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Periodic Potential Lab

By Abhijeet Paul1, Junzhe Geng1, Gerhard Klimeck1

1. Purdue University

Solve the time independent schrodinger eqn. for arbitrary periodic potentials

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Version 1.1.2 - published on 21 Jul 2014

doi:10.4231/D3VT1GQ74 cite this

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First-Time User Guide View All Supporting Documents

    SCREENSHOT #1 Wavefunction plot in well 50% Probability density plot Effective mass EK compared to reduced EK Free Electron EK compared to reduced EK SCREENSHOT #6 Wave function probability plot SCREENSHOT #8 fifty % wavefunction plot SCREENSHOT #10 1D DOS plot SCREENSHOT #12

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Tools

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Abstract

The Periodic Potential Lab solves the time independent Schroedinger Equation in a 1-D spatial potential variation. The user can determine energetic and spatial details of the potential profiles, compute the allowed and forbidden bands, plot the bands in a compact and an expanded zone, and compare the results against a simple effective mass parabolic band. Transmission is also calculated through the well for the given energy range.

Types of 1D periodic Potential in the tool:

Rectangular Potential Triangular Potential Parabolic (harmonic)Potential Coulombic Potential Sinosoidal Potential

New potentials included in V 1.0.6 Exponential Potential Gaussian Potential Polynomial Potential (upto order 4)


Recent Changes:


Version 1.0.4

Added predefined material masses, such as GaAs, InAs, InP. Reduced the maximum barrier height to a lower value in square well case. Version 1.0.5 Wavefunction plot added to the output. Completes this wish

  • % Wavefunction probability plot added to the output. Completes this wish New Sinosoidal Periodic potential added to the tool. Now the tool provides a log of the steps run in the tool. Version 1.0.6

    New periodic potentials have been added. Effective mass is provided in a separate table with E and K locations.

    Now the free electron EK starts from Emin=0eV, which provides a better comparison with the EK of the electron in periodic EK. Tool now provides the breakup of the time needed to obtain the solutions at different stages. Version 1.0.7

    A new 1D Density of States(DOS) plot included in the tool. Now the plots for allowed bands and reduced EK compared to effective mass EK are clearer.


    Bug Fixes: In Version 1.0.6: Effective masses calculation has been corrected and now values are correct. Can be seen in the effective mass table as well as the plot of reduced dispersion with effective mass EK plot. Allowed energy bands calculation has been modified to obtain all the correct energy bands.

    First Time User Guide This document explains some important details about the tool and details to use the tool. This is very useful if you are running the tool for the first time or want to understand the basic science behind the tool.


    Other useful documents: A list of some other useful documents associated with this tool. Demo: simple demonstration of how to use this toolLink Quantum Mechanics: Periodic Potentials and Kronig-Penney Model Link Kronig-Penney Model Explained . Simplified Band-Structure Model Link.


    WishList : See all the wishes here and add your wishes too.

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    References

    • Introduction to Solid State Physics, Charles Kittel

    Cite this work

    Researchers should cite this work as follows:

    • Abhijeet Paul; Junzhe Geng; Gerhard Klimeck (2008), "Periodic Potential Lab," http://nanohub.org/resources/kronig_penney. (DOI: 10.4231/D3VT1GQ74).

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