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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 **1.1.1**

Published on 14 Oct 2008, unpublished on 30 Oct 2008

Latest version: 1.2.8. All versions

doi:10.4231/D38C9R384 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:

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.

One can also use this tool to test the validity of first-order and second order stationary perturbation theory.

#### Sponsored by

NSF

#### References

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