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Transmission and the reflection coefficient of a five, seven, nine, eleven and 2n-segment piece-wise constant potential energy profile
Detailed description of the physics that needs to be understood to correctly use this tool and interpret the results obtained, is provided in the reading materials listed below:
Open Systems Double-Barrier Case Explained
Exercises that illustrate the importance of quantum-mechanical reflections in state of the art devices and the resonance width dependence upon the geometry in the double-barrier structure that is integral part of resonant tunneling diodes are given below:
Quantum-Mechanical Reflections Quantum-Mechanical Reflections in Nanodevices Double-Barrier Structure
The formation of bands in periodic potentials and how the width and the number of the energy bands varies by varying the geometry of the n-well potential is illustrated via the following homework assignments:
From one well, to two wells, to five wells, to periodic potentials Bands as a function of the geometry of the n-well potential
One can also use this tool to calculate the transmission coefficient through barriers that are approximated with piece-wise constant segments.
Tunneling through triangual barrier encountered in Schottky contacts
One can also use this tool to test the validity of first-order and second order stationary perturbation theory.
Application of stationary perturbation theory example
Improvements / modifications in subsequent releases:
- 1.2 – the energy and transmission coefficent axis are exchanged, so the resonance peaks now line up with the spatial resonances in the barrier structure.
- 1.2 – bug-fix: transmission through a single barrier can be simulated now in the “n” barrier case. The code no longer provides an empty output.
- 1.2 – the adaptive energy refinement was improved through a different algorithm. The tool no longer utilizes the Matlab built-in adaptive integration routine but an adaptive resonance finding and grid refinement technique as used in the NEMO1D tool or the Resonant Tunneling Diode Tool.
- 1.2 – The single barrier case has been corrected and should be functional.
- 1.2 – The tool now has a progress update for the adaptive resonance finding.
- 1.4- The tool now has the tight-binding Green’s function based formalism built into it. This will enable the user to make a comparison between the Transfer matrix method and the single band tight-binding calculation.
- 1.5- spatially varying effective masses are introduced.
Dragica Vasileska lecture notes on Quantum mechanics http://www.eas.asu.edu/~vasilesk .
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