Resonant Tunneling with Electron-Phonon Interaction: An Exactly Solvable Model

The probability for resonant tunneling through a quantum well is calculated for a model including electron-phonon coupling. The interaction of the tunneling electron with optic phonons produces resonant transmission sidebands, which are readily observable in $I-V$ characteristics. Our results confirm the recent experimental observation of phonon-assisted resonant tunneling in GaAs.