We have investigated electron transport in Nb doped SrTiO$_3$ single crystalsfor two doping densities. We find that the resistivity and mobility aretemperature dependent in both whereas the carrier concentration is almosttemperature invariant. We rationalize this using the hydrogenic theory forshallow donors. Further, we probe electrical transport across Schottkyinterfaces of Au on TiO$_2$ terminated n-type SrTiO$_3$. Quantitative analysisof macroscopic I-V measurements reveal thermionic emission dominated transportfor the low doped substrate whereas it deviates from such behavior for the highdoped substrate. This work is relevant for designing devices to studyelectronic transport using oxide-semiconductors.
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