Mapping the electronic wave functions by determining current-voltage curves

Resonant tunneling in double-barrier heterostructures in the presence of impurity planes is studied within the Green-function formalism following the diagram technique for nonequilibrium processes proposed by Keldysh [Sov. Phys. JETP 20, 1018 (1965)]. A simple one-band tight-binding Hamiltonian is adopted in the theoretical framework. The effects of an isoelectronic impurity plane, localized in the well region of a GaAs-Ga_1-xAlₓAs double-barrier heterostructure, on the resonant curves of the current are analyzed as a function of the impurity plane position. The theoretical results show that the evolution of the resonant bias, corresponding to the resonant peaks due to transport through quantum-well quasibound states, reflects the behavior of the spatial variation of the associated electronic wave function. This indicates unambiguously that transport measurements can be performed for a mapping of wave functions in quantum-well systems.