We investigated the etching characteristics of $HfAlO_3$ thin films in $O_2/Cl_2/Ar$ and $O_2/BCl_3/Ar$ gas, using a high-density plasma (HDP) system. The etch rates of the $HfAlO_3$ thin film obtained were 30.1 nm/min and 36 nm/min in the $O_2/Cl_2/Ar$ (3:4:16 sccm) and $O_2/BCl_3/Ar$ (3:4:16 sccm) gas mixtures, respectively. At the same time, the etch rate was measured as a function of the etching parameter, namely as the process pressure. The chemical states on the surface of the etched $HfAlO_3$ thin films were investigated by X-ray photoelectron spectroscopy. Auger electron spectroscopy was used for elemental analysis on the surface of the etched $HfAlO_3$ thin films. These surface analyses confirm that the surface of the etched $HfAlO_3$ thin film is formed with nonvolatile by-product. Also, Cl-O can protect the sidewall due to additional $O_2$.