Resonant transport in a double-barrier heterostructure Al_xGa_1−xAs/GaAs and mass discontinuity: a semiclassical path integral approach

Abstract In this paper, we investigate the dependence of the resonant carrier transport in an AlGaAs/GaAs double-barrier heterostructure on the electron’s effective mass discontinuity between the well and the barrier layer. We use a one-dimensional model for the effective potential and consider the activation of the resonant tunneling mechanism when a bias is applied between the emitter and the collector. We calculate the system’s Green’s function through semiclassical path integration to obtain the complex spectrum. Electron’s effective mass discontinuity affects our calculations through the contributions of the various propagations inside the heterostructure and the multiple reflections from the turning points. Our findings show that the lowest resonance energy decreases linearly with increasing bias, while the real energy shift of the resonance decreases in a non-linear manner with the mass discontinuity. We also observe that the resonant transport time increases nearly linearly with the mass discontinuity. These results demonstrate the impact of the carrier’s inertia enhancement on the resonance characteristics and are consistent with established concepts in quantum mechanics and previously published works. Furthermore, we identify a critical bias value that distinguishes the behavior of the symmetric and asymmetric heterostructure. Additionally, the derivative of the transport time with respect to mass discontinuity is found to be independent of the applied bias. Our results provide concise analytical relationships involving parameters such as barrier and well thickness and shape, enabling the prediction and optimization of various nanoscale devices’ performance.