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We calculate the tunneling process of a Dirac particle across two squarebarriers separated a distance $d$, as well as the scattering by a double cuspbarrier where the centers of the cusps are separated a distance larger thantheir screening lengths. Using the scattering matrix formalism, we obtain thetransmission and reflection amplitudes for the scattering processes of bothconfigurations. We show that, the presence of transmission resonances modifiesthe Lorentizian shape of the energy resonances and induces the appearance ofadditional maxima in the transmission coefficient in the range of energieswhere transmission resonances occur. We calculate the Wigner time-delay andshow how their maxima depend on the position of the transmission resonance.

Tunneling and transmission resonances of a Dirac particle by a double barrier