ballistic to the diffusive limit and we present
approximate analytical expressions that describe our results fairly well. Our
model suggests that a spin accumulation proportional to the current should be
observed even in clean ballistic sample. We further show good quantitative
agreement with recent experimental observations in GaAs suggesting that these
can be understood in terms of an intrinsic effect driven by the Rashba
interaction, although experiments on ZnSe likely have a different origin.
