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 f
ind 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.
