Energy Band Structure of an Electron in a One-Dimensional Periodic Potential

Abstract

<jats:p> It has been observed that electron in a perfect crystal moves in a spatially periodic field of force due to the ions and the averaged effect of all the electrons. This work shows the investigative work done to determine the energy band structure of an electron in a one-dimensional periodic potential. The application of the Kronig-Penney model was applied to an electron state in a delta-like potential. To fully understand the Kronig-Penney model, the concept of Bloch’s theorem was first introduced to describe the conduction of electrons in solids. It has been found that the periodic potential introduces gaps in the reduced representation with an increasing number of potential well/barrier strengths. It has been observed that the regions of non-propagating states, which give rise to energy band gaps, become larger with decreasing values. </jats:p>