  The observation of metallic behavior at the interface between insulating
oxides has triggered worldwide efforts to shed light on the physics of these
systems and clarify some still open issues, among which the dimensional
character of the conducting system. In order to address this issue, we measure
electrical transport (Seebeck effect, Hall effect and conductivity) in
LaAlO_{3}/SrTiO_{3} interfaces and, for comparison, in a doped SrTiO_{3} bulk
single crystal. In these experiments, the carrier concentration is tuned, using
the field effect in a back gate geometry. The combined analysis of all
experimental data at 77 K indicates that the thickness of the conducting layer
is ~7 nm and that the Seebeck effect data are well described by a
two-dimensional (2D) density of states. We find that the back gate voltage is
effective in varying not only the charge density, but also the thickness of the
conducting layer, which is found to change by a factor of ~2, using an electric
field between -4 and +4MV/m at 77K. No enhancement of the Seebeck effect due to
the electronic confinement and no evidence for two-dimensional quantization
steps are observed at the interfaces.
