  The band bending (BB) effect on the surface of the second-generation
topological insulators implies a serious challenge to design transport devices.
The BB is triggered by the effective electric field generated by charged
impurities close to the surface and by the inhomogeneous charge distribution of
the occupied surface states. Our self-consistent calculations in the
Korringa-Kohn-Rostoker framework showed that in contrast to the bulk bands, the
spectrum of the surface states is not bent at the surface. In turn, it is
possible to tune the energy level of the Dirac point via the deposited surface
dopants. In addition, the electrostatic modifications induced by the charged
impurities on the surface induce long range oscillations in the charge density.
For dopants located beneath the surface, however, these oscillations become
highly suppressed. Our findings are in good agreement with recent experiments,
however, our results indicate that the concentration of the surface doping
cannot be estimated from the energy shift of the Dirac cone within the scope of
the effective continuous model for the protected surface states.
