Electrical Transport in SrTiO$_{3}$ Under Biaxial Strain

Mobility engineering with strain is widely used for conventional semiconductors, but has only recently been proposed for complex oxides such as SrTiO$_{3}$. The conduction band structure of SrTiO$_{3}$ is complicated with multiple degenerate bands derived from the Ti 3d orbitals. Strain is thus expected to have a significant effect by lifting this degeneracy and altering the occupancy and curvature of the bands. Indeed, a 300{\%} increase in the electron mobility with values exceeding 128,000 cm$^{2}$/Vs at 1.8 K was demonstrated in MBE-grown SrTiO$_{3}$ films subjected to \textit{uniaxial} compressive strain [1]. For heterostructure engineering, the effect of \textit{biaxial} strain is relevant. Here, the electron mobilities in SrTiO$_{3}$ subjected to biaxial strain are investigated through growth of coherent films on lattice-mismatched substrates. Lightly-doped (high-mobility) strained SrTiO$_{3}$ films below the critical thickness are insulating because of significant surface depletion, which increases with decreasing temperature due to the high dielectric constant of SrTiO$_{3}$. We show that highly-doped, low-mobility capping layers address this problem, but require a multilayer model to analyze the Hall data in terms of the mobility in the lightly doped layer. [1] B. Jalan et al., Appl. Phys. Lett. \textbf{98}, 132102 (2011)