Electron-phonon interaction in double-barrier resonant tunneling

The electron-phonon-assisted tunneling in a quantum-well double-barrier structure is studied within the transfer-Hamiltonian approach. It is found that as the bias voltage increases, the tunneling current exhibits, besides the normal resonant peak, a series of small resonances when a magnetic field is applied along the direction of the tunneling current. These small resonant structures are attributed to the coupling of electrons with optical phonons. In the present study, two modes are considered: (a) electrons interact with phonons in the quantum well, resulting in additional structures in the electron density of states; (b) electrons couple with barrier phonons, introducing inter-Landau-level tunneling events. Our calculations may help to explain recent experimental observations.