We solve exactly an approximate model for inelastic resonant tunneling in the presence of a boson field. The model is based on the many-body tunneling Hamiltonian formalism, which, in the appropriate limits, is shown to precisely reproduce the elastic resonant tunneling results of ordinary single-particle scattering theory. Bosons coupling with arbitrary strength to the resonant level broaden the energy dependence of the effective transmission probability. Applications to resonant tunneling in quasi-one-dimensional GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures in the presence of LO phonons and to resonant tunneling in three-dimensional heterostructures in the presence of electromagnetic fields (laser beam or ac voltage) are discussed.

• Received 19 September 1988

DOI:https://doi.org/10.1103/PhysRevB.39.5924