3D Band Structure Visualization

This project was undertaken for a numerical analysis course. The project uses the tight binding model with the hamiltonian parameters supplied by Chadi and Cohen (D. J. Chadi and Marvin L. Cohen. Tight-binding calculations of the valence bands of diamond and zincblende crystals. phys. stat. sol., 68:405, 1975.). It calculates the eigenvalues for a 2D plane in the first Brillouin zone, and saves those eigen values to a 3D model file, where x and y are mapped to the position on the plane, and z is the eigenvalue in eV. This is then imported into Blender, skinned, scaled, and printed on a ZCorp 310 printer. As a future project, even more interesting shapes could be obtained by incorporating external fields into the calculation.

Diamond

GaAs

Poster presented at the undergraduate research symposium:

References

• Neil W. Ashcroft and N. David Mermin. Solid State Physics. Brooks/Cole, 1976.
• D. J. Chadi and Marvin L. Cohen. Tight-binding calculations of the valence bands of diamond and zincblende crystals. phys. stat. sol., 68:405, 1975.
• Walter A. Harrison. Electronic Structure and the Properties of Solids. Dover Publications, Inc., New York, 1989.
• Charles Kittel. Solid State Physics. John Wiley & Sons, Inc., 2nd edition, 1962.
• Richard P. Muller and William A. Goddard III. harrison.py. http://www.wag.caltech.edu/home/rpm/projects/tight-binding/, March 2005.