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Phonon scattering limited mobility in the representative cubic perovskite semiconductors SrGeO$_3$, BaSnO$_3$ and SrTiO$_3$

Cubic perovskite oxides are emerging high-mobility transparent conducting oxides (TCOs), but Ge-based TCOs had not been known until the discovery of metastable cubic SrGeO$_3$. $0.5 \times 0.4 \times 0.2$-mm$^3$ large single crystals of the cubic SrGeO$_3$ perovskite were successfully synthesized employing the high-pressure flux method. The phonon spectrum is determined from the IR optical reflectance and Raman-scattering analysis to evaluate the electron transport governed by optical phonon scattering. A calculated room-temperature mobility on the order of $3.9 \times 10^2$ cm$^2$V$^{-1}$s$^{-1}$ is obtained, identifying cubic SrGeO$_3$ as one of the most promising TCOs. Employing classical phonon theory and a combined experimental-theoretical approach, a comprehensive analysis of the intrinsic electron mobility in the cubic perovskite semiconductors SrGeO$_3$, BaSnO$_3$, and SrTiO$_3$ is provided based on the magnitude of polarization and eigenfrequency of optically active phonons.