  We show how to engineer enhanced skew scattering and gap-like opening in the
surface state of three-dimensional topological insulators using only
non-magnetic impurities. Enhanced skew scattering off non-magnetic impurities
is obtained as a finite size effect of the scattering potential. Intimately
related to the generated skew-scattering is the emergence of a gap-like density
of electron states locally around the impurities and surrounded by sharp
resonances, with an extended energy gap appearing in engineered impurity
structures.
