  We report on metalorganic chemical vapor deposition (MOCVD) growth of
controllably Si-doped 4.5 $\mu$m thick $\beta$-Ga$_2$O$_3$ films with electron
concentrations in the 10$^{15}$ cm$^{-3}$ range and record-high room
temperature Hall electron mobilities of up to 200 cm$^2$/V.s, reaching the
predicted theoretical maximum room temperature mobility value for
$\beta$-Ga$_2$O$_3$. Growth of the homoepitaxial films was performed on
Fe-doped (010) $\beta$-Ga$_2$O$_3$ substrates at a growth rate of 1.9 $\mu$m/hr
using TEGa as the Gallium precursor. To probe the background electron
concentration, an unintentionally doped film was grown with a Hall
concentration of 3.43 x 10$^{15}$ cm$^{-3}$ and Hall mobility of 196
cm$^2$/V.s. Growth of intentionally Si-Doped films was accomplished by fixing
all growth conditions and varying only the silane flow, with controllable Hall
electron concentrations ranging from 4.38 x 10$^{15}$ cm$^{-3}$ to 8.30 x
10$^{15}$ cm$^{-3}$ and exceptional Hall mobilities ranging from 194 - 200
cm$^2$/V.s demonstrated. C-V measurements showed a flat charge profile with the
N$_D^+$ - N$_A^-$ values correlating well with the Hall-measured electron
concentration in the films. SIMS measurements showed the silicon atomic
concentration matched the Hall electron concentration with Carbon and Hydrogen
below detection limit in the films. The Hall, C-V, and SIMS data indicate the
growth of high-quality 4.5 $\mu$m thick $\beta$-Ga$_2$O$_3$ films and
controllable doping into the mid 10$^{15}$ cm$^{-3}$ range. These results
demonstrate MOCVD growth of electronics grade record-high mobility, low carrier
density, and thick $\beta$-Ga$_2$O$_3$ drift layers for next generation
vertical $\beta$-Ga$_2$O$_3$ power devices.
