  $\beta$-Ga$_2$O$_3$ is a next-generation ultra wide bandgap semiconductor
(E$_g$ = 4.8 eV to 4.9 eV) that can be homoepitaxially grown on commercial
substrates, enabling next-generation power electronic devices among other
important applications. Analyzing the quality of deposited homoepitaxial layers
used in such devices is challenging, in part due to the large probing depth in
traditional x-ray diffraction (XRD) and also due to the surface-sensitive
nature of atomic force microscopy (AFM). Here, a combination of evanescent
grazing-incidence skew asymmetric XRD and AFM are investigated as an approach
to effectively characterize the quality of homoepitaxial $\beta$-Ga$_2$O$_3$
layers grown by molecular beam epitaxy at a variety of Ga/O flux ratios.
Accounting for both structure and morphology, optimal films are achieved at a
Ga/O ratio of $\sim$1.15, a conclusion that would not be possible to achieve by
either XRD or AFM methods alone. Finally, fabricated Schottky barrier diodes
with thicker homoepitaxial layers are characterized by $J-V$ and $C-V$
measurements, revealing an unintentional doping density of 4.3 $\times$
10$^{16}$ cm$^{-3}$ - 2 $\times$ 10$^{17}$ cm$^{-3}$ in the epilayer. These
results demonstrate the importance of complementary measurement methods for
improving the quality of the $\beta$-Ga$_2$O$_3$ homoepitaxial layers used in
power electronic and other devices.
