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## Piece-Wise Constant Potential Barriers Tool

Transmission and the reflection coefficient of a five, seven, nine, eleven and 2n-segment piece-wise constant potential energy profile

Launch Tool

**Archive** Version **1.1.7**

Published on 06 Apr 2009, unpublished on 06 Apr 2009

Latest version: 1.2.8. All versions

doi:10.4231/D3Q23R02J cite this

This tool is closed source.

#### Category

#### Published on

#### Abstract

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:
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

- From one well, to two wells, to five wells, to periodic potentials
- Bands as a function of the geometry of the n-well potential

**Improvements / modifications in subsequent releases:**- 1.1.2 - the energy and transmission coefficent axis are exchanged, so the resonance peaks now line up with the spatial resonances in the barrier structure.
- 1.1.2 - bug-fix: transmission through a single barrier can be simulated now in the "n" barrier case. The code no longer provides an empty output.
- 1.1.2 - 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.
- 1.1.2 - The single barrier case has been corrected and should be functional.
- 1.1.2 - The tool now has a progress update for the adaptive resonance finding.
- 1.1.4- 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.
- 1.1.5- spatially varying effective masses are introduced.
- 1.1.7 - the effective mass treatment in the tight binding approach has been corrected. The Transfer matrix approach still appears to have some problems when masses are varied across the device.
- 1.1.7 - the natural lattice constant is set to 0.5 for the tight binding calculation such that there is no rounding of the barrier and well heights which will result in deviations from the Transfer matrix method. Now if there is no effective mass variation the two methods give virtually the same results for the default structures.

#### Sponsored by

NSF

#### References

Dragica Vasileska lecture notes on Quantum mechanics http://www.eas.asu.edu/~vasilesk .

#### Cite this work

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