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In LaAlO3/SrTiO3 heterostructures, a commonly observed but poorly understoodphenomenon is that of electron trapping in back-gating experiments. In thiswork, by combining magnetotransport measurements and self-consistentSchroedinger-Poisson calculations, we obtain an empirical relation between theamount of trapped electrons and the gate voltage. We find that the trappedelectrons follow an exponentially decaying spatial distribution away from theinterface. However, contrary to earlier observations, we find that the Fermilevel remains well within the quantum well. The enhanced trapping of electronsinduced by the gate voltage can therefore not be explained by a thermal escapemechanism. Further gate sweeping experiments strengthen our conclusion that thethermal escape mechanism is not valid. We propose a new mechanism whichinvolves the electromigration and clustering of oxygen vacancies in SrTiO3. Ourwork indicates that electron trapping is a universal phenomenon in SrTiO3-basedtwo-dimensional electron systems.

New insights into the electron trapping mechanism in LaAlO_3 / SrTiO3 heterostructures