We report the structural characterization of $Bi_xZn_{1-x}O$ thin films grown on c-plane sapphire substrates by plasma-assisted molecular beam epitaxy. By increasing the Bi flux during the growth process, $Bi_xZn_{1-x}O$ thin films with various Bi contents (x = 0~13.17 atomic %) were prepared. X-ray diffraction (XRD) measurements revealed the formation of Bi-oxide phase in (Bi)ZnO after increasing the Bi content. However, it was impossible to determine whether the formed Bi-oxide phase was the monoclinic structure ${alpha}-Bi_2O_3$ or the tetragonal structure ${eta}-Bi_2O_3$ by means of XRD ${ heta}-2{ heta}$ measurements, as the observed diffraction peaks of the $2{ heta}$ value at ~28 were very close to reflection of the (012) plane for the monoclinic structure ${alpha}-Bi_2O_3$ at 28.064 and the reflection of the (201) plane for the tetragonal structure ${eta}-Bi_2O_3$ at 27.946. By means of transmission electron microscopy (TEM) using a diffraction pattern analysis and a high-resolution lattice image, it was finally determined as the monoclinic structure ${alpha}-Bi_2O_3$ phase. To investigate the distribution of the Bi and Bi-oxide phases in BiZnO films, elemental mapping using energy dispersive spectroscopy equipped with TEM was performed. Considering both the XRD and the elemental mapping results, it was concluded that hexagonal-structure wurtzite $Bi_xZn_{1-x}O$ thin films were grown at a low Bi content (x = ~2.37 atomic %) without the formation of ${alpha}-Bi_2O_3$. However, the increased Bi content (x = 4.63~13.17 atomic %) resulted in the formation of the ${alpha}-Bi_2O_3$ phase in the wurtzite (Bi)ZnO matrix.