  This work reports high carrier mobilities and growth rates, simultaneously in
low unintentionally-doped UID (10$^{15}$ cm$^{-3}$) MOCVD-grown thick
$\beta$-Ga$_2$O$_3$ epitaxial drift layers, with thicknesses reaching up to 6.3
$\mu$m, using triethylgallium (TEGa) as a precursor. Record high room
temperature Hall mobilities of 187-190 cm$^2$/Vs were measured for background
carrier density values of 2.4 - 3.5$\times$10$^{15}$ cm$^{-3}$ grown at a rate
of 2.2 $\mu$m/hr. A controlled background carrier density scaling from
3.3$\times$10$^{16}$ cm$^{-3}$ to 2.4$\times$10$^{15}$ cm$^{-3}$ is
demonstrated, without the use of intentional dopant gases such as silane, by
controlling the growth rate and O$_2$/TEGa ratio. Films show smooth surface
morphologies of 0.8-3.8 nm RMS roughness for film thicknesses of 1.24 -
6.3$\mu$m. Vertical Ni Schottky barrier diodes (SBDs) fabricated on UID MOCVD
material were compared with those fabricated on hydride vapor phase epitaxy
(HVPE) material, revealing superior material and device characteristics. MOCVD
SBDs on a 6.3 $\mu$m thick epitaxial layer show a uniform charge vs. depth
profile of $\sim$2.4$\times$10$^{15}$ cm$^{-3}$, an estimated $\mu$$_{drift}$
of 132 cm$^2$/Vs, a breakdown voltage (V$_{BR}$) close to 1.2 kV and a surface
parallel plane field of 2.05MV/cm without any electric field management -
setting record-high parameters for any MOCVD-grown $\beta$-Ga$_2$O$_3$ vertical
diode to date.
