Theoretical investigations of resonant tunneling in asymmetric multibarrier semiconductor heterostructures in an applied constant electric field

We solve the one-dimensional Schr\"odinger wave equation in the effective-mass approximation for the transmission coefficient T(E) of electrons through asymmetric multibarrier semiconductor heterostructures in the presence of a constant applied electric field, using an exact Airy-function formalism and the transfer-matrix technique. In particular, we show that for appropriate choices of asymmetry in the barrier widths and heights of the semiconductor heterostructure, the transmission coefficient is enhanced to yield resonances that are stronger than those calculated in symmetric structures, thus giving further validity to Mendez's concept of effective-barrier symmetry for obtaining optimal resonant tunneling in asymmetric double- and triple-barrier semiconductor heterostructures. These results should assist experimental efforts in designing resonant-tunneling systems that require optimum peaks both in the transmission spectrum and current density.