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High quality Bi2Te3 and Sb2Te3 topological insulators films were epitaxially grown on GaAs (111) substrate using solid source molecular beam epitaxy. Their growth and behavior on both vicinal and non-vicinal GaAs (111) substrates were investigated by reflection high-energy electron diffraction, atomic force microscopy, X-ray diffraction, and high resolution transmission electron microscopy. It is found that non-vicinal GaAs (111) substrate is better than a vicinal substrate to provide high quality Bi2Te3 and Sb2Te3 films. Hall and magnetoresistance measurements indicate that p type Sb2Te3 and n type Bi2Te3 topological insulator films can be directly grown on a GaAs (111) substrate, which may pave a way to fabricate topological insulator p-n junction on the same substrate, compatible with the fabrication process of present semiconductor optoelectronic devices.