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Bismuth selenide Bi$_2$Se$_3$ was grown by molecular beam epitaxy whilecarrier density and mobility were measured directly \emph{in situ} as afunction of film thickness. Carrier density shows high interface n-doping (1.5x 10$^{13}$ cm$^{-2}$) at the onset of film conduction, and bulk dopant densityof $\sim$5 x 10$^{18}$ cm$^{-3}$, roughly independent of growth temperatureprofile. Mobility depends more strongly on the growth temperature and isrelated to the crystalline quality of the samples quantified by \emph{ex-situ}AFM measurements. These results indicate that Bi$_2$Se$_3$ as prepared bywidely employed parameters is \emph{n}-doped before exposure to atmosphere, thedoping is largely interfacial in origin, and dopants are not the limitingdisorder in present Bi$_2$Se$_3$ films.

Thickness and growth-condition dependence of \emph{in-situ} mobility and carrier density of epitaxial thin-film Bi$_2$Se$_3$