Infrared ellipsometry study of the confined electrons in a high-mobility $\gamma$-Al${}_2$O${}_3$/SrTiO${}_3$ heterostructure

With infrared ellipsometry we studied the response of the confined electrons in a $\gamma$-Al${}_2$O${}_3$/SrTiO${}_3$ heterostructures in which they originate predominantly from oxygen vacancies. From the analysis of a so-called Berreman mode, that develops near the highest longitudinal optical phonon mode of SrTiO${}_3$, we derive the sheet carrier density, $N_s$, the mobility, $\mu$, and also the depth profile of the carrier concentration. Notably, we find that $N_s$ and the shape of the depth profile are similar as in LaAlO${}_3$/SrTiO${}_3$ heterostructures for which the itinerant carriers are believed to arise from a polar discontinuity. The main differences concern the higher mobility and a relatively stronger confinement of the electrons in $\gamma$-Al${}_2$O${}_3$/SrTiO${}_3$