Quasi-resonant tunneling states in triangular double-barrier nanostructures

Abstract

Quasi-resonant tunneling energy states and their corresponding lifetimes were examined in symmetric triangular double-barrier nanostructures composed of GaAs-AlyGa1-yAs. The present study employs the complex energy technique that involves solving two transcendental equations. One of these equations is associated with the even-energy state, while the other is associated with the odd-energy state of the resonant tunneling. The quasi- resonant tunneling energy is determined from the real part of the complex root while as the associated lifetime is found from the imaginary part of the complex root through the uncertainty energy-time relationship. The numerical investigation imposes a single wavefunction attributed to the spatial probability density of the electron inside the triangular barrier region. The results demonstrate that the quasi-resonant tunneling energies enhance by diminishing the well width and increasing the aluminum concentration within the barrier material for a fixed barrier thickness. In addition, enhancing both the aluminum concentration and the barrier thickness yield longer quasi-resonant tunneling lifetimes. The findings of the current study indicate that resonant tunneling energies and lifetimes align closely with the published data in the literature.

Towards the Analytical Generalization of the Transcendental Energy Equation, Group Velocity, and Effective Mass in One-Dimensional Periodic Potential Wells with a Computational Application to Common Coupled Potentials

“…For the simplest case (a rectangular-like barrier), the main goal is to determine the transmission and reflection coefficients through a potential barrier [17,18]. However, there are more complex barriers that involve combinations of potentials-for instance, a triangular-like potential coupled to a rectangular-like potential or a rectangular-like potential combined with a parabolic-like potential, i.e., potentials that approach a more realistic physical problems [19,20]. Again, Bloch's theorem can also be used to address the corresponding asymmetric-like potentials, which also reduces the computational costs.…”