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