In this exercise, various calculations of the electronic band structure of a one-dimensional crystal are performed with the Kronig-Penney (KP) model. 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. Nowadays, hypothetical (nonexistent) materials are often investigated by band structure calculations – and if they show attractive properties, researchers try to prepare these materials experimentally. The KP model is a strongly simplified one-dimensional quantum mechanical model of a crystal. Despite of the simplifications, the electronic band structure obtained from this model shares many features with band structures that result from more sophisticated models.
The exercise will enable you to learn the following:
1. Understand the concept of energy bands and energy gaps, their variations as a function of the size of the periodic potentials and energy