We have investigated electron transport in Nb doped SrTiO$_3$ single crystals for two doping densities. We find that the resistivity and mobility are temperature dependent in both whereas the carrier concentration is almost temperature invariant. We rationalize this using the hydrogenic theory for shallow donors. Further, we probe electrical transport across Schottky interfaces of Au on TiO$_2$ terminated n-type SrTiO$_3$. Quantitative analysis of macroscopic I-V measurements reveal thermionic emission dominated transport for the low doped substrate whereas it deviates from such behavior for the high doped substrate. This work is relevant for designing devices to study electronic transport using oxide-semiconductors. ; Comment: 10 Pages, 3 Figures