Bi$_4$-$_{x}$EU$_{x}$Ti$_3$O$_{12}$ (BET) thin films were etched by inductively coupled CF$_4$/Ar plasma. We obtained the maximum etch rate of 78 nm/min at the gas mixing ratio of CF$_4$(10%)/Ar(90%). The variation of volume density for F and Ar atoms are measured by the optical emission spectroscopy. As CF$_4$increased in CF$_4$/Ar plasma, the emission intensities of F increase, but Ar atoms decrease, which confirms our suggestion that emission intensity is proportional to the volume density of atoms. From X-ray photoelectron spectroscopy, the intensities of the Bi-O, the Eu-O and the Ti-O peaks are changed. By pure Ar plasma, intensity peak of the oxygen-metal (O-M : TiO$_2$, Bi$_2$O$_3$, Eu$_2$O$_3$) bond was seemed to disappear while the intensity of pure oxygen peak showed an opposite tendency. After the BET thin films was etched by CF$_4$/Ar plasma, the peak intensity of O-M bond increase slowly, but more quickly than that of peak belonged to pure oxygen atoms due to the decrease of Ar ion bombardment. Scanning electron microscopy was used to investigate etching Profile. The Profile of etched BET thin film was over 85$^{circ}$./TEX>.