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

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Archive Version 1.1.3
Published on 06 Nov 2008, unpublished on 19 Feb 2009 All versions

doi:10.4231/D35H7BT1W cite this



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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: 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: 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: One can also use this tool to calculate the transmission coefficient through barriers that are approximated with piece-wise constant segments. One can also use this tool to test the validity of first-order and second order stationary perturbation theory.
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.

Sponsored by



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

Cite this work

Researchers should cite this work as follows:

  • Dragica Vasileska; Gerhard Klimeck; Xufeng Wang; Samarth Agarwal (2016), "Piece-Wise Constant Potential Barriers Tool," http://nanohub.org/resources/pcpbt. (DOI: 10.4231/D35H7BT1W).

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