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.
The present work investigates the resonant tunneling of electrons in symmetric triangular double barrier triodes composed of GaAs-Ga1-xAlxAs nanostructures under a step bias voltage. This work employs the complex energy method to compute the resonant tunneling energy and the associated lifetimes. In the mathematical analysis of this work, the matching conditions are taken at specific points on both lateral sides of the triangular barrier. Results showed decreasing the resonant tunneling energies for both the lowest and excited states by applying step bias voltage and disappearing the lowest energy states at a specific applied bias voltage. The resonant tunneling lifetimes of the present structure exhibited nearly constant behavior at constant values of both well half-width and barrier half-thickness although the enhancement of the bias voltage. Moreover, the lifetimes of both the lowest and excited states increased nearly linearly and overlapped at a specific bias voltage, after which the lifetime of the excited state enhanced parabolically. The results showed considerable agreement with the data published in the literature for both magnitude and tendency. The present work highlights the importance of employing the mass-mismatch condition in studying heterostructures. It is found from the present study that resonant tunneling energies and their related lifetimes are more affected by the variations of the aluminum concentration in the barrier region, barrier thickness, and well width, which can be adjusted to improve the performance of the resonant tunneling triangular triodes and other nanostructure devices.
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