Resonance Condition in Asymmetrical Rectangular Double-Barrier Structures with Deep Well

Abstract

A theoretical study of resonant tunneling is carried out for asymmetrical rectangular double-barrier structures with a deep well. Analytical expressions for the transmission coefficient and the resonance condition are derived for the first time. 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 (MCPV) hold simultaneously; under-unity resonant tunneling occurs so that the peak value of the transmission coefficient at resonance is below unity when only PDCR holds. Wave functions of an electron at the resonance level are calculated and the confining phenomenon is confirmed. Moreover, the peak value variation of the resonant transmission coefficient under an applied field is discussed.