  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.
