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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-patterned 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 patterned 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. [ABSTRACT FROM AUTHOR]