Phonon-assisted tunneling from a two-dimensional emitter state

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Abstract
We present a theory of phonon-assisted tunneling in GaAs/AlAs double-barrier structures, which treats the electrons in the emitter as a two-dimensional electron gas. A complete set of confined and interface optical-phonon modes is calculated using a dielectric-continuum model, and we derive a general expression for the electron-phonon Hamiltonian valid for all optical-phonon modes in an arbitrary heterostructure. The electronic wave functions relevant to phonon-assisted tunneling are found by self-consistently solving the Schrödinger and Poisson equations in both the well and the emitter. Five different phonon modes are predicted to dominate the phonon-assisted tunneling current: three LO-like interface modes, the half-space modes in the emitter, and the confined modes in the well.