  The problem of the Klein tunneling across a potential barrier in bi-layer
graphene is addressed. The electron wave functions are treated as massive
chiral particles. This treatment allows us to compute the statistical
complexity and Fisher-Shannon information for each angle of incidence. The
comparison of these magnitudes with the transmission coefficient through the
barrier is performed. The role played by the evanescent waves on these
magnitudes is disclosed. Due to the influence of these waves, it is found that
the statistical measures take their minimum values not only in the situations
of total transparency through the barrier, a phenomenon highly anisotropic for
the Klein tunneling in bi-layer graphene.
