Seeking Resonances in a Al<sub>y</sub>ga<sub>1-y</sub>AS/GaAs Nanostructure via Semiclassical Path Integration

In this paper, we conducted an analytical study of the resonant tunneling mechanism in an AlGaAs/GaAs heterostructure. Our focus was on developing a method to determine the resonance complex positions of the system using semiclassical path integration. To achieve this, we started by employing a one-dimensional effective model potential to describe the carrier’s potential as it moves between layers. We then built the fixed energy amplitude of the structure by accounting for all changes in the phase of the carrier’s wave-function as it propagated through infinite paths. The resonance positions were identified as complex poles of the overall amplitude. We discovered that these positions depend on both the geometric characteristics of the nanostructure, such as the well and barrier widths and the barrier height, and material properties like the aluminum’s mole fraction. Our results provide clear analytical relationships and align with previously published findings, enabling us to predict and optimize the performance of various nanoscale devices.