Ⅲ-Ⅴ quantum dot (QD) lasers monolithically grown on CMOS-compatible Si substrates are considered as essential components for integrated silicon photonic circuits.However,epitaxial growth of Ⅲ-Ⅴ materials on Si substrates encounters three obstacles:mismatch defects,antiphase boundaries (APBs),and thermal cracks.We study the evolution of the structures on U-shaped trench-patteed Si (001) substrates with various trench orientations by homoepitaxy and the subsequent heteroepitaxial growth of GaAs film.The results show that the formation of (111)-faceted hollow structures on patteed Si (001) substrates with trenches oriented along [110] direction can effectively reduce the defect density and thermal stress in the GaAs/Si epilayers.The (111)-faceted silicon hollow structure can act as a promising platform for the direct growth of Ⅲ-Ⅴ materials for silicon based optoelectronic applications.