Theoretical study of resonant-tunneling and confining phenomena with mass variation in unsymmetrical rectangular double-barrier structures

Analytical expressions for the transmission coefficient and the resonance condition in unsymmetrical rectangular double-barrier structures are derived theoretically by taking into account the mass difference between well and barrier layers. It is found that resonant tunneling with a transmission peak equal to 1 (unity resonance) and resonant tunneling with a transmission peak less than 1 (below unity resonance) may occur in the unsymmetrical double-barrier structures. Two independent conditions are required for unity-resonant transmission: One is the Phase-Difference Condition for Resonance (PDCR) and the other is the Maximum Condition for the Peak Value (MCPV). The below-unity resonant transmission occurs when only condition PDCR holds. It is believed that the two conditions are useful for calculating values of the transmission coefficient and the resonance energy for the unsymmetrical double-barrier structures. They may be useful for resonant tunneling-device fabrication. Furthermore, wave functions of an electron at resonance level are calculated and the confining phenomenon is confirmed.