  $\beta$-Ga$_2$O$_3$ is a semiconductor with bandgap in the deep-UV ~ 5 eV.
Due to its strong phonon-hole coupling, holes are self-trapped inhibiting
bandgap luminescence at the deep-UV. In contrast, the self-trapped holes (STH)
can exhibit a strong luminescence at ~ 3.5 eV. This research addresses the
thermal response of the STH photoluminescence (PL), and the role of phonon
interactions at temperatures 77 K - 622 K in nanocrystalline films. It was
found that the PL intensity strongly diminishes as a function of increasing
temperature with activation energy ~ 72 meV. A study of the Raman modes
revealed that the intensity of the high frequency modes of the Ga$_I$O$_4$ site
decrease with temperature, implying a phonon annihilation process. These modes,
which have comparable energy to the STH activation energy, thus can couple to
the STH and transition them from a radiative to a non-radiative regime in
accordance with the configurational coordinate model at the strong phonon
coupling limit. The significantly broad Gaussian linewidth of the PL is also a
manifestation of a strong STH-phonon coupling. Furthermore, the peak position
of the STH exhibited a negligible temperature response, in contrast to the
redshift of ~ 220 meV of the bandedge of the film. In contrast to the intensity
behavior of the high frequency Raman modes, the low frequency ones were found
to follow the thermal Bose-Einstein phonon population.
