  Rutile Germanium Dioxide (r-GeO$_2$) has been identified as an ultrawide
bandgap (UWBG) semiconductor recently, featuring a bandgap of 4.68 eV,
comparable to Ga$_2$O$_3$ but offering bipolar dopability, higher electron
mobility, higher thermal conductivity, and higher Baliga's figure of merit
(BFOM).These superior properties position GeO$_2$ as a promising material for
various semiconductor applications. However, the epitaxial growth of r-GeO$_2$,
particularly in its most advantageous rutile polymorph, is still at an early
stage. This work explores the growth of r-GeO$_2$ using metal-organic chemical
vapor deposition (MOCVD) on an r-TiO$_2$ (001) substrate, utilizing tetraethyl
germane (TEGe) as the precursor. Our investigations reveal that higher growth
temperatures significantly enhance crystalline quality, achieving a full width
at half maximum (FWHM) of 0.181 degree at 925 degree C, compared to 0.54 degree
at 840 degree C and amorphous structures at 725 degree C. Additionally, we
found that longer growth durations increase surface roughness due to the
formation of faceted crystals. Meanwhile, adjusting the susceptor rotation
speed from 300 RPM to 170 RPM plays a crucial role in optimizing crystalline
quality, effectively reducing surface roughness by approximately 15 times. This
study offers a foundational guide for optimizing MOCVD growth conditions of
r-GeO$_2$ films, emphasizing the crucial need for precise control over
deposition temperature and rotation speed to enhance adatom mobility and
effectively minimize the boundary layer thickness.
