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Electron transmission through semiconductor superlattices is studied withtransfer matrix method and resonance theory. The formation of electronband-pass transmission is ascribed to the coupling of different modes in thosesemiconductor superlattices with the symmetric unit cell. Upon Fabry-P\'erotresonance condition, Bloch modes and two other resonant modes are identified tobe related to the nature of the superlattice and its unit cell, respectively.The bands related to the unit cell and the superlattice overlap spontaneouslyin the tunneling region due to the shared wells, and the coupling of perfectlyresonances results in the band-pass tunneling. Our findings provide a promisingway to study electronic systems with more complicated superlattices or evenoptical systems with photonic crystals.

Filtering electrons by mode coupling in finite semiconductor superlattices