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

With infrared ellipsometry we studied the response of the confined electrons in a $γ$-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, $μ$, 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 $γ$-Al$_2$O$_3$/SrTiO$_3$