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Three-dimensional topological insulators (3D-TIs) are a new generation of materials with insulating bulk and exotic metallic surface states that facilitate a wide variety of ground-breaking applications. However, utilization of the surface channels is often hampered by the presence of crystal defects, such as antisites, vacancies, and twin domains. For terahertz device applications, twinning is shown to be highly deleterious. Previous attempts to reduce twins using technologically important InP(111) substrates have been promising, but have failed to completely suppress twin domains while preserving high structural quality. Here we report growth of twin-free molecular beam epitaxial Bi2Se3 and Sb2Te3 structures on ultra-thin In2Se3 layers formed by a novel selenium passivation technique during the oxide desorption of smooth, non-vicinal InP(111)B substrates, without the use of an indium source. The formation of un-twinned In2Se3 provides a favorable template to fully suppress twin domains in 3D-TIs, greatly broadening novel device applications in the terahertz regime.