Resonant tunneling in asymmetrical double-barrier structures under an applied electric field

Abstract

Resonant tunneling is studied theoretically for the asymmetrical rectangular double-barrier structures with deep well when a dc bias field is applied. Analytical expressions for the transmission coefficient and the resonance condition are derived by assuming that the effect of the space charge buildup in the well is neglected. It is found that the resonant tunneling with unity transmission (unity resonance) occurs when both the phase difference condition for resonance (PDCR) and the maximum condition for peak value hold simultaneously, while occurs the under-unity resonance that the peak value of transmission coefficient at resonance is below unity when only PDCR holds. The values of transmission peak and the resonance energy are investigated by two methods, Airy function analysis and multistep rectangular approximation. Wave-functions of an electron at the resonance level are calculated and the confining phenomenon is confirmed. Moreover, the effect of the right-hand side barrier height on the transmission coefficient characteristics is investigated.