Correlation of strain and quantum corrections to resistance in very thin films of $SrTiO_{3-\delta } $ on Si through X-ray diffraction measurements

Our group has shown that a 2-d electron gas forms in strained thin films of oxygen deficient $SrTiO_{3-\delta } $(STO) grown epitaxially on Si(001). Low temperature magnetotransport measurements show quantum corrections to the Drude conductivity due to both quantum interference and electron-electron interaction (EEI) effects, and insulating behavior with Mott-Variable Range Hopping. The EEI are observed only for low carrier concentrations of $4-9\ast 10^{-12}cm^{-2}$, and for thicknesses less than 15 nm. The coherent growth of STO on Si produces a compressive in-plane strain of 1.7{\%} and a tetragonal distortion. A Mott insulating phase is predicted for STO for large distortions of the crystal structure with Ti-O-Ti angles of $165^{\circ }$ compared to $180^{\circ }$ in the cubic phase and for a high doping level.[1] We use x-ray diffraction to investigate the effect of film strain on EEI and the Mott insulating behavior. Wide angle $\theta -2\theta $ scans along with phi scans of the Si\textbraceleft 202\textbraceright and STO\textbraceleft 202\textbraceright family of planes show coherent crystal growth with STO(002)\textbar \textbar Si(004) and a $45^{\circ }$ in-plane rotation of STO on Si. Rocking curve measurements of STO(002) and the STO\textbraceleft 202\textbraceright verify the tetragonal distortion $\left( {a=b\ne c;\alpha =\beta =\gamma =90^{\circ }} \right)$. We use X-ray reflectivity to measure the thickness of the films, the interface roughness, and composition.