Electron Trapping and Detrapping in an Oxide Two-Dimensional Electron Gas: The Role of Ferroelastic Twin Walls

The choice of electrostatic gating over the conventional chemical doping for phase engineering of quantum materials is attributed to the fact that the former can reversibly tune the carrier density without affecting the system's level of disorder. However, this proposition seems to break down in field-effect transistors involving ${\mathrm{Sr}\mathrm{Ti}\mathrm{O}}_{3}$ (STO)-based two-dimensional electron gases. Such peculiar behavior is associated with electron trapping under an external electric field. However, the microscopic nature of the trapping centers remains an open question. In this paper, we investigate electric-field-induced charge-trapping and charge-detrapping phenomena at the conducting interface between the band insulators $\ensuremath{\gamma}$-${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and STO. Our transport measurements reveal that the charge trapping under a positive back-gate voltage (${V}_{g}$) above the tetragonal-to-cubic structural transition temperature (${T}_{c}$) of STO has a contribution from electric-field-assisted thermal escape of electrons from the quantum well, and from clustering of oxygen vacancies as well. We observe an additional source of trapping below ${T}_{c}$, which arises from the trapping of free carriers at ferroelastic twin walls in the STO. Application of a negative ${V}_{g}$ results in charge detrapping, which vanishes above ${T}_{c}$. This feature demonstrates the crucial role of structural domain walls in the electrical transport properties of STO-based heterostructures. The number of charges trapped (detrapped) at (from) a twin wall is controlled by the net polarity of the wall and is completely reversible with a sweep of ${V}_{g}$.