  The electronic transport properties of a series of LaAlO_3 / SrTiO_3
interfaces were investigated, and a systematic thickness dependence of the
sheet resistance and magnetoresistance was found for constant growth
conditions. This trend occurs above the critical thickness of four unit cells,
below which the LaAlO_3 / SrTiO_3 interface is not conducting. A dramatic
decrease in mobility of the electron gas of nearly two orders of magnitude was
observed with increasing LaAlO_3 thickness from five to 25 unit cells.
