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We provide a full account of our recent report (EPL, 141 (2023) 10001}) whichconstructed a quantized relativistic time-of-arrival operator for spin-0particles using a modified Weyl-ordering rule to calculate the traversal timeacross a square barrier. It was shown that the tunneling time of a relativisticspin-0 particle is instantaneous under the condition that the barrier height$V_o$ is less than the rest mass energy. This implies that instantaneoustunneling is an inherent quantum effect in the context of arrival times.

Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem