The naturally existing chalcogenide Bi 2 Se 3 is topologically nontrivial due to the band inversion caused by the strong spin-orbit coupling inside the bulk of the material. The surface states are spin polarized, protected by the time-inversion symmetry, and thus robust to the scattering caused by nonmagnetic defects. A high-purity topological insulator thin film can be easily grown via molecular beam epitaxy (MBE) on various substrates to enable novel electronics, optics, and spintronics applications. However, the unique surface state properties have historically been limited by the film quality, which is evaluated by crystallinity, surface morphology, and transport data. Here we propose and investigate different MBE growth strategies to improve the quality of Bi 2 Se 3 thin films grown by MBE. Based on the surface passivation status, we have classified the substrates into two categories, self-passivated or unpassivated, and determine the optimal growth mechanisms on the representative sapphire and GaAs, respectively. For Bi 2 Se 3 on GaAs, the surface passivation status determines the dominant growth mechanism. In the end, growths of the topological trivial insulator (Bi 0.5 In 0.5 ) 2 Se 3 (BIS) on GaAs are investigated following the protocols proposed.