  Bi$_{2}$Te$_{3}$ and Bi$_{2}$Se$_{3}$ are well known 3D-topological
insulators. Films made of these materials exhibit metal-like surface states
with a Dirac dispersion and possess high mobility. The high mobility metal-like
surface states can serve as channel material for TI-based field effect
transistors. While such a transistor offers superior terminal characteristics,
they suffer from an inherent zero band gap problem. The absence of a band gap
for the surface states prevents an easy turn-off mechanism. In this work,
techniques that can be employed to easily open a band gap for the TI surface
states is introduced. Two approaches are described: 1) Coating the surface
states with a ferromagnet which has a controllable magnetization axis. The
magnetization strength of the ferromagnet is incorporated as an exchange
interaction term in the Hamiltonian. 2) An \textit{s}-wave superconductor,
because of the proximity effect, when coupled to a 3D-TI opens a band gap on
the surface. This TI-superconductor heterostructure is modeled using the
Bogoliubov-de Gennes Hamiltonian. A comparison demonstrating the finite size
effects on surface states of a 3D-TI and edge states of a CdTe/HgTe/CdTe-based
2D-TI is also presented. 3D-TI nanostructures can be reduced to dimensions as
low as 10.0 $ \mathrm{nm} $ in contrast to 2D-TI structures which require a
thickness of at least 100.0 $ \mathrm{nm} $. All calculations are performed
using the continuum four-band k.p Hamiltonian.
