  Using scanning gate microscopy (SGM), we probe the scattering between a beam
of electrons and a two-dimensional electron gas (2DEG) as a function of the
beam's injection energy, and distance from the injection point. At low
injection energies, we find electrons in the beam scatter by small-angles, as
has been previously observed. At high injection energies, we find a surprising
result: placing the SGM tip where it back-scatters electrons increases the
differential conductance through the system. This effect is explained by a
non-equilibrium distribution of electrons in a localized region of 2DEG near
the injection point. Our data indicate that the spatial extent of this highly
non-equilibrium distribution is within ~1 micrometer of the injection point. We
approximate the non-equilibrium region as having an effective temperature that
depends linearly upon injection energy.
