Metallicity in Ultra-Thin Oxygen-Deficient SrTiO$_3$ Thin Films

We report on the observation of metallic behavior in thin films of oxygen-deficient SrTiO$_3$ - down to 9 unit cells - when coherently strained on (001) SrTiO$_3$ or DyScO$_3$-buffered (001) SrTiO$_3$ substrates. These films have carrier concentrations of up to 2$\times10^{22}$ cm$^{-3}$ and mobilities of up to 19,000 cm$^2$/V-s at 2 K. There exists a non-conducting layer in our SrTiO$_{3-\delta}$ films that is larger in films with lower carrier concentrations. This non-conducting layer can be attributed to a surface depletion layer due to a Fermi level pinning potential. The depletion width, transport, and structural properties are not greatly affected by the insertion of a DyScO$_3$ buffer between the SrTiO$_3$ film and SrTiO$_3$ substrate.