Resonance splitting effect in multibarrier tunneling

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Abstract
An exact analytical expression for the transmission probability of electron transport through the superlattice (SL) modeled by a finite number of periodic rectangular multibarrier structures (PRMBS’s) in one dimension is presented. The explicit correlation between the resonance properties and the SL potential structure as well as miniband structure is obtained. It is shown that (1) the resonances in multibarrier tunneling are confined in energy into the minibands of the corresponding SL; (2) the number of resonance splittings in each miniband is equal to the number of the wells in the structure; (3) in each set of splittings the peaks of the resonances are distributed equally about the energy asymptotically coinciding with the energy of the single-well structure, at which there is also a resonance peak if and only if the number of the barriers in the structure is even; and (4) for PRMBS’s each of the resonances provides an ideal energy window of 100% transparency for the electron with the resonant energy.