  We determined the complex dielectric functions of $\varepsilon$-Ga$_2$O$_3$
using optical transmittance and reflectance spectroscopies at temperatures from
10 K to room temperature. The measured dielectric-function spectra reveal
distinct structures at a bandgap energy. We fitted a model dielectric function
based on the electronic energy-band structure to these experimental data. We
analyzed the temperature dependence of the band-gap with a model based on
phonon dispersion effects. One could explain it in terms of phonon-related
parameters such as the optical phonon temperature. We compare phonon-related
properties of $\varepsilon$-Ga$_2$O$_3$ with those of a large variety of
element and binary semiconductors.
