We investigate Klein tunneling through finite potential barriers with space-time-resolved solutions to relativistic quantum field equations. We find that no particle actually tunnels through a finite supercritical barrier, even in the case of resonant tunneling. The transmission is instead mediated by modulations in pair production rates, at each edge of the barrier, caused by the incoming electron. We further examine the effect of the barrier's width on the numbers of produced pairs in the fermionic case (characterized by saturation) and in the bosonic case (characterized by exponential superradiance). This work paves the way to precise studies of the radiating dynamics of supercritical barriers, and could be applied to certain analogs of Klein tunneling observed in systems modeled by relativistic wave equations.

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• Light-matter interaction
• Quantum field theory
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• Relativistic wave equations