In situ monitoring of resistivity and carrier concentration during molecular beam epitaxy of topological insulator Bi$_2$Se$_3$

Bismuth selenide (Bi$_2$Se$_3$) is a three-dimensional strong topological insulator of particular interest due to its relatively large bulk band gap (300 meV) and single set of topologically non-trivial surface states. However, there are outstanding problems in isolating the surface state from the bulk (trivial) conduction: this problem is frequently attributed to doping from selenium vacancies and atmospheric exposure. To address this question of doping, we have constructed a molecular beam epitaxy system with the additional capability of doing real time, in situ measurement of resistivity and Hall carrier density. Bismuth selenide has a micaceous crystal structure of quintuple layer units weakly bonded to one another making it well suited to this growth (van der Waals epitaxy) and measurement technique. Cooling to 15 K and controlled exposure to atmospheric dopants is additionally possible without breaking vacuum. We have been able to achieve direct measurement of mobilities on the order of 300 cm$^2/$Vs and carrier densities of 3$\times$10$^{13}$cm$^{-2}$ measured at growth temperatures of 200 to 300 $^\circ$C. The latest results of carrier density and mobility as a function of film thickness and growth parameters will be reported.