The a-axis lattice parameter of Bi2Se3 is almost identical to the lattice periodicity of the InP (1 1 1) surface. We consequently obtain remarkably smooth Bi2Se3 (0 0 0 1) layers in hot-wall-epitaxy growth on InP (1 1 1)B substrates. The lattice-matched periodicity is preserved in the [1 1 0] and  directions of the (0 0 1) surface. The Bi2Se3 layers grown on InP (0 0 1) substrates exhibit 12-fold in-plane symmetry as the  direction of Bi2Se3 is aligned to either of the two directions. When the (1 1 1)-oriented InP substrates are inclined, the Bi2Se3 (0 0 0 1) layers are found to develop steps having a height of ~50 nm. The tilting of the Bi2Se3 [0 0 0 1] axis with respect to the growth surface is responsible for the creation of the steps. Epitaxial growth is thus evidenced to take place rather than van der Waals growth. We point out its implications on the surface states of topological insulators.
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