# Can electrons transition within energy bands, or must they transition from one band to another?

A while back, I asked a question about the absorption of different wavelengths by matter (see this post). I received some excellent answers that prompted to undertake some more in-depth research, especially concerning band structures / energy bands in materials. I did this and have a better understanding of this topic now, though it is still very rudimentary.

I will try to explain how I currently understand this topic, and then formulate my questions. By my knowledge, when multiple atoms, each with only a few discrete energy levels come together to form a more complex object, their energy levels overlap. However, due to the Pauli exclusion principle, no two electrons can exist on the same exact energy level, therefore each energy level breaks apart into 2 new levels. Expanding this process onto a large number of atoms results in complex materials having continuous energy "bands" instead of just a few discrete energy levels.

My first question concerns the absorption of light by electrons in these energy bands. Can a photon only be absorbed if it will transition an electron into a higher band? Or can it absorb a photon and just transition to a higher energy level within its current band? The first option would limit the amount of wavelengths that could be absorbed, while my second assumption means that many more wavelengths could be absorbed.

Additionally, my understanding is such that the size of a materials bandgap also determiens its conductivity, where large band gap (e.g glass) = insulator, moderate bandgap = semiconductor and no bandgap = conductor. I also read frequently that the band gap is responsible for determining the transmittance of the object. For example, a large bandgap of an insulator would mean that visible light could not excite photons across the band gap, making the object transparent to visible light. However, if this is the case, how can it be that some insulators like glass are transparent to visible light, but others such as wood are opaque?

I'd be happy if anyone could clear these misunderstandings up, or even recommend a good source. Thank you!

This is a brief answer but will hopefully point you in the right direction. There are some lower energy transitions in electronic energy bands, these are due to molecular vibration (and even lower energy transitions due to rotation) that can be stimulated via absorption of lower energy photons. With regard to electrons moving within the electronic band due to photons, it is more an indirect result of filling the hole left behind by an electron that crosses the band gap. The electron energy within an energy band is based on a Fermi-Dirac distribution (which some more physics based textbooks will be able to help with).

As far as your second question, someone else will be able to give a better answer, but I think there are lots of molecules in wood that lead to the opacity.

• Thanks very much, it definetely helps knowing that there are several tranistion possibilities within the bands themselves. I'll do some more research in that direction. Thanks! Commented May 16, 2020 at 15:03
• No worries, I feel I should clarify as I'm not sure I wrote it particularly well, the vibrational and rotational transitions aren't technically electronic transitions but molecular. Electrons when promoted to the conduction band may reach a higher vibrational level, the electrons then relax and release heat (through phonon emission). So that's another potential electron movement within an energy band. Commented May 16, 2020 at 15:14

You are discussing within the model of the band theory of solids.

Please note that the Y axis in this illustration is the energy. As you say there are specific energy levels in the conduction band too, except that they are in energy close enough to form practically a continuum.

Can a photon only be absorbed if it will transition an electron into a higher band? Or can it absorb a photon and just transition to a higher energy level within its current band?

Changing energy levels define the photon energy needed, E=hν. It will require a much higher energy photon to raise an electron from the valence band energy level to the conduction band. Very low energy photons will raise electrons within the conduction band, where the infrared photons of black body radiation would do the job.

while my second assumption means that many more wavelengths could be absorbed.

except these will be very low energy photons.