We present a detailed investigation of the electrical properties of epitaxial La0.7Sr0.3MnO3/SrTi0.98Nb0.02O3 Schottky junctions. A fabrication process that allows reduction of the junction dimensions to current electronic device size has been employed. A heavily doped semiconductor has been used as a substrate in order to suppress its series resistance. We show that, unlike standard semiconductors, high-quality oxide-based Schottky junctions maintain a highly rectifying behavior for doping concentration of the semiconductor larger than 10^20 cm^(-3). Moreover, the junctions show hysteretic current-voltage characteristics.