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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 1.1.1 - published on 16 Oct 2009

doi:10.4231/D3TT4FS6Z cite this

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First-Time User Guide View All Supporting Documents

Wavefunction plot in well SCREENSHOT #2 50% Probability density plot Effective mass EK compared to reduced EK SCREENSHOT #5 Free Electron EK compared to reduced EK Wave function probability plot SCREENSHOT #8 fifty % wavefunction plot 1D DOS plot SCREENSHOT #11 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.
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.
  • Video demo: demonstration of how to use the Periodic Potential Lab [Link]
  • Quantum Mechanics: Periodic Potentials and Kronig-Penney Model [Link]
  • Kronig-Penney Model Explained [Link ].
  • Simplified Band-Structure Model [ Link ].
  • Comparison of PCPBT Lab and Periodic Potential Lab [ Link ].
  • Learn more about the Periodic Potential Lab in the [ Topic page ].
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
  • 50% 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.
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 (2009), "Periodic Potential Lab," http://nanohub.org/resources/kronig_penney. (DOI: 10.4231/D3TT4FS6Z).

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