  In this paper we present detailed study of the density of states near defects
in Bi$_2$Se$_3$. In particular, we present data on the commonly found
triangular defects in this system. While we do not find any measurable
quasiparticle scattering interference effects, we do find localized resonances,
which can be well fitted by theory once the potential is taken to be extended
to properly account for the observed defects. The data together with the fits
confirm that while the local density of states around the Dirac point of the
electronic spectrum at the surface is significantly disrupted near the impurity
by the creation of low-energy resonance state, the Dirac point is not locally
destroyed. We discuss our results in terms of the expected protected surface
state of topological insulators.
