  The in-situ metalorganic chemical vapor deposition (MOCVD) growth of
Al$_2$O$_3$ dielectrics on $\beta$-Ga$_2$O$_3$ and
$\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ films is investigated as a function of
crystal orientations and Al compositions of $\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$
films. The interface and film qualities of Al$_2$O$_3$ dielectrics are
evaluated by high resolution X-ray diffraction (HR-XRD) and scanning
transmission electron microscopy (HR-STEM) imaging, which indicate the growth
of high quality amorphous Al$_2$O$_3$ dielectrics with abrupt interfaces on
(010), (100) and (-201) oriented $\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ films. The
surface stoichiometries of Al$_2$O$_3$ deposited on all orientations of
$\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ are found to be well maintained with a
bandgap energy of 6.91 eV as evaluated by high resolution x-ray photoelectron
spectroscopy, which is consistent with the atomic layer deposited (ALD)
Al$_2$O$_3$ dielectrics. The evolution of band offsets at both in-situ MOCVD
and ex-situ ALD deposited Al$_2$O$_3$/$\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ are
determined as a function of Al composition, indicating the influence of the
deposition method, orientation, and Al composition of
$\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ films on resulting band alignments. Type II
band alignments are determined at the MOCVD grown
Al$_2$O$_3$/$\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ interfaces for (010) and (100)
orientations, whereas type I band alignments with relatively lower conduction
band offsets are observed along (-201) orientation. Results from this work
revealed that the in-situ MOCVD deposited high quality Al$_2$O$_3$ dielectrics
with sharp interfaces can be considered as a viable alternative of commonly
used ex-situ deposited (ALD) Al$_2$O$_3$ for developing high performance
$\beta$-Ga$_2$O$_3$ and $\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ based devices.
