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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This tool version is unpublished and cannot be run. If you would like to have this version staged, you can put a request through HUB Support.

Archive Version 1.1.5
Published on 01 Apr 2009, unpublished on 01 Apr 2009 All versions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: 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.
  • 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.

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/D3707WN5N).

    BibTex | EndNote


  1. nanoelectronics
  2. nanoelectronics
  3. quantum mechanics
  4. reflection coefficient
  5. transmission coefficient
  6. quantum transport
  7. nanoelectronics
  8. quantum mechanics
  9. reflection coefficient
  10. transmission coefficient
  11. tunneling
  12. nanoelectronics
  13. quantum mechanics
  14. quantum transport
  15. reflection coefficient
  16. transmission coefficient
  17. tunneling
  18. NCN Supported
  19. NCN@Purdue Supported
  20. NCN Supported
  21. NCN@Purdue Supported
  22. nanoelectronics
  23. quantum mechanics
  24. quantum transport
  25. reflection coefficient
  26. transmission coefficient
  27. tunneling
  28. NCN Supported
  29. NCN@Purdue Supported
  30. nanoelectronics
  31. NCN Supported
  32. NCN@Purdue Supported
  33. quantum mechanics
  34. quantum transport
  35. reflection coefficient
  36. transmission coefficient
  37. tunneling
  38. AQME
  39. ACUTE
  40. ANTSY
  41. nanoelectronics
  42. NCN Supported
  43. NCN@Purdue Supported
  44. quantum mechanics
  45. quantum transport
  46. reflection coefficient
  47. transmission coefficient
  48. tunneling
  49. ACUTE
  50. ANTSY
  51. AQME
  52. PCPBT