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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 **1.1.3**

Published on 06 Nov 2008, unpublished on 19 Feb 2009

Latest version: 1.2.9. All versions

doi:10.4231/D35H7BT1W 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:

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:

- 1.2 – the energy and transmission coefficent axis are exchanged, so the resonance peaks now line up with the spatial resonances in the barrier structure.

- 1.2 – bug-fix: transmission through a single barrier can be simulated now in the “n” barrier case. The code no longer provides an empty output.

- 1.2 – 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.

- 1.2 – The single barrier case has been corrected and should be functional.

- 1.2 – The tool now has a progress update for the adaptive resonance finding.

#### Sponsored by

NSF

#### References

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

#### Cite this work

Researchers should cite this work as follows: