  The tunneling time problem earlier studied in Phys. Rev. Lett 108 170402
(2012) using a non-relativistic time-of-arrival (TOA) operator predicted that
tunneling time is instantaneous. This raises the question on whether
instantaneous tunneling time is a consequence of using a non-relativistic
theory. Here, we extend the analysis by proposing a formalism on the
construction of relativistic TOA-operators for spin-0 particles in the presence
of an interaction potential via quantization. We then construct the
corresponding barrier traversal time operator and impose the condition that the
barrier height is less than the rest mass energy of the particle. We show that
only the above-barrier energy components of the incident wavepacket's momentum
distribution contribute to the barrier traversal time while the below-barrier
components are transmitted instantaneously.
