  Motivated by recent scanning tunneling microscopy experiments on surfaces of
Bi$_{1-x}$Sb$_{x'}$\cite{yazdanistm,gomesstm} and
Bi$_2$Te$_3$,\cite{kaptunikstm,xuestm} we theoretically study the electronic
structure of a 3-dimensional (3D) topological insulator in the presence of a
local impurity or a domain wall on its surface using a 3D lattice model. While
the local density of states (LDOS) oscillates significantly in space at
energies above the bulk gap, the oscillation due to the in-gap surface Dirac
fermions are very weak. The extracted modulation wave number as a function of
energy satisfies the Dirac dispersion for in-gap energies and follows the
border of the bulk continuum above the bulk gap. We have also examined
analytically the effects of the defects by using a pure Dirac fermion model for
the surface states and found that the LDOS decays asymptotically faster at
least by a factor of 1/r than that in normal metals, consistent with the
results obtained from our lattice model.
