Optical Band Structure

/ edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
In this video, I talk about where the band diagrams we have been using to this point fall short, and how band structure (or E/k diagrams) are much more useful when dealing with optical transitions. This band structure will allow us to use what we have learned about two-level systems and apply it to figure out the absorption spectrum of a semiconductor.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.

[@ellenorgeraffy5401]

I have been struggling to understand this for ages. Thanks for making it so clear!

[@Galileosays]

Very clear explanation of the E-k band diagram.

[@CanErtugay]

This is the most clear lecture I have ever seen. Thanks thousands

[@abogerebmedia5627]

Wow nice lecture it helps me my studying

[@JordanEdmundsEECS]

Thanks!

[@buktoptravel9314]

Hey everyone, I'm confused about what happens when a photon with more energy than the band gap passes by a valence electron in a material. On the one hand, some people say that absorption only occurs when the photon energy perfectly matches the energy gap between the initial and final states, and if the energy is higher, the matter may be transparent to that photon. On the other hand, some people say that the electron absorbs the extra energy and emits it in the form of phonons, through thermalisation. I'm having trouble reconciling these two opinions, so if anyone can help shed some light on this topic, I'd really appreciate it!

[@buktoptravel9314]

I asked gpt4, I'll put its answer here: The discrepancy you've pointed out arises from the simplification of the actual processes involved in the interaction between photons and materials. Both of the explanations you've mentioned have some truth to them, but they describe different aspects of a more complex process. Let's break it down. When a photon interacts with a material, its energy can be absorbed by an electron if the photon's energy is close to or greater than the band gap. The band gap is the energy difference between the valence band (where the valence electrons reside) and the conduction band (where the electrons can move more freely). Resonant absorption: If the photon's energy perfectly matches the band gap, then the absorption is most efficient. This is called resonant absorption. In this case, the electron is promoted from the valence band to the conduction band, creating an electron-hole pair. Non-resonant absorption: If the photon's energy is higher than the band gap but still within a range where the material can absorb it, the electron can still be promoted to the conduction band. However, the excess energy will be absorbed as well, and the electron will occupy a higher energy state in the conduction band. The process of thermalisation comes into play after the electron has been promoted to the conduction band. In this process, the excited electron relaxes to the lowest available energy state within the conduction band by releasing the excess energy in the form of phonons (quanta of lattice vibrations). This energy transfer to the lattice eventually results in the material heating up.

[@omaralrawi8624]

You are awesome, thanks a lot for sharing these information

[@mayteylg]

Really enjoyed the video! It was very clear. Thank you!

[@user-ie4zx1xy7l]

Keep up the good work!👍

[@VictorOguroth]

Amazing lecture!

[@israrahmad6637]

sir thank you very much for so clear explanation

[@federicosonnino7188]

very clear, thank you!

[@akhilkumar3090]

So basically, photon can not transfer its momentum to an electron (because not an integral multiple?) Leading to the transition being a vertical line, but then how can photon transfer the energy to the electron? (Because energy and momentum are interrelated and energy transfer would mean a momentum transfer as well)

[@PedMan47]

This is amazing.

[@lirabin]

Each electron has its own momentom. So what happens if the electron that you marked has 0.2eV gets the 2eV of the photon (which gives total of 2.2 and does not suit the gap)? It also cannot jump? I thought that in the case of additional energy the electron jumps and the rest of the energy becomes heat.

[@hongbinbin24]

Thank you. It's helpful.

[@dougklotz4926]

Hi Jordan, you said the electron could not absorb the 2eV photon. But why not? Cant the electron "ionize"? Or, how does the electron "resist" not absorbing THAT photon? Does it have a choice? Does the 2eV photon simply not "see" THAT electron? (i.e. cross section of absorption) Does it then therefore come down to quantum resonance patterns as described in the SE? And lastly, if that is in fact the case, how did the electron "know" that it was/was not "allowed" to absorb THAT photon until AFTER it had been raised in energy and momentum only to find that there was no available energy level to "land" on. Thanks for putting up with my remedial questions here but you very much just moved right past the obvious question when you said that that electron could not absorb the 2eV photon. Blaming it on quantum mechanics is totally acceptable but I have been trying for many decades to get a satisfactory answer to this question that doesn't invoke Schrodinger or Dirac. Great video!

[@DeepakGupta-or8qh]

But what is the difference between optical and electrical bandgap?

[@simonlinser8286]

It's a big difference in terms of eV s But it depends on if you're talking about the photo electro chemical effect, or something to do with absorption etc

[@DeepakGupta-or8qh]

Thanks a lot for the information

[@ekhibaathaiyaar1610]

Hey, very awesome video. Though i've a doubt pls clarify, why the Ki is 0, I mean it can't be a reference game right, coz you'll have some actual momentum of those electrons. Also what do you exactly mean by crystal momentum, I understood the momentum conservation argumnent and equation(apart from why Ki is 0), but I could't gat what's that Kmax(what u said to be crystal momentum).

[@hanserdadu6886]

Thank you

[@tejasgowdakr4700]

❤

[@Ahmad-py7wz]

Very good explanation. Could you explain the momentum band structure, in term of radiative recombination? Thanks

[@Simply--Science]

Thanks a lot for all your videos, they are very helpful! In this video, @3:41, you have shown a diagram of Energy vs k. As much as I know, energy of electron depends on its frequency. So how is it possible to have electron with same k having a higher energy? according to this video, electron can do transition vertically, i.e. no change in momentum but increase in energy. How can this be even possible? Shouldn't there be one to one mapping between energy and k or frequency of electron?

[@Simply--Science]

I can see part of response in notifications but not here :( some bug in youtube

[@JordanEdmundsEECS]

Huh, funky. Trying again, in free space you would be correct - each k has only one possible energy. In a crystal, things get more complicated. Because the crystal is periodic, there end up being many possible values of E. See the Kronig-Penney model for a mathematical treatment of this.

[@drscott1]

👍🏼

[@sahabuddin9140]

Why we are calculating the band gap of a material? What are the purpose of band gap calculation and its application? please

[@basharabbass8955]

nice

[@eranfalek]

How should one approach the band diagram if the semiconductor is amorphous? There is no latice constant then, so does the electrons still go straight up? Thanks for this very clear lecture!

[@user-mn9ob8he7z]

Hi nice vid, what about for indirect transition.

[@JordanEdmundsEECS]

0.0 it’s complicated, I actually haven’t studied it yet.

[@ShakeelAhmad-tf6lz]

when electron de-excited from conduction band to valence band what happen in that place in conduction band hole create same as created in valance band ? explain please

[@landau165]

thanks, but I have a question. What about vibration states?

[@JordanEdmundsEECS]

These are called "phonons" and they aren't states of the electrons, but states of the underlying lattice (the atomic nuclei). Since the electrons are what causes most of the interesting optical phenomena (absorption, emission, etc)., vibration only comes in tangentially. They can get absorbed by electrons to allow non-vertical optical transitions (this is why silicon can absorb photons despite having an indirect bandgap).

[@yongchaojia4610]

@@JordanEdmundsEECS then, the comment of only vertical transition is problematic.