Nonlinear interlayer tunneling in a double-electron-layer structure

Abstract

We present a theory for nonequilibrium two-dimensional to two-dimensional tunneling between two weakly tunnel-coupled electron layers when the chemical potentials of the two electron gases are arbitrarily biased. We first present an intuitive but rigorous second-order perturbation theory based on a transition-rate approach. Contributions from electron-impurity, interface-roughness, electron-electron, and electron-phonon interactions are considered. The validity of this result is established using a more general field-theoretic formalism by expressing the tunneling current as a current-current correlation function which can be evaluated employing a standard temperature-ordered Green's function technique and a Feynman-graph expansion. The formalism is exact to the second order in the tunneling integral and to all orders in the interactions and is useful for studying higher-order interaction effect. The relevance of the numerical results to recent experimental data from a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ double-electron-layer tunneling transistor (DELTT) at 77 K are discussed. These data show a large peak-to-valley ratio of the $I\ensuremath{-}V$ curve. The room-temperature numerical results for the $I\ensuremath{-}V$ curve show a reasonably large peak-to-valley ratio indicating the feasibility of room-temperature DELTT's.