  The generation and manipulation of carrier spin polarization in
semiconductors solely by electric fields has garnered significant attention as
both an interesting manifestation of spin-orbit physics as well as a valuable
capability for potential spintronics devices. One realization of these
spin-orbit phenomena, the spin Hall effect (SHE), has been studied as a means
of all-electrical spin current generation and spin separation in both
semiconductor and metallic systems. Previous measurements of the spin Hall
effect have focused on steady-state generation and time-averaged detection,
without directly addressing the accumulation dynamics on the timescale of the
spin coherence time. Here, we demonstrate time-resolved measurement of the
dynamics of spin accumulation generated by the extrinsic spin Hall effect in a
doped GaAs semiconductor channel. Using electrically-pumped time-resolved Kerr
rotation, we image the accumulation, precession, and decay dynamics near the
channel boundary with spatial and temporal resolution and identify multiple
evolution time constants. We model these processes using time-dependent
diffusion analysis utilizing both exact and numerical solution techniques and
find that the underlying physical spin coherence time differs from the
dynamical rates of spin accumulation and decay observed near the sample edges.
