A two-dimensional electron gas (2DEG) can form in a layered crystal because of divergencies in the perpendicular electric potential arising from polar materials. The electrons move freely in the plane that forms at the interface between two different materials in the crystal. Much interest has developed in complex oxide heterostructures that exhibit interfacial 2DEGs, capable of having unique properties such as superconductivity and strong electron correlation effects. One such system with which this study is concerned is GdTiO₃/SrTiO₃. By analyzing the conductive and capacitive properties of the 2DEG and contacts deposited on top of the material stack we can extract information on the spatial carrier distribution and details of the band structure can be determined. We obtained the electron depletion width and tunability from capacitance-voltage measurements. To determine the Schottky barrier heights, contact resistance and verify the sheet resistance, we used the current-voltage method. Barrier heights were measured with Pt/Au and Ni contacts on HfO₂ with an Al₂O₃ buffer layer beneath as well as Pt/Au directly on Al₂O₃. The barriers of Pt/Au were found to be the highest, annealing showed an increase in barrier height, and sheet resistivity was found to be consistent with earlier measurements. Pt/Au showed good mechanical durability whereas Al₂O₃ provided a fragile contact. The methods can be used for further investigations of similar material systems and help to characterize the device processing and compositions for potential use in technical applications.