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Piece-Wise Constant Potential Barriers Tool

By Dragica Vasileska1, Gerhard Klimeck2, Xufeng Wang2, Samarth Agarwal3

1. Arizona State University 2. Purdue University 3. IBM

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

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Archive Version 1.1.3
Published on 06 Nov 2008, unpublished on 19 Feb 2009
Latest version: 1.2.8. All versions

doi:10.4231/D35H7BT1W cite this

This tool is closed source.



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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. 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.

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Dragica Vasileska lecture notes on Quantum mechanics .

Cite this work

Researchers should cite this work as follows:

  • Dragica Vasileska; Gerhard Klimeck; Xufeng Wang; Samarth Agarwal (2014), "Piece-Wise Constant Potential Barriers Tool," (DOI: 10.4231/D35H7BT1W).

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Tags, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.