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Kronig-Penney Model

Solid State Physics student laboratory Kronig-Penney Model S ren Kahl (2005) 08 790 4186 Original Version: sten Rapp (1998) Fasta Tillst ndets Fysik Introduction In this student laboratory, various calculations of the electronic bandstructure of a one-dimensional crystal are performed with the Kronig-Penney (KP) This Model has an analytical solution and therefore allows for simple calculations. More realistic models always require extensive numeric calculations, often on the fastest computers available. The electronic band structure is directly related to many macroscopic properties of the material and therefore of large interest.

Can you find any energy gap between the first and second band? – Zoom into the figure in order to determine the size of the bandgap. Note that you will obtain too large a value if you plot in large steps. Steps of 0.1 eV, e.g., are too large here. For nearly free electrons, the following can be shown (compare Kittel or Hook&Hall):

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