Achieving true bulk insulating behavior in Bi$_2$Se$_3$, the archetypal topological insulator with a simplistic one-band electronic structure and sizable band gap, has been prohibited by a well-known self-doping effect caused by selenium vacancies, whose extra electrons shift the chemical potential into the bulk conduction band. We report a new synthesis method for achieving stoichiometric Bi$_2$Se$_3$ crystals that exhibit nonmetallic behavior in electrical transport down to low temperatures. Hall effect measurements indicate the presence of both electron- and hole-like carriers, with the latter identified with surface state conduction and the achievement of ambipolar transport in bulk Bi$_2$Se$_3$ crystals without gating techniques. With carrier mobilities surpassing the highest values yet reported for topological surface states in this material, the achievement of ambipolar transport via upward band bending is found to provide a key method to advancing the potential of this material for future study and applications.
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