Editing Band gap (section)

===Direct and indirect band gap===
{{main|Direct and indirect bandgaps}}
Based on their band structure, materials are characterised with a direct band gap or indirect band gap. In the free-electron model, k is the momentum of a free electron and assumes unique values within the Brillouin zone that outlines the periodicity of the crystal lattice. If the momentum of the lowest energy state in the conduction band and the highest energy state of the valence band of a material have the same value, then the material has a direct bandgap. If they are not the same, then the material has an indirect band gap and the electronic transition must undergo momentum transfer to satisfy conservation. Such indirect "forbidden" transitions still occur, however at very low probabilities and weaker energy.<ref name="Pankove"/><ref name="Yu&Cardona"/><ref name="Fox"/><ref>{{Cite book |last1=Böer |first1=K.W. |author-link=Karl Wolfgang Boer |title=Semiconductor Physics |last2=Pohl |first2=U.W. |author-link2=Udo W. Pohl |date=2023 |publisher=Springer |isbn=9783031182853}}</ref> For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In contrast, for materials with an indirect band gap, a photon and [[phonon]] must both be involved in a transition from the valence band top to the conduction band bottom, involving a [[Direct and indirect band gaps|momentum change]]. Therefore, direct bandgap materials tend to have stronger light emission and absorption properties and tend to be better suited for [[photovoltaics]] (PVs), [[light-emitting diode]]s (LEDs), and [[laser diode]]s;<ref name="Sze">{{cite book |title=Physics of semiconductor devices |last1=Sze|first1=S.M. |year=1981 |chapter=Chapters 12–14|publisher=John Wiley & Sons | isbn=0471056618 }}</ref> however, indirect bandgap materials are frequently used in PVs and LEDs when the materials have other favorable properties.