Condensed Matter Physics - Band Theory of Solids : An Introduction

The free electron theory was successful in explaining various electronic and thermal properties of metals,such as specific heat,paramagnetism,etc. This theory fails in explaining the properties of insulators and semiconductors. The failure of the free electron model is due to the oversimplified assumption that a conduction electron experiences zero potential. The band theory assumes that the potential in which electrons move varies periodically with a period equal to the lattice constant. The behavior of the electron in this potential is described by constructing the electron wave functions using one electron approximation.In this condition it is found that there exists energy bands separated by forbidden regions or band gaps.