  Using a density functional based electronic structure method, we study the
effect of perturbations on the surface state Dirac cone of a strong topological
insulator Bi$_2$Se$_3$ from both the intrinsic and extrinsic sources. We
consider atomic relaxations, and film thickness as intrinsic and interfacial
thin dielectric films as an extrinsic source of perturbation to the surface
states. We find that atomic relaxations has no effect on the degeneracy of the
Dirac cone whereas film thickness has considerable effect on the surface states
inducing a gap which increases monotonically with decrease in film thickness.
We consider two insulating substrates BN and quartz as dielectric films and
show that surface terminations of quartz with or without passivation plays
critical role in preserving Dirac cone degeneracy whereas BN is more inert to
the TI surface states. The relative orbital contribution with respect to bulk
is mapped out using a simple algorithm, and with the help of it we demonstrate
the bulk band inversion when spin-orbit coupling is switched on. The layer
projected charge density distributions of the surface states shows that these
states are not strictly confined to the surface. The spatial confinement of
these states extends up to two to three quintuple layers, a quintuple layer
consists of five atomic layers of Bi and Se
