  Using a combination of vertical transport measurements across and lateral
transport measurements along the LaAlO$_{3}$/SrTiO$_{3}$ heterointerface, we
demonstrate that significant potential barrier lowering and band bending are
the cause of interfacial metallicity. Barrier lowering and enhanced band
bending extends over 2.5 nm into LaAlO$_{3}$ as well as SrTiO$_{3}$. We explain
origins of high-temperature carrier saturation, lower carrier concentration,
and higher mobility in the sample with the thinnest LaAlO$_{3}$ film on a
SrTiO$_{3}$ substrate. Lateral transport results suggest that parasitic
interface scattering centers limit the low-temperature lateral electron
mobility of the metallic channel.
