  Two-dimensional effective continuous models are derived for the surface
states and thin films of the three-dimensional topological insulator (3DTI).
Starting from an effective model for 3DTI based on the first principles
calculation [Zhang \emph{et al}, Nat. Phys. 5, 438 (2009)], we present
solutions for both the surface states in a semi-infinite boundary condition and
in the thin film with finite thickness. An effective continuous model was
derived for surface states and the thin film 3DTI. The coupling between
opposite topological surfaces and structure inversion asymmetry (SIA) give rise
to gapped Dirac hyperbolas with Rashba-like splittings in energy spectrum.
Besides, the SIA leads to asymmetric distributions of wavefunctions along the
film growth direction, making some branches in the energy spectra much harder
than others to be probed by light. These features agree well with the recent
angle-resolved photoemission spectra of Bi$_{2}$Se $_{3}$ films grown on SiC
substrate [Zhang et al, arXiv: 0911.3706]. More importantly, we use the
effective model to fit the experimental data and determine the model
parameters. The result indicates that the thin film Bi$_{2}$Se$_{3}$ lies in
quantum spin Hall region based on the calculation of the Chern number and the
$Z_{2}$ invariant. In addition, strong SIA always intends to destroy the
quantum spin Hall state.
