Heteroepitaxial growth of GaAs/Ge/SiGe films on submicrostructured Si substrates is reported. One-dimensional, nanometer-linewidth, submicrometer period features were fabricated in Si substrates using interferometric lithography, reactive ion etching, and wet-chemical etching techniques. The quality of the GaAs layers grown on these structures was investigated using high-resolution x-ray diffraction, transmission electron microscopy, scanning electron microscopy, photoluminescence, and etch pit density measurements. The defect density of GaAs epilayers grown on submicrostructured Si at ∼6×105 cm-2 was two orders of magnitude lower compared with that grown on planar silicon. The optical quality of the GaAs/Ge/SiGe on submicrostructured Si was comparable to that of single crystal GaAs.