We report comprehensive x-ray diffraction studies of the crystal structure and epitaxy of thin films of the topological insulator Bi 2 Te 3 grown on Si (1 1 1 Recently, new quantum materials called topological insulators, in which metallic surface states located in the band gap of their insulating bulk are protected by time-reversal symmetry, have been discovered 1-4 and attracted considerable attention due to fascinating properties such as almost dissipationless surface transport and potential for "spintronic" applications. 5,6 Bi 2 Te 3 (BT) is such a topological insulator with the advantages of a nominally stoichiometric material and a large bulk gap. 3 Bulk single crystals of this substance, however, have a considerable disadvantage over the MBE grown II-VI heterostructures for which many of the interesting effects have been first observed 1 in that transport, which is supposed to occur only through the surface states, also involves unwanted bulk channels due to crystal imperfections. 3,7 For electronic device research and applications it is required not only to eliminate these charge carriers but also to fabricate low-dimensional nanostructures. Therefore, growth of undoped thin films of topological insulators with low defect concentration, in which the Fermi level intersects only the metallic surface states, is essential and has been attempted using various methods. Large progress has been made in thin film growth of topological insulators on Si (1 1 1) substrates using the molecular beam epitaxy (MBE) technique. 8 While the authors of ref. 8 have demonstrated the crystal structure of the surface to correspond to that of BT using RHEED, and shown the presence of metallic surface states using ARPES, so far, no quantitative structural