Built-in electric fields across heterojunctions between semiconducting materials underpin the functionality of modern device technologies. Heterojunctions between semiconductors and epitaxially grown crystalline oxides provide a rich setting in which built-in fields can be explored. Here, we present an electrical transport and hard X-ray photoelectron spectroscopy study of epitaxial SrNbxTi1-xO3-{delta} / Si heterojunctions. A non-monotonic anomaly in the sheet resistance is observed near room temperature, which is accompanied by a crossover in sign of the Hall resistance. The crossover is consistent with the formation of a hole gas in the Si and the presence of a built-in field. Hard X-ray photoelectron spectroscopy measurements reveal pronounced asymmetric features in both the SrNbxTi1-xO3-{delta} and Si core-level spectra that we show arise from built-in fields. The extended probe depth of hard X-ray photoelectron spectroscopy enables band bending across the SrNbxTi1-xO3-{delta} / Si heterojunction to be spatially mapped. Band alignment at the interface and surface depletion in SrNbxTi1-xO3-{delta} are implicated in the formation of the hole gas and built-in fields. Control of charge transfer and built-in electric fields across semiconductor-crystalline oxide interfaces opens a pathway to novel functional heterojunctions.