  We study local density of state (LDOS) oscillations arising from the
scattering of electrons at atomic edge defects in topological insulator (TI)
surfaces. To create edge scattering on the surface of a TI, we assume that half
of its surface is covered with a semiconductor. In addition to modifying the TI
states in the covered half, the presence of the semiconductor leads to a
localized edge potential at the vacuum-semiconductor boundary. We study the
induced LDOS by imposing time-reversal (TR) invariance and current conservation
across the boundary. Additionally, we explore how the scattering of TI
junctions with dissimilar spin textures and anisotropic Fermi velocities affect
the modulations of the LDOS away from the junction edge. In all cases, for
energies close to the Dirac point, we find that the decay envelope of the LDOS
oscillations is insensitive to the scattering at the atomic edge defect, with a
decay power given by $x^{-3/2}$. Quantitative differences in the amplitude of
these oscillations depend on the details of the interface and the spin
textures, while the period of the oscillations is defined by the size of the
Fermi surface.
