  Using a low-temperature conductive-tip atomic force microscope in
cross-section geometry we have characterized the local transport properties of
the metallic electron gas that forms at the interface between LaAlO3 and
SrTiO3. At low temperature, we find that the carriers do not spread away from
the interface but are confined within ~10 nm, just like at room temperature.
Simulations taking into account both the large temperature and electric-field
dependence of the permittivity of SrTiO3 predict a confinement over a few nm
for sheet carrier densities larger than ~6 10^13 cm-2. We discuss the
experimental and simulations results in terms of a multi-band carrier system.
Remarkably, the Fermi wavelength estimated from Hall measurements is ~16 nm,
indicating that the electron gas in on the verge of two-dimensionality.
