  We investigated SrFeO$_{3-x}$ thin films on a SrTiO$_3$ (001) substrate
prepared via pulsed laser epitaxy using an optical spectroscopy technique. The
oxygen vacancy level ($x$) was controlled by post-annealing processes at
different oxygen partial pressures. We achieved a brownmillerite(BM) structure
at $x =$ 0.5 and observed the evolution of the crystal structure from BM into
perovskite(PV) as the oxygen concentration increased. We observed the evolution
of infrared-active phonons with respect to the oxygen concentration, which was
closely related to the structural evolution observed via X-ray diffraction. We
identified the phonons using the shell-model calculation. Furthermore, we
studied temperature-dependent behaviors of the phonon modes of three
representative samples: PV, and two BMs (BM$_{\mathrm{oop}}$ and
BM$_{\mathrm{ip}}$) with different orientations of the oxygen vacancy channel.
In the BM$_{\mathrm{oop}}$ sample, we observed a phonon mode, which exhibited
an unusual red-shift with decreasing temperature; this behavior may have been
due to the apical oxygen instability in the FeO$_6$ octahedron. Our results
provide important information regarding the ionic conduction mechanism in
SrFeO$_{3-x}$ material systems.
