  Thin films of topological insulators (TI) usually exhibit multiple parallel
conduction channels for the transport of electrical current. Beside the
topologically protected surface states (TSS), parallel channels may exist,
namely the interior of the not-ideally insulating TI film, the interface layer
to the substrate, and the substrate itself. To be able to take advantage of the
auspicious transport properties of the TSS, the influence of the parasitic
parallel channels on the total current transport has to be minimized. Because
the conductivity of the interior (bulk) of the thin TI film is difficult to
access by measurements, we propose here an approach for calculating the mobile
charge carrier concentration in the TI film. To this end, we calculate the
near-surface band bending using parameters obtained experimentally from
surface-sensitive measurements, namely (gate-dependent) four-point resistance
measurements and angle-resolved photoelectron spectroscopy (ARPES). While in
most cases another parameter in the calculations, i.e. the concentration of
unintentional dopants inside the thin TI film, is unknown, it turns out that in
the thin-film limit the band bending is largely independent of the dopant
concentration in the film. Thus, a well-founded estimate of the total mobile
charge carrier concentration and the conductivity of the interior of the thin
TI film proves possible. Since the interface and substrate conductivities can
be measured by a four-probe conductance measurement prior to the deposition of
the TI film, the total contribution of all parasitic channels, and therefore
also the contribution of the vitally important TSS, can be determined reliably.
