  Oxide heterointerfaces are ideal for investigating strong correlation effects
to electron transport, relevant for oxide-electronics. Using hot-electrons, we
probe electron transport perpendicular to the La$_{0.7}$Sr$_{0.3}$MnO$_{3}$
(LSMO)- Nb-doped SrTiO$_3$ (Nb:STO) interface and find the characteristic
hot-electron attenuation length in LSMO to be 1.48 $\pm$ 0.10 unit cells (u.c.)
at -1.9 V, increasing to 2.02 $\pm$ 0.16 u.c. at -1.3 V at room temperature.
Theoretical analysis of this energy dispersion reveals the dominance of
electron-electron and polaron scattering. Direct visualization of the local
electron transport shows different transmission at the terraces and at the
step-edges.
