Bloch Theorem and Kronig-Penney Model: Band Theory Insights

This lecture introduces the Bloch theorem and the Kronig-Penney model, fundamental concepts in semiconductor band theory. The instructor begins by discussing the periodic arrangement of atoms in solids and how this periodicity influences electronic states. The Bloch theorem is presented, explaining how wave functions in periodic potentials can be expressed as a product of a plane wave and a periodic function. The discussion then shifts to the Kronig-Penney model, which simplifies the analysis of electron behavior in a periodic potential. The model illustrates how the strength of the potential barrier affects the band structure and energy levels of electrons. The instructor emphasizes the relationship between the effective mass of electrons and the curvature of energy bands, highlighting how these concepts relate to the behavior of electrons and holes in semiconductors. The lecture concludes with a discussion on the implications of these theories for understanding semiconductor properties and the significance of the effective mass in practical applications.