A bulk phantom scalar field (with negative kinetic energy) in a sine--Gordon
type potential is used to generate an exact thick brane solution with an
increasing warp factor. It is shown that the growing nature of the warp factor
allows the localisation of massive as well as massless spin-half fermions on
the brane even without any additional non--gravitational interactions. The
exact solutions for the localised massive fermionic modes are presented and
discussed. The inclusion of a fermion--scalar Yukawa coupling appears to change
the mass spectrum and wave functions of the localised fermion though it does
not play the crucial role it did in the case of a decreasing warp factor.Comment: 11 pages, 3 figures, RevTex
