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 1.1.5
Published on 01 Apr 2009, unpublished on 01 Apr 2009
Latest version: 1.2.9. All versions

doi:10.4231/D3707WN5N 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:

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.
  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.
  2. 1.5- spatially varying effective masses are introduced.

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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/D3707WN5N).

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