## Why does the band gap exist?

Hello, do you know why no electron can stay in the band gap? Is it impossible at every energy?

Thank you!

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 Do you know no electron can stay between -13.6eV and -3.4eV energy levels in an isolated Hydrogen atom? Now, apply the analogy.
 Yes but why they cannot stay there? What does impede them to stay in that levels^

## 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.

 Recognitions: Science Advisor Because there are no energy levels for them to sit in. Energy levels are time-independent solutions to the Schrodinger equation. Claude.