# Why does the band gap exist?

by scientifico
Tags: band, exist
 P: 135 Why does the band gap exist? Bloch's theorem says that anytime you have a periodic potential (like in a lattice of a metal or semiconductor where the atoms are equally spaced apart), then the solutions to Schrodinger's Equation will be plane waves, i.e. $\psi$ ~ $e^{i kx}$ where k is the wave number. When you actually solve a particular problem, you will find certain restrictions on k, that is, you will find for certain values of k, no such plane wave solutions exist. Since k is related to the energy, then you also get restrictions on the energy. That is, for certain values of the energy, there will be no valid solutions to Shrodinger's Equation. These energy levels where no solution exists are referred to as Energy gaps, or Band gaps. The reason the electron can't be on one of these gaps is because there is no solution to Shrodinger's equation in these regions, hence they are forbidden.